Daily Papers

This paper presents X3D, a family of efficient video networks that progressively expand a tiny 2D image classification architecture along multiple network axes, in space, time, width and depth. Inspired by feature selection methods in machine learning, a simple stepwise network expansion approach is employed that expands a single axis in each step, such that good accuracy to complexity trade-off is achieved. To expand X3D to a specific target complexity, we perform progressive forward expansion followed by backward contraction. X3D achieves state-of-the-art performance while requiring 4.8x and 5.5x fewer multiply-adds and parameters for similar accuracy as previous work. Our most surprising finding is that networks with high spatiotemporal resolution can perform well, while being extremely light in terms of network width and parameters. We report competitive accuracy at unprecedented efficiency on video classification and detection benchmarks. Code will be available at: https://github.com/facebookresearch/SlowFast

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective on limited, unimodal data (i.e., data following a single pattern), these methods struggle as target data complexity increases. Specifically, in multimodal distributions, these heuristics fail to account for multiple inherent patterns, leading to suboptimal data selection. This work identifies two primary factors contributing to this limitation: (i) the disproportionate impact of dominant feature components in high-dimensional influence estimation, and (ii) the restrictive linear additive assumptions inherent in greedy selection strategies. To address these challenges, TAROT incorporates whitened feature distance to mitigate dominant feature bias, providing a more reliable measure of data influence. Building on this, TAROT uses whitened feature distance to quantify and minimize the optimal transport distance between the selected data and target domains. Notably, this minimization also facilitates the estimation of optimal selection ratios. We evaluate TAROT across multiple tasks, including semantic segmentation, motion prediction, and instruction tuning. Results consistently show that TAROT outperforms state-of-the-art methods, highlighting its versatility across various deep learning tasks. Code is available at https://github.com/vita-epfl/TAROT.

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by loss minimization. Using random weights for a hidden layer is an effective method to avoid non-convex optimization in standard gradient descent learning. It has also been adopted in recent deep learning theories. Despite the well-known fact that a neural network is a universal approximator, in this study, we mathematically show that when hidden parameters are distributed in a bounded domain, the network may not achieve zero approximation error. In particular, we derive a new nontrivial approximation error lower bound. The proof utilizes the technique of ridgelet analysis, a harmonic analysis method designed for neural networks. This method is inspired by fundamental principles in classical signal processing, specifically the idea that signals with limited bandwidth may not always be able to perfectly recreate the original signal. We corroborate our theoretical results with various simulation studies, and generally, two main take-home messages are offered: (i) Not any distribution for selecting random weights is feasible to build a universal approximator; (ii) A suitable assignment of random weights exists but to some degree is associated with the complexity of the target function.

Recent advances in synthetic methods enable designing subunits that self-assemble into structures with well-defined sizes and architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (number of distinct inter-subunit interaction types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we use icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are a class of disclinations. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large sizes. Optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction.

Sentiment analysis is a highly subjective and challenging task. Its complexity further increases when applied to the Arabic language, mainly because of the large variety of dialects that are unstandardized and widely used in the Web, especially in social media. While many datasets have been released to train sentiment classifiers in Arabic, most of these datasets contain shallow annotation, only marking the sentiment of the text unit, as a word, a sentence or a document. In this paper, we present the Arabic Sentiment Twitter Dataset for the Levantine dialect (ArSenTD-LEV). Based on findings from analyzing tweets from the Levant region, we created a dataset of 4,000 tweets with the following annotations: the overall sentiment of the tweet, the target to which the sentiment was expressed, how the sentiment was expressed, and the topic of the tweet. Results confirm the importance of these annotations at improving the performance of a baseline sentiment classifier. They also confirm the gap of training in a certain domain, and testing in another domain.

Toeplitz Neural Networks (TNNs) have exhibited outstanding performance in various sequence modeling tasks. They outperform commonly used Transformer-based models while benefiting from log-linear space-time complexities. On the other hand, State Space Models (SSMs) achieve lower performance than TNNs in language modeling but offer the advantage of constant inference complexity. In this paper, we aim to combine the strengths of TNNs and SSMs by converting TNNs to SSMs during inference, thereby enabling TNNs to achieve the same constant inference complexities as SSMs. To accomplish this, we formulate the conversion process as an optimization problem and provide a closed-form solution. We demonstrate how to transform the target equation into a Vandermonde linear system problem, which can be efficiently solved using the Discrete Fourier Transform (DFT). Notably, our method requires no training and maintains numerical stability. It can be also applied to any LongConv-based model. To assess its effectiveness, we conduct extensive experiments on language modeling tasks across various settings. Additionally, we compare our method to other gradient-descent solutions, highlighting the superior numerical stability of our approach. The source code is available at https://github.com/OpenNLPLab/ETSC-Exact-Toeplitz-to-SSM-Conversion.

Accurately detecting rice flowering time is crucial for timely pollination in hybrid rice seed production. This not only enhances pollination efficiency but also ensures higher yields. However, due to the complexity of field environments and the characteristics of rice spikelets, such as their small size and short flowering period, automated and precise recognition remains challenging. To address this, this study proposes a rice spikelet flowering recognition method based on an improved YOLOv8 object detection model. First, a Bidirectional Feature Pyramid Network (BiFPN) replaces the original PANet structure to enhance feature fusion and improve multi-scale feature utilization. Second, to boost small object detection, a p2 small-object detection head is added, using finer feature mapping to reduce feature loss commonly seen in detecting small targets. Given the lack of publicly available datasets for rice spikelet flowering in field conditions, a high-resolution RGB camera and data augmentation techniques are used to construct a dedicated dataset, providing reliable support for model training and testing. Experimental results show that the improved YOLOv8s-p2 model achieves an [email protected] of 65.9%, precision of 67.6%, recall of 61.5%, and F1-score of 64.41%, representing improvements of 3.10%, 8.40%, 10.80%, and 9.79%, respectively, over the baseline YOLOv8. The model also runs at 69 f/s on the test set, meeting practical application requirements. Overall, the improved YOLOv8s-p2 offers high accuracy and speed, providing an effective solution for automated monitoring in hybrid rice seed production.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

How can "weak teacher models" such as average human annotators or existing AI systems, effectively supervise LLMs to improve performance on hard reasoning tasks, especially those that challenge and requires expertise or daily practice from the teacher models? In this paper, we seek for empirical answers to this question by investigating various data-driven strategies that offer supervision data at different quality levels upon tasks of varying complexity. Two intuitive strategies emerge for teacher models to provide supervision during alignment training: 1) using lower-quality supervision from complete tasks that match the difficulty of the target reasoning tasks, and 2) leveraging higher-quality supervision from easier subtasks that are less challenging. Interestingly, we find that even when the outcome error rate for hard task supervision is high (e.g., 90\%), training on such data can outperform perfectly correct supervision on easier subtasks on multiple hard math benchmarks. We further identify a more critical factor influencing training performance: step-wise error rates, which indicate the severity of errors in solutions. Specifically, training on hard task supervision with the same outcome error rates but disparate step-wise error rates can lead to a 30\% accuracy gap on MATH benchmark. Our results also reveal that supplementing hard task supervision with the corresponding subtask supervision can yield notable performance improvements than simply combining rephrased hard full task supervision, suggesting new avenues for data augmentation. Data and code are released at https://github.com/hexuan21/Weak-to-Strong.

This paper presents TextComplexityDE, a dataset consisting of 1000 sentences in German language taken from 23 Wikipedia articles in 3 different article-genres to be used for developing text-complexity predictor models and automatic text simplification in German language. The dataset includes subjective assessment of different text-complexity aspects provided by German learners in level A and B. In addition, it contains manual simplification of 250 of those sentences provided by native speakers and subjective assessment of the simplified sentences by participants from the target group. The subjective ratings were collected using both laboratory studies and crowdsourcing approach.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-state pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

Recent progress has pushed AI frontiers from pattern recognition tasks toward problems that require step by step, System2 style reasoning, especially with large language models. Yet, unlike learning, where generalization and out of distribution (OoD) evaluation concepts are well formalized, there is no clear, consistent definition or metric for reasoning ability. We propose Complexity Out of Distribution (Complexity OoD) generalization as a framework and problem setting to define and measure reasoning. A model exhibits Complexity OoD generalization when it maintains performance on test instances whose minimal required solution complexity, either representational (richer solution structure) or computational (more reasoning steps/program length), exceeds that of all training examples. We formalize complexity via solution description Kolmogorov complexity and operational proxies (e.g., object/relation counts; reasoning step counts), clarifying how Complexity OoD differs from length and compositional OoD. This lens unifies learning and reasoning: many cases solvable with System1 like processing at low complexity become System2 like under complexity pressure, while System2 can be viewed as generalization over solution structures. We translate this perspective into practice with recommendations for operationalizing Complexity OoD across the stack: incorporating complexity into benchmark and evaluation metric design, rethinking supervision to target solution traces, seeking and designing inductive biases for Complexity OoD generalization, addressing learning to reason spillovers such as spurious shortcuts, semantic robustness, catastrophic forgetting, and step wise calibration. Because Complexity OoD cannot be solved by scaling data alone, progress toward robust reasoning will require architectures and training regimes that explicitly model and allocate computation with respect to complexity.

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number n of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the mean of the generated mixture and the mean of the target mixture, which we show decays as Theta_n(1{n}). Finally, this rate is shown to be in fact Bayes-optimal.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

Universal Information Extraction (UIE) has garnered significant attention due to its ability to address model explosion problems effectively. Extractive UIE can achieve strong performance using a relatively small model, making it widely adopted. Extractive UIEs generally rely on task instructions for different tasks, including single-target instructions and multiple-target instructions. Single-target instruction UIE enables the extraction of only one type of relation at a time, limiting its ability to model correlations between relations and thus restricting its capability to extract complex relations. While multiple-target instruction UIE allows for the extraction of multiple relations simultaneously, the inclusion of irrelevant relations introduces decision complexity and impacts extraction accuracy. Therefore, for multi-relation extraction, we propose LDNet, which incorporates multi-aspect relation modeling and a label drop mechanism. By assigning different relations to different levels for understanding and decision-making, we reduce decision confusion. Additionally, the label drop mechanism effectively mitigates the impact of irrelevant relations. Experiments show that LDNet outperforms or achieves competitive performance with state-of-the-art systems on 9 tasks, 33 datasets, in both single-modal and multi-modal, few-shot and zero-shot settings.https://github.com/Lu-Yang666/LDNet

Model size and inference speed/power have become a major challenge in the deployment of Neural Networks for many applications. A promising approach to address these problems is quantization. However, uniformly quantizing a model to ultra low precision leads to significant accuracy degradation. A novel solution for this is to use mixed-precision quantization, as some parts of the network may allow lower precision as compared to other layers. However, there is no systematic way to determine the precision of different layers. A brute force approach is not feasible for deep networks, as the search space for mixed-precision is exponential in the number of layers. Another challenge is a similar factorial complexity for determining block-wise fine-tuning order when quantizing the model to a target precision. Here, we introduce Hessian AWare Quantization (HAWQ), a novel second-order quantization method to address these problems. HAWQ allows for the automatic selection of the relative quantization precision of each layer, based on the layer's Hessian spectrum. Moreover, HAWQ provides a deterministic fine-tuning order for quantizing layers, based on second-order information. We show the results of our method on Cifar-10 using ResNet20, and on ImageNet using Inception-V3, ResNet50 and SqueezeNext models. Comparing HAWQ with state-of-the-art shows that we can achieve similar/better accuracy with 8times activation compression ratio on ResNet20, as compared to DNAS~wu2018mixed, and up to 1% higher accuracy with up to 14% smaller models on ResNet50 and Inception-V3, compared to recently proposed methods of RVQuant~park2018value and HAQ~wang2018haq. Furthermore, we show that we can quantize SqueezeNext to just 1MB model size while achieving above 68% top1 accuracy on ImageNet.

Detecting traversable pathways in unstructured outdoor environments remains a significant challenge for autonomous robots, especially in critical applications such as wide-area search and rescue, as well as incident management scenarios like forest fires. Existing datasets and models primarily target urban settings or wide, vehicle-traversable off-road tracks, leaving a substantial gap in addressing the complexity of narrow, trail-like off-road scenarios. To address this, we introduce the Trail-based Off-road Multimodal Dataset (TOMD), a comprehensive dataset specifically designed for such environments. TOMD features high-fidelity multimodal sensor data -- including 128-channel LiDAR, stereo imagery, GNSS, IMU, and illumination measurements -- collected through repeated traversals under diverse conditions. We also propose a dynamic multiscale data fusion model for accurate traversable pathway prediction. The study analyzes the performance of early, cross, and mixed fusion strategies under varying illumination levels. Results demonstrate the effectiveness of our approach and the relevance of illumination in segmentation performance. We publicly release TOMD at https://github.com/yyyxs1125/TMOD to support future research in trail-based off-road navigation.

RNN-T models are widely used in ASR, which rely on the RNN-T loss to achieve length alignment between input audio and target sequence. However, the implementation complexity and the alignment-based optimization target of RNN-T loss lead to computational redundancy and a reduced role for predictor network, respectively. In this paper, we propose a novel model named CIF-Transducer (CIF-T) which incorporates the Continuous Integrate-and-Fire (CIF) mechanism with the RNN-T model to achieve efficient alignment. In this way, the RNN-T loss is abandoned, thus bringing a computational reduction and allowing the predictor network a more significant role. We also introduce Funnel-CIF, Context Blocks, Unified Gating and Bilinear Pooling joint network, and auxiliary training strategy to further improve performance. Experiments on the 178-hour AISHELL-1 and 10000-hour WenetSpeech datasets show that CIF-T achieves state-of-the-art results with lower computational overhead compared to RNN-T models.

With the rapid advancement of AI-generated videos, there is an urgent need for effective detection tools to mitigate societal risks such as misinformation and reputational harm. In addition to accurate classification, it is essential that detection models provide interpretable explanations to ensure transparency for regulators and end users. To address these challenges, we introduce VidGuard-R1, the first video authenticity detector that fine-tunes a multi-modal large language model (MLLM) using group relative policy optimization (GRPO). Our model delivers both highly accurate judgments and insightful reasoning. We curate a challenging dataset of 140k real and AI-generated videos produced by state-of-the-art generation models, carefully designing the generation process to maximize discrimination difficulty. We then fine-tune Qwen-VL using GRPO with two specialized reward models that target temporal artifacts and generation complexity. Extensive experiments demonstrate that VidGuard-R1 achieves state-of-the-art zero-shot performance on existing benchmarks, with additional training pushing accuracy above 95%. Case studies further show that VidGuard-R1 produces precise and interpretable rationales behind its predictions. The code is publicly available at https://VidGuard-R1.github.io.

Attention layers -- which map a sequence of inputs to a sequence of outputs -- are core building blocks of the Transformer architecture which has achieved significant breakthroughs in modern artificial intelligence. This paper presents a rigorous theoretical study on the learning and generalization of a single multi-head attention layer, with a sequence of key vectors and a separate query vector as input. We consider the random feature setting where the attention layer has a large number of heads, with randomly sampled frozen query and key matrices, and trainable value matrices. We show that such a random-feature attention layer can express a broad class of target functions that are permutation invariant to the key vectors. We further provide quantitative excess risk bounds for learning these target functions from finite samples, using random feature attention with finitely many heads. Our results feature several implications unique to the attention structure compared with existing random features theory for neural networks, such as (1) Advantages in the sample complexity over standard two-layer random-feature networks; (2) Concrete and natural classes of functions that can be learned efficiently by a random-feature attention layer; and (3) The effect of the sampling distribution of the query-key weight matrix (the product of the query and key matrix), where Gaussian random weights with a non-zero mean result in better sample complexities over the zero-mean counterpart for learning certain natural target functions. Experiments on simulated data corroborate our theoretical findings and further illustrate the interplay between the sample size and the complexity of the target function.

Speculative Decoding (SD) is a technique to accelerate the inference of Large Language Models (LLMs) by using a lower complexity draft model to propose candidate tokens verified by a larger target model. To further improve efficiency, Multi-Candidate Speculative Decoding (MCSD) improves upon this by sampling multiple candidate tokens from the draft model at each step and verifying them in parallel, thus increasing the chances of accepting a token and reducing generation time. Existing MCSD methods rely on the draft model to initialize the multi-candidate sequences and use static length and tree attention structure for draft generation. However, such an approach suffers from the draft and target model's output distribution differences, especially in dynamic generation context. In this work, we introduce an improved version of MCSD that includes a target model initialized multi-candidate process, dynamic sliced topology-aware causal mask for dynamic length adjustment, and decision models to optimize early stopping. Our framework improves the acceptance rate, defined as the ratio of the longest draft sequence length accepted by the target model over the maximum draft sequence length, by a maximum of 164% and gains a maximum of 75% generation speed up over the MCSD baseline. We also conduct an ablation study to evaluate the impact of the decision model.

This paper introduces the Balanced Arabic Readability Evaluation Corpus (BAREC), a large-scale, fine-grained dataset for Arabic readability assessment. BAREC consists of 69,441 sentences spanning 1+ million words, carefully curated to cover 19 readability levels, from kindergarten to postgraduate comprehension. The corpus balances genre diversity, topical coverage, and target audiences, offering a comprehensive resource for evaluating Arabic text complexity. The corpus was fully manually annotated by a large team of annotators. The average pairwise inter-annotator agreement, measured by Quadratic Weighted Kappa, is 81.8%, reflecting a high level of substantial agreement. Beyond presenting the corpus, we benchmark automatic readability assessment across different granularity levels, comparing a range of techniques. Our results highlight the challenges and opportunities in Arabic readability modeling, demonstrating competitive performance across various methods. To support research and education, we make BAREC openly available, along with detailed annotation guidelines and benchmark results.

Data augmentation is critical to the empirical success of modern self-supervised representation learning, such as contrastive learning and masked language modeling. However, a theoretical understanding of the exact role of augmentation remains limited. Recent work has built the connection between self-supervised learning and the approximation of the top eigenspace of a graph Laplacian operator, suggesting that learning a linear probe atop such representation can be connected to RKHS regression. Building on this insight, this work delves into a statistical analysis of augmentation-based pretraining. Starting from the isometry property, a geometric characterization of the target function given by the augmentation, we disentangle the effects of the model and the augmentation, and prove two generalization bounds that are free of model complexity. Our first bound works for an arbitrary encoder, where the prediction error is decomposed as the sum of an estimation error incurred by fitting a linear probe with RKHS regression, and an approximation error entailed by RKHS approximation. Our second bound specifically addresses the case where the encoder is near-optimal, that is it approximates the top-d eigenspace of the RKHS induced by the augmentation. A key ingredient in our analysis is the augmentation complexity, which we use to quantitatively compare different augmentations and analyze their impact on downstream performance.

Large language models (LLMs) have brought exciting new advances to mobile UI agents, a long-standing research field that aims to complete arbitrary natural language tasks through mobile UI interactions. However, existing UI agents usually demand high reasoning capabilities of powerful large models that are difficult to be deployed locally on end-users' devices, which raises huge concerns about user privacy and centralized serving cost. One way to reduce the required model size is to customize a smaller domain-specific model with high-quality training data, e.g. large-scale human demonstrations of diverse types of apps and tasks, while such datasets are extremely difficult to obtain. Inspired by the remarkable coding abilities of recent small language models (SLMs), we propose to convert the UI task automation problem to a code generation problem, which can be effectively solved by an on-device SLM and efficiently executed with an on-device code interpreter. Unlike normal coding tasks that can be extensively pretrained with public datasets, generating UI automation code is challenging due to the diversity, complexity, and variability of target apps. Therefore, we adopt a document-centered approach that automatically builds fine-grained API documentation for each app and generates diverse task samples based on this documentation. By guiding the agent with the synthetic documents and task samples, it learns to generate precise and efficient scripts to complete unseen tasks. Based on detailed comparisons with state-of-the-art mobile UI agents, our approach effectively improves the mobile task automation with significantly higher success rates and lower latency/token consumption. Code will be open-sourced.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample complexity) if its individual components align well with the target algorithm. Specifically, GNNs are claimed to align with dynamic programming (DP), a general problem-solving strategy which expresses many polynomial-time algorithms. However, has this alignment truly been demonstrated and theoretically quantified? Here we show, using methods from category theory and abstract algebra, that there exists an intricate connection between GNNs and DP, going well beyond the initial observations over individual algorithms such as Bellman-Ford. Exposing this connection, we easily verify several prior findings in the literature, produce better-grounded GNN architectures for edge-centric tasks, and demonstrate empirical results on the CLRS algorithmic reasoning benchmark. We hope our exposition will serve as a foundation for building stronger algorithmically aligned GNNs.

Incorporating expert demonstrations has empirically helped to improve the sample efficiency of reinforcement learning (RL). This paper quantifies theoretically to what extent this extra information reduces RL's sample complexity. In particular, we study the demonstration-regularized reinforcement learning that leverages the expert demonstrations by KL-regularization for a policy learned by behavior cloning. Our findings reveal that using N^{E} expert demonstrations enables the identification of an optimal policy at a sample complexity of order mathcal{O}(Poly(S,A,H)/(varepsilon^2 N^{E})) in finite and mathcal{O}(Poly(d,H)/(varepsilon^2 N^{E})) in linear Markov decision processes, where varepsilon is the target precision, H the horizon, A the number of action, S the number of states in the finite case and d the dimension of the feature space in the linear case. As a by-product, we provide tight convergence guarantees for the behaviour cloning procedure under general assumptions on the policy classes. Additionally, we establish that demonstration-regularized methods are provably efficient for reinforcement learning from human feedback (RLHF). In this respect, we provide theoretical evidence showing the benefits of KL-regularization for RLHF in tabular and linear MDPs. Interestingly, we avoid pessimism injection by employing computationally feasible regularization to handle reward estimation uncertainty, thus setting our approach apart from the prior works.

To leverage the copious amount of data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, most existing works design a source task selection strategy from a purely empirical perspective. Recently, chen2022active gave the first active multi-task representation learning (A-MTRL) algorithm which adaptively samples from source tasks and can provably reduce the total sample complexity using the L2-regularized-target-source-relevance parameter nu^2. But their work is theoretically suboptimal in terms of total source sample complexity and is less practical in some real-world scenarios where sparse training source task selection is desired. In this paper, we address both issues. Specifically, we show the strict dominance of the L1-regularized-relevance-based (nu^1-based) strategy by giving a lower bound for the nu^2-based strategy. When nu^1 is unknown, we propose a practical algorithm that uses the LASSO program to estimate nu^1. Our algorithm successfully recovers the optimal result in the known case. In addition to our sample complexity results, we also characterize the potential of our nu^1-based strategy in sample-cost-sensitive settings. Finally, we provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method.

With the incorporation of the UNet architecture, diffusion probabilistic models have become a dominant force in image generation tasks. One key design in UNet is the skip connections between the encoder and decoder blocks. Although skip connections have been shown to improve training stability and model performance, we reveal that such shortcuts can be a limiting factor for the complexity of the transformation. As the sampling steps decrease, the generation process and the role of the UNet get closer to the push-forward transformations from Gaussian distribution to the target, posing a challenge for the network's complexity. To address this challenge, we propose Skip-Tuning, a simple yet surprisingly effective training-free tuning method on the skip connections. Our method can achieve 100% FID improvement for pretrained EDM on ImageNet 64 with only 19 NFEs (1.75), breaking the limit of ODE samplers regardless of sampling steps. Surprisingly, the improvement persists when we increase the number of sampling steps and can even surpass the best result from EDM-2 (1.58) with only 39 NFEs (1.57). Comprehensive exploratory experiments are conducted to shed light on the surprising effectiveness. We observe that while Skip-Tuning increases the score-matching losses in the pixel space, the losses in the feature space are reduced, particularly at intermediate noise levels, which coincide with the most effective range accounting for image quality improvement.

In this paper, we explore the impact of augmenting pre-trained Encoder-Decoder models, specifically T5, with linguistic knowledge for the prediction of a target task. In particular, we investigate whether fine-tuning a T5 model on an intermediate task that predicts structural linguistic properties of sentences modifies its performance in the target task of predicting sentence-level complexity. Our study encompasses diverse experiments conducted on Italian and English datasets, employing both monolingual and multilingual T5 models at various sizes. Results obtained for both languages and in cross-lingual configurations show that linguistically motivated intermediate fine-tuning has generally a positive impact on target task performance, especially when applied to smaller models and in scenarios with limited data availability.

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features, represented as directions in the penultimate layer, that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity and find a spectrum of simple to complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features flow, and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features complexity and their importance in driving the networks decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a sedimentation process, allowing the model to build upon these foundational elements.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

We resolve the open question regarding the sample complexity of policy learning for maximizing the long-run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of widetilde O(|S||A|t_{mix}^2 epsilon^{-2}) and a lower bound of Omega(|S||A|t_{mix} epsilon^{-2}). In these expressions, |S| and |A| denote the cardinalities of the state and action spaces respectively, t_{mix} serves as a uniform upper limit for the total variation mixing times, and epsilon signifies the error tolerance. Therefore, a notable gap of t_{mix} still remains to be bridged. Our primary contribution is the development of an estimator for the optimal policy of average reward MDPs with a sample complexity of widetilde O(|S||A|t_{mix}epsilon^{-2}). This marks the first algorithm and analysis to reach the literature's lower bound. Our new algorithm draws inspiration from ideas in Li et al. (2020), Jin and Sidford (2021), and Wang et al. (2023). Additionally, we conduct numerical experiments to validate our theoretical findings.

We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer [1], we define the objective of learning the set of ε-optimal goal-conditioned policies attaining all states that are incrementally reachable within L steps (in expectation) from a reference state s_0. In this paper, we introduce a novel model-based approach that interleaves discovering new states from s_0 and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as O(L^5 S_{L+ε} Γ_{L+ε} A ε^{-2}), where A is the number of actions, S_{L+ε} is the number of states that are incrementally reachable from s_0 in L+ε steps, and Γ_{L+ε} is the branching factor of the dynamics over such states. This improves over the algorithm proposed in [1] in both ε and L at the cost of an extra Γ_{L+ε} factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an ε/c_{min}-optimal policy for any cost-sensitive shortest-path problem defined on the L-reachable states with minimum cost c_{min}. Finally, we report preliminary empirical results confirming our theoretical findings.

When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational "phase transitions". Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

Every data selection method inherently has a target. In practice, these targets often emerge implicitly through benchmark-driven iteration: researchers develop selection strategies, train models, measure benchmark performance, then refine accordingly. This raises a natural question: what happens when we make this optimization explicit? To explore this, we propose benchmark-targeted ranking (BETR), a simple method that selects pretraining documents based on similarity to benchmark training examples. BETR embeds benchmark examples and a sample of pretraining documents in a shared space, scores this sample by similarity to benchmarks, then trains a lightweight classifier to predict these scores for the full corpus. We compare data selection methods by training over 500 models spanning 10^{19} to 10^{22} FLOPs and fitting scaling laws to them. From this, we find that simply aligning pretraining data to evaluation benchmarks using BETR achieves a 2.1x compute multiplier over DCLM-Baseline (4.7x over unfiltered data) and improves performance on 9 out of 10 tasks across all scales. BETR also generalizes well: when targeting a diverse set of benchmarks disjoint from our evaluation suite, it still matches or outperforms baselines. Our scaling analysis further reveals a clear trend: larger models require less aggressive filtering. Overall, our findings show that directly matching pretraining data to target tasks precisely shapes model capabilities and highlight that optimal selection strategies must adapt to model scale.

We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to predict these rules. Our study focuses on elementary cellular automata (ECA), simple yet powerful one-dimensional systems that generate behaviors ranging from trivial to highly complex. By training distinct Large Language Models (LLMs) on different ECAs, we evaluated the relationship between the complexity of the rules' behavior and the intelligence exhibited by the LLMs, as reflected in their performance on downstream tasks. Our findings reveal that rules with higher complexity lead to models exhibiting greater intelligence, as demonstrated by their performance on reasoning and chess move prediction tasks. Both uniform and periodic systems, and often also highly chaotic systems, resulted in poorer downstream performance, highlighting a sweet spot of complexity conducive to intelligence. We conjecture that intelligence arises from the ability to predict complexity and that creating intelligence may require only exposure to complexity.

Large Language Models (LLMs) are increasingly used for tasks involving Knowledge Graphs (KGs), whose evaluation typically focuses on accuracy and output correctness. We propose a complementary task characterization approach using three complexity frameworks from cognitive psychology. Applying this to the LLM-KG-Bench framework, we highlight value distributions, identify underrepresented demands and motivate richer interpretation and diversity for benchmark evaluation tasks.

In the realm of embodied artificial intelligence, the reasoning capabilities of Large Language Models (LLMs) play a pivotal role. Although there are effective methods like program-of-thought prompting for LLMs which uses programming language to tackle complex reasoning tasks, the specific impact of code data on the improvement of reasoning capabilities remains under-explored. To address this gap, we propose complexity-impacted reasoning score (CIRS), which combines structural and logical attributes, to measure the correlation between code and reasoning abilities. Specifically, we use the abstract syntax tree to encode the structural information and calculate logical complexity by considering the difficulty and the cyclomatic complexity. Through an empirical analysis, we find not all code data of complexity can be learned or understood by LLMs. Optimal level of complexity is critical to the improvement of reasoning abilities by program-aided prompting. Then we design an auto-synthesizing and stratifying algorithm, and apply it to instruction generation for mathematical reasoning and code data filtering for code generation tasks. Extensive results demonstrates the effectiveness of our proposed approach. Code will be integrated into the EasyInstruct framework at https://github.com/zjunlp/EasyInstruct.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

We study the representation complexity of model-based and model-free reinforcement learning (RL) in the context of circuit complexity. We prove theoretically that there exists a broad class of MDPs such that their underlying transition and reward functions can be represented by constant depth circuits with polynomial size, while the optimal Q-function suffers an exponential circuit complexity in constant-depth circuits. By drawing attention to the approximation errors and building connections to complexity theory, our theory provides unique insights into why model-based algorithms usually enjoy better sample complexity than model-free algorithms from a novel representation complexity perspective: in some cases, the ground-truth rule (model) of the environment is simple to represent, while other quantities, such as Q-function, appear complex. We empirically corroborate our theory by comparing the approximation error of the transition kernel, reward function, and optimal Q-function in various Mujoco environments, which demonstrates that the approximation errors of the transition kernel and reward function are consistently lower than those of the optimal Q-function. To the best of our knowledge, this work is the first to study the circuit complexity of RL, which also provides a rigorous framework for future research.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by 1, we show that our algorithm only needs to explore tilde O( d^2varepsilon^{-2}) episodes to find an varepsilon-optimal policy, where d is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is ``horizon-free''. In addition, we provide an Omega(d^2varepsilon^{-2}) sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

In this paper, we investigate which questions are challenging for retrieval-based Question Answering (QA). We (i) propose retrieval complexity (RC), a novel metric conditioned on the completeness of retrieved documents, which measures the difficulty of answering questions, and (ii) propose an unsupervised pipeline to measure RC given an arbitrary retrieval system. Our proposed pipeline measures RC more accurately than alternative estimators, including LLMs, on six challenging QA benchmarks. Further investigation reveals that RC scores strongly correlate with both QA performance and expert judgment across five of the six studied benchmarks, indicating that RC is an effective measure of question difficulty. Subsequent categorization of high-RC questions shows that they span a broad set of question shapes, including multi-hop, compositional, and temporal QA, indicating that RC scores can categorize a new subset of complex questions. Our system can also have a major impact on retrieval-based systems by helping to identify more challenging questions on existing datasets.

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses of all the neighbors of the action. This problem was introduced by mannor2011 and received considerable attention in recent years. It is generally stated in the literature that the minimax regret rate for this problem is of order alpha T, where alpha is the independence number of the graph, and T is the time horizon. However, this is proven only when the number of rounds T is larger than alpha^3, which poses a significant restriction for the usability of this result in large graphs. In this paper, we define a new quantity R^*, called the problem complexity, and prove that the minimax regret is proportional to R^* for any graph and time horizon T. Introducing an intricate exploration strategy, we define the \mainAlgorithm algorithm that achieves the minimax optimal regret bound and becomes the first provably optimal algorithm for this setting, even if T is smaller than alpha^3.

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in learning a family of sub-Gaussian probability distributions. We introduce a notion of complexity for probability distributions in terms of their relative density with respect to the standard Gaussian measure. We prove that if the log-relative density can be locally approximated by a neural network whose parameters can be suitably bounded, then the distribution generated by empirical score matching approximates the target distribution in total variation with a dimension-independent rate. We illustrate our theory through examples, which include certain mixtures of Gaussians. An essential ingredient of our proof is to derive a dimension-free deep neural network approximation rate for the true score function associated with the forward process, which is interesting in its own right.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

To make AI systems broadly useful for challenging real-world tasks, we need them to learn complex human goals and preferences. One approach to specifying complex goals asks humans to judge during training which agent behaviors are safe and useful, but this approach can fail if the task is too complicated for a human to directly judge. To help address this concern, we propose training agents via self play on a zero sum debate game. Given a question or proposed action, two agents take turns making short statements up to a limit, then a human judges which of the agents gave the most true, useful information. In an analogy to complexity theory, debate with optimal play can answer any question in PSPACE given polynomial time judges (direct judging answers only NP questions). In practice, whether debate works involves empirical questions about humans and the tasks we want AIs to perform, plus theoretical questions about the meaning of AI alignment. We report results on an initial MNIST experiment where agents compete to convince a sparse classifier, boosting the classifier's accuracy from 59.4% to 88.9% given 6 pixels and from 48.2% to 85.2% given 4 pixels. Finally, we discuss theoretical and practical aspects of the debate model, focusing on potential weaknesses as the model scales up, and we propose future human and computer experiments to test these properties.

In this work, we conduct an experiment using state-of-the-art LLMs to translate MiniF2F into Rocq. The translation task focuses on generating a Rocq theorem based on three sources: a natural language description, the Lean formalization, and the Isabelle formalization. We conducted our experiment in 3 stages of increasing complexity, from basic one-shot prompting to multi-turn conversations that incorporate feedback from unsuccessful attempts. At each stage, we perform multiple rounds of translation using increasingly advanced models: GPT-4o mini, Claude 3.5 Sonnet, o1 mini, and o1. We successfully translated 478 out of 488 theorems. The dataset is opensource: https://github.com/LLM4Rocq/miniF2F-rocq.

We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface iota and an explicit per-step information budget B(d,n)=c,dlog_2 n . With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, Psi -Fooling, and Psi -Fano, with worked examples L_k and L_k^{phase} . We prove an oracle-relative separation P^{Psi} neq NP^{Psi} and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of iota_k using many calls to iota_{k-1} under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC^{0}/IC-NC^{1}) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside iota yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback is given in the format of preferences over pairs of trajectories. In the linear MDP model, using randomization in algorithm design, we present an algorithm that is sample efficient (i.e., has near-optimal worst-case regret bounds) and has polynomial running time (i.e., computational complexity is polynomial with respect to relevant parameters). Our algorithm further minimizes the query complexity through a novel randomized active learning procedure. In particular, our algorithm demonstrates a near-optimal tradeoff between the regret bound and the query complexity. To extend the results to more general nonlinear function approximation, we design a model-based randomized algorithm inspired by the idea of Thompson sampling. Our algorithm minimizes Bayesian regret bound and query complexity, again achieving a near-optimal tradeoff between these two quantities. Computation-wise, similar to the prior Thompson sampling algorithms under the regular RL setting, the main computation primitives of our algorithm are Bayesian supervised learning oracles which have been heavily investigated on the empirical side when applying Thompson sampling algorithms to RL benchmark problems.

Instruction tuning has been widely used to unleash the complete potential of large language models. Notably, complex and diverse instructions are of significant importance as they can effectively align models with various downstream tasks. However, current approaches to constructing large-scale instructions predominantly favour powerful models such as GPT-4 or those with over 70 billion parameters, under the empirical presumption that such larger language models (LLMs) inherently possess enhanced capabilities. In this study, we question this prevalent assumption and conduct an in-depth exploration into the potential of smaller language models (SLMs) in the context of instruction evolution. Extensive experiments across three scenarios of instruction evolution reveal that smaller language models (SLMs) can synthesize more effective instructions than LLMs. Further analysis demonstrates that SLMs possess a broader output space during instruction evolution, resulting in more complex and diverse variants. We also observe that the existing metrics fail to focus on the impact of the instructions. Thus, we propose Instruction Complex-Aware IFD (IC-IFD), which introduces instruction complexity in the original IFD score to evaluate the effectiveness of instruction data more accurately. Our source code is available at: https://github.com/HypherX/Evolution-Analysis{https://github.com/HypherX/Evolution-Analysis}

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

Understanding how humans perceive visual complexity is a key area of study in visual cognition. Previous approaches to modeling visual complexity assessments have often resulted in intricate, difficult-to-interpret algorithms that employ numerous features or sophisticated deep learning architectures. While these complex models achieve high performance on specific datasets, they often sacrifice interpretability, making it challenging to understand the factors driving human perception of complexity. Recently (Shen, et al. 2024) proposed an interpretable segmentation-based model that accurately predicted complexity across various datasets, supporting the idea that complexity can be explained simply. In this work, we investigate the failure of their model to capture structural, color and surprisal contributions to complexity. To this end, we propose Multi-Scale Sobel Gradient (MSG) which measures spatial intensity variations, Multi-Scale Unique Color (MUC) which quantifies colorfulness across multiple scales, and surprise scores generated using a Large Language Model. We test our features on existing benchmarks and a novel dataset (Surprising Visual Genome) containing surprising images from Visual Genome. Our experiments demonstrate that modeling complexity accurately is not as simple as previously thought, requiring additional perceptual and semantic factors to address dataset biases. Our model improves predictive performance while maintaining interpretability, offering deeper insights into how visual complexity is perceived and assessed. Our code, analysis and data are available at https://github.com/Complexity-Project/Complexity-in-Complexity.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward g(gamma, v) depends on the proposed threshold gamma and latent value v and it can be only achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most epsilon smaller than the optimum and prove that the number of queries needed can be infinitely large even when g(gamma, v) is monotone with respect to both gamma and v. On the positive side, we provide a tight query complexity Theta(1/epsilon^3) when g is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight Theta(1/epsilon^3) query complexity can be achieved as long as g satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight Theta(T^{2/3}) regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

Large Language Models (LLMs) have emerged as a milestone in artificial intelligence, and their performance can improve as the model size increases. However, this scaling brings great challenges to training and inference efficiency, particularly for deploying LLMs in resource-constrained environments, and the scaling trend is becoming increasingly unsustainable. This paper introduces the concept of ``capacity density'' as a new metric to evaluate the quality of the LLMs across different scales and describes the trend of LLMs in terms of both effectiveness and efficiency. To calculate the capacity density of a given target LLM, we first introduce a set of reference models and develop a scaling law to predict the downstream performance of these reference models based on their parameter sizes. We then define the effective parameter size of the target LLM as the parameter size required by a reference model to achieve equivalent performance, and formalize the capacity density as the ratio of the effective parameter size to the actual parameter size of the target LLM. Capacity density provides a unified framework for assessing both model effectiveness and efficiency. Our further analysis of recent open-source base LLMs reveals an empirical law (the densing law)that the capacity density of LLMs grows exponentially over time. More specifically, using some widely used benchmarks for evaluation, the capacity density of LLMs doubles approximately every three months. The law provides new perspectives to guide future LLM development, emphasizing the importance of improving capacity density to achieve optimal results with minimal computational overhead.

This systematic review explores the application of Large Language Models (LLMs) in Combinatorial Optimization (CO). We report our findings using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. We conduct a literature search via Scopus and Google Scholar, examining over 2,000 publications. We assess publications against four inclusion and four exclusion criteria related to their language, research focus, publication year, and type. Eventually, we select 103 studies. We classify these studies into semantic categories and topics to provide a comprehensive overview of the field, including the tasks performed by LLMs, the architectures of LLMs, the existing datasets specifically designed for evaluating LLMs in CO, and the field of application. Finally, we identify future directions for leveraging LLMs in this field.

Large Language Models (LLMs) demonstrate promising capabilities in solving simple scientific problems but often produce hallucinations for complex ones. While integrating LLMs with tools can increase reliability, this approach typically results in over-reliance on tools, diminishing the model's ability to solve simple problems through basic reasoning. In contrast, human experts first assess problem complexity using domain knowledge before choosing an appropriate solution approach. Inspired by this human problem-solving process, we propose a novel two-component fine-tuning method. In the first component World Knowledge Distillation (WKD), LLMs learn directly from solutions generated using tool's information to internalize domain knowledge. In the second component Tool Usage Adaptation (TUA), we partition problems into easy and hard categories based on the model's direct answering accuracy. While maintaining the same alignment target for easy problems as in WKD, we train the model to intelligently switch to tool usage for more challenging problems. We validate our method on six scientific benchmark datasets, spanning mathematics, climate science and epidemiology. On average, our models demonstrate a 28.18% improvement in answer accuracy and a 13.89% increase in tool usage precision across all datasets, surpassing state-of-the-art models including GPT-4o and Claude-3.5.

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate O(k^{-1/4}). As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss-Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.

Techniques that learn improved representations via offline data or self-supervised objectives have shown impressive results in traditional reinforcement learning (RL). Nevertheless, it is unclear how improved representation learning can benefit reinforcement learning from human feedback (RLHF) on language models (LMs). In this work, we propose training reward models (RMs) in a contrastive, goal-conditioned fashion by increasing the representation similarity of future states along sampled preferred trajectories and decreasing the similarity along randomly sampled dispreferred trajectories. This objective significantly improves RM performance by up to 0.09 AUROC across challenging benchmarks, such as MATH and GSM8k. These findings extend to general alignment as well -- on the Helpful-Harmless dataset, we observe 2.3% increase in accuracy. Beyond improving reward model performance, we show this way of training RM representations enables improved steerability because it allows us to evaluate the likelihood of an action achieving a particular goal-state (e.g., whether a solution is correct or helpful). Leveraging this insight, we find that we can filter up to 55% of generated tokens during majority voting by discarding trajectories likely to end up in an "incorrect" state, which leads to significant cost savings. We additionally find that these representations can perform fine-grained control by conditioning on desired future goal-states. For example, we show that steering a Llama 3 model towards helpful generations with our approach improves helpfulness by 9.6% over a supervised-fine-tuning trained baseline. Similarly, steering the model towards complex generations improves complexity by 21.6% over the baseline. Overall, we find that training RMs in this contrastive, goal-conditioned fashion significantly improves performance and enables model steerability.

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

Automatically estimating the complexity of texts for readers has a variety of applications, such as recommending texts with an appropriate complexity level to language learners or supporting the evaluation of text simplification approaches. In this paper, we present our submission to the Text Complexity DE Challenge 2022, a regression task where the goal is to predict the complexity of a German sentence for German learners at level B. Our approach relies on more than 220,000 pseudo-labels created from the German Wikipedia and other corpora to train Transformer-based models, and refrains from any feature engineering or any additional, labeled data. We find that the pseudo-label-based approach gives impressive results yet requires little to no adjustment to the specific task and therefore could be easily adapted to other domains and tasks.

Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length curve as input, what is the length of the resulting curve of outputs? It has been widely believed that this length grows exponentially in network depth. We prove that in fact this is not the case: the expected length distortion does not grow with depth, and indeed shrinks slightly, for ReLU networks with standard random initialization. We also generalize this result by proving upper bounds both for higher moments of the length distortion and for the distortion of higher-dimensional volumes. These theoretical results are corroborated by our experiments.

While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly generating valid plans for complex planning problems such as multi-constraint or long-horizon tasks. On the other hand, many frameworks aiming to solve complex planning problems often rely on task-specific preparatory efforts, such as task-specific in-context examples and pre-defined critics/verifiers, which limits their cross-task generalization capability. In this paper, we tackle these challenges by observing that the core of many planning problems lies in optimization problems: searching for the optimal solution (best plan) with goals subject to constraints (preconditions and effects of decisions). With LLMs' commonsense, reasoning, and programming capabilities, this opens up the possibilities of a universal LLM-based approach to planning problems. Inspired by this observation, we propose LLMFP, a general-purpose framework that leverages LLMs to capture key information from planning problems and formally formulate and solve them as optimization problems from scratch, with no task-specific examples needed. We apply LLMFP to 9 planning problems, ranging from multi-constraint decision making to multi-step planning problems, and demonstrate that LLMFP achieves on average 83.7% and 86.8% optimal rate across 9 tasks for GPT-4o and Claude 3.5 Sonnet, significantly outperforming the best baseline (direct planning with OpenAI o1-preview) with 37.6% and 40.7% improvements. We also validate components of LLMFP with ablation experiments and analyzed the underlying success and failure reasons.

Code based Language Models (LMs) have shown very promising results in the field of software engineering with applications such as code refinement, code completion and generation. However, the task of time and space complexity classification from code has not been extensively explored due to a lack of datasets, with prior endeavors being limited to Java. In this project, we aim to address these gaps by creating a labelled dataset of code snippets spanning multiple languages (Python and C++ datasets currently, with C, C#, and JavaScript datasets being released shortly). We find that existing time complexity calculation libraries and tools only apply to a limited number of use-cases. The lack of a well-defined rule based system motivates the application of several recently proposed code-based LMs. We demonstrate the effectiveness of dead code elimination and increasing the maximum sequence length of LMs. In addition to time complexity, we propose to use LMs to find space complexities from code, and to the best of our knowledge, this is the first attempt to do so. Furthermore, we introduce a novel code comprehension task, called cross-language transfer, where we fine-tune the LM on one language and run inference on another. Finally, we visualize the activation of the attention fed classification head of our LMs using Non-negative Matrix Factorization (NMF) to interpret our results.

Recent advances in reinforcement learning for large language models have converged on increasing complexity: multi-stage training pipelines, dynamic hyperparameter schedules, and curriculum learning strategies. This raises a fundamental question: Is this complexity necessary? We present JustRL, a minimal approach using single-stage training with fixed hyperparameters that achieves state-of-the-art performance on two 1.5B reasoning models (54.9\% and 64.3\% average accuracy across nine mathematical benchmarks) while using 2times less compute than sophisticated approaches. The same hyperparameters transfer across both models without tuning, and training exhibits smooth, monotonic improvement over 4,000+ steps without the collapses or plateaus that typically motivate interventions. Critically, ablations reveal that adding ``standard tricks'' like explicit length penalties and robust verifiers may degrade performance by collapsing exploration. These results suggest that the field may be adding complexity to solve problems that disappear with a stable, scaled-up baseline. We release our models and code to establish a simple, validated baseline for the community.

Building upon our previous investigations of O1 replication (Part 1: Journey Learning [Qin et al., 2024] and Part 2: Distillation [Huang et al., 2024]), this work explores the potential of inference-time scaling in large language models (LLMs) for medical reasoning tasks, ranging from diagnostic decision-making to treatment planning. Through extensive experiments on medical benchmarks of varying complexity (MedQA, Medbullets, and JAMA Clinical Challenges), our investigation reveals several key insights: (1) Increasing inference time does lead to improved performance. With a modest training set of 500 samples, our model yields substantial performance improvements of 6%-11%. (2) Task complexity directly correlates with the required length of reasoning chains, confirming the necessity of extended thought processes for challenging problems. (3) The differential diagnoses generated by our model adhere to the principles of the hypothetico-deductive method, producing a list of potential conditions that may explain a patient's symptoms and systematically narrowing these possibilities by evaluating the evidence. These findings demonstrate the promising synergy between inference-time scaling and journey learning in advancing LLMs' real-world clinical reasoning capabilities.

Large language models (LLMs) have shown promising results in a wide array of generative NLP tasks, such as summarization and machine translation. In the context of narrative generation, however, existing models still do not capture factors that contribute to producing consistent text. For instance, it is logical that a piece of text or a story should be uniformly readable throughout and that this form of complexity should be controllable. As such, if the complexity of an input text prompt is rated first-grade reading level in the Flesch Reading Ease test, then the generated text continuing the plot should also be within this range of complexity. With this in mind, we introduce Uniform Complexity for Text Generation (UCTG), a new benchmark test which raises the challenge of making generative models observe uniform linguistic properties with respect to prompts. We experiment with over 150+ linguistically and cognitively motivated features for evaluating text complexity in humans and generative models. From our results, we find that models such as GPT-2 struggle to preserve the complexity of input prompts used in its generations, even if finetuned with professionally written texts.

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision trees) is generally NP-hard. We often do not know whether the search for a simpler model will be worthwhile, and thus we do not go to the trouble of searching for one. In this work, we ask an important practical question: can accurate-yet-simple models be proven to exist, or shown likely to exist, before explicitly searching for them? We hypothesize that there is an important reason that simple-yet-accurate models often do exist. This hypothesis is that the size of the Rashomon set is often large, where the Rashomon set is the set of almost-equally-accurate models from a function class. If the Rashomon set is large, it contains numerous accurate models, and perhaps at least one of them is the simple model we desire. In this work, we formally present the Rashomon ratio as a new gauge of simplicity for a learning problem, depending on a function class and a data set. The Rashomon ratio is the ratio of the volume of the set of accurate models to the volume of the hypothesis space, and it is different from standard complexity measures from statistical learning theory. Insight from studying the Rashomon ratio provides an easy way to check whether a simpler model might exist for a problem before finding it, namely whether several different machine learning methods achieve similar performance on the data. In that sense, the Rashomon ratio is a powerful tool for understanding why and when an accurate-yet-simple model might exist. If, as we hypothesize in this work, many real-world data sets admit large Rashomon sets, the implications are vast: it means that simple or interpretable models may often be used for high-stakes decisions without losing accuracy.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

Efficiently tackling combinatorial reasoning problems, particularly the notorious NP-hard tasks, remains a significant challenge for AI research. Recent efforts have sought to enhance planning by incorporating hierarchical high-level search strategies, known as subgoal methods. While promising, their performance against traditional low-level planners is inconsistent, raising questions about their application contexts. In this study, we conduct an in-depth exploration of subgoal-planning methods for combinatorial reasoning. We identify the attributes pivotal for leveraging the advantages of high-level search: hard-to-learn value functions, complex action spaces, presence of dead ends in the environment, or using data collected from diverse experts. We propose a consistent evaluation methodology to achieve meaningful comparisons between methods and reevaluate the state-of-the-art algorithms.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

It is imperative for Large language models (LLMs) to follow instructions with elaborate requirements (i.e. Complex Instructions Following). Yet, it remains under-explored how to enhance the ability of LLMs to follow complex instructions with multiple constraints. To bridge the gap, we initially study what training data is effective in enhancing complex constraints following abilities. We found that training LLMs with instructions containing multiple constraints enhances their understanding of complex instructions, especially those with lower complexity levels. The improvement can even generalize to compositions of out-of-domain constraints. Additionally, we further propose methods addressing how to obtain and utilize the effective training data. Finally, we conduct extensive experiments to prove the effectiveness of our methods in terms of overall performance and training efficiency. We also demonstrate that our methods improve models' ability to follow instructions generally and generalize effectively across out-of-domain, in-domain, and adversarial settings, while maintaining general capabilities.

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 (ge 175B) to T5 variants (le 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

This paper details the work of the University of Groningen for the BabyLM Challenge. We follow the idea that, like babies, language models should be introduced to simpler concepts first and build off of that knowledge to understand more complex concepts. We examine this strategy of simple-then-complex through a variety of lenses, namely context size, vocabulary, and overall linguistic complexity of the data. We find that only one, context size, is truly beneficial to training a language model. However this simple change to context size gives us improvements of 2 points on average on (Super)GLUE tasks, 1 point on MSGS tasks, and 12\% on average on BLiMP tasks. Our context-limited model outperforms the baseline that was trained on 10times the amount of data.

The use of target networks is a popular approach for estimating value functions in deep Reinforcement Learning (RL). While effective, the target network remains a compromise solution that preserves stability at the cost of slowly moving targets, thus delaying learning. Conversely, using the online network as a bootstrapped target is intuitively appealing, albeit well-known to lead to unstable learning. In this work, we aim to obtain the best out of both worlds by introducing a novel update rule that computes the target using the MINimum estimate between the Target and Online network, giving rise to our method, MINTO. Through this simple, yet effective modification, we show that MINTO enables faster and stable value function learning, by mitigating the potential overestimation bias of using the online network for bootstrapping. Notably, MINTO can be seamlessly integrated into a wide range of value-based and actor-critic algorithms with a negligible cost. We evaluate MINTO extensively across diverse benchmarks, spanning online and offline RL, as well as discrete and continuous action spaces. Across all benchmarks, MINTO consistently improves performance, demonstrating its broad applicability and effectiveness.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.

For a two-player imperfect-information extensive-form game (IIEFG) with K time steps and a player action space of size U, the game tree complexity is U^{2K}, causing existing IIEFG solvers to struggle with large or infinite (U,K), e.g., differential games with continuous action spaces. To partially address this scalability challenge, we focus on an important class of 2p0s games where the informed player (P1) knows the payoff while the uninformed player (P2) only has a belief over the set of I possible payoffs. Such games encompass a wide range of scenarios in sports, defense, cybersecurity, and finance. We prove that under mild conditions, P1's (resp. P2's) equilibrium strategy at any infostate concentrates on at most I (resp. I+1) action prototypes. When Ill U, this equilibrium structure causes the game tree complexity to collapse to I^K for P1 when P2 plays pure best responses, and (I+1)^K for P2 in a dual game where P1 plays pure best responses. We then show that exploiting this structure in standard learning modes, i.e., model-free multiagent reinforcement learning and model predictive control, is straightforward, leading to significant improvements in learning accuracy and efficiency from SOTA IIEFG solvers. Our demonstration solves a 22-player football game (K=10, U=infty) where the attacking team has to strategically conceal their intention until a critical moment in order to exploit information advantage. Code is available at https://github.com/ghimiremukesh/cams/tree/iclr

State-of-the-art large language models (LLMs) exhibit impressive problem-solving capabilities but may struggle with complex reasoning and factual correctness. Existing methods harness the strengths of chain-of-thought and retrieval-augmented generation (RAG) to decompose a complex problem into simpler steps and apply retrieval to improve factual correctness. These methods work well on straightforward reasoning tasks but often falter on challenging tasks such as competitive programming and mathematics, due to frequent reasoning errors and irrelevant knowledge retrieval. To address this, we introduce Critic-guided planning with Retrieval-augmentation, CR-Planner, a novel framework that leverages fine-tuned critic models to guide both reasoning and retrieval processes through planning. CR-Planner solves a problem by iteratively selecting and executing sub-goals. Initially, it identifies the most promising sub-goal from reasoning, query generation, and retrieval, guided by rewards given by a critic model named sub-goal critic. It then executes this sub-goal through sampling and selecting the optimal output based on evaluations from another critic model named execution critic. This iterative process, informed by retrieved information and critic models, enables CR-Planner to effectively navigate the solution space towards the final answer. We employ Monte Carlo Tree Search to collect the data for training the critic models, allowing for a systematic exploration of action sequences and their long-term impacts. We validate CR-Planner on challenging domain-knowledge-intensive and reasoning-heavy tasks, including competitive programming, theorem-driven math reasoning, and complex domain retrieval problems. Our experiments demonstrate that CR-Planner significantly outperforms baselines, highlighting its effectiveness in addressing challenging problems by improving both reasoning and retrieval.

We study the complexity of sampling from a distribution over all index subsets of the set {1,...,n} with the probability of a subset S proportional to the determinant of the submatrix L_S of some ntimes n p.s.d. matrix L, where L_S corresponds to the entries of L indexed by S. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets S with small expected size k = E[|S|] ll n from a very large matrix L, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to L, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is n cdot poly(k), i.e., sublinear in the size of L, and (2) its sampling cost is poly(k), i.e., independent of the size of L. Prior to our results, state-of-the-art exact samplers required O(n^3) preprocessing time and sampling time linear in n or dependent on the spectral properties of L. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with ncdotpoly(k) time preprocessing.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

We study what actually works and what doesn't for training large language models as agents via multi-turn reinforcement learning. Despite rapid progress, existing frameworks and definitions are fragmented, and there is no systematic formulation or analysis of which design choices matter across tasks. We address this gap by first breaking down the design space into three inter-related pillars -- environment, reward, and policy -- and empirically derive a recipe for training LLM agents in situated textual domains. In particular, we test TextWorld and ALFWorld, popular domains for testing situated embodied reasoning, as well as SWE-Gym for more software engineering style tasks. (i) For the environment, we analyze the impacts of task complexity in terms of sizes of the state and action spaces as well as optimal solution length, finding that even simple environments within a domain can provide signal on how well an agent can generalize to more complex tasks. (ii) For the reward, we ablate relative reward sparsity, observing that while dense turn-level rewards accelerate training, performance and stability is highly dependent on the choice of RL algorithm. (iii) And for the agent's policy, we explore the interplay between reward sparsity and biased (PPO, GRPO) and unbiased (RLOO) policy gradient methods in addition to showing how to find the optimal Supervised Fine-tuning (SFT) to RL training ratio given a fixed budget. We distill these findings into a training recipe that guides co-design across the three pillars, facilitating research and practical efforts in multi-turn agentic RL. Code: https://github.com/pearls-lab/meow-tea-taro

Interactively learning from observation and language feedback is an increasingly studied area driven by the emergence of large language model (LLM) agents. While impressive empirical demonstrations have been shown, so far a principled framing of these decision problems remains lacking. In this paper, we formalize the Learning from Language Feedback (LLF) problem, assert sufficient assumptions to enable learning despite latent rewards, and introduce transfer eluder dimension as a complexity measure to characterize the hardness of LLF problems. We show that transfer eluder dimension captures the intuition that information in the feedback changes the learning complexity of the LLF problem. We demonstrate cases where learning from rich language feedback can be exponentially faster than learning from reward. We develop a no-regret algorithm, called HELiX, that provably solves LLF problems through sequential interactions, with performance guarantees that scale with the transfer eluder dimension of the problem. Across several empirical domains, we show that HELiX performs well even when repeatedly prompting LLMs does not work reliably. Our contributions mark a first step towards designing principled interactive learning algorithms from generic language feedback.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

We address the problem of optimizing a Brownian motion. We consider a (random) realization W of a Brownian motion with input space in [0,1]. Given W, our goal is to return an ε-approximation of its maximum using the smallest possible number of function evaluations, the sample complexity of the algorithm. We provide an algorithm with sample complexity of order log^2(1/ε). This improves over previous results of Al-Mharmah and Calvin (1996) and Calvin et al. (2017) which provided only polynomial rates. Our algorithm is adaptive---each query depends on previous values---and is an instance of the optimism-in-the-face-of-uncertainty principle.

Assessing the effectiveness of large language models (LLMs) in addressing diverse tasks is essential for comprehending their strengths and weaknesses. Conventional evaluation techniques typically apply a single prompting strategy uniformly across datasets, not considering the varying degrees of task complexity. We introduce the Hierarchical Prompting Taxonomy (HPT), a taxonomy that employs a Hierarchical Prompt Framework (HPF) composed of five unique prompting strategies, arranged from the simplest to the most complex, to assess LLMs more precisely and to offer a clearer perspective. This taxonomy assigns a score, called the Hierarchical Prompting Score (HP-Score), to datasets as well as LLMs based on the rules of the taxonomy, providing a nuanced understanding of their ability to solve diverse tasks and offering a universal measure of task complexity. Additionally, we introduce the Adaptive Hierarchical Prompt framework, which automates the selection of appropriate prompting strategies for each task. This study compares manual and adaptive hierarchical prompt frameworks using four instruction-tuned LLMs, namely Llama 3 8B, Phi 3 3.8B, Mistral 7B, and Gemma 7B, across four datasets: BoolQ, CommonSenseQA (CSQA), IWSLT-2017 en-fr (IWSLT), and SamSum. Experiments demonstrate the effectiveness of HPT, providing a reliable way to compare different tasks and LLM capabilities. This paper leads to the development of a universal evaluation metric that can be used to evaluate both the complexity of the datasets and the capabilities of LLMs. The implementation of both manual HPF and adaptive HPF is publicly available.

Reinforcement learning with AI feedback (RLAIF) is a popular paradigm for improving the instruction-following abilities of powerful pre-trained language models. RLAIF first performs supervised fine-tuning (SFT) using demonstrations from a teacher model and then further fine-tunes the model with reinforcement learning (RL), using feedback from a critic model. While recent popular open-source models have demonstrated substantial improvements in performance from the RL step, in this paper we question whether the complexity of this RL step is truly warranted for AI feedback. We show that the improvements of the RL step are virtually entirely due to the widespread practice of using a weaker teacher model (e.g. GPT-3.5) for SFT data collection than the critic (e.g., GPT-4) used for AI feedback generation. Specifically, we show that simple supervised fine-tuning with GPT-4 as the teacher outperforms existing RLAIF pipelines. More generally, we find that the gains from RLAIF vary substantially across base model families, test-time evaluation protocols, and critic models. Finally, we provide a mechanistic explanation for when SFT may outperform the full two-step RLAIF pipeline as well as suggestions for making RLAIF maximally useful in practice.

It has been observed that the input space of deep neural network classifiers can exhibit `fragmentation', where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the double descent curve, achieving a maximum at the interpolation regime. We study this phenomenon in the context of image classification and ask whether fragmentation could be predictive of generalization performance. Using a fragmentation-based complexity measure, we show this to be possible by achieving good performance on the PGDL (Predicting Generalization in Deep Learning) benchmark. In addition, we report on new observations related to fragmentation, namely (i) fragmentation is not limited to the input space but occurs in the hidden representations as well, (ii) fragmentation follows the trends in the validation error throughout training, and (iii) fragmentation is not a direct result of increased weight norms. Together, this indicates that fragmentation is a phenomenon worth investigating further when studying the generalization ability of deep neural networks.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

This paper analyzes Large Language Model (LLM) security vulnerabilities based on data from Crucible, encompassing 214,271 attack attempts by 1,674 users across 30 LLM challenges. Our findings reveal automated approaches significantly outperform manual techniques (69.5% vs 47.6% success rate), despite only 5.2% of users employing automation. We demonstrate that automated approaches excel in systematic exploration and pattern matching challenges, while manual approaches retain speed advantages in certain creative reasoning scenarios, often solving problems 5x faster when successful. Challenge categories requiring systematic exploration are most effectively targeted through automation, while intuitive challenges sometimes favor manual techniques for time-to-solve metrics. These results illuminate how algorithmic testing is transforming AI red-teaming practices, with implications for both offensive security research and defensive measures. Our analysis suggests optimal security testing combines human creativity for strategy development with programmatic execution for thorough exploration.

Characterizing samples that are difficult to learn from is crucial to developing highly performant ML models. This has led to numerous Hardness Characterization Methods (HCMs) that aim to identify "hard" samples. However, there is a lack of consensus regarding the definition and evaluation of "hardness". Unfortunately, current HCMs have only been evaluated on specific types of hardness and often only qualitatively or with respect to downstream performance, overlooking the fundamental quantitative identification task. We address this gap by presenting a fine-grained taxonomy of hardness types. Additionally, we propose the Hardness Characterization Analysis Toolkit (H-CAT), which supports comprehensive and quantitative benchmarking of HCMs across the hardness taxonomy and can easily be extended to new HCMs, hardness types, and datasets. We use H-CAT to evaluate 13 different HCMs across 8 hardness types. This comprehensive evaluation encompassing over 14K setups uncovers strengths and weaknesses of different HCMs, leading to practical tips to guide HCM selection and future development. Our findings highlight the need for more comprehensive HCM evaluation, while we hope our hardness taxonomy and toolkit will advance the principled evaluation and uptake of data-centric AI methods.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the N users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with N user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When N is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

In the classical transformer attention scheme, we are given three n times d size matrices Q, K, V (the query, key, and value tokens), and the goal is to compute a new n times d size matrix D^{-1} exp(QK^top) V where D = diag( exp(QK^top) {bf 1}_n ). In this work, we study a generalization of attention which captures triple-wise correlations. This generalization is able to solve problems about detecting triple-wise connections that were shown to be impossible for transformers. The potential downside of this generalization is that it appears as though computations are even more difficult, since the straightforward algorithm requires cubic time in n. However, we show that in the bounded-entry setting (which arises in practice, and which is well-studied in both theory and practice), there is actually a near-linear time algorithm. More precisely, we show that bounded entries are both necessary and sufficient for quickly performing generalized computations: bullet On the positive side, if all entries of the input matrices are bounded above by o(sqrt[3]{log n}) then we show how to approximate the ``tensor-type'' attention matrix in n^{1+o(1)} time. bullet On the negative side, we show that if the entries of the input matrices may be as large as Omega(sqrt[3]{log n}), then there is no algorithm that runs faster than n^{3-o(1)} (assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory). We also show that our construction, algorithms, and lower bounds naturally generalize to higher-order tensors and correlations. Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm. Our results thus yield a natural tradeoff between the boundedness of the entries, and order of the tensor one may use for more expressive, efficient attention computation.

A fundamental open challenge in modern LLM scaling is the lack of understanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable as a function of compute. However, downstream capabilities are far less predictable -- sometimes even exhibiting emergent jumps -- which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few-shot accuracy on a task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., "emergence laws"). We validate this approach using four standard NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA, and CoLA). Using only small-scale LLMs, we find that, in some cases, we can accurately predict whether models trained with up to 4x more compute have emerged. Finally, we present a case study of two realistic uses for emergence prediction.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

Reinforcement Learning (RL) has demonstrated tremendous empirical success across numerous challenging domains. However, we lack a strong theoretical understanding of the statistical complexity of RL in environments with large state spaces, where function approximation is required for sample-efficient learning. This thesis addresses this gap by rigorously examining the statistical complexity of RL with function approximation from a learning theoretic perspective. Departing from a long history of prior work, we consider the weakest form of function approximation, called agnostic policy learning, in which the learner seeks to find the best policy in a given class Pi, with no guarantee that Pi contains an optimal policy for the underlying task. We systematically explore agnostic policy learning along three key axes: environment access -- how a learner collects data from the environment; coverage conditions -- intrinsic properties of the underlying MDP measuring the expansiveness of state-occupancy measures for policies in the class Pi, and representational conditions -- structural assumptions on the class Pi itself. Within this comprehensive framework, we (1) design new learning algorithms with theoretical guarantees and (2) characterize fundamental performance bounds of any algorithm. Our results reveal significant statistical separations that highlight the power and limitations of agnostic policy learning.

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

Large Language Models (LLMs) suffer from reliability issues on complex tasks, as existing decomposition methods are heuristic and rely on agent or manual decomposition. This work introduces a novel, systematic decomposition framework that we call Analysis of CONstraint-Induced Complexity (ACONIC), which models the task as a constraint problem and leveraging formal complexity measures to guide decomposition. On combinatorial (SATBench) and LLM database querying tasks (Spider), we find that by decomposing the tasks following the measure of complexity, agent can perform considerably better (10-40 percentage point).

We trained 13,440 large language models and found that entropy minimization requires only a single unlabeled data and 10 steps optimization to achieve performance improvements comparable to or even greater than those obtained using thousands of data and carefully designed rewards in rule-based reinforcement learning. This striking result may prompt a rethinking of post-training paradigms for large language models. Our code is avaliable at https://github.com/zitian-gao/one-shot-em.

Large Reasoning Models (LRMs) have demonstrated impressive performance on complex tasks, including logical puzzle games that require deriving solutions satisfying all constraints. However, whether they can flexibly apply appropriate rules to varying conditions, particularly when faced with non-canonical game variants, remains an open question. Existing corpora focus on popular puzzles like 9x9 Sudoku, risking overfitting to canonical formats and memorization of solution patterns, which can mask deficiencies in understanding novel rules or adapting strategies to new variants. To address this, we introduce HardcoreLogic, a challenging benchmark of over 5,000 puzzles across 10 games, designed to test the robustness of LRMs on the "long-tail" of logical games. HardcoreLogic systematically transforms canonical puzzles through three dimensions: Increased Complexity (IC), Uncommon Elements (UE), and Unsolvable Puzzles (UP), reducing reliance on shortcut memorization. Evaluations on a diverse set of LRMs reveal significant performance drops, even for models achieving top scores on existing benchmarks, indicating heavy reliance on memorized stereotypes. While increased complexity is the dominant source of difficulty, models also struggle with subtle rule variations that do not necessarily increase puzzle difficulty. Our systematic error analysis on solvable and unsolvable puzzles further highlights gaps in genuine reasoning. Overall, HardcoreLogic exposes the limitations of current LRMs and establishes a benchmark for advancing high-level logical reasoning.

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance tau. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision Processes (MDPs) setting. To extend CVaR RL to settings where state space is large, function approximation must be deployed. We study CVaR RL in low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the underlying transition kernel admits a low-rank decomposition, but unlike prior linear models, low-rank MDPs do not assume the feature or state-action representation is known. We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to carefully balance the interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of Oleft(H^7 A^2 d^4{tau^2 epsilon^2}right) to yield an epsilon-optimal CVaR, where H is the length of each episode, A is the capacity of action space, and d is the dimension of representations. Computational-wise, we design a novel discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR objective as the planning oracle and show that we can find the near-optimal policy in a polynomial running time with a Maximum Likelihood Estimation oracle. To our knowledge, this is the first provably efficient CVaR RL algorithm in low-rank MDPs.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.