Daily Papers

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Linear Mode Connectivity (LMC) refers to the phenomenon that performance remains consistent for linearly interpolated models in the parameter space. For independently optimized model pairs from different random initializations, achieving LMC is considered crucial for validating the stable success of the non-convex optimization in modern machine learning models and for facilitating practical parameter-based operations such as model merging. While LMC has been achieved for neural networks by considering the permutation invariance of neurons in each hidden layer, its attainment for other models remains an open question. In this paper, we first achieve LMC for soft tree ensembles, which are tree-based differentiable models extensively used in practice. We show the necessity of incorporating two invariances: subtree flip invariance and splitting order invariance, which do not exist in neural networks but are inherent to tree architectures, in addition to permutation invariance of trees. Moreover, we demonstrate that it is even possible to exclude such additional invariances while keeping LMC by designing decision list-based tree architectures, where such invariances do not exist by definition. Our findings indicate the significance of accounting for architecture-specific invariances in achieving LMC.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

Recent studies have shown that reducing symmetries in neural networks enhances linear mode connectivity between networks without requiring parameter space alignment, leading to improved performance in linearly interpolated neural networks. However, in practical applications, neural network interpolation is rarely used; instead, ensembles of networks are more common. In this paper, we empirically investigate the impact of reducing symmetries on the performance of deep ensembles and Mixture of Experts (MoE) across five datasets. Additionally, to explore deeper linear mode connectivity, we introduce the Mixture of Interpolated Experts (MoIE). Our results show that deep ensembles built on asymmetric neural networks achieve significantly better performance as ensemble size increases compared to their symmetric counterparts. In contrast, our experiments do not provide conclusive evidence on whether reducing symmetries affects both MoE and MoIE architectures.

Deep networks often suffer from vanishing or exploding gradients due to inefficient signal propagation, leading to long training times or convergence difficulties. Various architecture designs, sophisticated residual-style networks, and initialization schemes have been shown to improve deep signal propagation. Recently, Pennington et al. used free probability theory to show that dynamical isometry plays an integral role in efficient deep learning. We show that the simplest architecture change of gating each residual connection using a single zero-initialized parameter satisfies initial dynamical isometry and outperforms more complex approaches. Although much simpler than its predecessors, this gate enables training thousands of fully connected layers with fast convergence and better test performance for ResNets trained on CIFAR-10. We apply this technique to language modeling and find that we can easily train 120-layer Transformers. When applied to 12 layer Transformers, it converges 56% faster on enwiki8.

Deep ensemble is a simple yet powerful way to improve the performance of deep neural networks. Under this motivation, recent works on mode connectivity have shown that parameters of ensembles are connected by low-loss subspaces, and one can efficiently collect ensemble parameters in those subspaces. While this provides a way to efficiently train ensembles, for inference, multiple forward passes should still be executed using all the ensemble parameters, which often becomes a serious bottleneck for real-world deployment. In this work, we propose a novel framework to reduce such costs. Given a low-loss subspace connecting two modes of a neural network, we build an additional neural network that predicts the output of the original neural network evaluated at a certain point in the low-loss subspace. The additional neural network, which we call a "bridge", is a lightweight network that takes minimal features from the original network and predicts outputs for the low-loss subspace without forward passes through the original network. We empirically demonstrate that we can indeed train such bridge networks and significantly reduce inference costs with the help of bridge networks.

Multi-controlled single-target (MC) gates are some of the most crucial building blocks for varied quantum algorithms. How to implement them optimally is thus a pivotal question. To answer this question in an architecture-independent manner, and to get a worst-case estimate, we should look at a linear nearest-neighbor (LNN) architecture, as this can be embedded in almost any qubit connectivity. Motivated by the above, here we describe a method which implements MC gates using no more than sim 4k+8n CNOT gates -- up-to 60% reduction over state-of-the-art -- while allowing for complete flexibility to choose the locations of n controls, the target, and a dirty ancilla out of k qubits. More strikingly, in case k approx n, our upper bound is sim 12n -- the best known for unrestricted connectivity -- and if n = 1, our upper bound is sim 4k -- the best known for a single long-range CNOT gate over k qubits -- therefore, if our upper bound can be reduced, then the cost of one or both of these simpler versions of MC gates will be immediately reduced accordingly. In practice, our method provides circuits that tend to require fewer CNOT gates than our upper bound for almost any given instance of MC gates.

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounding methods. Still, we lack an understanding of the mechanisms making IBP so successful. In this work, we thoroughly investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models, tightness decreases with width and depth at initialization, but improves with IBP training, given sufficient network width. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, explaining the empirically observed trade-off between robustness and accuracy in certified training. Our extensive experimental evaluation validates our theoretical predictions for ReLU networks, including that wider networks improve performance, yielding state-of-the-art results. Interestingly, we observe that while all IBP-based training methods lead to high tightness, this is neither sufficient nor necessary to achieve high certifiable robustness. This hints at the existence of new training methods that do not induce the strong regularization required for tight IBP bounds, leading to improved robustness and standard accuracy.

We study neural network loss landscapes through the lens of mode connectivity, the observation that minimizers of neural networks retrieved via training on a dataset are connected via simple paths of low loss. Specifically, we ask the following question: are minimizers that rely on different mechanisms for making their predictions connected via simple paths of low loss? We provide a definition of mechanistic similarity as shared invariances to input transformations and demonstrate that lack of linear connectivity between two models implies they use dissimilar mechanisms for making their predictions. Relevant to practice, this result helps us demonstrate that naive fine-tuning on a downstream dataset can fail to alter a model's mechanisms, e.g., fine-tuning can fail to eliminate a model's reliance on spurious attributes. Our analysis also motivates a method for targeted alteration of a model's mechanisms, named connectivity-based fine-tuning (CBFT), which we analyze using several synthetic datasets for the task of reducing a model's reliance on spurious attributes.

The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However, finding the right permutation is challenging, and current optimization techniques are not differentiable, which makes it difficult to integrate into a gradient-based optimization, and often leads to sub-optimal solutions. In this paper, we propose a Sinkhorn re-basin network with the ability to obtain the transportation plan that better suits a given objective. Unlike the current state-of-art, our method is differentiable and, therefore, easy to adapt to any task within the deep learning domain. Furthermore, we show the advantage of our re-basin method by proposing a new cost function that allows performing incremental learning by exploiting the linear mode connectivity property. The benefit of our method is compared against similar approaches from the literature, under several conditions for both optimal transport finding and linear mode connectivity. The effectiveness of our continual learning method based on re-basin is also shown for several common benchmark datasets, providing experimental results that are competitive with state-of-art results from the literature.

This paper reveals a novel linear characteristic exclusive to transformer decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We analyze embedding transformations between sequential layers, uncovering a near-perfect linear relationship (Procrustes similarity score of 0.99). However, linearity decreases when the residual component is removed due to a consistently low output norm of the transformer layer. Our experiments show that removing or linearly approximating some of the most linear blocks of transformers does not affect significantly the loss or model performance. Moreover, in our pretraining experiments on smaller models we introduce a cosine-similarity-based regularization, aimed at reducing layer linearity. This regularization improves performance metrics on benchmarks like Tiny Stories and SuperGLUE and as well successfully decreases the linearity of the models. This study challenges the existing understanding of transformer architectures, suggesting that their operation may be more linear than previously assumed.

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.

Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, multi-layer architectures, which are required to propagate knowledge to distant nodes in the graph, dilute the knowledge by performing extensive Laplacian smoothing at each layer and thereby consequently decrease performance. In order to still enjoy the benefit brought by the graph structure while preventing dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node to improve information propagation in the graph. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches.

It has recently been conjectured that neural network solution sets reachable via stochastic gradient descent (SGD) are convex, considering permutation invariances (Entezari et al., 2022). This means that a linear path can connect two independent solutions with low loss, given the weights of one of the models are appropriately permuted. However, current methods to test this theory often require very wide networks to succeed. In this work, we conjecture that more generally, the SGD solution set is a "star domain" that contains a "star model" that is linearly connected to all the other solutions via paths with low loss values, modulo permutations. We propose the Starlight algorithm that finds a star model of a given learning task. We validate our claim by showing that this star model is linearly connected with other independently found solutions. As an additional benefit of our study, we demonstrate better uncertainty estimates on the Bayesian Model Averaging over the obtained star domain. Further, we demonstrate star models as potential substitutes for model ensembles. Our code is available at https://github.com/aktsonthalia/starlight.

In diffusion models, UNet is the most popular network backbone, since its long skip connects (LSCs) to connect distant network blocks can aggregate long-distant information and alleviate vanishing gradient. Unfortunately, UNet often suffers from unstable training in diffusion models which can be alleviated by scaling its LSC coefficients smaller. However, theoretical understandings of the instability of UNet in diffusion models and also the performance improvement of LSC scaling remain absent yet. To solve this issue, we theoretically show that the coefficients of LSCs in UNet have big effects on the stableness of the forward and backward propagation and robustness of UNet. Specifically, the hidden feature and gradient of UNet at any layer can oscillate and their oscillation ranges are actually large which explains the instability of UNet training. Moreover, UNet is also provably sensitive to perturbed input, and predicts an output distant from the desired output, yielding oscillatory loss and thus oscillatory gradient. Besides, we also observe the theoretical benefits of the LSC coefficient scaling of UNet in the stableness of hidden features and gradient and also robustness. Finally, inspired by our theory, we propose an effective coefficient scaling framework ScaleLong that scales the coefficients of LSC in UNet and better improves the training stability of UNet. Experimental results on four famous datasets show that our methods are superior to stabilize training and yield about 1.5x training acceleration on different diffusion models with UNet or UViT backbones. Code: https://github.com/sail-sg/ScaleLong

Satellite connectivity is gaining increased attention as the demand for seamless internet access, especially in transportation and remote areas, continues to grow. For fast-moving objects such as aircraft, vehicles, or trains, satellite connectivity is critical due to their mobility and frequent presence in areas without terrestrial coverage. Maintaining reliable connectivity in these cases requires frequent switching between satellite beams, constellations, or orbits. To enhance user experience and address challenges like long switching times, Machine Learning (ML) algorithms can analyze historical connectivity data and predict network quality at specific locations. This allows for proactive measures, such as network switching before connectivity issues arise. In this paper, we analyze a real dataset of communication between a Geostationary Orbit (GEO) satellite and aircraft over multiple flights, using ML to predict signal quality. Our prediction model achieved an F1 score of 0.97 on the test data, demonstrating the accuracy of machine learning in predicting signal quality during flight. By enabling seamless broadband service, including roaming between different satellite constellations and providers, our model addresses the need for real-time predictions of signal quality. This approach can further be adapted to automate satellite and beam-switching mechanisms to improve overall communication efficiency. The model can also be retrained and applied to any moving object with satellite connectivity, using customized datasets, including connected vehicles and trains.

This paper challenges the well-established paradigm for building any-to-any networks for training Large Language Models (LLMs). We show that LLMs exhibit a unique communication pattern where only small groups of GPUs require high-bandwidth any-to-any communication within them, to achieve near-optimal training performance. Across these groups of GPUs, the communication is insignificant, sparse, and homogeneous. We propose a new network architecture that closely resembles the communication requirement of LLMs. Our architecture partitions the cluster into sets of GPUs interconnected with non-blocking any-to-any high-bandwidth interconnects that we call HB domains. Across the HB domains, the network only connects GPUs with communication demands. We call this network a "rail-only" connection, and show that our proposed architecture reduces the network cost by up to 75% compared to the state-of-the-art any-to-any Clos networks without compromising the performance of LLM training.

Fine-tuning large language models (LLMs) remains resource-intensive due to their sheer scale. While zeroth-order (ZO) optimization provides a memory-efficient alternative by eliminating backward passes, its application to multi-hundred-billion-parameter models is constrained by GPU memory and compute throughput. The ZO2 framework addresses the memory bottleneck by offloading model parameters to CPU memory and overlapping transformer block transfer with dual forward computation on a single GPU. However, ZO2 remains limited by its single-device execution and achieves modest throughput. In this work, we present DistZO2, a high-throughput, memory-efficient framework for distributed zeroth-order fine-tuning of LLMs. DistZO2 introduces three parallel strategies: (1) Perturbation Parallelism (PertP), which parallelizes the two perturbed forward passes across devices; (2) Distributed Data Parallelism (DDP), adapted to the scalar-gradient nature of ZO training; and (3) a unified 2D Parallelism design that combines PertP and DDP. To further mitigate communication bottlenecks introduced by parameter offloading, we propose a hardware-aware communication strategy that slices parameter blocks and redistributes them across GPUs via high-speed interconnects such as NVLink. DistZO2 scales zeroth-order fine-tuning to modern multi-GPU systems, preserving ZO2's memory efficiency while substantially improving training throughput. In our experiments on OPT-175B, DistZO2 achieves a 3x speedup over ZO2 with distributed computing. DistZO2's code has been open-sourced in https://github.com/liangyuwang/zo2.

Scaling up Large Language Model(LLM) training involves fitting a tremendous amount of training parameters across a limited number of workers. However, methods like ZeRO-3 that drastically reduce GPU memory pressure often incur heavy communication to ensure global synchronization and consistency. Established efforts such as ZeRO++ use secondary partitions to avoid inter-node communications, given that intra-node GPU-GPU transfer generally has more bandwidth and lower latency than inter-node connections. However, as more capable infrastructure like Frontier, equipped with AMD GPUs, emerged with impressive computing capability, there is a need for investigations on the hardware topology and to develop targeted strategies to improve training efficiency. In this work, we propose a collection of communication and optimization strategies for ZeRO++ to reduce communication costs and improve memory utilization. In this paper, we propose a 3-level hierarchical partitioning specifically for the current Top-1 supercomputing cluster, Frontier, which aims at leveraging various bandwidths across layers of communications (GCD-GCD, GPU-GPU, and inter-node) to reduce communication overhead. For a 20B GPT model, we observe a 1.71x increase in TFLOPS per GPU when compared with ZeRO++ up to 384 GCDs and a scaling efficiency of 0.94 for up to 384 GCDs. To the best of our knowledge, our work is also the first effort to efficiently optimize LLM workloads on Frontier AMD GPUs.

Modern diffusion models, particularly those utilizing a Transformer-based UNet for denoising, rely heavily on self-attention operations to manage complex spatial relationships, thus achieving impressive generation performance. However, this existing paradigm faces significant challenges in generating high-resolution visual content due to its quadratic time and memory complexity with respect to the number of spatial tokens. To address this limitation, we aim at a novel linear attention mechanism as an alternative in this paper. Specifically, we begin our exploration from recently introduced models with linear complexity, e.g., Mamba, Mamba2, and Gated Linear Attention, and identify two key features-attention normalization and non-causal inference-that enhance high-resolution visual generation performance. Building on these insights, we introduce a generalized linear attention paradigm, which serves as a low-rank approximation of a wide spectrum of popular linear token mixers. To save the training cost and better leverage pre-trained models, we initialize our models and distill the knowledge from pre-trained StableDiffusion (SD). We find that the distilled model, termed LinFusion, achieves performance on par with or superior to the original SD after only modest training, while significantly reducing time and memory complexity. Extensive experiments on SD-v1.5, SD-v2.1, and SD-XL demonstrate that LinFusion delivers satisfactory zero-shot cross-resolution generation performance, generating high-resolution images like 16K resolution. Moreover, it is highly compatible with pre-trained SD components, such as ControlNet and IP-Adapter, requiring no adaptation efforts. Codes are available at https://github.com/Huage001/LinFusion.

Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently provided an equivalent convex training problem. However, extending this result to deeper networks remains to be an open problem. In this paper, we prove that the duality gap for deeper linear networks with vector outputs is non-zero. In contrast, we show that the zero duality gap can be obtained by stacking standard deep networks in parallel, which we call a parallel architecture, and modifying the regularization. Therefore, we prove the strong duality and existence of equivalent convex problems that enable globally optimal training of deep networks. As a by-product of our analysis, we demonstrate that the weight decay regularization on the network parameters explicitly encourages low-rank solutions via closed-form expressions. In addition, we show that strong duality holds for three-layer standard ReLU networks given rank-1 data matrices.

Transformers face quadratic complexity and memory issues with long sequences, prompting the adoption of linear attention mechanisms using fixed-size hidden states. However, linear models often suffer from limited recall performance, leading to hybrid architectures that combine linear and full attention layers. Despite extensive hybrid architecture research, the choice of linear attention component has not been deeply explored. We systematically evaluate various linear attention models across generations - vector recurrences to advanced gating mechanisms - both standalone and hybridized. To enable this comprehensive analysis, we trained and open-sourced 72 models: 36 at 340M parameters (20B tokens) and 36 at 1.3B parameters (100B tokens), covering six linear attention variants across five hybridization ratios. Benchmarking on standard language modeling and recall tasks reveals that superior standalone linear models do not necessarily excel in hybrids. While language modeling remains stable across linear-to-full attention ratios, recall significantly improves with increased full attention layers, particularly below a 3:1 ratio. Our study highlights selective gating, hierarchical recurrence, and controlled forgetting as critical for effective hybrid models. We recommend architectures such as HGRN-2 or GatedDeltaNet with a linear-to-full ratio between 3:1 and 6:1 to achieve Transformer-level recall efficiently. Our models are open-sourced at https://huggingface.co/collections/m-a-p/hybrid-linear-attention-research-686c488a63d609d2f20e2b1e.

Time series forecasting (TSF) is critical in domains like energy, finance, healthcare, and logistics, requiring models that generalize across diverse datasets. Large pre-trained models such as Chronos and Time-MoE show strong zero-shot (ZS) performance but suffer from high computational costs. In this work, We introduce Super-Linear, a lightweight and scalable mixture-of-experts (MoE) model for general forecasting. It replaces deep architectures with simple frequency-specialized linear experts, trained on resampled data across multiple frequency regimes. A lightweight spectral gating mechanism dynamically selects relevant experts, enabling efficient, accurate forecasting. Despite its simplicity, Super-Linear matches state-of-the-art performance while offering superior efficiency, robustness to various sampling rates, and enhanced interpretability. The implementation of Super-Linear is available at https://github.com/azencot-group/SuperLinear{https://github.com/azencot-group/SuperLinear}

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear complexity by approximating the Softmax operation through carefully designed mapping functions. However, current linear attention approaches either suffer from significant performance degradation or introduce additional computation overhead from the mapping functions. In this paper, we propose a novel Focused Linear Attention module to achieve both high efficiency and expressiveness. Specifically, we first analyze the factors contributing to the performance degradation of linear attention from two perspectives: the focus ability and feature diversity. To overcome these limitations, we introduce a simple yet effective mapping function and an efficient rank restoration module to enhance the expressiveness of self-attention while maintaining low computation complexity. Extensive experiments show that our linear attention module is applicable to a variety of advanced vision Transformers, and achieves consistently improved performances on multiple benchmarks. Code is available at https://github.com/LeapLabTHU/FLatten-Transformer.

We show that introducing a weighting factor to reduce the influence of identity shortcuts in residual networks significantly enhances semantic feature learning in generative representation learning frameworks, such as masked autoencoders (MAEs) and diffusion models. Our modification notably improves feature quality, raising ImageNet-1K K-Nearest Neighbor accuracy from 27.4% to 63.9% and linear probing accuracy from 67.8% to 72.7% for MAEs with a ViT-B/16 backbone, while also enhancing generation quality in diffusion models. This significant gap suggests that, while residual connection structure serves an essential role in facilitating gradient propagation, it may have a harmful side effect of reducing capacity for abstract learning by virtue of injecting an echo of shallower representations into deeper layers. We ameliorate this downside via a fixed formula for monotonically decreasing the contribution of identity connections as layer depth increases. Our design promotes the gradual development of feature abstractions, without impacting network trainability. Analyzing the representations learned by our modified residual networks, we find correlation between low effective feature rank and downstream task performance.

The derivation of ultimate limits to communication over certain quantum repeater networks have provided extremely valuable benchmarks for assessing near-term quantum communication protocols. However, these bounds are usually derived in the limit of ideal devices and leave questions about the performance of practical implementations unanswered. To address this challenge, we quantify how the presence of loss in repeater stations affect the maximum attainable rates for quantum communication over linear repeater chains and more complex quantum networks. Extending the framework of node splitting, we model the loss introduced at the repeater stations and then prove the corresponding limits. In the linear chain scenario we show that, by increasing the number of repeater stations, the maximum rate cannot overcome a quantity which solely depends on the loss of a single station. We introduce a way of adapting the standard machinery for obtaining bounds to this realistic scenario. The difference is that whilst ultimate limits for any strategy can be derived given a fixed channel, when the repeaters introduce additional decoherence, then the effective overall channel is itself a function of the chosen repeater strategy (e.g., one-way versus two-way classical communication). Classes of repeater strategies can be analysed using additional modelling and the subsequent bounds can be interpreted as the optimal rate within that class.

We present 1d-qt-ideal-solver, an open-source Python library for simulating one-dimensional quantum tunneling dynamics under idealized coherent conditions. The solver implements the split-operator method with second-order Trotter-Suzuki factorization, utilizing FFT-based spectral differentiation for the kinetic operator and complex absorbing potentials to eliminate boundary reflections. Numba just-in-time compilation achieves performance comparable to compiled languages while maintaining code accessibility. We validate the implementation through two canonical test cases: rectangular barriers modeling field emission through oxide layers and Gaussian barriers approximating scanning tunneling microscopy interactions. Both simulations achieve exceptional numerical fidelity with machine-precision energy conservation over femtosecond-scale propagation. Comparative analysis employing information-theoretic measures and nonparametric hypothesis tests reveals that rectangular barriers exhibit moderately higher transmission coefficients than Gaussian barriers in the over-barrier regime, though Jensen-Shannon divergence analysis indicates modest practical differences between geometries. Phase space analysis confirms complete decoherence when averaged over spatial-temporal domains. The library name reflects its scope: idealized signifies deliberate exclusion of dissipation, environmental coupling, and many-body interactions, limiting applicability to qualitative insights and pedagogical purposes rather than quantitative experimental predictions. Distributed under the MIT License, the library provides a deployable tool for teaching quantum mechanics and preliminary exploration of tunneling dynamics.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NP- and #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

We present hyper-connections, a simple yet effective method that can serve as an alternative to residual connections. This approach specifically addresses common drawbacks observed in residual connection variants, such as the seesaw effect between gradient vanishing and representation collapse. Theoretically, hyper-connections allow the network to adjust the strength of connections between features at different depths and dynamically rearrange layers. We conduct experiments focusing on the pre-training of large language models, including dense and sparse models, where hyper-connections show significant performance improvements over residual connections. Additional experiments conducted on vision tasks also demonstrate similar improvements. We anticipate that this method will be broadly applicable and beneficial across a wide range of AI problems.

Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.

The new barrier mode in Apache Spark allows embedding distributed deep learning training as a Spark stage to simplify the distributed training workflow. In Spark, a task in a stage does not depend on any other tasks in the same stage, and hence it can be scheduled independently. However, several algorithms require more sophisticated inter-task communications, similar to the MPI paradigm. By combining distributed message passing (using asynchronous network IO), OpenJDK's new auto-vectorization and Spark's barrier execution mode, we can add non-map/reduce based algorithms, such as Cannon's distributed matrix multiplication to Spark. We document an efficient distributed matrix multiplication using Cannon's algorithm, which improves significantly on the performance of the existing MLlib implementation. Used within a barrier task, the algorithm described herein results in an up to 24 percent performance increase on a 10,000x10,000 square matrix with a significantly lower memory footprint. Applications of efficient matrix multiplication include, among others, accelerating the training and implementation of deep convolutional neural network based workloads, and thus such efficient algorithms can play a ground-breaking role in faster, more efficient execution of even the most complicated machine learning tasks.

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.

One of the core pillars of efficient deep learning methods is architectural improvements such as the residual/skip connection, which has led to significantly better model convergence and quality. Since then the residual connection has become ubiquitous in not just convolutional neural networks but also transformer-based architectures, the backbone of LLMs. In this paper we introduce Learned Augmented Residual Layer (LAuReL) -- a novel generalization of the canonical residual connection -- with the goal to be an in-situ replacement of the latter while outperforming on both model quality and footprint metrics. Our experiments show that using \laurel can help boost performance for both vision and language models. For example, on the ResNet-50, ImageNet 1K task, it achieves 60% of the gains from adding an extra layer, while only adding 0.003% more parameters, and matches it while adding 2.6times fewer parameters.

We perform an empirical study of the behaviour of deep networks when fully linearizing some of its feature channels through a sparsity prior on the overall number of nonlinear units in the network. In experiments on image classification and machine translation tasks, we investigate how much we can simplify the network function towards linearity before performance collapses. First, we observe a significant performance gap when reducing nonlinearity in the network function early on as opposed to late in training, in-line with recent observations on the time-evolution of the data-dependent NTK. Second, we find that after training, we are able to linearize a significant number of nonlinear units while maintaining a high performance, indicating that much of a network's expressivity remains unused but helps gradient descent in early stages of training. To characterize the depth of the resulting partially linearized network, we introduce a measure called average path length, representing the average number of active nonlinearities encountered along a path in the network graph. Under sparsity pressure, we find that the remaining nonlinear units organize into distinct structures, forming core-networks of near constant effective depth and width, which in turn depend on task difficulty.

In commonly used sub-quadratic complexity modules, linear attention benefits from simplicity and high parallelism, making it promising for image synthesis tasks. However, the architectural design and learning strategy for linear attention remain underexplored in this field. In this paper, we offer a suite of ready-to-use solutions for efficient linear diffusion Transformers. Our core contributions include: (1) Simplified Linear Attention using few heads, observing the free-lunch effect of performance without latency increase. (2) Weight inheritance from a fully pre-trained diffusion Transformer: initializing linear Transformer using pre-trained diffusion Transformer and loading all parameters except for those related to linear attention. (3) Hybrid knowledge distillation objective: using a pre-trained diffusion Transformer to help the training of the student linear Transformer, supervising not only the predicted noise but also the variance of the reverse diffusion process. These guidelines lead to our proposed Linear Diffusion Transformer (LiT), an efficient text-to-image Transformer that can be deployed offline on a laptop. Experiments show that in class-conditional 256*256 and 512*512 ImageNet benchmark LiT achieves highly competitive FID while reducing training steps by 80% and 77% compared to DiT. LiT also rivals methods based on Mamba or Gated Linear Attention. Besides, for text-to-image generation, LiT allows for the rapid synthesis of up to 1K resolution photorealistic images. Project page: https://techmonsterwang.github.io/LiT/.

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios in (0,1], and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural networks has emerged as an essential area of research to enhance adversarial robustness and network certifiability. This paper presents a rigorous approach to the general design of L-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. Initially, the ResNet architecture was reformulated as a cyclic tridiagonal LMI, and closed-form constraints on network parameters were derived to ensure L-Lipschitz continuity; however, using a new LDL^top decomposition approach for certifying LMI feasibility, we extend the construction of L-Lipchitz networks to any other nonlinear architecture. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained residual networks and other hierarchical architectures. Cholesky decomposition is also used for efficient parameterization. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. The LDL^top formulation is shown to be a tight relaxation of the SDP-based network, maintaining full expressiveness and achieving 3\%-13\% accuracy gains over SLL Layers on 121 UCI data sets.

Coronary microvascular disease constitutes a substantial risk to human health. Employing computer-aided analysis and diagnostic systems, medical professionals can intervene early in disease progression, with 3D vessel segmentation serving as a crucial component. Nevertheless, conventional U-Net architectures tend to yield incoherent and imprecise segmentation outcomes, particularly for small vessel structures. While models with attention mechanisms, such as Transformers and large convolutional kernels, demonstrate superior performance, their extensive computational demands during training and inference lead to increased time complexity. In this study, we leverage Fourier domain learning as a substitute for multi-scale convolutional kernels in 3D hierarchical segmentation models, which can reduce computational expenses while preserving global receptive fields within the network. Furthermore, a zero-parameter frequency domain fusion method is designed to improve the skip connections in U-Net architecture. Experimental results on a public dataset and an in-house dataset indicate that our novel Fourier transformation-based network achieves remarkable dice performance (84.37\% on ASACA500 and 80.32\% on ImageCAS) in tubular vessel segmentation tasks and substantially reduces computational requirements without compromising global receptive fields.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

Multi-layer perceptrons (MLPs) conventionally follow a narrow-wide-narrow design where skip connections operate at the input/output dimensions while processing occurs in expanded hidden spaces. We challenge this convention by proposing wide-narrow-wide (Hourglass) MLP blocks where skip connections operate at expanded dimensions while residual computation flows through narrow bottlenecks. This inversion leverages higher-dimensional spaces for incremental refinement while maintaining computational efficiency through parameter-matched designs. Implementing Hourglass MLPs requires an initial projection to lift input signals to expanded dimensions. We propose that this projection can remain fixed at random initialization throughout training, enabling efficient training and inference implementations. We evaluate both architectures on generative tasks over popular image datasets, characterizing performance-parameter Pareto frontiers through systematic architectural search. Results show that Hourglass architectures consistently achieve superior Pareto frontiers compared to conventional designs. As parameter budgets increase, optimal Hourglass configurations favor deeper networks with wider skip connections and narrower bottlenecks-a scaling pattern distinct from conventional MLPs. Our findings suggest reconsidering skip connection placement in modern architectures, with potential applications extending to Transformers and other residual networks.

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute (access) time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

Zero Redundancy Optimizer (ZeRO) has been used to train a wide range of large language models on massive GPUs clusters due to its ease of use, efficiency, and good scalability. However, when training on low-bandwidth clusters, or at scale which forces batch size per GPU to be small, ZeRO's effective throughput is limited because of high communication volume from gathering weights in forward pass, backward pass, and averaging gradients. This paper introduces three communication volume reduction techniques, which we collectively refer to as ZeRO++, targeting each of the communication collectives in ZeRO. First is block-quantization based all-gather. Second is data remapping that trades-off communication for more memory. Third is a novel all-to-all based quantized gradient averaging paradigm as replacement of reduce-scatter collective, which preserves accuracy despite communicating low precision data. Collectively, ZeRO++ reduces communication volume of ZeRO by 4x, enabling up to 2.16x better throughput at 384 GPU scale.

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and M\"obius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8\% improvement on heterophilic graphs and 8.4\% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

Generalized Zero-Shot Learning (GZSL) is a challenging topic that has promising prospects in many realistic scenarios. Using a gating mechanism that discriminates the unseen samples from the seen samples can decompose the GZSL problem to a conventional Zero-Shot Learning (ZSL) problem and a supervised classification problem. However, training the gate is usually challenging due to the lack of data in the unseen domain. To resolve this problem, in this paper, we propose a boundary based Out-of-Distribution (OOD) classifier which classifies the unseen and seen domains by only using seen samples for training. First, we learn a shared latent space on a unit hyper-sphere where the latent distributions of visual features and semantic attributes are aligned class-wisely. Then we find the boundary and the center of the manifold for each class. By leveraging the class centers and boundaries, the unseen samples can be separated from the seen samples. After that, we use two experts to classify the seen and unseen samples separately. We extensively validate our approach on five popular benchmark datasets including AWA1, AWA2, CUB, FLO and SUN. The experimental results demonstrate the advantages of our approach over state-of-the-art methods.

The human brain is a complex, dynamic network, which is commonly studied using functional magnetic resonance imaging (fMRI) and modeled as network of Regions of interest (ROIs) for understanding various brain functions. Recent studies utilize deep learning approaches to learn the brain network representation based on functional connectivity (FC) profile, broadly falling into two main categories. The Fixed-FC approaches, utilizing the FC profile which represents the linear temporal relation within the brain network, are limited by failing to capture informative brain temporal dynamics. On the other hand, the Dynamic-FC approaches, modeling the evolving FC profile over time, often exhibit less satisfactory performance due to challenges in handling the inherent noisy nature of fMRI data. To address these challenges, we propose Brain Masked Auto-Encoder (BrainMAE) for learning representations directly from fMRI time-series data. Our approach incorporates two essential components: a region-aware graph attention mechanism designed to capture the relationships between different brain ROIs, and a novel self-supervised masked autoencoding framework for effective model pre-training. These components enable the model to capture rich temporal dynamics of brain activity while maintaining resilience to inherent noise in fMRI data. Our experiments demonstrate that BrainMAE consistently outperforms established baseline methods by significant margins in four distinct downstream tasks. Finally, leveraging the model's inherent interpretability, our analysis of model-generated representations reveals findings that resonate with ongoing research in the field of neuroscience.

Masked graph autoencoders have emerged as a powerful graph self-supervised learning method that has yet to be fully explored. In this paper, we unveil that the existing discrete edge masking and binary link reconstruction strategies are insufficient to learn topologically informative representations, from the perspective of message propagation on graph neural networks. These limitations include blocking message flows, vulnerability to over-smoothness, and suboptimal neighborhood discriminability. Inspired by these understandings, we explore non-discrete edge masks, which are sampled from a continuous and dispersive probability distribution instead of the discrete Bernoulli distribution. These masks restrict the amount of output messages for each edge, referred to as "bandwidths". We propose a novel, informative, and effective topological masked graph autoencoder using bandwidth masking and a layer-wise bandwidth prediction objective. We demonstrate its powerful graph topological learning ability both theoretically and empirically. Our proposed framework outperforms representative baselines in both self-supervised link prediction (improving the discrete edge reconstructors by at most 20%) and node classification on numerous datasets, solely with a structure-learning pretext. Our implementation is available at https://github.com/Newiz430/Bandana.

Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as CIFAR-10. This paper investigates strategies for expanding certifiably robust training to larger, deeper models. A key challenge in certifying deep networks is efficient calculation of the Lipschitz bound for residual blocks found in ResNet and ViT architectures. We show that fast ways of bounding the Lipschitz constant for conventional ResNets are loose, and show how to address this by designing a new residual block, leading to the Linear ResNet (LiResNet) architecture. We then introduce Efficient Margin MAximization (EMMA), a loss function that stabilizes robust training by simultaneously penalizing worst-case adversarial examples from all classes. Together, these contributions yield new state-of-the-art robust accuracy on CIFAR-10/100 and Tiny-ImageNet under ell_2 perturbations. Moreover, for the first time, we are able to scale up fast deterministic robustness guarantees to ImageNet, demonstrating that this approach to robust learning can be applied to real-world applications. We release our code on Github: https://github.com/klasleino/gloro.

We present an end-to-end deep learning segmentation method by combining a 3D UNet architecture with a graph neural network (GNN) model. In this approach, the convolutional layers at the deepest level of the UNet are replaced by a GNN-based module with a series of graph convolutions. The dense feature maps at this level are transformed into a graph input to the GNN module. The incorporation of graph convolutions in the UNet provides nodes in the graph with information that is based on node connectivity, in addition to the local features learnt through the downsampled paths. This information can help improve segmentation decisions. By stacking several graph convolution layers, the nodes can access higher order neighbourhood information without substantial increase in computational expense. We propose two types of node connectivity in the graph adjacency: i) one predefined and based on a regular node neighbourhood, and ii) one dynamically computed during training and using the nearest neighbour nodes in the feature space. We have applied this method to the task of segmenting the airway tree from chest CT scans. Experiments have been performed on 32 CTs from the Danish Lung Cancer Screening Trial dataset. We evaluate the performance of the UNet-GNN models with two types of graph adjacency and compare it with the baseline UNet.

The optimization of multilayer neural networks typically leads to a solution with zero training error, yet the landscape can exhibit spurious local minima and the minima can be disconnected. In this paper, we shed light on this phenomenon: we show that the combination of stochastic gradient descent (SGD) and over-parameterization makes the landscape of multilayer neural networks approximately connected and thus more favorable to optimization. More specifically, we prove that SGD solutions are connected via a piecewise linear path, and the increase in loss along this path vanishes as the number of neurons grows large. This result is a consequence of the fact that the parameters found by SGD are increasingly dropout stable as the network becomes wider. We show that, if we remove part of the neurons (and suitably rescale the remaining ones), the change in loss is independent of the total number of neurons, and it depends only on how many neurons are left. Our results exhibit a mild dependence on the input dimension: they are dimension-free for two-layer networks and depend linearly on the dimension for multilayer networks. We validate our theoretical findings with numerical experiments for different architectures and classification tasks.

Various common deep learning architectures, such as LSTMs, GRUs, Resnets and Highway Networks, employ state passthrough connections that support training with high feed-forward depth or recurrence over many time steps. These "Passthrough Networks" architectures also enable the decoupling of the network state size from the number of parameters of the network, a possibility has been studied by Sak2014 with their low-rank parametrization of the LSTM. In this work we extend this line of research, proposing effective, low-rank and low-rank plus diagonal matrix parametrizations for Passthrough Networks which exploit this decoupling property, reducing the data complexity and memory requirements of the network while preserving its memory capacity. This is particularly beneficial in low-resource settings as it supports expressive models with a compact parametrization less susceptible to overfitting. We present competitive experimental results on several tasks, including language modeling and a near state of the art result on sequential randomly-permuted MNIST classification, a hard task on natural data.

Existing works have extensively studied adversarial examples, which are minimal perturbations that can mislead the output of deep neural networks (DNNs) while remaining imperceptible to humans. However, in this work, we reveal the existence of a harmless perturbation space, in which perturbations drawn from this space, regardless of their magnitudes, leave the network output unchanged when applied to inputs. Essentially, the harmless perturbation space emerges from the usage of non-injective functions (linear or non-linear layers) within DNNs, enabling multiple distinct inputs to be mapped to the same output. For linear layers with input dimensions exceeding output dimensions, any linear combination of the orthogonal bases of the nullspace of the parameter consistently yields no change in their output. For non-linear layers, the harmless perturbation space may expand, depending on the properties of the layers and input samples. Inspired by this property of DNNs, we solve for a family of general perturbation spaces that are redundant for the DNN's decision, and can be used to hide sensitive data and serve as a means of model identification. Our work highlights the distinctive robustness of DNNs (i.e., consistency under large magnitude perturbations) in contrast to adversarial examples (vulnerability for small imperceptible noises).

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

Residual connections are central to modern deep learning architectures, enabling the training of very deep networks by mitigating gradient vanishing. Hyper-Connections recently generalized residual connections by introducing multiple connection strengths at different depths, thereby addressing the seesaw effect between gradient vanishing and representation collapse. However, Hyper-Connections increase memory access costs by expanding the width of hidden states. In this paper, we propose Frac-Connections, a novel approach that divides hidden states into multiple parts rather than expanding their width. Frac-Connections retain partial benefits of Hyper-Connections while reducing memory consumption. To validate their effectiveness, we conduct large-scale experiments on language tasks, with the largest being a 7B MoE model trained on up to 3T tokens, demonstrating that Frac-Connections significantly outperform residual connections.

Efficient training strategies for large-scale diffusion models have recently emphasized the importance of improving discriminative feature representations in these models. A central line of work in this direction is representation alignment with features obtained from powerful external encoders, which improves the representation quality as assessed through linear probing. Alignment-based approaches show promise but depend on large pretrained encoders, which are computationally expensive to obtain. In this work, we propose an alternative regularization for training, based on promoting the Linear SEParability (LSEP) of intermediate layer representations. LSEP eliminates the need for an auxiliary encoder and representation alignment, while incorporating linear probing directly into the network's learning dynamics rather than treating it as a simple post-hoc evaluation tool. Our results demonstrate substantial improvements in both training efficiency and generation quality on flow-based transformer architectures such as SiTs, achieving an FID of 1.46 on 256 times 256 ImageNet dataset.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed ell^2 Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from mathbb R^N onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at https://github.com/acfr/LBDN.

Vector Quantization (VQ) is a widely used method for converting continuous representations into discrete codes, which has become fundamental in unsupervised representation learning and latent generative models. However, VQ models are often hindered by the problem of representation collapse in the latent space, which leads to low codebook utilization and limits the scalability of the codebook for large-scale training. Existing methods designed to mitigate representation collapse typically reduce the dimensionality of latent space at the expense of model capacity, which do not fully resolve the core issue. In this study, we conduct a theoretical analysis of representation collapse in VQ models and identify its primary cause as the disjoint optimization of the codebook, where only a small subset of code vectors are updated through gradient descent. To address this issue, we propose SimVQ, a novel method which reparameterizes the code vectors through a linear transformation layer based on a learnable latent basis. This transformation optimizes the entire linear space spanned by the codebook, rather than merely updating the code vector selected by the nearest-neighbor search in vanilla VQ models. Although it is commonly understood that the multiplication of two linear matrices is equivalent to applying a single linear layer, our approach works surprisingly well in resolving the collapse issue in VQ models with just one linear layer. We validate the efficacy of SimVQ through extensive experiments across various modalities, including image and audio data with different model architectures. Our code is available at https://github.com/youngsheen/SimVQ.

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging. In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural networks has emerged as an essential area of research for enhancing adversarial robustness and network certifiability. This paper uses a rigorous approach to design L-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. The ResNet architecture was reformulated as a pseudo-tri-diagonal LMI with off-diagonal elements and derived closed-form constraints on network parameters to ensure L-Lipschitz continuity. To address the lack of explicit eigenvalue computations for such matrix structures, the Gershgorin circle theorem was employed to approximate eigenvalue locations, guaranteeing the LMI's negative semi-definiteness. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained networks and a compositional framework for managing recursive systems within hierarchical architectures. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. However, a limitation was identified in the Gershgorin-based approximations, which over-constrain the system, suppressing non-linear dynamics and diminishing the network's expressive capacity.

Gated Linear Units (GLUs) have become essential components in the feed-forward networks of state-of-the-art Large Language Models (LLMs). However, they require twice as many memory reads compared to feed-forward layers without gating, due to the use of separate weight matrices for the gate and value streams. To address this bottleneck, we introduce Masked Gated Linear Units (MGLUs), a novel family of GLUs with an efficient kernel implementation. The core contribution of MGLUs include: (1) the Mixture of Element-wise Gating (MoEG) architecture that learns multiple binary masks, each determining gate or value assignments at the element level on a single shared weight matrix resulting in reduced memory transfer, and (2) FlashMGLU, a hardware-friendly kernel that yields up to a 19.7 times inference-time speed-up over a naive PyTorch MGLU and is 47% more memory-efficient and 34% faster than standard GLUs despite added architectural complexity on an RTX5090 GPU. In LLM experiments, the Swish-activated variant SwiMGLU preserves its memory advantages while matching - or even surpassing - the downstream accuracy of the SwiGLU baseline.

Airway segmentation on CT scans is critical for pulmonary disease diagnosis and endobronchial navigation. Manual extraction of airway requires strenuous efforts due to the complicated structure and various appearance of airway. For automatic airway extraction, convolutional neural networks (CNNs) based methods have recently become the state-of-the-art approach. However, there still remains a challenge for CNNs to perceive the tree-like pattern and comprehend the connectivity of airway. To address this, we propose a voxel-connectivity aware approach named AirwayNet for accurate airway segmentation. By connectivity modeling, conventional binary segmentation task is transformed into 26 tasks of connectivity prediction. Thus, our AirwayNet learns both airway structure and relationship between neighboring voxels. To take advantage of context knowledge, lung distance map and voxel coordinates are fed into AirwayNet as additional semantic information. Compared to existing approaches, AirwayNet achieved superior performance, demonstrating the effectiveness of the network's awareness of voxel connectivity.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

Hypergraphs are widely being employed to represent complex higher-order relations in real-world applications. Most existing research on hypergraph learning focuses on node-level or edge-level tasks. A practically relevant and more challenging task, edge-dependent node classification (ENC), is still under-explored. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node features unique to each hyperedge. The state-of-the-art ENC solution, WHATsNet, only outputs single node and edge representations, leading to the limitations of entangled edge-specific features and non-adaptive representation sizes when applied to ENC. Additionally, WHATsNet suffers from the common oversmoothing issue in most HGNNs. To address these limitations, we propose CoNHD, a novel HGNN architecture specifically designed to model edge-specific features for ENC. Instead of learning separate representations for nodes and edges, CoNHD reformulates within-edge and within-node interactions as a hypergraph diffusion process over node-edge co-representations. We develop a neural implementation of the proposed diffusion process, leveraging equivariant networks as diffusion operators to effectively learn the diffusion dynamics from data. Extensive experiments demonstrate that CoNHD achieves the best performance across all benchmark ENC datasets and several downstream tasks without sacrificing efficiency. Our implementation is available at https://github.com/zhengyijia/CoNHD.

We present a model for chi^{(2)} waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter-space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single frequency pump pulse to back up its formation and stability properties.

The efficacy of deep residual networks is fundamentally predicated on the identity shortcut connection. While this mechanism effectively mitigates the vanishing gradient problem, it imposes a strictly additive inductive bias on feature transformations, thereby limiting the network's capacity to model complex state transitions. In this paper, we introduce Deep Delta Learning (DDL), a novel architecture that generalizes the standard residual connection by modulating the identity shortcut with a learnable, data-dependent geometric transformation. This transformation, termed the Delta Operator, constitutes a rank-1 perturbation of the identity matrix, parameterized by a reflection direction vector k(X) and a gating scalar β(X). We provide a spectral analysis of this operator, demonstrating that the gate β(X) enables dynamic interpolation between identity mapping, orthogonal projection, and geometric reflection. Furthermore, we restructure the residual update as a synchronous rank-1 injection, where the gate acts as a dynamic step size governing both the erasure of old information and the writing of new features. This unification empowers the network to explicitly control the spectrum of its layer-wise transition operator, enabling the modeling of complex, non-monotonic dynamics while preserving the stable training characteristics of gated residual architectures.

We propose a simple yet efficient anchor-free instance segmentation, called CenterMask, that adds a novel spatial attention-guided mask (SAG-Mask) branch to anchor-free one stage object detector (FCOS) in the same vein with Mask R-CNN. Plugged into the FCOS object detector, the SAG-Mask branch predicts a segmentation mask on each box with the spatial attention map that helps to focus on informative pixels and suppress noise. We also present an improved backbone networks, VoVNetV2, with two effective strategies: (1) residual connection for alleviating the optimization problem of larger VoVNet lee2019energy and (2) effective Squeeze-Excitation (eSE) dealing with the channel information loss problem of original SE. With SAG-Mask and VoVNetV2, we deign CenterMask and CenterMask-Lite that are targeted to large and small models, respectively. Using the same ResNet-101-FPN backbone, CenterMask achieves 38.3%, surpassing all previous state-of-the-art methods while at a much faster speed. CenterMask-Lite also outperforms the state-of-the-art by large margins at over 35fps on Titan Xp. We hope that CenterMask and VoVNetV2 can serve as a solid baseline of real-time instance segmentation and backbone network for various vision tasks, respectively. The Code is available at https://github.com/youngwanLEE/CenterMask.

Multi-agent multi-lidar sensor fusion between connected vehicles for cooperative perception has recently been recognized as the best technique for minimizing the blind zone of individual vehicular perception systems and further enhancing the overall safety of autonomous driving systems. This technique relies heavily on the reliability and availability of vehicle-to-everything (V2X) communication. In practical sensor fusion application scenarios, the non-line-of-sight (NLOS) issue causes blind zones for not only the perception system but also V2X direct communication. To counteract underlying communication issues, we introduce an abstract perception matrix matching method for quick sensor fusion matching procedures and mobility-height hybrid relay determination procedures, proactively improving the efficiency and performance of V2X communication to serve the upper layer application fusion requirements. To demonstrate the effectiveness of our solution, we design a new simulation framework to consider autonomous driving, sensor fusion and V2X communication in general, paving the way for end-to-end performance evaluation and further solution derivation.

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs) that focuses on hidden representations analysis rather than pure downstream task performance. Different from existing efforts, we analyze the models through a three-part evaluation: Embedding Geometry Analysis to assess representation space utilization, Metric Alignment Assessment to measure correspondence with domain-expert features, and Causal Sensitivity Testing to evaluate robustness to protocol perturbations. Using five diverse network datasets spanning controlled and real-world environments, we evaluate four state-of-the-art NFMs, revealing that they all exhibit significant anisotropy, inconsistent feature sensitivity patterns, an inability to separate the high-level context, payload dependency, and other properties. Our work identifies numerous limitations across all models and demonstrates that addressing them can significantly improve model performance (by up to +0.35 F_1 score without architectural changes).

Diffusion Transformers (DiT) have become a leading architecture in image generation. However, the quadratic complexity of attention mechanisms, which are responsible for modeling token-wise relationships, results in significant latency when generating high-resolution images. To address this issue, we aim at a linear attention mechanism in this paper that reduces the complexity of pre-trained DiTs to linear. We begin our exploration with a comprehensive summary of existing efficient attention mechanisms and identify four key factors crucial for successful linearization of pre-trained DiTs: locality, formulation consistency, high-rank attention maps, and feature integrity. Based on these insights, we introduce a convolution-like local attention strategy termed CLEAR, which limits feature interactions to a local window around each query token, and thus achieves linear complexity. Our experiments indicate that, by fine-tuning the attention layer on merely 10K self-generated samples for 10K iterations, we can effectively transfer knowledge from a pre-trained DiT to a student model with linear complexity, yielding results comparable to the teacher model. Simultaneously, it reduces attention computations by 99.5% and accelerates generation by 6.3 times for generating 8K-resolution images. Furthermore, we investigate favorable properties in the distilled attention layers, such as zero-shot generalization cross various models and plugins, and improved support for multi-GPU parallel inference. Models and codes are available here: https://github.com/Huage001/CLEAR.

Linear attention has emerged as a viable alternative to softmax attention by reducing complexity from quadratic to linear in sequence length. To preserve two fundamental properties of softmax, non-negativity and entropy reduction, current works employ various linearly separatable kernel functions with L1 normalization instead of softmax operator. However, query norms are neglected by the normalization operation in linear attention, such degradation heavily leads to an entropy gap. Meanwhile, existing works inhibit negative values of query and key vectors resulting in a missing inner-product interactions after being mapped. To address these dual challenges, we propose a novel Norm-Aware Linear Attention mechanism serving to restore norm-guided dynamic spikiness and recover kernel-perturbed norm distributions. Specifically, we first decouple query and key matrices into two components: norm and direction, to achieve norm-aware spikiness control and norm consistency, respectively. We mathematically reveal that the extent of entropy reduction varies with the query norm in softmax normalization, motivating a query-norm aware kernel function for dynamic control over entropy reduction. Furthermore, to ensure norm consistency and enforce non-negativity constraints, we employ a norm-preserving mapping to project all elements of the angular matrix into positive values, leveraging cosine similarity to inhibit dimensions with opposite directions. We conduct extensive experiments demonstrating that the NaLaFormer improves performance on vision and language tasks, enhancing both expressiveness and efficiency by up to 4.2\%.

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a "convex relaxation barrier" that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive downstream tasks. Drawing inspiration from neuroscience, particularly the brain's ability to maintain robust long-term memory while mitigating "memory interference", we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM significantly outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models. The code is released at https://github.com/OpenSparseLLMs/MoM and is also released as a part of https://github.com/OpenSparseLLMs/Linear-MoE.

As more devices connect to the internet, it becomes crucial to address their limitations and basic security needs. While much research focuses on utilizing ML and DL to tackle security challenges, there is often a tendency to overlook the practicality and feasibility of implementing these methods in real-time settings. This oversight stems from the constrained processing power and memory of certain devices (IoT devices), as well as concerns about the generalizability of these approaches. Focusing on the detection of DNS-tunneling attacks in a router as a case study, we present an end-to-end process designed to effectively address these challenges. The process spans from developing a lightweight DNS-tunneling detection model to integrating it into a resource-constrained device for real-time detection. Through our experiments, we demonstrate that utilizing stateless features for training the ML model, along with features chosen to be independent of the network configuration, leads to highly accurate results. The deployment of this carefully crafted model, optimized for embedded devices across diverse environments, resulted in high DNS-tunneling attack detection with minimal latency. With this work, we aim to encourage solutions that strike a balance between theoretical advancements and the practical applicability of ML approaches in the ever-evolving landscape of device security.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem we must look at the articulated decisions in entirety. If we could capture the actions of non-linear units for a particular input, we would be able to replay the whole system back and forth as if it was always linear. It would also reveal the actions of non-linearities because the resulting linear system, a Linear Interpreter, depends on the input image. We introduce a hooking layer, called a LinearScope, which allows us to run the network and the linear interpreter in parallel. Its implementation is simple, flexible and efficient. From here we can make many curious inquiries: how do these linear systems look like? When the rows and columns of the transformation matrix are images, how do they look like? What type of basis do these linear transformations rely on? The answers depend on the problems presented, through which we take a tour to some popular architectures used for classification, super-resolution (SR) and image-to-image translation (I2I). For classification we observe that popular networks use a pixel-wise vote per class strategy and heavily rely on bias parameters. For SR and I2I we find that CNNs use wavelet-type basis similar to the human visual system. For I2I we reveal copy-move and template-creation strategies to generate outputs.

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis.

Diffusion models have advanced from text-to-image (T2I) to image-to-image (I2I) generation by incorporating structured inputs such as depth maps, enabling fine-grained spatial control. However, existing methods either train separate models for each condition or rely on unified architectures with entangled representations, resulting in poor generalization and high adaptation costs for novel conditions. To this end, we propose DivControl, a decomposable pretraining framework for unified controllable generation and efficient adaptation. DivControl factorizes ControlNet via SVD into basic components-pairs of singular vectors-which are disentangled into condition-agnostic learngenes and condition-specific tailors through knowledge diversion during multi-condition training. Knowledge diversion is implemented via a dynamic gate that performs soft routing over tailors based on the semantics of condition instructions, enabling zero-shot generalization and parameter-efficient adaptation to novel conditions. To further improve condition fidelity and training efficiency, we introduce a representation alignment loss that aligns condition embeddings with early diffusion features. Extensive experiments demonstrate that DivControl achieves state-of-the-art controllability with 36.4times less training cost, while simultaneously improving average performance on basic conditions. It also delivers strong zero-shot and few-shot performance on unseen conditions, demonstrating superior scalability, modularity, and transferability.

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit intrinsic correlations over time. Capitalizing on this, we introduce Correlation Mode Decomposition (CMD). This algorithm clusters the parameter space into groups, termed modes, that display synchronized behavior across epochs. This enables CMD to efficiently represent the training dynamics of complex networks, like ResNets and Transformers, using only a few modes. Moreover, test set generalization is enhanced. We introduce an efficient CMD variant, designed to run concurrently with training. Our experiments indicate that CMD surpasses the state-of-the-art method for compactly modeled dynamics on image classification. Our modeling can improve training efficiency and lower communication overhead, as shown by our preliminary experiments in the context of federated learning.

The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices u and v in the graph, there exists a path between u and v that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch 1+varepsilon and O(1) many trees for any fixed varepsilon in (0,1). However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the "planarity barrier" to construct a shortcut partition for K_r-minor-free graphs for any r. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for K_r-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for K_r-minor-free graphs, with 1+varepsilon stretch, linear space, and constant query time for any fixed varepsilon in (0,1). The previous best distance oracle [AG06] uses O(nlog n) space and O(log n) query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of O(1) size for minor-free graphs with stretch 1+varepsilon, while the previous best (1+varepsilon)-tree cover has size O(log^2 n) [BFN19].

For any positive integer k, there exist neural networks with Θ(k^3) layers, Θ(1) nodes per layer, and Θ(1) distinct parameters which can not be approximated by networks with O(k) layers unless they are exponentially large --- they must possess Ω(2^k) nodes. This result is proved here for a class of nodes termed "semi-algebraic gates" which includes the common choices of ReLU, maximum, indicator, and piecewise polynomial functions, therefore establishing benefits of depth against not just standard networks with ReLU gates, but also convolutional networks with ReLU and maximization gates, sum-product networks, and boosted decision trees (in this last case with a stronger separation: Ω(2^{k^3}) total tree nodes are required).

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform transformers especially on tasks that require in-context retrieval. While more expressive variants of linear transformers which replace the additive outer-product update in linear transformers with the delta rule have been found to be more effective at associative recall, existing algorithms for training such models do not parallelize over sequence length and are thus inefficient to train on modern hardware. This work describes a hardware-efficient algorithm for training linear transformers with the delta rule, which exploits a memory-efficient representation for computing products of Householder matrices. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B model for 100B tokens and find that it outperforms recent linear-time baselines such as Mamba and GLA in terms of perplexity and zero-shot performance on downstream tasks (including on tasks that focus on recall). We also experiment with two hybrid models which combine DeltaNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrid models outperform strong transformer baselines.

We numerically study excitation transfer in an artificial LH1-RC complex -- an N-site donor ring coupled to a central acceptor -- driven by a narrowband optical mode and evolved under a Lindblad master equation with loss and dephasing. In the absence of disorder, the light-driven system exhibits a tall, narrow on-resonance efficiency peak (near unity for our parameters); dephasing lowers and narrows this peak without shifting its position. Off resonance, the efficiency shows environmentally assisted transport with a clear non-monotonic dependence on dephasing and a finite optimum. Under static disorder, two regimes emerge: photon-ring coupling and diagonal energetic disorder mix the drive into dark ring modes, activate dissipative channels, and depress efficiency over a detuning window, whereas intra-ring coupling disorder has a much smaller impact in the tested range; increasing the intra-ring coupling g moves dark-mode crossings away from the operating detuning and restores near-peak performance. In the ordered, symmetric, single-excitation, narrowband limit we analytically derive closed-form transfer efficiencies by projecting onto the k{=}0 bright mode and solving the photon--bright mode--acceptor trimer via a Laplace/linear-algebra (determinant) formula; these expressions include a probability-conservation identity eta + sum_k L_k = 1 that benchmarks the simulations and quantitatively predicts the resonant line shape and its dephasing-induced narrowing. A minimal ring toy model further reproduces coherent trapping and its relief by moderate dephasing (ENAQT). These analytics are exact in the ordered limit and serve as mechanistic guides outside this limit, yielding practical design rules for robust, bio-inspired light-harvesting devices.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

Non-line-of-sight (NLOS) imaging is conducted to infer invisible scenes from indirect light on visible objects. The neural transient field (NeTF) was proposed for representing scenes as neural radiance fields in NLOS scenes. We propose NLOS neural implicit surface (NLOS-NeuS), which extends the NeTF to neural implicit surfaces with a signed distance function (SDF) for reconstructing three-dimensional surfaces in NLOS scenes. We introduce two constraints as loss functions for correctly learning an SDF to avoid non-zero level-set surfaces. We also introduce a lower bound constraint of an SDF based on the geometry of the first-returning photons. The experimental results indicate that these constraints are essential for learning a correct SDF in NLOS scenes. Compared with previous methods with discretized representation, NLOS-NeuS with the neural continuous representation enables us to reconstruct smooth surfaces while preserving fine details in NLOS scenes. To the best of our knowledge, this is the first study on neural implicit surfaces with volume rendering in NLOS scenes.

We present ControlNet, a neural network architecture to add spatial conditioning controls to large, pretrained text-to-image diffusion models. ControlNet locks the production-ready large diffusion models, and reuses their deep and robust encoding layers pretrained with billions of images as a strong backbone to learn a diverse set of conditional controls. The neural architecture is connected with "zero convolutions" (zero-initialized convolution layers) that progressively grow the parameters from zero and ensure that no harmful noise could affect the finetuning. We test various conditioning controls, eg, edges, depth, segmentation, human pose, etc, with Stable Diffusion, using single or multiple conditions, with or without prompts. We show that the training of ControlNets is robust with small (<50k) and large (>1m) datasets. Extensive results show that ControlNet may facilitate wider applications to control image diffusion models.

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

The Mixture-of-Experts (MoE) approach has demonstrated outstanding scalability in multi-task learning including low-level upstream tasks such as concurrent removal of multiple adverse weather effects. However, the conventional MoE architecture with parallel Feed Forward Network (FFN) experts leads to significant parameter and computational overheads that hinder its efficient deployment. In addition, the naive MoE linear router is suboptimal in assigning task-specific features to multiple experts which limits its further scalability. In this work, we propose an efficient MoE architecture with weight sharing across the experts. Inspired by the idea of linear feature modulation (FM), our architecture implicitly instantiates multiple experts via learnable activation modulations on a single shared expert block. The proposed Feature Modulated Expert (FME) serves as a building block for the novel Mixture-of-Feature-Modulation-Experts (MoFME) architecture, which can scale up the number of experts with low overhead. We further propose an Uncertainty-aware Router (UaR) to assign task-specific features to different FM modules with well-calibrated weights. This enables MoFME to effectively learn diverse expert functions for multiple tasks. The conducted experiments on the multi-deweather task show that our MoFME outperforms the baselines in the image restoration quality by 0.1-0.2 dB and achieves SOTA-compatible performance while saving more than 72% of parameters and 39% inference time over the conventional MoE counterpart. Experiments on the downstream segmentation and classification tasks further demonstrate the generalizability of MoFME to real open-world applications.

Transformers with linear recurrent modeling offer linear-time training and constant-memory inference. Despite their demonstrated efficiency and performance, pretraining such non-standard architectures from scratch remains costly and risky. The linearization of large language models (LLMs) transforms pretrained standard models into linear recurrent structures, enabling more efficient deployment. However, current linearization methods typically introduce additional feature map modules that require extensive fine-tuning and overlook the gating mechanisms used in state-of-the-art linear recurrent models. To address these issues, this paper presents Liger, short for Linearizing LLMs to gated recurrent structures. Liger is a novel approach for converting pretrained LLMs into gated linear recurrent models without adding extra parameters. It repurposes the pretrained key matrix weights to construct diverse gating mechanisms, facilitating the formation of various gated recurrent structures while avoiding the need to train additional components from scratch. Using lightweight fine-tuning with Low-Rank Adaptation (LoRA), Liger restores the performance of the linearized gated recurrent models to match that of the original LLMs. Additionally, we introduce Liger Attention, an intra-layer hybrid attention mechanism, which significantly recovers 93\% of the Transformer-based LLM at 0.02\% pre-training tokens during the linearization process, achieving competitive results across multiple benchmarks, as validated on models ranging from 1B to 8B parameters. Code is available at https://github.com/OpenSparseLLMs/Linearization.

State-of-the-art supervised stereo matching methods have achieved remarkable performance on various benchmarks. However, their generalization to real-world scenarios remains challenging due to the scarcity of annotated real-world stereo data. In this paper, we propose ZeroStereo, a novel stereo image generation pipeline for zero-shot stereo matching. Our approach synthesizes high-quality right images from arbitrary single images by leveraging pseudo disparities generated by a monocular depth estimation model. Unlike previous methods that address occluded regions by filling missing areas with neighboring pixels or random backgrounds, we fine-tune a diffusion inpainting model to recover missing details while preserving semantic structure. Additionally, we propose Training-Free Confidence Generation, which mitigates the impact of unreliable pseudo labels without additional training, and Adaptive Disparity Selection, which ensures a diverse and realistic disparity distribution while preventing excessive occlusion and foreground distortion. Experiments demonstrate that models trained with our pipeline achieve state-of-the-art zero-shot generalization across multiple datasets with only a dataset volume comparable to Scene Flow. Code: https://github.com/Windsrain/ZeroStereo.

Foundation multi-modal models are often designed by stitching of multiple existing pretrained uni-modal models: for example, an image classifier with an text model. This stitching process is performed by training a connector module that aims to align the representation spaces of these uni-modal models towards a multi-modal objective. However, given the complexity of training such connectors on large scale web-based datasets coupled with the ever-increasing number of available pretrained uni-modal models, the task of uni-modal models selection and subsequent connector module training becomes computationally demanding. To address this under-studied critical problem, we propose Hypernetwork Model Alignment (Hyma), a novel all-in-one solution for optimal uni-modal model selection and connector training by leveraging hypernetworks. Specifically, our framework utilizes the parameter prediction capability of a hypernetwork to obtain jointly trained connector modules for N times M combinations of uni-modal models. In our experiments, Hyma reduces the cost of searching for the best performing uni-modal model pair by 10times, while matching the ranking and trained connector performance obtained via grid search across a suite of diverse multi-modal benchmarks.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Linear transformers aim to reduce the quadratic space-time complexity of vanilla transformers. However, they usually suffer from degraded performances on various tasks and corpus. In this paper, we examine existing kernel-based linear transformers and identify two key issues that lead to such performance gaps: 1) unbounded gradients in the attention computation adversely impact the convergence of linear transformer models; 2) attention dilution which trivially distributes attention scores over long sequences while neglecting neighbouring structures. To address these issues, we first identify that the scaling of attention matrices is the devil in unbounded gradients, which turns out unnecessary in linear attention as we show theoretically and empirically. To this end, we propose a new linear attention that replaces the scaling operation with a normalization to stabilize gradients. For the issue of attention dilution, we leverage a diagonal attention to confine attention to only neighbouring tokens in early layers. Benefiting from the stable gradients and improved attention, our new linear transformer model, transNormer, demonstrates superior performance on text classification and language modeling tasks, as well as on the challenging Long-Range Arena benchmark, surpassing vanilla transformer and existing linear variants by a clear margin while being significantly more space-time efficient. The code is available at https://github.com/OpenNLPLab/Transnormer .

We introduce a 3D-aware diffusion model, ZeroNVS, for single-image novel view synthesis for in-the-wild scenes. While existing methods are designed for single objects with masked backgrounds, we propose new techniques to address challenges introduced by in-the-wild multi-object scenes with complex backgrounds. Specifically, we train a generative prior on a mixture of data sources that capture object-centric, indoor, and outdoor scenes. To address issues from data mixture such as depth-scale ambiguity, we propose a novel camera conditioning parameterization and normalization scheme. Further, we observe that Score Distillation Sampling (SDS) tends to truncate the distribution of complex backgrounds during distillation of 360-degree scenes, and propose "SDS anchoring" to improve the diversity of synthesized novel views. Our model sets a new state-of-the-art result in LPIPS on the DTU dataset in the zero-shot setting, even outperforming methods specifically trained on DTU. We further adapt the challenging Mip-NeRF 360 dataset as a new benchmark for single-image novel view synthesis, and demonstrate strong performance in this setting. Our code and data are at http://kylesargent.github.io/zeronvs/

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

The self-attention mechanism utilizes large implicit weight matrices, programmed through dot product-based activations with very few trainable parameters, to enable long sequence modeling. In this paper, we investigate the possibility of discarding residual learning by employing large implicit kernels to achieve full context interaction at each layer of the network. To accomplish it, we introduce coordinate-based implicit MLPs as a slow network to generate hyper-kernels for another fast convolutional network. To get context-varying weights for fast dynamic encoding, we propose a HyperZ{cdotZ{cdot}W} operator that connects hyper-kernels (W) and hidden activations (Z) through simple elementwise multiplication, followed by convolution of Z using the context-dependent W. Based on this design, we present a novel Terminator architecture that integrates hyper-kernels of different sizes to produce multi-branch hidden representations for enhancing the feature extraction capability of each layer. Additionally, a bottleneck layer is employed to compress the concatenated channels, allowing only valuable information to propagate to the subsequent layers. Notably, our model incorporates several innovative components and exhibits excellent properties, such as introducing local feedback error for updating the slow network, stable zero-mean features, faster training convergence, and fewer model parameters. Extensive experimental results on pixel-level 1D and 2D image classification benchmarks demonstrate the superior performance of our architecture.

Window attention and linear attention represent two principal strategies for mitigating the quadratic complexity and ever-growing KV cache in Vision-Language Models (VLMs). However, we observe that window-based VLMs suffer performance degradation when sequence length exceeds the window size, while linear attention underperforms on information-intensive tasks such as OCR and document understanding. To overcome these limitations, we propose InfiniteVL, a linear-complexity VLM architecture that synergizes sliding window attention (SWA) with Gated DeltaNet. For achieving competitive multimodal performance under constrained resources, we design a three-stage training strategy comprising distillation pretraining, instruction tuning, and long-sequence SFT. Remarkably, using less than 2\% of the training data required by leading VLMs, InfiniteVL not only substantially outperforms previous linear-complexity VLMs but also matches the performance of leading Transformer-based VLMs, while demonstrating effective long-term memory retention. Compared to similar-sized Transformer-based VLMs accelerated by FlashAttention-2, InfiniteVL achieves over 3.6\times inference speedup while maintaining constant latency and memory footprint. In streaming video understanding scenarios, it sustains a stable 24 FPS real-time prefill speed while preserving long-term memory cache. Code and models are available at https://github.com/hustvl/InfiniteVL.

We quantify the upper bound on the size of the implicit neural representation (INR) model from a digital perspective. The upper bound of the model size increases exponentially as the required bit-precision increases. To this end, we present a bit-plane decomposition method that makes INR predict bit-planes, producing the same effect as reducing the upper bound of the model size. We validate our hypothesis that reducing the upper bound leads to faster convergence with constant model size. Our method achieves lossless representation in 2D image and audio fitting, even for high bit-depth signals, such as 16-bit, which was previously unachievable. We pioneered the presence of bit bias, which INR prioritizes as the most significant bit (MSB). We expand the application of the INR task to bit depth expansion, lossless image compression, and extreme network quantization. Our source code is available at https://github.com/WooKyoungHan/LosslessINR

Linear Sequence Modeling (LSM) like linear attention, state space models and linear RNNs, and Mixture-of-Experts (MoE) have recently emerged as significant architectural improvements. In this paper, we introduce Linear-MoE, a production-level system for modeling and training large-scale models that integrate LSM with MoE. Linear-MoE leverages the advantages of both LSM modules for linear-complexity sequence modeling and MoE layers for sparsely activation, aiming to offer high performance with efficient training. The Linear-MoE system comprises: 1) Modeling subsystem, which provides a unified framework supporting all instances of LSM. and 2) Training subsystem, which facilitates efficient training by incorporating various advanced parallelism technologies, particularly Sequence Parallelism designed for Linear-MoE models. Additionally, we explore hybrid models that combine Linear-MoE layers with standard Transformer-MoE layers with its Sequence Parallelism to further enhance model flexibility and performance. Evaluations on two model series, A0.3B-2B and A1B-7B, demonstrate Linear-MoE achieves efficiency gains while maintaining competitive performance on various benchmarks, showcasing its potential as a next-generation foundational model architecture. Code: https://github.com/OpenSparseLLMs/Linear-MoE.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from O(D^2L) to O(D^3L) for an L-layered model that accepts D-dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods. The experimental results demonstrate that our approach achieves a significant speedup compared to maximum likelihood estimation while outperforming prior methods with a noticeable margin in terms of negative log-likelihood (NLL).

Large deep learning models offer significant accuracy gains, but training billions to trillions of parameters is challenging. Existing solutions such as data and model parallelisms exhibit fundamental limitations to fit these models into limited device memory, while obtaining computation, communication and development efficiency. We develop a novel solution, Zero Redundancy Optimizer (ZeRO), to optimize memory, vastly improving training speed while increasing the model size that can be efficiently trained. ZeRO eliminates memory redundancies in data- and model-parallel training while retaining low communication volume and high computational granularity, allowing us to scale the model size proportional to the number of devices with sustained high efficiency. Our analysis on memory requirements and communication volume demonstrates: ZeRO has the potential to scale beyond 1 Trillion parameters using today's hardware. We implement and evaluate ZeRO: it trains large models of over 100B parameter with super-linear speedup on 400 GPUs, achieving throughput of 15 Petaflops. This represents an 8x increase in model size and 10x increase in achievable performance over state-of-the-art. In terms of usability, ZeRO can train large models of up to 13B parameters (e.g., larger than Megatron GPT 8.3B and T5 11B) without requiring model parallelism which is harder for scientists to apply. Last but not the least, researchers have used the system breakthroughs of ZeRO to create the world's largest language model (Turing-NLG, 17B parameters) with record breaking accuracy.

We analyze the layerwise effective dimension (rank of the feature matrix) in fully-connected ReLU networks of finite width. Specifically, for a fixed batch of m inputs and random Gaussian weights, we derive closed-form expressions for the expected rank of the \mtimes n hidden activation matrices. Our main result shows that E[EDim(ell)]=m[1-(1-2/pi)^ell]+O(e^{-c m}) so that the rank deficit decays geometrically with ratio 1-2 / pi approx 0.3634. We also prove a sub-Gaussian concentration bound, and identify the "revival" depths at which the expected rank attains local maxima. In particular, these peaks occur at depths ell_k^*approx(k+1/2)pi/log(1/rho) with height approx (1-e^{-pi/2}) m approx 0.79m. We further show that this oscillatory rank behavior is a finite-width phenomenon: under orthogonal weight initialization or strong negative-slope leaky-ReLU, the rank remains (nearly) full. These results provide a precise characterization of how random ReLU layers alternately collapse and partially revive the subspace of input variations, adding nuance to prior work on expressivity of deep networks.

This work investigates an important phenomenon in centroid-based deep clustering (DC) algorithms: Performance quickly saturates after a period of rapid early gains. Practitioners commonly address early saturation with periodic reclustering, which we demonstrate to be insufficient to address performance plateaus. We call this phenomenon the "reclustering barrier" and empirically show when the reclustering barrier occurs, what its underlying mechanisms are, and how it is possible to Break the Reclustering Barrier with our algorithm BRB. BRB avoids early over-commitment to initial clusterings and enables continuous adaptation to reinitialized clustering targets while remaining conceptually simple. Applying our algorithm to widely-used centroid-based DC algorithms, we show that (1) BRB consistently improves performance across a wide range of clustering benchmarks, (2) BRB enables training from scratch, and (3) BRB performs competitively against state-of-the-art DC algorithms when combined with a contrastive loss. We release our code and pre-trained models at https://github.com/Probabilistic-and-Interactive-ML/breaking-the-reclustering-barrier .

We introduce ReplaceMe, a generalized training-free depth pruning method that effectively replaces transformer blocks with a linear operation, while maintaining high performance for low compression ratios. In contrast to conventional pruning approaches that require additional training or fine-tuning, our approach requires only a small calibration dataset that is used to estimate a linear transformation to approximate the pruned blocks. This estimated linear mapping can be seamlessly merged with the remaining transformer blocks, eliminating the need for any additional network parameters. Our experiments show that ReplaceMe consistently outperforms other training-free approaches and remains highly competitive with state-of-the-art pruning methods that involve extensive retraining/fine-tuning and architectural modifications. Applied to several large language models (LLMs), ReplaceMe achieves up to 25% pruning while retaining approximately 90% of the original model's performance on open benchmarks - without any training or healing steps, resulting in minimal computational overhead (see Fig.1). We provide an open-source library implementing ReplaceMe alongside several state-of-the-art depth pruning techniques, available at this repository.

Latent diffusion models (LDMs) exhibit an impressive ability to produce realistic images, yet the inner workings of these models remain mysterious. Even when trained purely on images without explicit depth information, they typically output coherent pictures of 3D scenes. In this work, we investigate a basic interpretability question: does an LDM create and use an internal representation of simple scene geometry? Using linear probes, we find evidence that the internal activations of the LDM encode linear representations of both 3D depth data and a salient-object / background distinction. These representations appear surprisingly early in the denoising process-well before a human can easily make sense of the noisy images. Intervention experiments further indicate these representations play a causal role in image synthesis, and may be used for simple high-level editing of an LDM's output. Project page: https://yc015.github.io/scene-representation-diffusion-model/

Recent advancements in Large Language Models (LLMs) have set themselves apart with their exceptional performance in complex language modelling tasks. However, these models are also known for their significant computational and storage requirements, primarily due to the quadratic computation complexity of softmax attention. To mitigate this issue, linear attention has been designed to reduce the quadratic space-time complexity that is inherent in standard transformers. In this work, we embarked on a comprehensive exploration of three key components that substantially impact the performance of the Gated Linear Attention module: feature maps, normalization, and the gating mechanism. We developed a feature mapping function to address some crucial issues that previous suggestions overlooked. Then we offered further rationale for the integration of normalization layers to stabilize the training process. Moreover, we explored the saturation phenomenon of the gating mechanism and augmented it with a refining module. We conducted extensive experiments and showed our architecture outperforms previous Gated Linear Attention mechanisms in extensive tasks including training from scratch and post-linearization with continual pre-training.

In this paper, we propose a general framework for universal zero-shot goal-oriented navigation. Existing zero-shot methods build inference framework upon large language models (LLM) for specific tasks, which differs a lot in overall pipeline and fails to generalize across different types of goal. Towards the aim of universal zero-shot navigation, we propose a uniform graph representation to unify different goals, including object category, instance image and text description. We also convert the observation of agent into an online maintained scene graph. With this consistent scene and goal representation, we preserve most structural information compared with pure text and are able to leverage LLM for explicit graph-based reasoning. Specifically, we conduct graph matching between the scene graph and goal graph at each time instant and propose different strategies to generate long-term goal of exploration according to different matching states. The agent first iteratively searches subgraph of goal when zero-matched. With partial matching, the agent then utilizes coordinate projection and anchor pair alignment to infer the goal location. Finally scene graph correction and goal verification are applied for perfect matching. We also present a blacklist mechanism to enable robust switch between stages. Extensive experiments on several benchmarks show that our UniGoal achieves state-of-the-art zero-shot performance on three studied navigation tasks with a single model, even outperforming task-specific zero-shot methods and supervised universal methods.

Generating high-quality stereo videos that mimic human binocular vision requires maintaining consistent depth perception and temporal coherence across frames. While diffusion models have advanced image and video synthesis, generating high-quality stereo videos remains challenging due to the difficulty of maintaining consistent temporal and spatial coherence between left and right views. We introduce StereoCrafter-Zero, a novel framework for zero-shot stereo video generation that leverages video diffusion priors without the need for paired training data. Key innovations include a noisy restart strategy to initialize stereo-aware latents and an iterative refinement process that progressively harmonizes the latent space, addressing issues like temporal flickering and view inconsistencies. Comprehensive evaluations, including quantitative metrics and user studies, demonstrate that StereoCrafter-Zero produces high-quality stereo videos with improved depth consistency and temporal smoothness, even when depth estimations are imperfect. Our framework is robust and adaptable across various diffusion models, setting a new benchmark for zero-shot stereo video generation and enabling more immersive visual experiences. Our code can be found in~https://github.com/shijianjian/StereoCrafter-Zero.

Outdoor-to-indoor (OtI) signal propagation further challenges the already tight link budgets at millimeter-wave (mmWave). To gain insight into OtI mmWave scenarios at 28 GHz, we conducted an extensive measurement campaign consisting of over 2,200 link measurements. In total, 43 OtI scenarios were measured in West Harlem, New York City, covering seven highly diverse buildings. The measured OtI path gain can vary by up to 40 dB for a given link distance, and the empirical path gain model for all data shows an average of 30 dB excess loss over free space at distances beyond 50 m, with an RMS fitting error of 11.7 dB. The type of glass is found to be the single dominant feature for OtI loss, with 20 dB observed difference between empirical path gain models for scenarios with low-loss and high-loss glass. The presence of scaffolding, tree foliage, or elevated subway tracks, as well as difference in floor height are each found to have an impact between 5-10 dB. We show that for urban buildings with high-loss glass, OtI coverage can support 500 Mbps for 90% of indoor user equipment (UEs) with a base station (BS) antenna placed up to 49 m away. For buildings with low-loss glass, such as our case study covering multiple classrooms of a public school, data rates over 2.5/1.2 Gbps are possible from a BS 68/175 m away from the school building, when a line-of-sight path is available. We expect these results to be useful for the deployment of mmWave networks in dense urban environments as well as the development of relevant scheduling and beam management algorithms.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

Linear attention is an efficient attention mechanism that has recently emerged as a promising alternative to conventional softmax attention. With its ability to process tokens in linear computational complexities, linear attention, in theory, can handle sequences of unlimited length without sacrificing speed, i.e., maintaining a constant training speed for various sequence lengths with a fixed memory consumption. However, due to the issue with cumulative summation (cumsum), current linear attention algorithms cannot demonstrate their theoretical advantage in a causal setting. In this paper, we present Lightning Attention-2, the first linear attention implementation that enables linear attention to realize its theoretical computational benefits. To achieve this, we leverage the thought of tiling, separately handling the intra-block and inter-block components in linear attention calculation. Specifically, we utilize the conventional attention computation mechanism for the intra-blocks and apply linear attention kernel tricks for the inter-blocks. A tiling technique is adopted through both forward and backward procedures to take full advantage of the GPU hardware. We implement our algorithm in Triton to make it IO-aware and hardware-friendly. Various experiments are conducted on different model sizes and sequence lengths. Lightning Attention-2 retains consistent training and inference speed regardless of input sequence length and is significantly faster than other attention mechanisms. The source code is available at https://github.com/OpenNLPLab/lightning-attention.

Segmentation of anatomical structures and pathological regions in medical images is essential for modern clinical diagnosis, disease research, and treatment planning. While significant advancements have been made in deep learning-based segmentation techniques, many of these methods still suffer from limitations in data efficiency, generalizability, and interactivity. As a result, developing precise segmentation methods that require fewer labeled datasets remains a critical challenge in medical image analysis. Recently, the introduction of foundation models like CLIP and Segment-Anything-Model (SAM), with robust cross-domain representations, has paved the way for interactive and universal image segmentation. However, further exploration of these models for data-efficient segmentation in medical imaging is still needed and highly relevant. In this paper, we introduce MedCLIP-SAMv2, a novel framework that integrates the CLIP and SAM models to perform segmentation on clinical scans using text prompts, in both zero-shot and weakly supervised settings. Our approach includes fine-tuning the BiomedCLIP model with a new Decoupled Hard Negative Noise Contrastive Estimation (DHN-NCE) loss, and leveraging the Multi-modal Information Bottleneck (M2IB) to create visual prompts for generating segmentation masks from SAM in the zero-shot setting. We also investigate using zero-shot segmentation labels within a weakly supervised paradigm to enhance segmentation quality further. Extensive testing across four diverse segmentation tasks and medical imaging modalities (breast tumor ultrasound, brain tumor MRI, lung X-ray, and lung CT) demonstrates the high accuracy of our proposed framework. Our code is available at https://github.com/HealthX-Lab/MedCLIP-SAMv2.

The problems of detecting and recovering planted structures/subgraphs in Erdős-Rényi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques. However, prior work has largely focused on specific ad hoc planted structures and inferential settings, while a general theory has remained elusive. In this paper, we bridge this gap by investigating the detection of an arbitrary planted subgraph Γ= Γ_n in an Erdős-Rényi random graph G(n, q_n), where the edge probability within Γ is p_n. We examine both the statistical and computational aspects of this problem and establish the following results. In the dense regime, where the edge probabilities p_n and q_n are fixed, we tightly characterize the information-theoretic and computational thresholds for detecting Γ, and provide conditions under which a computational-statistical gap arises. Most notably, these thresholds depend on Γ only through its number of edges, maximum degree, and maximum subgraph density. Our lower and upper bounds are general and apply to any value of p_n and q_n as functions of n. Accordingly, we also analyze the sparse regime where q_n = Θ(n^{-α}) and p_n-q_n =Θ(q_n), with αin[0,2], as well as the critical regime where p_n=1-o(1) and q_n = Θ(n^{-α}), both of which have been widely studied, for specific choices of Γ. For these regimes, we show that our bounds are tight for all planted subgraphs investigated in the literature thus farand many more. Finally, we identify conditions under which detection undergoes sharp phase transition, where the boundaries at which algorithms succeed or fail shift abruptly as a function of q_n.

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: "Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?" We answer this question in the affirmative by giving a particular construction of an Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded gradients at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.