Daily Papers

Fine-tuning is a widespread technique that allows practitioners to transfer pre-trained capabilities, as recently showcased by the successful applications of foundation models. However, fine-tuning reinforcement learning (RL) models remains a challenge. This work conceptualizes one specific cause of poor transfer, accentuated in the RL setting by the interplay between actions and observations: forgetting of pre-trained capabilities. Namely, a model deteriorates on the state subspace of the downstream task not visited in the initial phase of fine-tuning, on which the model behaved well due to pre-training. This way, we lose the anticipated transfer benefits. We identify conditions when this problem occurs, showing that it is common and, in many cases, catastrophic. Through a detailed empirical analysis of the challenging NetHack and Montezuma's Revenge environments, we show that standard knowledge retention techniques mitigate the problem and thus allow us to take full advantage of the pre-trained capabilities. In particular, in NetHack, we achieve a new state-of-the-art for neural models, improving the previous best score from 5K to over 10K points in the Human Monk scenario.

Benefiting from massive corpora and advanced hardware, large language models (LLMs) exhibit remarkable capabilities in language understanding and generation. However, their performance degrades in scenarios where multiple tasks are encountered sequentially, also known as catastrophic forgetting. In this paper, we propose orthogonal low-rank adaptation (O-LoRA), a simple and efficient approach for continual learning in language models, effectively mitigating catastrophic forgetting while learning new tasks. Specifically, O-LoRA learns tasks in different (low-rank) vector subspaces that are kept orthogonal to each other in order to minimize interference. Our method induces only marginal additional parameter costs and requires no user data storage for replay. Experimental results on continual learning benchmarks show that our method outperforms state-of-the-art methods. Furthermore, compared to previous approaches, our method excels in preserving the generalization ability of LLMs on unseen tasks.

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when adapting to new tasks. Recently, approaches leveraging pre-trained models have gained increasing popularity in mitigating this issue, due to the strong generalization ability of foundation models. To adjust pre-trained models for new tasks, existing methods usually employ low-rank adaptation, which restricts parameter updates to a fixed low-rank subspace. However, constraining the optimization space inherently compromises the model's learning capacity, resulting in inferior performance. To address this limitation, we propose Continuous Subspace Optimization for Continual Learning (CoSO) to fine-tune the model in a series of subspaces rather than a single one. These sequential subspaces are dynamically determined through the singular value decomposition of the gradients. CoSO updates the model by projecting gradients onto these subspaces, ensuring memory-efficient optimization. To mitigate forgetting, the optimization subspace of each task is constrained to be orthogonal to the historical task subspace. During task learning, CoSO maintains a task-specific component that captures the critical update directions for the current task. Upon completing a task, this component is used to update the historical task subspace, laying the groundwork for subsequent learning. Extensive experiments on multiple datasets demonstrate that CoSO significantly outperforms state-of-the-art methods, especially in challenging scenarios with long task sequences.

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes mathcal{O}(d^{,3/2}/epsilon) queries to the time-evolution operator of the system and mathcal{O}(d^{,3/2}) queries to a block-encoding of the perturbation, for d cooling steps and an epsilon-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

Class-Incremental Learning (CIL) requires a learning system to continually learn new classes without forgetting. Despite the strong performance of Pre-Trained Models (PTMs) in CIL, a critical issue persists: learning new classes often results in the overwriting of old ones. Excessive modification of the network causes forgetting, while minimal adjustments lead to an inadequate fit for new classes. As a result, it is desired to figure out a way of efficient model updating without harming former knowledge. In this paper, we propose ExpAndable Subspace Ensemble (EASE) for PTM-based CIL. To enable model updating without conflict, we train a distinct lightweight adapter module for each new task, aiming to create task-specific subspaces. These adapters span a high-dimensional feature space, enabling joint decision-making across multiple subspaces. As data evolves, the expanding subspaces render the old class classifiers incompatible with new-stage spaces. Correspondingly, we design a semantic-guided prototype complement strategy that synthesizes old classes' new features without using any old class instance. Extensive experiments on seven benchmark datasets verify EASE's state-of-the-art performance. Code is available at: https://github.com/sun-hailong/CVPR24-Ease

This paper describes a new technique for finding disentangled semantic directions in the latent space of StyleGAN. Our method identifies meaningful orthogonal subspaces that allow editing of one human face attribute, while minimizing undesired changes in other attributes. Our model is capable of editing a single attribute in multiple directions, resulting in a range of possible generated images. We compare our scheme with three state-of-the-art models and show that our method outperforms them in terms of face editing and disentanglement capabilities. Additionally, we suggest quantitative measures for evaluating attribute separation and disentanglement, and exhibit the superiority of our model with respect to those measures.

Continual learning in large language models (LLMs) is prone to catastrophic forgetting, where adapting to new tasks significantly degrades performance on previously learned ones. Existing methods typically rely on low-rank, parameter-efficient updates that limit the model's expressivity and introduce additional parameters per task, leading to scalability issues. To address these limitations, we propose a novel continual full fine-tuning approach leveraging adaptive singular value decomposition (SVD). Our method dynamically identifies task-specific low-rank parameter subspaces and constrains updates to be orthogonal to critical directions associated with prior tasks, thus effectively minimizing interference without additional parameter overhead or storing previous task gradients. We evaluate our approach extensively on standard continual learning benchmarks using both encoder-decoder (T5-Large) and decoder-only (LLaMA-2 7B) models, spanning diverse tasks including classification, generation, and reasoning. Empirically, our method achieves state-of-the-art results, up to 7% higher average accuracy than recent baselines like O-LoRA, and notably maintains the model's general linguistic capabilities, instruction-following accuracy, and safety throughout the continual learning process by reducing forgetting to near-negligible levels. Our adaptive SVD framework effectively balances model plasticity and knowledge retention, providing a practical, theoretically grounded, and computationally scalable solution for continual learning scenarios in large language models.

Transformer-based methods have demonstrated impressive performance in 4D light field (LF) super-resolution by effectively modeling long-range spatial-angular correlations, but their quadratic complexity hinders the efficient processing of high resolution 4D inputs, resulting in slow inference speed and high memory cost. As a compromise, most prior work adopts a patch-based strategy, which fails to leverage the full information from the entire input LFs. The recently proposed selective state-space model, Mamba, has gained popularity for its efficient long-range sequence modeling. In this paper, we propose a Mamba-based Light Field Super-Resolution method, named MLFSR, by designing an efficient subspace scanning strategy. Specifically, we tokenize 4D LFs into subspace sequences and conduct bi-directional scanning on each subspace. Based on our scanning strategy, we then design the Mamba-based Global Interaction (MGI) module to capture global information and the local Spatial- Angular Modulator (SAM) to complement local details. Additionally, we introduce a Transformer-to-Mamba (T2M) loss to further enhance overall performance. Extensive experiments on public benchmarks demonstrate that MLFSR surpasses CNN-based models and rivals Transformer-based methods in performance while maintaining higher efficiency. With quicker inference speed and reduced memory demand, MLFSR facilitates full-image processing of high-resolution 4D LFs with enhanced performance.

Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a state-dependent, sparse expansion of a shared basis bank. Formally, DSC models the weight update as a residual trajectory within a Star- Shaped Domain, employing a Magnitude-Gated Simplex Interpolation to ensure continuity at the identity. Unlike standard Mixture-of-LoRAs, which incurs O(M rd) parameter complexity by retrieving independent rank-r matrices, DSC constructs a compositional rank-K approximation from decoupled unit-norm basis vectors. This reduces parameter complexity to O(M d) and memory traffic to O(Kd), while Frame-Theoretic regularization and spectral constraints provide rigorous worst-case bounds on the dynamic update. The code is available at https://github. com/VladimerKhasia/DSC

The capability of the self-attention mechanism to model the long-range dependencies has catapulted its deployment in vision models. Unlike convolution operators, self-attention offers infinite receptive field and enables compute-efficient modeling of global dependencies. However, the existing state-of-the-art attention mechanisms incur high compute and/or parameter overheads, and hence unfit for compact convolutional neural networks (CNNs). In this work, we propose a simple yet effective "Ultra-Lightweight Subspace Attention Mechanism" (ULSAM), which infers different attention maps for each feature map subspace. We argue that leaning separate attention maps for each feature subspace enables multi-scale and multi-frequency feature representation, which is more desirable for fine-grained image classification. Our method of subspace attention is orthogonal and complementary to the existing state-of-the-arts attention mechanisms used in vision models. ULSAM is end-to-end trainable and can be deployed as a plug-and-play module in the pre-existing compact CNNs. Notably, our work is the first attempt that uses a subspace attention mechanism to increase the efficiency of compact CNNs. To show the efficacy of ULSAM, we perform experiments with MobileNet-V1 and MobileNet-V2 as backbone architectures on ImageNet-1K and three fine-grained image classification datasets. We achieve approx13% and approx25% reduction in both the FLOPs and parameter counts of MobileNet-V2 with a 0.27% and more than 1% improvement in top-1 accuracy on the ImageNet-1K and fine-grained image classification datasets (respectively). Code and trained models are available at https://github.com/Nandan91/ULSAM.

Model merging integrates the weights of multiple task-specific models into a single multi-task model. Despite recent interest in the problem, a significant performance gap between the combined and single-task models remains. In this paper, we investigate the key characteristics of task matrices -- weight update matrices applied to a pre-trained model -- that enable effective merging. We show that alignment between singular components of task-specific and merged matrices strongly correlates with performance improvement over the pre-trained model. Based on this, we propose an isotropic merging framework that flattens the singular value spectrum of task matrices, enhances alignment, and reduces the performance gap. Additionally, we incorporate both common and task-specific subspaces to further improve alignment and performance. Our proposed approach achieves state-of-the-art performance across multiple scenarios, including various sets of tasks and model scales. This work advances the understanding of model merging dynamics, offering an effective methodology to merge models without requiring additional training. Code is available at https://github.com/danielm1405/iso-merging .

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

Training large language models (LLMs) is often bottlenecked by extreme memory demands, with optimizer states dominating the footprint. Recent works mitigates this cost by projecting gradients into low-dimensional subspaces using sophisticated update strategies. In this paper, we analyze the dynamics of gradient space and its underlying subspaces. We find that while a small subspace captures most gradient energy, a significant portion still resides in the residual bulk; moreover, the influence of the core subspace diminishes over time and in deeper layers. We also observe that the gradient space exhibits near-flat curvature, calling for algorithms that explicitly account for this geometry. Motivated by these insights, we introduce a suite of randomized algorithms, GrassWalk and GrassJump, which exploit subspace and achieve state-of-the-art memory savings while improving performance on LLaMA-1B and LLaMA-7B pretraining.

We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank real symmetric tensors. This algorithm calculates one new CP component at a time, alternating between applying the shifted symmetric higher-order power method (SS-HOPM) to a certain modified tensor, constructed from a matrix flattening of the original tensor; and using appropriate deflation steps. We obtain rigorous guarantees for SPM regarding convergence and global optima for input tensors of dimension d and order m of CP rank up to O(d^{lfloor m/2rfloor}), via results in classical algebraic geometry and optimization theory. As a by-product of our analysis we prove that SS-HOPM converges unconditionally, settling a conjecture in [Kolda, T.G., Mayo, J.R.: Shifted power method for computing tensor eigenpairs. SIAM Journal on Matrix Analysis and Applications 32(4), 1095-1124 (2011)]. We present numerical experiments which demonstrate that SPM is efficient and robust to noise, being up to one order of magnitude faster than state-of-the-art CP decomposition algorithms in certain experiments. Furthermore, prior knowledge of the CP rank is not required by SPM.

Model merging aims to cheaply combine individual task-specific models into a single multitask model. In this work, we view past merging methods as leveraging different notions of a ''task subspace'' in which models are matched before being merged. We connect the task subspace of a given model to its loss landscape and formalize how this approach to model merging can be seen as solving a linear system of equations. While past work has generally been limited to linear systems that have a closed-form solution, we consider using the conjugate gradient method to find a solution. We show that using the conjugate gradient method can outperform closed-form solutions, enables merging via linear systems that are otherwise intractable to solve, and flexibly allows choosing from a wide variety of initializations and estimates for the ''task subspace''. We ultimately demonstrate that our merging framework called ''Matching Models in their Task Subspace'' (MaTS) achieves state-of-the-art results in multitask and intermediate-task model merging. We release all of the code and checkpoints used in our work at https://github.com/r-three/mats.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

One-class learning is the classic problem of fitting a model to data for which annotations are available only for a single class. In this paper, we propose a novel objective for one-class learning. Our key idea is to use a pair of orthonormal frames -- as subspaces -- to "sandwich" the labeled data via optimizing for two objectives jointly: i) minimize the distance between the origins of the two subspaces, and ii) to maximize the margin between the hyperplanes and the data, either subspace demanding the data to be in its positive and negative orthant respectively. Our proposed objective however leads to a non-convex optimization problem, to which we resort to Riemannian optimization schemes and derive an efficient conjugate gradient scheme on the Stiefel manifold. To study the effectiveness of our scheme, we propose a new dataset~Dash-Cam-Pose, consisting of clips with skeleton poses of humans seated in a car, the task being to classify the clips as normal or abnormal; the latter is when any human pose is out-of-position with regard to say an airbag deployment. Our experiments on the proposed Dash-Cam-Pose dataset, as well as several other standard anomaly/novelty detection benchmarks demonstrate the benefits of our scheme, achieving state-of-the-art one-class accuracy.

Temporal knowledge graphs represent temporal facts (s,p,o,tau) relating a subject s and an object o via a relation label p at time tau, where tau could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by singular value decomposition (SVD). However, convergence of these algorithms is highly dependent on the update rules of their projection matrix. In this work, we provide the first convergence guarantee for arbitrary update rules of projection matrix. This guarantee is generally applicable to optimizers that can be analyzed with Hamiltonian Descent, including most common ones, such as LION, Adam. Inspired by our theoretical understanding, we propose Online Subspace Descent, a new family of subspace descent optimizer without SVD. Instead of updating the projection matrix with eigenvectors, Online Subspace Descent updates the projection matrix with online PCA. Online Subspace Descent is flexible and introduces only minimum overhead to training. We show that for the task of pretraining LLaMA models ranging from 60M to 7B parameters on the C4 dataset, Online Subspace Descent achieves lower perplexity and better downstream tasks performance than state-of-the-art low-rank training methods across different settings and narrows the gap with full-rank baselines.

Growing amount and quality of AI-generated texts makes detecting such content more difficult. In most real-world scenarios, the domain (style and topic) of generated data and the generator model are not known in advance. In this work, we focus on the robustness of classifier-based detectors of AI-generated text, namely their ability to transfer to unseen generators or semantic domains. We investigate the geometry of the embedding space of Transformer-based text encoders and show that clearing out harmful linear subspaces helps to train a robust classifier, ignoring domain-specific spurious features. We investigate several subspace decomposition and feature selection strategies and achieve significant improvements over state of the art methods in cross-domain and cross-generator transfer. Our best approaches for head-wise and coordinate-based subspace removal increase the mean out-of-distribution (OOD) classification score by up to 9% and 14% in particular setups for RoBERTa and BERT embeddings respectively. We release our code and data: https://github.com/SilverSolver/RobustATD

The objective of pre-trained language models is to learn contextual representations of textual data. Pre-trained language models have become mainstream in natural language processing and code modeling. Using probes, a technique to study the linguistic properties of hidden vector spaces, previous works have shown that these pre-trained language models encode simple linguistic properties in their hidden representations. However, none of the previous work assessed whether these models encode the whole grammatical structure of a programming language. In this paper, we prove the existence of a syntactic subspace, lying in the hidden representations of pre-trained language models, which contain the syntactic information of the programming language. We show that this subspace can be extracted from the models' representations and define a novel probing method, the AST-Probe, that enables recovering the whole abstract syntax tree (AST) of an input code snippet. In our experimentations, we show that this syntactic subspace exists in five state-of-the-art pre-trained language models. In addition, we highlight that the middle layers of the models are the ones that encode most of the AST information. Finally, we estimate the optimal size of this syntactic subspace and show that its dimension is substantially lower than those of the models' representation spaces. This suggests that pre-trained language models use a small part of their representation spaces to encode syntactic information of the programming languages.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge quickly for large linear inverse problems. For example, the conjugate gradient method (CG), one of the most popular Krylov subspace methods, is based on the idea of minimizing the residual error in the Krylov subspace. However, with the recent advancement of high-performance diffusion solvers for inverse problems, it is not clear how classical wisdom can be synergistically combined with modern diffusion models. In this study, we propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if the tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG initialized with the denoised data ensures the data consistency update to remain in the tangent space. This negates the need to compute the manifold-constrained gradient (MCG), leading to a more efficient diffusion sampling method. Our method is applicable regardless of the parametrization and setting (i.e., VE, VP). Notably, we achieve state-of-the-art reconstruction quality on challenging real-world medical inverse imaging problems, including multi-coil MRI reconstruction and 3D CT reconstruction. Moreover, our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method. Code is available at https://github.com/HJ-harry/DDS

Large language model (LLM) training and finetuning are often bottlenecked by limited GPU memory. While existing projection-based optimization methods address this by projecting gradients into a lower-dimensional subspace to reduce optimizer state memory, they typically rely on dense projection matrices, which can introduce computational and memory overheads. In this work, we propose Grass (GRAdient Stuctured Sparsification), a novel approach that leverages sparse projections to transform gradients into structured sparse updates. This design not only significantly reduces memory usage for optimizer states but also minimizes gradient memory footprint, computation, and communication costs, leading to substantial throughput improvements. Extensive experiments on pretraining and finetuning tasks demonstrate that Grass achieves competitive performance to full-rank training and existing projection-based methods. Notably, Grass enables half-precision pretraining of a 13B parameter LLaMA model on a single 40GB A100 GPU--a feat infeasible for previous methods--and yields up to a 2times throughput improvement on an 8-GPU system. Code can be found at https://github.com/aashiqmuhamed/GRASS .

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems. This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data. A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables. A method is also presented for balanced model reduction of over-specified EDMD systems in feature space. Nonlinear reconstruction using partially linear multi-kernel regression aims to improve reconstruction accuracy from the low-dimensional state when the data has complex but intrinsically low-dimensional structure. The techniques demonstrate the ability to identify Koopman eigenfunctions of the unforced Duffing equation, create accurate low-dimensional models of an unstable cylinder wake flow, and make short-time predictions of the chaotic Kuramoto-Sivashinsky equation.

Parameter-efficient fine-tuning (PEFT) methods seek to adapt large models via updates to a small number of weights. However, much prior interpretability work has shown that representations encode rich semantic information, suggesting that editing representations might be a more powerful alternative. Here, we pursue this hypothesis by developing a family of Representation Finetuning (ReFT) methods. ReFT methods operate on a frozen base model and learn task-specific interventions on hidden representations. We define a strong instance of the ReFT family, Low-rank Linear Subspace ReFT (LoReFT). LoReFT is a drop-in replacement for existing PEFTs and learns interventions that are 10x-50x more parameter-efficient than prior state-of-the-art PEFTs. We showcase LoReFT on eight commonsense reasoning tasks, four arithmetic reasoning tasks, Alpaca-Eval v1.0, and GLUE. In all these evaluations, LoReFT delivers the best balance of efficiency and performance, and almost always outperforms state-of-the-art PEFTs. We release a generic ReFT training library publicly at https://github.com/stanfordnlp/pyreft.

Large language models (LLMs) have revolutionized natural language understanding and generation but face significant memory bottlenecks during training. GaLore, Gradient Low-Rank Projection, addresses this issue by leveraging the inherent low-rank structure of weight gradients, enabling substantial memory savings without sacrificing performance. Recent works further extend GaLore from various aspects, including low-bit quantization and higher-order tensor structures. However, there are several remaining challenges for GaLore, such as the computational overhead of SVD for subspace updates and the integration with state-of-the-art training parallelization strategies (e.g., FSDP). In this paper, we present GaLore 2, an efficient and scalable GaLore framework that addresses these challenges and incorporates recent advancements. In addition, we demonstrate the scalability of GaLore 2 by pre-training Llama 7B from scratch using up to 500 billion training tokens, highlighting its potential impact on real LLM pre-training scenarios.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

Recent unsupervised domain adaptation methods have utilized vicinal space between the source and target domains. However, the equilibrium collapse of labels, a problem where the source labels are dominant over the target labels in the predictions of vicinal instances, has never been addressed. In this paper, we propose an instance-wise minimax strategy that minimizes the entropy of high uncertainty instances in the vicinal space to tackle the stated problem. We divide the vicinal space into two subspaces through the solution of the minimax problem: contrastive space and consensus space. In the contrastive space, inter-domain discrepancy is mitigated by constraining instances to have contrastive views and labels, and the consensus space reduces the confusion between intra-domain categories. The effectiveness of our method is demonstrated on public benchmarks, including Office-31, Office-Home, and VisDA-C, achieving state-of-the-art performances. We further show that our method outperforms the current state-of-the-art methods on PACS, which indicates that our instance-wise approach works well for multi-source domain adaptation as well. Code is available at https://github.com/NaJaeMin92/CoVi.

Evaluations of large language model (LLM) risks and capabilities are increasingly being incorporated into AI risk management and governance frameworks. Currently, most risk evaluations are conducted by designing inputs that elicit harmful behaviors from the system. However, a fundamental limitation of this approach is that the harmfulness of the behaviors identified during any particular evaluation can only lower bound the model's worst-possible-case behavior. As a complementary method for eliciting harmful behaviors, we propose evaluating LLMs with model tampering attacks which allow for modifications to latent activations or weights. We pit state-of-the-art techniques for removing harmful LLM capabilities against a suite of 5 input-space and 6 model tampering attacks. In addition to benchmarking these methods against each other, we show that (1) model resilience to capability elicitation attacks lies on a low-dimensional robustness subspace; (2) the attack success rate of model tampering attacks can empirically predict and offer conservative estimates for the success of held-out input-space attacks; and (3) state-of-the-art unlearning methods can easily be undone within 16 steps of fine-tuning. Together these results highlight the difficulty of removing harmful LLM capabilities and show that model tampering attacks enable substantially more rigorous evaluations than input-space attacks alone. We release models at https://huggingface.co/LLM-GAT