ICML 2025 Papers

We theoretically characterize gradient descent dynamics in deep linear networks trained at large width from random initialization and on large quantities of random data. Our theory captures the ``wider is better" effect of mean-field/maximum-update parameterized networks as well as hyperparameter transfer effects, which can be contrasted with the neural-tangent parameterization where optimal learning rates shift with model width. We provide asymptotic descriptions of both non-residual and residual neural networks, the latter of which enables an infinite depth limit when branches are scaled as $1/\sqrt{\text{depth}}$. We also compare training with one-pass stochastic gradient descent to the dynamics when training data are repeated at each iteration. Lastly, we show that this model recovers the accelerated power law training dynamics for power law structured data in the rich regime observed in recent works.

We introduce a new approach to systematically map features discovered by sparse autoencoder across consecutive layers of large language models, extending earlier work that examined inter-layer feature links. By using a data-free cosine similarity technique, we trace how specific features persist, transform, or first appear at each stage. This method yields granular flow graphs of feature evolution, enabling fine-grained interpretability and mechanistic insights into model computations. Crucially, we demonstrate how these cross-layer feature maps facilitate direct steering of model behavior by amplifying or suppressing chosen features, achieving targeted thematic control in text generation. Together, our findings highlight the utility of a causal, cross-layer interpretability framework that not only clarifies how features develop through forward passes but also provides new means for transparent manipulation of large language models.

Recent advancements in Large Language Models (LLMs) have spurred interest in numerous applications requiring robust long-range capabilities, essential for processing extensive input contexts and continuously generating extended outputs. As sequence lengths increase, the number of Key-Value (KV) pairs in LLMs escalates, creating a significant efficiency bottleneck. In this paper, we propose a new KV cache optimization paradigm called LaCache, a training-free method for efficient and accurate generative inference of LLMs. LaCache enables LLMs to simultaneously address both of the critical challenges in long-range modeling: robust long-range capabilities and continuous generation without running out-of-memory (OOM). Specifically, LaCache integrates two key innovations: (1) a ladder-shaped KV cache pattern that stores KV pairs not only sequentially (left-to-right within each layer) but also across layers (from shallow to deep), providing an extended span for capturing long-range dependencies under a fixed storage budget, thereby boosting long-range capabilities; and (2) an iterative compaction mechanism that progressively compresses older caches, freeing up space for new tokens within a fixed cache size. This token distance-based dynamic compression enables more effective continuous generation under constrained cache budgets. Experiments across various tasks, benchmarks, and LLM models consistently validate LaCache's effectiveness in enhancing LLMs' long-range capabilities. Our code is available at https://github.com/GATECH-EIC/LaCache.

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the eigenbasis of the coupling matrix, exploiting the independent evolution of eigenmodes and revealing that the learning timescales are tied to the spectral decomposition of the empirical covariance matrix. We see that optimal points for early stopping arise from the interplay between these timescales and the initial conditions of training. Moreover, we show that finite data corrections can be accurately modeled through asymptotic random matrix theory calculations and provide the counterpart of generalized cross-validation in the energy based model context. Our analytical framework extends to binary-variable maximum-entropy pairwise models with minimal variations. These findings offer strategies to control overfitting in discrete-variable models through empirical shrinkage corrections, improving the management of overfitting in energy-based generative models. Finally, we propose a generalization to arbitrary energy-based models by deriving the neural tangent kernel dynamics of the score function under the score-matching algorithm.

We present DriveGPT, a scalable behavior model for autonomous driving. We model driving as a sequential decision-making task, and learn a transformer model to predict future agent states as tokens in an autoregressive fashion. We scale up our model parameters and training data by multiple orders of magnitude, enabling us to explore the scaling properties in terms of dataset size, model parameters, and compute. We evaluate DriveGPT across different scales in a planning task, through both quantitative metrics and qualitative examples, including closed-loop driving in complex real-world scenarios. In a separate prediction task, DriveGPT outperforms state-of-the-art baselines and exhibits improved performance by pretraining on a large-scale dataset, further validating the benefits of data scaling.

Activation sparsity denotes the existence of substantial weakly-contributed neurons within feed-forward networks of large language models (LLMs), providing wide potential benefits such as computation acceleration. However, existing works lack thorough quantitative studies on this useful property, in terms of both its measurement and influential factors. In this paper, we address three underexplored research questions: (1) How can activation sparsity be measured more accurately? (2) How is activation sparsity affected by the model architecture and training process? (3) How can we build a more sparsely activated and efficient LLM? Specifically, we develop a generalizable and performance-friendly metric, named CETT-PPL-1\%, to measure activation sparsity. Based on CETT-PPL-1\%, we quantitatively study the influence of various factors and observe several important phenomena, such as the convergent power-law relationship between sparsity and training data amount, the higher competence of ReLU activation than mainstream SiLU activation, the potential sparsity merit of a small width-depth ratio, and the scale insensitivity of activation sparsity. Finally, we provide implications for building sparse and effective LLMs, and demonstrate the reliability of our findings by training a 2.4B model with a sparsity ratio of 93.52\%, showing 4.1$\times$ speedup compared with its dense version. The codes and checkpoints are available at https://github.com/thunlp/SparsingLaw/.

Diffusion models have emerged as a powerful framework for generative modeling, with guidance techniques playing a crucial role in enhancing sample quality. Despite their empirical success, a comprehensive theoretical understanding of the guidance effect remains limited. Existing studies only focus on case studies, where the distribution conditioned on each class is either isotropic Gaussian or supported on a one-dimensional interval with some extra conditions. How to analyze the guidance effect beyond these case studies remains an open question. Towards closing this gap, we make an attempt to analyze diffusion guidance under general data distributions. Rather than demonstrating uniform sample quality improvement, which does not hold in some distributions, we prove that guidance can improve the whole sample quality, in the sense that the ratio of bad samples (measured by the classifier probability) decreases in the presence of guidance. This aligns with the motivation of introducing guidance.

Reinforcement learning (RL) with delays is challenging as sensory perceptions lag behind the actual events: the RL agent needs to estimate the real state of its environment based on past observations. State-of-the-art (SOTA) methods typically employ recursive, step-by-step forecasting of states. This can cause the accumulation of compounding errors. To tackle this problem, our novel belief estimation method, named Directly Forecasting Belief Transformer (DFBT), directly forecasts states from observations without incrementally estimating intermediate states step-by-step. We theoretically demonstrate that DFBT greatly reduces compounding errors of existing recursively forecasting methods, yielding stronger performance guarantees. In experiments with D4RL offline datasets, DFBT reduces compounding errors with remarkable prediction accuracy. DFBT's capability to forecast state sequences also facilitates multi-step bootstrapping, thus greatly improving learning efficiency. On the MuJoCo benchmark, our DFBT-based method substantially outperforms SOTA baselines. Code is available at \href{https://github.com/QingyuanWuNothing/DFBT}{https://github.com/QingyuanWuNothing/DFBT}.

Training large language models to predict beyond their training context lengths has drawn much attention in recent years, yet the principles driving such behavior of length generalization remain underexplored. We propose a new theoretical framework to study length generalization for the next-token prediction task, as performed by decoder-only transformers. Conceptually, we show that length generalization occurs as long as each predicted token depends on a small (fixed) number of previous tokens. We formalize such tasks via a notion we call k-sparse planted correlation distributions, and show that an idealized model of transformers which generalize attention heads successfully length-generalize on such tasks. As a bonus, our theoretical model allows us to provide justifications for techniques to modify positional embeddings which have been introduced to improve length generalization, such as position coupling. We support our theoretical results with experiments on synthetic tasks and natural language, which confirm that a key factor driving length generalization is indeed a ``sparse'' dependency structure of each token on the previous ones. Further, inspired by our theory, we introduce Predictive Position Coupling, a generalization of position coupling which trains the transformer to predict the position IDs used in a positional coupling approach. Predictive Position Coupling thereby allows us to broaden the array of tasks to which Position Coupling can successfully be applied to achieve length generalization.

The evaluation of machine learning models using human-labeled validation data can be expensive and time-consuming. AI-labeled synthetic data can be used to decrease the number of human annotations required for this purpose in a process called autoevaluation. We suggest efficient and statistically principled algorithms for this purpose that improve sample efficiency while remaining unbiased.

Graph Neural Networks (GNNs) effectively learn from relational data by leveraging graph symmetries. However, many real-world systems---such as biological or social networks---feature multi-way interactions that GNNs fail to capture. Topological Deep Learning (TDL) addresses this by modeling and leveraging higher-order structures, with Combinatorial Complex Neural Networks (CCNNs) offering a general and expressive approach that has been shown to outperform GNNs. However, TDL lacks the principled and standardized frameworks that underpin GNN development, restricting its accessibility and applicability. To address this issue, we introduce Generalized CCNNs (GCCNs), a simple yet powerful family of TDL models that can be used to systematically transform any (graph) neural network into its TDL counterpart. We prove that GCCNs generalize and subsume CCNNs, while extensive experiments on a diverse class of GCCNs show that these architectures consistently match or outperform CCNNs, often with less model complexity. In an effort to accelerate and democratize TDL, we introduce TopoTune, a lightweight software for defining, building, and training GCCNs with unprecedented flexibility and ease.

A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier of sharp behaviour is the softmax function, with its capability to perform differentiable query-key lookups. It is a common belief that the predictive power of networks leveraging softmax arises from "circuits" which sharply perform certain kinds of computations consistently across many diverse inputs. However, for these circuits to be robust, they would need to generalise well to arbitrary valid inputs. In this paper, we dispel this myth: even for tasks as simple as finding the maximum key, any learned circuitry must disperse as the number of items grows at test time. We attribute this to a fundamental limitation of the softmax function to robustly approximate sharp functions with increasing problem size, prove this phenomenon theoretically, and propose adaptive temperature as an ad-hoc technique for improving the sharpness of softmax at inference time.

With the integration of image modality, the semantic space of multimodal large language models (MLLMs) is more complex than text-only models, making their interpretability more challenging and their alignment less stable, particularly susceptible to low-quality data, which can lead to inconsistencies between modalities, hallucinations, and biased outputs. As a result, developing interpretability methods for MLLMs is crucial for improving alignment quality and efficiency. In text-only LLMs, Sparse Autoencoders (SAEs) have gained attention for their ability to interpret latent representations. However, extending SAEs to multimodal settings presents new challenges due to modality fusion and the difficulty of isolating cross-modal representations. To address these challenges, we introduce SAE-V, a mechanistic interpretability framework that extends the SAE paradigm to MLLMs. By identifying and analyzing interpretable features along with their corresponding data, SAE-V enables fine-grained interpretation of both model behavior and data quality, facilitating a deeper understanding of cross-modal interactions and alignment dynamics. Moreover, by utilizing cross-modal feature weighting, SAE-V provides an intrinsic data filtering mechanism to enhance model alignment without requiring additional models. Specifically, when applied to the alignment process of MLLMs, SAE-V-based data filtering methods could achieve more than 110% performance with less than 50% data. Our results highlight SAE-V’s ability to enhance interpretability and alignment in MLLMs, providing insights into their internal mechanisms.

Many applications in machine learning and decision-making rely on procedures to aggregate human preferences.In such tasks, individual express ordinal preferences over a set of items through votes, ratings, or pairwise comparisons. We then summarize their collective preferences as a ranking. Standard methods for preference aggregation are designed to return rankings that arbitrate individual disagreements in ways that are faithful and fair. In this work, we introduce a paradigm for *selective aggregation*, where we can avoid the need to arbitrate dissent by abstaining from comparison. We summarize collective preferences as a *selective ranking* -- i.e., a partial order where we can only compare items where at least $100\cdot(1 - \tau)\%$ of individuals agree. We develop algorithms to build selective rankings that achieve all possible trade-offs between comparability and disagreement, and derive formal guarantees on their safety and stability. We conduct an extensive set of experiments on real-world datasets to benchmark our approach and demonstrate its functionality. Our results show selective aggregation can promote transparency and robustness by revealing disagreement and abstaining from arbitration.

Pruning is a widely used technique for compressing large neural networks that eliminates weights that have minimal impact on the model's performance. Current pruning methods, exemplified by magnitude pruning, assign an importance score to each weight based on its magnitude and remove weights with scores below a certain threshold. Nonetheless, these methods often create a gap between the original dense and the pruned sparse model, potentially impairing performance. Especially when the sparsity ratio is high, the gap becomes more pronounced. To mitigate this issue, we introduce a method to bridge the gap left by pruning by utilizing a low-rank approximation of the difference between the dense and sparse matrices. Our method entails the iterative refinement of the sparse weight matrix augmented by a low-rank adjustment. This technique captures and retains the essential information often lost during pruning, thereby improving the performance of the pruned model. Furthermore, we offer a comprehensive theoretical analysis of our approach, emphasizing its convergence properties and establishing a solid basis for its efficacy. Experimental results on LLaMa models validate its effectiveness on large language models across various pruning techniques and sparsity levels. Our method shows significant improvements: at 50\% sparsity, it reduces perplexity by 53.9\% compared to conventional magnitude pruning on LLaMa-7B. Furthermore, to achieve a specific performance target, our approach enables an 8.6\% reduction in model parameters while maintaining a sparsity ratio of about 50\%.

In reinforcement learning, offline value function learning is the procedure of using an offline dataset to estimate the expected discounted return from each state when taking actions according to a fixed target policy. The stability of this procedure, i.e., whether it converges to its fixed-point, critically depends on the representations of the state-action pairs. Poorly learned representations can make value function learning unstable, or even divergent. Therefore, it is critical to stabilize value function learning by explicitly shaping the state-action representations. Recently, the class of bisimulation-based algorithms have shown promise in shaping representations for control. However, it is still unclear if this class of methods can \emph{stabilize} value function learning. In this work, we investigate this question and answer it affirmatively. We introduce a bisimulation-based algorithm called kernel representations for offline policy evaluation (\textsc{krope}). \textsc{krope} uses a kernel to shape state-action representations such that state-action pairs that have similar immediate rewards and lead to similar next state-action pairs under the target policy also have similar representations. We show that \textsc{krope}: 1) learns stable representations and 2) leads to lower value error than baselines. Our analysis provides new theoretical insight into the stability properties of bisimulation-based methods and suggests that practitioners can use these methods to improve the stability and accuracy of offline evaluation of reinforcement learning agents.

In this paper, we propose ZipAR, a training-free, plug-and-play parallel decoding framework for accelerating autoregressive (AR) visual generation. The motivation stems from the observation that images exhibit local structures, and spatially distant regions tend to have minimal interdependence. Given a partially decoded set of visual tokens, in addition to the original next-token prediction scheme in the row dimension, the tokens corresponding to spatially adjacent regions in the column dimension can be decoded in parallel. To ensure alignment with the contextual requirements of each token, we employ an adaptive local window assignment scheme with rejection sampling analogous to speculative decoding. By decoding multiple tokens in a single forward pass, the number of forward passes required to generate an image is significantly reduced, resulting in a substantial improvement in generation efficiency. Experiments demonstrate that ZipAR can reduce the number of model forward passes by up to 91% on the Emu3-Gen model without requiring any additional retraining.

The sparse-group lasso performs both variable and group selection, simultaneously using the strengths of the lasso and group lasso. It has found widespread use in genetics, a field that regularly involves the analysis of high-dimensional data, due to its sparse-group penalty, which allows it to utilize grouping information. However, the sparse-group lasso can be computationally expensive, due to the added shrinkage complexity, and its additional hyperparameter that needs tuning. This paper presents a novel feature reduction method, Dual Feature Reduction (DFR), that uses strong screening rules for the sparse-group lasso and the adaptive sparse-group lasso to reduce their input space before optimization, without affecting solution optimality. DFR applies two layers of screening through the application of dual norms and subdifferentials. Through synthetic and real data studies, it is shown that DFR drastically reduces the computational cost under many different scenarios.

Transformer-based Large Language Models rely critically on the KV cache to efficiently handle extended contexts during the decode phase. Yet, the size of the KV cache grows proportionally with the input length, burdening both memory bandwidth and capacity as decoding progresses. To address this challenge, we present RocketKV, a training-free KV cache compression strategy containing two consecutive stages. In the first stage, it performs coarse-grain permanent KV cache eviction on the input sequence tokens. In the second stage, it adopts a hybrid sparse attention method to conduct fine-grain top-k sparse attention, approximating the attention scores by leveraging both head and sequence dimensionality reductions. We show that RocketKV provides a compression ratio of up to 400×, end-to-end speedup of up to 3.7× as well as peak memory reduction of up to 32.6% in the decode phase on an NVIDIA A100 GPU compared to the full KV cache baseline, while achieving negligible accuracy loss on a variety of long-context tasks. We also propose a variant of RocketKV for multi-turn scenarios, which consistently outperforms other existing methods and achieves accuracy nearly on par with an oracle top-k attention scheme.