NeurIPS 2025 论文列表

Conference on Neural Information Processing Systems

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5,812篇论文

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    73912.7%
  • Poster
    4,98085.7%

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CrossSpectra: Exploiting Cross-Layer Smoothness for Parameter-Efficient Fine-Tuning

Yifei Zhang, Hao Zhu, Junhao Dong, Haoran Shi, Ziqiao Meng, Piotr Koniusz, Han Yu

展开摘要

Parameter-efficient fine-tuning (PEFT) is essential for adapting large foundation models without excessive storage cost. However, current approaches such as LoRA treat each layer’s adaptation independently, overlooking correlations across layers. This independence causes the number of trainable parameters to grow linearly with model depth. We provide theoretical and empirical evidence that skip connections in transformers create smooth gradient propagation across layers. This smoothness leads to weight adaptations that concentrate most of their energy in low-frequency spectral components, especially along the layer dimension. Empirical analysis confirms this effect, showing that most of adaptation energy lies in low frequencies. Building on this insight, we propose CrossSpectra, which parameterizes all attention-weight adaptations $(Q, K, V)$ across layers as a single 3D tensor and represents them with sparse spectral coefficients ($\kappa_1, \kappa_2$). Using $\kappa_{1}$ non-zero coefficients within each layer’s frequency space and truncating to $\kappa_{2}$ frequencies across layers, CrossSpectra requires $\mathcal{O}(\kappa_{1}\kappa_{2})$ parameters instead of LoRA’s $\mathcal{O}(Lrd)$, where $L$ is the number of layers and $r$ the rank. Across natural-language and vision benchmarks, \methodname{} matches or surpasses baseline performance while using fewer parameters than LoRA, achieving only $0.36\%$ of LoRA’s parameter count when fine-tuning LLaMA-7B on instruction-following tasks. These results show that exploiting the \textbf{architectural smoothness of transformers} through spectral analysis yields major efficiency gains in PEFT.

Poster
LoRATv2: Enabling Low-Cost Temporal Modeling in One-Stream Trackers

Liting Lin, Heng Fan, Zhipeng Zhang, Yuqing Huang, Yaowei Wang, Yong Xu, Haibin Ling

展开摘要

Transformer-based algorithms, such as LoRAT, have significantly enhanced object-tracking performance. However, these approaches rely on a standard attention mechanism, which incurs quadratic token complexity, making real-time inference computationally expensive. In this paper, we introduce LoRATv2, a novel tracking framework that addresses these limitations with three main contributions. First, LoRATv2 integrates frame-wise causal attention, which ensures full self-attention within each frame while enabling causal dependencies across frames, significantly reducing computational overhead. Moreover, key-value (KV) caching is employed to efficiently reuse past embeddings for further speedup. Second, building on LoRAT's parameter-efficient fine-tuning, we propose Stream-Specific LoRA Adapters (SSLA). As frame-wise causal attention introduces asymmetry in how streams access temporal information, SSLA assigns dedicated LoRA modules to the template and each search stream, with the main ViT backbone remaining frozen. This allows specialized adaptation for each stream's role in temporal tracking. Third, we introduce a two-phase progressive training strategy, which first trains a single-search-frame tracker and then gradually extends it to multi-search-frame inputs by introducing additional LoRA modules. This curriculum-based learning paradigm improves long-term tracking while maintaining training efficiency. In extensive experiments on multiple benchmarks, LoRATv2 achieves state-of-the-art performance, substantially improved efficiency, and a superior performance-to-FLOPs ratio over state-of-the-art trackers. The code is available at https://github.com/LitingLin/LoRATv2.

Spotlight
Self Iterative Label Refinement via Robust Unlabeled Learning

Hikaru Asano, Tadashi Kozuno, Yukino Baba

展开摘要

Recent advances in large language models (LLMs) have yielded impressive performance on various tasks, yet they often depend on high-quality feedback that can be costly. Self-refinement methods attempt to leverage LLMs' internal evaluation mechanisms with minimal human supervision; however, these approaches frequently suffer from inherent biases and overconfidence, especially in domains where the models lack sufficient internal knowledge, resulting in performance degradation. As an initial step toward enhancing self-refinement for broader applications, we introduce an iterative refinement pipeline that employs the Unlabeled-Unlabeled learning framework to improve LLM-generated pseudo-labels for classification tasks. By exploiting two unlabeled datasets with differing positive class ratios, our approach iteratively denoises and refines the initial pseudo-labels, thereby mitigating the adverse effects of internal biases with minimal human supervision. Evaluations on diverse datasets, including low-resource language corpora, patent classifications, and protein structure categorizations, demonstrate that our method consistently outperforms both initial LLM's classification performance and the self-refinement approaches by cutting-edge models (e.g., GPT-4o and DeepSeek-R1). Moreover, we experimentally confirm that our refined classifier facilitates effective post-training alignment for safety in LLMs and demonstrate successful self-refinement in generative tasks as well. Our code is available at https://github.com/HikaruAsano/self-iterative-label-refinement.

Poster
DP-LLM: Runtime Model Adaptation with Dynamic Layer-wise Precision Assignment

Sangwoo Kwon, Seong Hoon Seo, Jae W. Lee, Yeonhong Park

展开摘要

How can we effectively handle queries for on-device large language models (LLMs) with varying runtime constraints, such as latency and accuracy? Multi-scale quantization addresses this challenge by enabling memory-efficient runtime model adaptation of LLMs through the overlaying of multiple model variants quantized to different bitwidths. Meanwhile, an important question still remains open-ended: how can models be properly configured to match a target precision or latency? While mixed-precision offers a promising solution, we take this further by leveraging the key observation that the sensitivity of each layer dynamically changes across decoding steps. Building on this insight, we introduce DP-LLM, a novel mechanism that dynamically assigns precision to each layer based on input values. Experimental results across multiple models and benchmarks demonstrate that DP-LLM achieves a superior performance-latency trade-off, outperforming prior approaches.

Poster
Rethinking Hebbian Principle: Low-Dimensional Structural Projection for Unsupervised Learning

Shikuang Deng, Jiayuan Zhang, Yuhang Wu, Ting Chen, Shi Gu

展开摘要

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the connections and the lack of accounting for feedback mediation. Such shortcomings limit its effective scaling to complex network architectures and tasks. To this end, here we introduce the Structural Projection Hebbian Representation (SPHeRe), a novel unsupervised learning method that integrates orthogonality and structural information preservation through a local auxiliary nonlinear block. The loss for structural information preservation backpropagates to the input through an auxiliary lightweight projection that conceptually serves as feedback mediation while the orthogonality constraints account for the boundedness of updating magnitude. Extensive experimental results show that SPHeRe achieves SOTA performance among unsupervised synaptic plasticity approaches on standard image classification benchmarks, including CIFAR-10, CIFAR-100, and Tiny-ImageNet. Furthermore, the method exhibits strong effectiveness in continual learning and transfer learning scenarios, and image reconstruction tasks show the robustness and generalizability of the extracted features. This work demonstrates the competitiveness and potential of Hebbian unsupervised learning rules within modern deep learning frameworks, demonstrating the possibility of efficient and biologically inspired learning algorithms without the strong dependence on strict backpropagation. Our code is available at https://github.com/brain-intelligence-lab/SPHeRe.

Poster
Parameter Dynamics of Online Machine Learning and Test-time Adaptation

Jae-Hong Lee

展开摘要

Pre-trained models based on deep neural networks hold strong potential for cross-domain adaptability. However, this potential is often impeded in online machine learning (OML) settings, where the breakdown of the independent and identically distributed (i.i.d.) assumption leads to unstable adaptation. While recent advances in test-time adaptation (TTA) have addressed aspects of this challenge under unsupervised learning, most existing methods focus exclusively on unsupervised objectives and overlook the risks posed by non-i.i.d. environments and the resulting dynamics of model parameters. In this work, we present a probabilistic framework that models the adaptation process using stochastic differential equations, enabling a principled analysis of parameter distribution dynamics over time. Within this framework, we find that the log-variance of the parameter transition distribution aligns closely with an inverse-gamma distribution under stable and high-performing adaptation conditions. Motivated by this insight, we propose Structured Inverse-Gamma Model Alignment (SIGMA), a novel algorithm that dynamically regulates parameter evolution to preserve inverse-gamma alignment throughout adaptation. Extensive experiments across diverse models, datasets, and adaptation scenarios show that SIGMA consistently enhances the performance of state-of-the-art TTA methods, highlighting the critical role of parameter dynamics in ensuring robust adaptation.

Poster
CoIDO: Efficient Data Selection for Visual Instruction Tuning via Coupled Importance-Diversity Optimization

Yichen Yan, Ming Zhong, Qi Zhu, Xiaoling Gu, Jinpeng Chen, Huan Li

展开摘要

Multimodal large language models (MLLMs) rely heavily on instruction tuning to align vision and language capabilities, yet the computational cost of training on large-scale datasets remains a major bottleneck. Existing data selection methods aim to mitigate this by selecting important and diverse subsets, but they often suffer from two critical drawbacks: high computational overhead from processing the entire dataset and suboptimal data selection due to separate treatment of importance and diversity. We introduce CoIDO, a novel dual-objective framework that jointly optimizes data importance and diversity to overcome these challenges. Unlike existing approaches that require costly evaluations across the whole dataset, CoIDO employs a lightweight plug-in scorer. This scorer is trained on just a small random sample of data to learn the distribution of the candidate set, drastically reducing computational demands. By leveraging a homoscedastic uncertainty-based formulation, CoIDO effectively balances importance and diversity during training, enabling the scorer to assign CoIDO scores to all data points. This unified scoring approach allows for direct ranking and selection of the most valuable subsets, completely bypassing the need for specialized algorithms. In our experiments, we trained the CoIDO Scorer using only 20% of randomly sampled data. Once trained, CoIDO was applied to the entire dataset to select a 20% subset for instruction tuning. On the widely used LLaVA-1.5-7B model across ten downstream tasks, this selected subset achieved an impressive 98.2% of the performance of full-data fine-tuning, on average. Moreover, CoIDO outperforms all competitors in terms of both efficiency (lowest training FLOPs) and aggregated accuracy. Our code is available at: https://github.com/SuDIS-ZJU/CoIDO

Poster
LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossing

Ruijie Zhang, Ziyue Liu, Zhengyang Wang, Zheng Zhang

展开摘要

Training foundation models such as ViTs and LLMs requires tremendous computing cost. Low-rank matrix or tensor factorization offers a parameter-efficient alternative, but often downgrades performance due to the restricted parameter space. In this work, we introduce ${\textbf{Latent Crossing (LaX)}}$ -- a simple yet effective plug-and-play module that enhances the capacity of low-rank models by enabling information flow across low-rank subspaces. We extensively validate the benefits of LaX on pre-training tasks with ViT-Base/Large and LLaMA-like models ranging from 60M to 1B parameters. LaX boosts low-rank model performance to match or exceed the full-rank baselines while using 2-3$\times$ fewer parameters. When equipped with low-rank adapters (i.e., LoRA) for fine-tuning LLaMA-7/13B, LaX consistently improves performance on arithmetic and common sense reasoning tasks with negligible cost.

Poster
Sample complexity of data-driven tuning of model hyperparameters in neural networks with structured parameter-dependent dual function

Maria Florina Balcan, Anh Tuan Nguyen, Dravyansh Sharma

展开摘要

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

Poster
Memory-Efficient Training with In-Place FFT Implementation

Xinyu Ding, Bangtian Liu, Siyu Liao, Zhongfeng Wang

展开摘要

Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation. In particular, rFFT maps an input of size $n$ to a complex output of size $\frac{n}{2}+1$, causing dimensional mismatch and requiring additional memory allocation. We propose the first real-domain, fully in-place FFT framework (rdFFT) that preserves input-output dimensional consistency ($n \rightarrow n$). By leveraging butterfly operation symmetry and conjugate properties in the frequency domain, we design an implicit complex encoding scheme that eliminates intermediate cache usage entirely. Theoretically, our method reduces memory usage by 50\% compared to rFFTs. Moreover, it enables zero-cache parameter updates by utilizing the derivative property of the Fourier transform to compute matrix inverses efficiently without intermediate storage. Experiments on multiple natural language understanding tasks demonstrate the method’s effectiveness in maintaining model performance while significantly lowering memory overhead, offering a promising direction for frequency-domain lightweight adaptation.

Poster
MokA: Multimodal Low-Rank Adaptation for MLLMs

Yake Wei, Yu Miao, Dongzhan Zhou, Di Hu

展开摘要

In this paper, we reveal that most current efficient multimodal fine-tuning methods are hindered by a key limitation: they are directly borrowed from LLMs, often neglecting the intrinsic differences of multimodal scenarios and even affecting the full utilization of all modalities. Inspired by our empirical observation, we argue that unimodal adaptation and cross-modal adaptation are two essential parts for the effective fine-tuning of MLLMs. From this perspective, we propose Multimodal Low-rank Adaptation (MokA), a multimodal-aware efficient fine-tuning strategy that takes multimodal characteristics into consideration. It compresses unimodal information by modality-specific parameters while explicitly enhancing cross-modal interaction, ensuring both unimodal and cross-modal adaptation. Extensive experiments cover three representative multimodal scenarios (audio-visual-text, visual-text, and speech-text), and multiple LLM backbones (LLaMA2, Qwen2, Qwen2.5-VL, etc). Consistent improvements indicate the efficacy and versatility of the proposed method. Ablation studies and efficiency evaluation are also conducted to fully asses our method. Overall, we think MokA provides a more targeted solution for efficient adaptation of MLLMs, paving the way for further exploration.

Oral
VIPAMIN: Visual Prompt Initialization via Embedding Selection and Subspace Expansion

Jaekyun Park, Hye Won Chung

展开摘要

In the era of large-scale foundation models, fully fine-tuning pretrained networks for each downstream task is often prohibitively resource-intensive. Prompt tuning offers a lightweight alternative by introducing tunable prompts while keeping the backbone frozen. However, existing visual prompt tuning methods often fail to specialize the prompts or enrich the representation space--especially when applied to self-supervised backbones. We show that these limitations become especially pronounced in challenging tasks and data-scarce settings, where effective adaptation is most critical. In this work, we introduce VIPAMIN, a visual prompt initialization strategy that enhances adaptation of self-supervised models by (1) aligning prompts with semantically informative regions in the embedding space, and (2) injecting novel representational directions beyond the pretrained subspace. Despite its simplicity--requiring only a single forward pass and lightweight operations--VIPAMIN consistently improves performance across diverse tasks and dataset sizes, setting a new state of the art in visual prompt tuning.

Poster
FlyLoRA: Boosting Task Decoupling and Parameter Efficiency via Implicit Rank-Wise Mixture-of-Experts

Heming Zou, Yunliang Zang, Wutong Xu, Yao Zhu, Xiangyang Ji

展开摘要

Low-Rank Adaptation (LoRA) is a widely used parameter-efficient fine-tuning method for foundation models, but it suffers from parameter interference, resulting in suboptimal performance. Although Mixture-of-Experts (MoE)-based LoRA variants show promise in mitigating intra-task correlations in single-task instruction tuning, they introduce additional router parameters and remain ineffective in multi-task model merging where inter-task interference arises. Inspired by the fly olfactory circuit, we propose FlyLoRA, an implicit MoE-based LoRA variant that introduces: (1) rank-wise expert activation in the up-projection matrix, and (2) an implicit router that unifies expert routing and down-projection, where a frozen sparse random projection matrix replaces the traditional dense trainable version. This design resolves the trade-off between intra-task decorrelation and computational efficiency by eliminating the need for an explicit router, while inherently mitigating inter-task interference due to the orthogonality property of random matrices. Extensive experiments across four domains---general knowledge understanding, scientific question answering, mathematical reasoning, and code generation---demonstrate consistent performance improvements over existing methods. Beyond empirical gains, FlyLoRA highlights how biological structures can inspire innovations in AI technologies. Code is available at https://github.com/gfyddha/FlyLoRA.

Poster
Generalization Bounds for Rank-sparse Neural Networks

Antoine Ledent, Rodrigo Alves, Yunwen Lei

展开摘要

It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of approximately low rank. In fact, the rank of the activations of each layer converges to a fixed value referred to as the ``bottleneck rank", which is the minimum rank required to represent the training data. This perspective is in line with the observation that regularizing linear networks (without activations) with weight decay is equivalent to minimizing the Schatten $p$ quasi norm of the neural network. In this paper we investigate the implications of this phenomenon for generalization. More specifically, we prove generalization bounds for neural networks which exploit the approximate low rank structure of the weight matrices if present. The final results rely on the Schatten $p$ quasi norms of the weight matrices: for small p, the bounds exhibit a sample complexity $ \widetilde{O}(WrL^2)$ where $W$ and $L$ are the width and depth of the neural network respectively and where $r$ is the rank of the weight matrices. As $p$ increases, the bound behaves more like a norm-based bound instead. The proof techniques involve a careful interpolation between the parametric and norm based regimes. We also demonstrate in experiments that this bound outperforms both classic parameter counting and norm based bounds in the typical overparametrized regime.

Poster
Parameter Efficient Fine-tuning via Explained Variance Adaptation

Fabian Paischer, Lukas Hauzenberger, Thomas Schmied, Benedikt Alkin, Marc Peter Deisenroth, Sepp Hochreiter

展开摘要

Foundation models (FMs) are pre-trained on large-scale datasets and then fine-tuned for a specific downstream task. The most common fine-tuning method is to update pretrained weights via low-rank adaptation (LoRA). Existing initialization strategies for LoRA often rely on singular value decompositions (SVD) of gradients or weight matrices. However, they do not provably maximize the expected gradient signal, which is critical for fast adaptation. To this end, we introduce **E**xplained **V**ariance **A**daptation (EVA), an initialization scheme that uses the directions capturing the most activation variance, provably maximizing the expected gradient signal and accelerating fine-tuning. EVA performs incremental SVD on minibatches of activation vectors and selects the right-singular vectors for initialization once they converged. Further, by selecting the directions that capture the most activation-variance for a given rank budget, EVA accommodates adaptive ranks that reduce the number of trainable parameters. We apply EVA to a variety of fine-tuning tasks as language generation and understanding, image classification, and reinforcement learning. EVA exhibits faster convergence than competitors and achieves the highest average score across a multitude of tasks per domain while reducing the number of trainable parameters through rank redistribution. In summary, EVA establishes a new Pareto frontier compared to existing LoRA initialization schemes in both accuracy and efficiency.

Poster
Low-Rank Head Avatar Personalization with Registers

Sai Tanmay Reddy Chakkera, Aggelina Chatziagapi, Md Moniruzzaman, Chen-ping Yu, Yi-Hsuan Tsai, Dimitris Samaras

展开摘要

We introduce a novel method for low-rank personalization of a generic model for head avatar generation. Prior work proposes generic models that achieve high-quality face animation by leveraging large-scale datasets of multiple identities. However, such generic models usually fail to synthesize unique identity-specific details, since they learn a general domain prior. To adapt to specific subjects, we find that it is still challenging to capture high-frequency facial details via popular solutions like low-rank adaptation (LoRA). This motivates us to propose a specific architecture, a Register Module, that enhances the performance of LoRA, while requiring only a small number of parameters to adapt to an unseen identity. Our module is applied to intermediate features of a pre-trained model, storing and re-purposing information in a learnable 3D feature space. To demonstrate the efficacy of our personalization method, we collect a dataset of talking videos of individuals with distinctive facial details, such as wrinkles and tattoos. Our approach faithfully captures unseen faces, outperforming existing methods quantitatively and qualitatively.

Poster
Ridge Boosting is Both Robust and Efficient

David Bruns-Smith, Zhongming Xie, Avi Feller

展开摘要

Estimators in statistics and machine learning must typically trade off between efficiency, having low variance for a fixed target, and distributional robustness, such as \textit{multiaccuracy}, or having low bias over a range of possible targets. In this paper, we consider a simple estimator, \emph{ridge boosting}: starting with any initial predictor, perform a single boosting step with (kernel) ridge regression. Surprisingly, we show that ridge boosting simultaneously achieves both efficiency and distributional robustness: for target distribution shifts that lie within an RKHS unit ball, this estimator maintains low bias across all such shifts and has variance at the semiparametric efficiency bound for each target. In addition to bridging otherwise distinct research areas, this result has immediate practical value. Since ridge boosting uses only data from the source distribution, researchers can train a single model to obtain both robust and efficient estimates for multiple target estimands at the same time, eliminating the need to fit separate semiparametric efficient estimators for each target. We assess this approach through simulations and an application estimating the age profile of retirement income.

Spotlight
Magical: Medical Lay Language Generation via Semantic Invariance and Layperson-tailored Adaptation

Weibin Liao, Tianlong Wang, Yinghao Zhu, Yasha Wang, Junyi Gao, Liantao Ma

展开摘要

Medical Lay Language Generation (MLLG) plays a vital role in improving the accessibility of complex scientific content for broader audiences. Recent literature to MLLG commonly employ parameter-efficient fine-tuning methods such as Low-Rank Adaptation (LoRA) to fine-tuning large language models (LLMs) using paired expert-lay language datasets. However, LoRA struggles with the challenges posed by multi-source heterogeneous MLLG datasets. Specifically, through a series of exploratory experiments, we reveal that standard LoRA fail to meet the requirement for semantic fidelity and diverse lay-style generation in MLLG task. To address these limitations, we propose Magical, an asymmetric LoRA architecture tailored for MLLG under heterogeneous data scenarios. Magical employs a shared matrix A for abstractive summarization, along with multiple isolated matrices B for diverse lay-style generation. To preserve semantic fidelity during the lay language generation process, Magical introduces a Semantic Invariance Constraint to mitigate semantic subspace shifts on matrix A. Furthermore, to better adapt to diverse lay-style generation, Magical incorporates the Recommendation-guided Switch, an externally interface to prompt the LLM to switch between different matrices B. Experimental results on three real-world lay language generation datasets demonstrate that Magical consistently outperforms prompt-based methods, vanilla LoRA, and its recent variants, while also reducing trainable parameters by 31.66%. Our code is publicly available at https://github.com/tianlwang/Magical.git.

Poster
Efficient Large Language Model Inference with Neural Block Linearization

Mete Erdogan, Francesco Tonin, Volkan Cevher

展开摘要

The high inference demands of transformer-based Large Language Models (LLMs) pose substantial challenges in their deployment. To this end, we introduce *Neural Block Linearization* (NBL), a novel framework for accelerating transformer model inference by replacing self-attention layers with linear approximations derived from Linear Minimum Mean Squared Error estimators. NBL leverages Canonical Correlation Analysis to compute a theoretical upper bound on the approximation error. Then, we use this bound as a criterion for substitution, selecting the LLM layers with the lowest linearization error. NBL can be efficiently applied to pre-trained LLMs without the need for fine-tuning. In experiments, NBL achieves notable computational speed-ups while preserving competitive accuracy on multiple reasoning benchmarks. For instance, applying NBL to 12 self-attention layers in *DeepSeek-R1-Distill-Llama-8B* increases the inference speed by 32% with less than 1% accuracy trade-off, making it a flexible and promising solution to improve the inference efficiency of LLMs.

Poster
Shift Before You Learn: Enabling Low-Rank Representations in Reinforcement Learning

Bastien Dubail, Stefan Stojanovic, Alexandre Proutiere

展开摘要

Low-rank structure is a common implicit assumption in many modern reinforcement learning (RL) algorithms. For instance, reward-free and goal-conditioned RL methods often presume that the successor measure admits a low-rank representation. In this work, we challenge this assumption by first remarking that the successor measure itself is not approximately low-rank. Instead, we demonstrate that a low-rank structure naturally emerges in the shifted successor measure, which captures the system dynamics after bypassing a few initial transitions. We provide finite-sample performance guarantees for the entry-wise estimation of a low-rank approximation of the shifted successor measure from sampled entries. Our analysis reveals that both the approximation and estimation errors are primarily governed by a newly introduced quantitity: the spectral recoverability of the corresponding matrix. To bound this parameter, we derive a new class of functional inequalities for Markov chains that we call Type II Poincaré inequalities and from which we can quantify the amount of shift needed for effective low-rank approximation and estimation. This analysis shows in particular that the required shift depends on decay of the high-order singular values of the shifted successor measure and is hence typically small in practice. Additionally, we establish a connection between the necessary shift and the local mixing properties of the underlying dynamical system, which provides a natural way of selecting the shift. Finally, we validate our theoretical findings with experiments, and demonstrate that shifting the successor measure indeed leads to improved performance in goal-conditioned RL.

Spotlight