Generalization Error Analysis for Selective State-Space Models Through the Lens of Attention

• URL: http://arxiv.org/abs/2502.01473v1
• Date: Mon, 03 Feb 2025 16:05:31 GMT
• Title: Generalization Error Analysis for Selective State-Space Models Through the Lens of Attention
• Authors: Arya Honarpisheh, Mustafa Bozdag, Mario Sznaier, Octavia Camps,
• Abstract summary: State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers.<n>This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures.
• Score: 2.8998926117101367
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

Related papers

• Algorithm- and Data-Dependent Generalization Bounds for Score-Based Generative Models [27.78637798976204]
  Score-based generative models (SGMs) have emerged as one of the most popular classes of generative models.<n>This paper provides the first algorithmic- and data-dependent analysis for SGMs.<n>In particular, we account for the dynamics of the learning algorithm, offering new insights into the behavior of SGMs.
  arXiv  Detail & Related papers  (2025-06-04T11:33:04Z)
• Advancing Generalization Across a Variety of Abstract Visual Reasoning Tasks [0.0]
  We present the Pathways of Normalized Group Convolution model (PoNG)<n>PoNG is a novel neural architecture that features group convolution, normalization, and a parallel design.<n>Experiments demonstrate strong capabilities of the proposed model, which in several settings outperforms the existing literature methods.
  arXiv  Detail & Related papers  (2025-05-19T17:32:07Z)
• Learning to Dissipate Energy in Oscillatory State-Space Models [55.09730499143998]
  State-space models (SSMs) are a class of networks for sequence learning.<n>We show that D-LinOSS consistently outperforms previous LinOSS methods on long-range learning tasks.
  arXiv  Detail & Related papers  (2025-05-17T23:15:17Z)
• Sensitivity Meets Sparsity: The Impact of Extremely Sparse Parameter Patterns on Theory-of-Mind of Large Language Models [55.46269953415811]
  We identify ToM-sensitive parameters and show that perturbing as little as 0.001% of these parameters significantly degrades ToM performance. Our results have implications for enhancing model alignment, mitigating biases, and improving AI systems designed for human interaction.
  arXiv  Detail & Related papers  (2025-04-05T17:45:42Z)
• SeRpEnt: Selective Resampling for Expressive State Space Models [5.7918134313332414]
  State Space Models (SSMs) have recently enjoyed a rise to prominence in the field of deep learning for sequence modeling.<n>We show how selective time intervals in Mamba act as linear approximators of information.<n>We propose our SeRpEnt architecture, a SSM that further exploits selectivity to compress sequences in an information-aware fashion.
  arXiv  Detail & Related papers  (2025-01-20T20:27:50Z)
• Understanding and Mitigating Bottlenecks of State Space Models through the Lens of Recency and Over-smoothing [56.66469232740998]
  We show that Structured State Space Models (SSMs) are inherently limited by strong recency bias.<n>This bias impairs the models' ability to recall distant information and introduces robustness issues.<n>We propose to polarize two channels of the state transition matrices in SSMs, setting them to zero and one, respectively, simultaneously addressing recency bias and over-smoothing.
  arXiv  Detail & Related papers  (2024-12-31T22:06:39Z)
• On the Expressiveness and Length Generalization of Selective State-Space Models on Regular Languages [56.22289522687125]
  Selective state-space models (SSMs) are an emerging alternative to the Transformer.<n>We analyze their expressiveness and length generalization performance on regular language tasks.<n>We introduce the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization.
  arXiv  Detail & Related papers  (2024-12-26T20:53:04Z)
• Deep Learning-based Approaches for State Space Models: A Selective Review [15.295157876811066]
  State-space models (SSMs) offer a powerful framework for dynamical system analysis.<n>This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs.
  arXiv  Detail & Related papers  (2024-12-15T15:04:35Z)
• Autocorrelation Matters: Understanding the Role of Initialization Schemes for State Space Models [14.932318540666547]
  Current methods for initializing state space model (SSM) parameters rely on the HiPPO framework. We take a further step to investigate the roles of SSM schemes by considering the autocorrelation of input sequences. We show that the imaginary part of the eigenvalues of the SSM state matrix determines the conditioning of SSM optimization problems.
  arXiv  Detail & Related papers  (2024-11-29T03:55:19Z)
• Comparative Analysis of Pooling Mechanisms in LLMs: A Sentiment Analysis Perspective [0.0]
  Transformer-based models like BERT and GPT rely on pooling layers to aggregate token-level embeddings into sentence-level representations.<n>Common pooling mechanisms such as Mean, Max, and Weighted Sum play a pivotal role in this aggregation process.<n>This paper investigates the effects of these pooling mechanisms on two prominent LLM families -- BERT and GPT, in the context of sentence-level sentiment analysis.
  arXiv  Detail & Related papers  (2024-11-22T00:59:25Z)
• Provable Benefits of Complex Parameterizations for Structured State Space Models [51.90574950170374]
  Structured state space models (SSMs) are linear dynamical systems adhering to a specified structure. In contrast to typical neural network modules, whose parameterizations are real, SSMs often use complex parameterizations. This paper takes a step towards explaining the benefits of complex parameterizations for SSMs by establishing formal gaps between real and complex diagonal SSMs.
  arXiv  Detail & Related papers  (2024-10-17T22:35:50Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences.<n>We train the model using maximum likelihood estimation with Markov chain Monte Carlo.<n> Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Enhanced Structured State Space Models via Grouped FIR Filtering and Attention Sink Mechanisms [0.6718184400443239]
  We propose an advanced architecture that mitigates challenges by decomposing A-multiplications into multiple groups. Inspired by the "attention sink" phenomenon identified in streaming language models, we incorporate a similar mechanism to enhance the stability and performance of our model.
  arXiv  Detail & Related papers  (2024-08-01T02:49:58Z)
• The Buffer Mechanism for Multi-Step Information Reasoning in Language Models [52.77133661679439]
  Investigating internal reasoning mechanisms of large language models can help us design better model architectures and training strategies. In this study, we constructed a symbolic dataset to investigate the mechanisms by which Transformer models employ vertical thinking strategy. We proposed a random matrix-based algorithm to enhance the model's reasoning ability, resulting in a 75% reduction in the training time required for the GPT-2 model.
  arXiv  Detail & Related papers  (2024-05-24T07:41:26Z)
• From Generalization Analysis to Optimization Designs for State Space Models [14.932318540666547]
  A State Space Model (SSM) is a foundation model in time series analysis. We propose improvements to training algorithms based on the generalization results.
  arXiv  Detail & Related papers  (2024-05-04T13:58:03Z)
• State Space Models as Foundation Models: A Control Theoretic Overview [3.3222241150972356]
  In recent years, there has been a growing interest in integrating linear state-space models (SSM) in deep neural network architectures. This paper is intended as a gentle introduction to SSM-based architectures for control theorists. It provides a systematic review of the most successful SSM proposals and highlights their main features from a control theoretic perspective.
  arXiv  Detail & Related papers  (2024-03-25T16:10:47Z)
• A Novel Energy based Model Mechanism for Multi-modal Aspect-Based Sentiment Analysis [85.77557381023617]
  We propose a novel framework called DQPSA for multi-modal sentiment analysis. PDQ module uses the prompt as both a visual query and a language query to extract prompt-aware visual information. EPE module models the boundaries pairing of the analysis target from the perspective of an Energy-based Model.
  arXiv  Detail & Related papers  (2023-12-13T12:00:46Z)
• Sparse Modular Activation for Efficient Sequence Modeling [94.11125833685583]
  Recent models combining Linear State Space Models with self-attention mechanisms have demonstrated impressive results across a range of sequence modeling tasks. Current approaches apply attention modules statically and uniformly to all elements in the input sequences, leading to sub-optimal quality-efficiency trade-offs. We introduce Sparse Modular Activation (SMA), a general mechanism enabling neural networks to sparsely activate sub-modules for sequence elements in a differentiable manner.
  arXiv  Detail & Related papers  (2023-06-19T23:10:02Z)
• Representer Point Selection for Explaining Regularized High-dimensional Models [105.75758452952357]
  We introduce a class of sample-based explanations we term high-dimensional representers. Our workhorse is a novel representer theorem for general regularized high-dimensional models. We study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets.
  arXiv  Detail & Related papers  (2023-05-31T16:23:58Z)
• Understanding Best Subset Selection: A Tale of Two C(omplex)ities [18.83617956033111]
  We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. In particular, we establish both necessary and sufficient margin conditions depending on the identifiability margin and the two complexity measures.
  arXiv  Detail & Related papers  (2023-01-16T04:52:46Z)
• Distributed Bayesian Learning of Dynamic States [65.7870637855531]
  The proposed algorithm is a distributed Bayesian filtering task for finite-state hidden Markov models. It can be used for sequential state estimation, as well as for modeling opinion formation over social networks under dynamic environments.
  arXiv  Detail & Related papers  (2022-12-05T19:40:17Z)
• On the Generalization and Adaption Performance of Causal Models [99.64022680811281]
  Differentiable causal discovery has proposed to factorize the data generating process into a set of modules. We study the generalization and adaption performance of such modular neural causal models. Our analysis shows that the modular neural causal models outperform other models on both zero and few-shot adaptation in low data regimes.
  arXiv  Detail & Related papers  (2022-06-09T17:12:32Z)
• A comprehensive comparative evaluation and analysis of Distributional Semantic Models [61.41800660636555]
  We perform a comprehensive evaluation of type distributional vectors, either produced by static DSMs or obtained by averaging the contextualized vectors generated by BERT. The results show that the alleged superiority of predict based models is more apparent than real, and surely not ubiquitous. We borrow from cognitive neuroscience the methodology of Representational Similarity Analysis (RSA) to inspect the semantic spaces generated by distributional models.
  arXiv  Detail & Related papers  (2021-05-20T15:18:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.