State Space Models are Provably Comparable to Transformers in Dynamic Token Selection

• URL: http://arxiv.org/abs/2405.19036v2
• Date: Wed, 05 Mar 2025 10:15:19 GMT
• Title: State Space Models are Provably Comparable to Transformers in Dynamic Token Selection
• Authors: Naoki Nishikawa, Taiji Suzuki,
• Abstract summary: Deep neural networks based on state space models (SSMs) are attracting significant attention in sequence modeling.<n>We show that SSMs are comparable to Transformers in extracting the essential tokens depending on the input.
• Score: 41.617269918948686
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep neural networks based on state space models (SSMs) are attracting significant attention in sequence modeling since their computational cost is much smaller than that of Transformers. While the capabilities of SSMs have been demonstrated through experiments in various tasks, theoretical understanding of SSMs is still limited. In particular, most theoretical studies discuss the capabilities of SSM layers without nonlinear layers, and there is a lack of discussion on their combination with nonlinear layers. In this paper, we explore the capabilities of SSMs combined with fully connected neural networks, and show that they are comparable to Transformers in extracting the essential tokens depending on the input. As concrete examples, we consider two synthetic tasks, which are challenging for a single SSM layer, and demonstrate that SSMs combined with nonlinear layers can efficiently solve these tasks. Furthermore, we study the nonparametric regression task, and prove that the ability of SSMs is equivalent to that of Transformers in estimating functions belonging to a certain class.

Related papers

• Multiscale Tensor Summation Factorization as a New Neural Network Layer (MTS Layer) for Multidimensional Data Processing [18.557169937152967]
  Multiscale Summation (MTS) Factorization is a novel neural network operator that implements tensor summation at multiple scales. MTS not only reduces the number of parameters required while enhancing the efficiency of weight optimization, but it also demonstrates clear advantages over convolutional layers. The corresponding neural network, MTSNet, demonstrates a more favorable complexity-performance tradeoff compared to state-of-the-art transformers in various computer vision applications.
  arXiv  Detail & Related papers  (2025-04-17T22:19:59Z)
• 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. This bias impairs the models' ability to recall distant information and introduces robustness issues. 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)
• 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)
• SMR: State Memory Replay for Long Sequence Modeling [19.755738298836526]
  This paper proposes a novel non-recursive non-uniform sample processing strategy to overcome compatibility limitations in parallel convolutional computation. We introduce State Memory Replay (SMR), which utilizes learnable memories to adjust the current state with multi-step information for generalization at sampling points different from those in the training data. Experiments on long-range modeling tasks in autoregressive language modeling and Long Range Arena demonstrate the general effectiveness of the SMR mechanism for a series of SSM models.
  arXiv  Detail & Related papers  (2024-05-27T17:53:32Z)
• The Expressive Capacity of State Space Models: A Formal Language Perspective [0.8948475969696075]
  recurrent models based on linear state space models (SSMs) have shown promising performance in language modeling (LM), competititve with transformers. We present a comprehensive theoretical study of the capacity of such SSMs as it compares to that of transformers and traditional RNNs.
  arXiv  Detail & Related papers  (2024-05-27T17:46:57Z)
• The Illusion of State in State-Space Models [27.57426601905237]
  State-space models (SSMs) have emerged as a potential alternative architecture for building large language models. We show that SSMs have similar limitations to non-recurrent models like transformers, which may limit their ability to solve real-world state-tracking problems.
  arXiv  Detail & Related papers  (2024-04-12T21:30:06Z)
• Theoretical Foundations of Deep Selective State-Space Models [13.971499161967083]
  Deep SSMs demonstrate outstanding performance across a diverse set of domains. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states. We show that when random linear recurrences are equipped with simple input-controlled transitions, then the hidden state is provably a low-dimensional projection of a powerful mathematical object.
  arXiv  Detail & Related papers  (2024-02-29T11:20:16Z)
• Repeat After Me: Transformers are Better than State Space Models at Copying [53.47717661441142]
  We show that while generalized state space models are promising in terms of inference-time efficiency, they are limited compared to transformer models on tasks that require copying from the input context.
  arXiv  Detail & Related papers  (2024-02-01T21:44:11Z)
• Understanding Self-attention Mechanism via Dynamical System Perspective [58.024376086269015]
  Self-attention mechanism (SAM) is widely used in various fields of artificial intelligence. We show that intrinsic stiffness phenomenon (SP) in the high-precision solution of ordinary differential equations (ODEs) also widely exists in high-performance neural networks (NN) We show that the SAM is also a stiffness-aware step size adaptor that can enhance the model's representational ability to measure intrinsic SP.
  arXiv  Detail & Related papers  (2023-08-19T08:17:41Z)
• 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)
• Approximation and Estimation Ability of Transformers for Sequence-to-Sequence Functions with Infinite Dimensional Input [50.83356836818667]
  We study the approximation and estimation ability of Transformers as sequence-to-sequence functions with infinite dimensional inputs. Our theoretical results support the practical success of Transformers for high dimensional data.
  arXiv  Detail & Related papers  (2023-05-30T02:44:49Z)
• Simplicity Bias in Transformers and their Ability to Learn Sparse Boolean Functions [29.461559919821802]
  Recent works have found that Transformers struggle to model several formal languages when compared to recurrent models. This raises the question of why Transformers perform well in practice and whether they have any properties that enable them to generalize better than recurrent models.
  arXiv  Detail & Related papers  (2022-11-22T15:10:48Z)
• Your Transformer May Not be as Powerful as You Expect [88.11364619182773]
  We mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. We present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is. We develop a novel attention module, called Universal RPE-based (URPE) Attention, which satisfies the conditions.
  arXiv  Detail & Related papers  (2022-05-26T14:51:30Z)
• Bayesian Transformer Language Models for Speech Recognition [59.235405107295655]
  State-of-the-art neural language models (LMs) represented by Transformers are highly complex. This paper proposes a full Bayesian learning framework for Transformer LM estimation.
  arXiv  Detail & Related papers  (2021-02-09T10:55:27Z)
• Understanding Self-supervised Learning with Dual Deep Networks [74.92916579635336]
  We propose a novel framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks. We prove that in each SGD update of SimCLR with various loss functions, the weights at each layer are updated by a emphcovariance operator. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a emphhierarchical latent tree model (HLTM)
  arXiv  Detail & Related papers  (2020-10-01T17:51:49Z)
• Variational Transformers for Diverse Response Generation [71.53159402053392]
  Variational Transformer (VT) is a variational self-attentive feed-forward sequence model. VT combines the parallelizability and global receptive field computation of the Transformer with the variational nature of the CVAE. We explore two types of VT: 1) modeling the discourse-level diversity with a global latent variable; and 2) augmenting the Transformer decoder with a sequence of finegrained latent variables.
  arXiv  Detail & Related papers  (2020-03-28T07:48:02Z)

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.