State Space Models as Foundation Models: A Control Theoretic Overview

• URL: http://arxiv.org/abs/2403.16899v1
• Date: Mon, 25 Mar 2024 16:10:47 GMT
• Title: State Space Models as Foundation Models: A Control Theoretic Overview
• Authors: Carmen Amo Alonso, Jerome Sieber, Melanie N. Zeilinger,
• Abstract summary: 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.
• Score: 3.3222241150972356
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years, there has been a growing interest in integrating linear state-space models (SSM) in deep neural network architectures of foundation models. This is exemplified by the recent success of Mamba, showing better performance than the state-of-the-art Transformer architectures in language tasks. Foundation models, like e.g. GPT-4, aim to encode sequential data into a latent space in order to learn a compressed representation of the data. The same goal has been pursued by control theorists using SSMs to efficiently model dynamical systems. Therefore, SSMs can be naturally connected to deep sequence modeling, offering the opportunity to create synergies between the corresponding research areas. This paper is intended as a gentle introduction to SSM-based architectures for control theorists and summarizes the latest research developments. It provides a systematic review of the most successful SSM proposals and highlights their main features from a control theoretic perspective. Additionally, we present a comparative analysis of these models, evaluating their performance on a standardized benchmark designed for assessing a model's efficiency at learning long sequences.

Related papers

• Mamba-CL: Optimizing Selective State Space Model in Null Space for Continual Learning [54.19222454702032]
  Continual Learning aims to equip AI models with the ability to learn a sequence of tasks over time, without forgetting previously learned knowledge. State Space Models (SSMs) have achieved notable success in computer vision. We introduce Mamba-CL, a framework that continuously fine-tunes the core SSMs of the large-scale Mamba foundation model.
  arXiv  Detail & Related papers  (2024-11-23T06:36:16Z)
• Exploring Model Kinship for Merging Large Language Models [52.01652098827454]
  We introduce model kinship, the degree of similarity or relatedness between Large Language Models. We find that there is a certain relationship between model kinship and the performance gains after model merging. We propose a new model merging strategy: Top-k Greedy Merging with Model Kinship, which can yield better performance on benchmark datasets.
  arXiv  Detail & Related papers  (2024-10-16T14:29:29Z)
• Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods [8.654571696634825]
  State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in non-linear cases for long-sequence modelling. This research contributes insights into the physical modelling of dynamical systems by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement.
  arXiv  Detail & Related papers  (2024-08-29T15:55:27Z)
• GenBench: A Benchmarking Suite for Systematic Evaluation of Genomic Foundation Models [56.63218531256961]
  We introduce GenBench, a benchmarking suite specifically tailored for evaluating the efficacy of Genomic Foundation Models. GenBench offers a modular and expandable framework that encapsulates a variety of state-of-the-art methodologies. We provide a nuanced analysis of the interplay between model architecture and dataset characteristics on task-specific performance.
  arXiv  Detail & Related papers  (2024-06-01T08:01:05Z)
• Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting [22.84798547604491]
  State Space Models (SSMs) approximate continuous systems using a set of basis functions and discretize them to handle input data. This paper proposes a novel theoretical framework termed Dynamic Spectral Operator, offering more intuitive and general guidance on applying SSMs to time series data. We introduce Time-SSM, a novel SSM-based foundation model with only one-seventh of the parameters compared to Mamba.
  arXiv  Detail & Related papers  (2024-05-25T17:42:40Z)
• Understanding the differences in Foundation Models: Attention, State Space Models, and Recurrent Neural Networks [50.29356570858905]
  We introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation. We provide principled comparisons between softmax attention and other model classes, discussing the theoretical conditions under which softmax attention can be approximated. This shows the DSF's potential to guide the systematic development of future more efficient and scalable foundation models.
  arXiv  Detail & Related papers  (2024-05-24T17:19:57Z)
• State Space Model for New-Generation Network Alternative to Transformers: A Survey [52.812260379420394]
  In the post-deep learning era, the Transformer architecture has demonstrated its powerful performance across pre-trained big models and various downstream tasks. To further reduce the complexity of attention models, numerous efforts have been made to design more efficient methods. Among them, the State Space Model (SSM), as a possible replacement for the self-attention based Transformer model, has drawn more and more attention in recent years.
  arXiv  Detail & Related papers  (2024-04-15T07:24:45Z)
• 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)
• Replicability Study: Corpora For Understanding Simulink Models & Projects [8.261117235807607]
  The study reviews methodologies and data sources employed in prior Simulink model studies and replicates the previous analysis using SLNET. We found that open-source Simulink models follow good modeling practices and contain models comparable in size and properties to proprietary models.
  arXiv  Detail & Related papers  (2023-08-03T18:14:54Z)
• S2RMs: Spatially Structured Recurrent Modules [105.0377129434636]
  We take a step towards exploiting dynamic structure that are capable of simultaneously exploiting both modular andtemporal structures. We find our models to be robust to the number of available views and better capable of generalization to novel tasks without additional training.
  arXiv  Detail & Related papers  (2020-07-13T17:44:30Z)
• Relational State-Space Model for Stochastic Multi-Object Systems [24.234120525358456]
  This paper introduces the relational state-space model (R-SSM), a sequential hierarchical latent variable model. R-SSM makes use of graph neural networks (GNNs) to simulate the joint state transitions of multiple correlated objects. The utility of R-SSM is empirically evaluated on synthetic and real time-series datasets.
  arXiv  Detail & Related papers  (2020-01-13T03:45:21Z)

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.