The Illusion of State in State-Space Models (AI summary)

Key Points

1. The paper discusses state-space models (SSMs) as a potential alternative to transformer architectures for building large language models. There is a focus on the ability of SSMs to address sequential computation and state tracking, but it is revealed that SSMs have limitations in expressive power for state tracking problems. Empirical experiments show that SSMs struggle with state tracking compared to recurrent neural networks (RNNs).

2. The paper explores the theoretical limitations of linear and Mamba-style SSMs, highlighting their inability to solve inherently sequential problems like composing permutations. It is shown that SSMs cannot express certain state-tracking problems, such as the tracking of chess moves, evaluating code, or tracking entities in a narrative.

3. The study examines the complexity hierarchy within NC1 and TC0, revealing that both transformers and SSMs cannot express the "hard state tracking" captured by certain problems, such as permutation composition.

4. A theoretical analysis of SSM architectures, using circuit complexity and logic formalisms, showcases the limitations of SSMs in expressing inherently sequential problems. The paper presents detailed results demonstrating that SSMs are unable to solve NC1-hard problems.

5. Two minimal extensions of linear SSMs are proposed to increase their expressive power for state tracking, allowing them to solve permutation composition. The extensions, however, may negatively impact parallelism as well as learning dynamics, prompting further research.

6. The study provides a comprehensive theoretical and empirical analysis of the state tracking capabilities of SSMs, comparing them with other architectural variants and models like transformers and RNNs.

7. The paper discusses the implications of the findings for the practical viability of SSMs and their potential to be deployed as the next generation of large language models.

8. The research shows how SSMs can be extended to close the gap in expressive power with RNNs, enabling them to solve more complex state-tracking problems. Two specific approaches are suggested to achieve this.

9. The study concludes with insights into the practical implications and potential societal impacts of advancing the foundational understanding of state-space architectures for deep learning. However, it is acknowledged that further research is needed to fully explore the practical viability and downstream impacts of SSMs.

Summary

The paper examines the expressive power of state-space models (SSMs) compared to transformers for state tracking tasks, with a focus on their limitations and experimental evidence. The research aims to address the theoretical weaknesses of transformers and SSMs in expressing certain kinds of sequential computation and state tracking. The paper reveals that SSMs, despite their architectural similarity to recurrent neural networks (RNNs), do not have an advantage in expressive power for state tracking compared to transformers. The analysis shows that the expressive power of SSMs is limited similarly to transformers, as they cannot express computation outside the complexity class TC0.

The limitations imply that SSMs are unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. The paper also reports experiments showing that SSMs struggle with state tracking, confirming the theoretical findings. The paper further discusses the theoretical weakness of linear SSMs and near generalizations, showing that they are in the complexity class L-uniform TC0 and cannot solve inherently sequential problems, including state-tracking problems like permutation composition.

Additionally, the paper examines the potential extensions of linear SSMs to increase their expressive power for state tracking, including the addition of a nonlinearity to make the SSM more like an RNN or allowing the A matrix to be input-dependent to make the SSM more like a weighted finite automaton (WFA). Empirical investigation of the SSM variants demonstrates their limitations and challenges in learning dynamics and learning permutations in practice.

Collectively, the study provides insights into the limitations and potential extensions of SSMs for state tracking tasks and highlights the need for further research in developing SSM-like models with greater expressivity for state tracking while maintaining strong parallelizability and learning dynamics. The paper presents a comprehensive analysis of the theoretical and practical aspects of using SSMs for state tracking tasks, informing future research directions in the development of neural architectures for language models.

Reference: https://arxiv.org/abs/2404.088...