Technologies on Effectiveness and Efficiency: A Survey of State Spaces Models (2503.11224v1)

Abstract: State Space Models (SSMs) have emerged as a promising alternative to the popular transformer-based models and have been increasingly gaining attention. Compared to transformers, SSMs excel at tasks with sequential data or longer contexts, demonstrating comparable performances with significant efficiency gains. In this survey, we provide a coherent and systematic overview for SSMs, including their theoretical motivations, mathematical formulations, comparison with existing model classes, and various applications. We divide the SSM series into three main sections, providing a detailed introduction to the original SSM, the structured SSM represented by S4, and the selective SSM typified by Mamba. We put an emphasis on technicality, and highlight the various key techniques introduced to address the effectiveness and efficiency of SSMs. We hope this manuscript serves as an introduction for researchers to explore the theoretical foundations of SSMs.

The Evolution and Application of State Space Models in Machine Learning

State Space Models (SSMs) have increasingly gained traction within the field of machine learning as a viable alternative to transformer-based models particularly for tasks involving sequential data and long-context dependencies. This comprehensive survey paper traces the evolutionary trajectory of SSMs, delineating their theoretical underpinnings, mathematical formulations, significant developments, and wide-ranging applications.

Theoretical Foundations and Structure

The paper elucidates how SSMs, originally conceptualized for modeling dynamical systems in continuous time, have been discretized for analyzing sequential data computationally. The seminal work on the Kalman filter showcased linear dynamic systems utilizing SSMs. The initial models, however, faced limitations like weak data-fitting capabilities and lack of parallel computing, motivating further advancements.

A substantial development was the introduction of structured SSMs, articulated through the Structured State Space Sequence model (S4). S4 integrates structured parameters using the HiPPO framework to address memory decay and gradient issues inherent in long-sequence modeling. It also incorporates the DPLR structure to enhance computational efficiency, reducing complexity from $O(LN_s^2)$ to $O(L+N)$. This transformation leverages the convolutional form of SSMs, scalable through efficient algorithms like FFT.

Advances in Selectivity and Model Enhancements

Furthering the capabilities of SSMs, models like Mamba have introduced selectivity, enabling dynamic adaptation of model parameters based on input context. This development allows SSMs to efficiently prioritize critical input information, providing nuanced handling of sequences. Mamba achieves computational efficiency through hardware-aware methods and reformulates the SSM into matrix-vector multiplication, aligning with modern GPU architectures.

Building upon these foundational enhancements, variants of Mamba, such as DenseMamba and Hierarchical SSM, utilize mixture-of-experts or hierarchical structuring to optimize handling of complex sequences and multidimensional data.

Comparative Analysis with Other Architectures

The paper discusses the alignment of SSMs with other neural architectures, notably RNNs and CNNs, due to their mathematical underpinnings. S4’s convolutional equivalence has facilitated its use in CNN-like applications. Moreover, the convergence with transformer architectures has been significant, as Mamba and its derivatives adopt structural elements reminiscent of transformers for enhanced scalability and real-world applicability.

Applications Across Domains

The paper meticulously covers the deployment of SSMs across various domains such as video modeling, speech and audio processing, molecular sequence analysis, 3D signal processing, time series forecasting, and structured data analysis. SSM-based frameworks, especially Mamba, demonstrate proficient handling of long-range dependencies in video and audio tasks, efficient spatiotemporal modeling in point clouds, and superior predictive power in genomic sequencing and chemical data.

These applications underscore the versatility of SSMs, driven by their efficiency in managing sequence data and capturing dependencies over extensive contexts, making them a powerful tool for a wide array of tasks from biomedical modeling to spatiotemporal forecasting.

Future Prospects and Conclusions

As SSMs continue to evolve, they promise to further challenge conventional transformer models, offering significant efficiency gains and nuanced sequence modeling capabilities. This survey provides a pivotal resource for researchers aiming to leverage the structured efficiency and selectivity of SSMs in multifarious applications, setting a stage for future endeavors to refine their adaptability and computational finesse. The potential for combining SSMs with other architectures to address more complex challenges is particularly promising, suggesting a fertile ground for further research and optimization.