Unifying Transformers and State-Space Models in Sequence Modeling

The fields of artificial intelligence and deep learning are continuously evolving, with innovations in sequence modeling standing at the forefront. Transformers and state-space models represent two distinct paradigms for modeling sequential data. While transformers have revolutionized the field with their self-attention mechanisms and scalability, state-space models offer interpretable and theoretically grounded frameworks for capturing temporal dependencies. This exploration delves into the possibility of unifying these paradigms to create more robust and versatile models for tasks ranging from natural language processing to time-series forecasting.

Transformers, introduced in the 2017 paper by Vaswani et al., leverage self-attention to weigh input elements dynamically during computation. This architecture enables parallel processing and has demonstrated exceptional performance on tasks like machine translation and text summarization. However, transformers are resource-intensive and lack an inherent mechanism for modeling long-term dependencies in the same way recurrent models do.

On the other hand, state-space models (SSMs) are grounded in control theory and linear systems. These models represent temporal dynamics using a set of state variables that evolve over time. SSMs are known for their efficiency and interpretability, as well as their ability to capture long-term dependencies. Recent advances, such as the use of structured matrices and efficient inference algorithms, have made SSMs competitive in sequence modeling tasks.

This exploration proposes a hybrid model that combines the strengths of both architectures. The attention mechanisms of transformers can be adapted to operate over the latent state trajectories generated by a state-space model. By doing so, the model benefits from the attention-based global context awareness of transformers while maintaining the temporal modeling precision of state-space models. This hybrid approach could enable more efficient and effective modeling of complex sequential data.

To explore this idea, we begin by analyzing the mathematical formulations of both architectures. Transformers employ a linear combination of value vectors weighted by the attention scores between queries and keys. In contrast, SSMs define the next state as a function of the current state and input, typically through linear transformations. The challenge lies in mapping the attention mechanism into a state-space framework or vice versa.

One potential direction is to reinterpret the attention weights as dynamic state transitions. For example, the attention mechanism can be seen as a non-linear update rule for the state, where each attention head provides a distinct trajectory for the state to evolve. By incorporating such a mechanism into a state-space model, we can create a more flexible and adaptive model for time-series data.

Another avenue is to use the structure of SSMs to regularize the attention weights in transformers. By constraining the attention matrix to follow certain properties (e.g., sparsity or low-rank structure), we can improve the interpretability and efficiency of the transformer model. This could also reduce overfitting and enhance generalization.

Empirical validation is crucial for this exploration. We propose to implement a prototype model that integrates a state-space core with a transformer-style attention layer. The model can be tested on benchmark datasets such as Penn Treebank for language modeling and NAB (Numenta Anomaly Benchmark) for time-series forecasting. Evaluation metrics will include accuracy, perplexity, and inference speed to assess the trade-offs between performance and efficiency.

The implications of this research are far-reaching. A unified model could bridge the gap between the high-performance but high-compute transformers and the efficient but less expressive state-space models. This could lead to a new class of models that are both powerful and scalable, suitable for deployment on devices with limited computational resources. Furthermore, the theoretical insights gained from this integration could inspire new methodologies in sequence modeling and time-series analysis.

In conclusion, the unification of transformers and state-space models represents a promising frontier in the field of AI. By combining their strengths, we can build models that are not only capable of handling complex sequential data but also interpretable, efficient, and adaptable to diverse applications.