Subgroups of $U(d)$ Induce Natural RNN and Transformer Architectures
arXiv:2602.18417v1 Announce Type: cross Abstract: This paper presents a direct framework for sequence models with hidden states on closed subgroups of U(d). We use a minimal axiomatic setup and derive recurrent and transformer templates from a shared skeleton in which subgroup choice acts as a drop-in replacement for state space, tangent projection, and update map. We then specialize to O(d) and evaluate orthogonal-state RNN and transformer models on Tiny Shakespeare and Penn Treebank under parameter-matched settings. We also report a general linear-mixing extension in tangent space, which applies across subgroup choices and improves finite-budget performance in the current O(d) experiments.
arXiv:2602.18417v1 Announce Type: cross Abstract: This paper presents a direct framework for sequence models with hidden states on closed subgroups of U(d). We use a minimal axiomatic setup and derive recurrent and transformer templates from a shared skeleton in which subgroup choice acts as a drop-in replacement for state space, tangent projection, and update map. We then specialize to O(d) and evaluate orthogonal-state RNN and transformer models on Tiny Shakespeare and Penn Treebank under parameter-matched settings. We also report a general linear-mixing extension in tangent space, which applies across subgroup choices and improves finite-budget performance in the current O(d) experiments.
Executive Summary
This article presents a novel framework for sequence models with hidden states on closed subgroups of U(d). The authors derive recurrent and transformer templates from a shared skeleton, where subgroup choice acts as a drop-in replacement for state space, tangent projection, and update map. They specialize to O(d) and evaluate orthogonal-state RNN and transformer models on two benchmark datasets, Tiny Shakespeare and Penn Treebank. The results show improved performance and a general linear-mixing extension in tangent space, which applies across subgroup choices. This work has significant implications for the design and optimization of sequence models, particularly in the context of recurrent neural networks and transformers.
Key Points
- ▸ Derivation of recurrent and transformer templates from a shared skeleton
- ▸ Use of subgroups of U(d) as a drop-in replacement for state space, tangent projection, and update map
- ▸ Evaluation of orthogonal-state RNN and transformer models on benchmark datasets
Merits
Strength
The article presents a unified framework for sequence models, which allows for a more systematic exploration of different subgroup choices. This framework has the potential to lead to improved performance and better understanding of the underlying dynamics of sequence models.
Demerits
Limitation
The article focuses primarily on the theoretical framework and evaluation on two benchmark datasets, which may not be representative of real-world applications. Further research is needed to explore the practical implications of this work and to generalize the results to more complex scenarios.
Expert Commentary
This article presents a significant contribution to the field of sequence models, particularly in the context of recurrent neural networks and transformers. The authors' framework provides a unified approach to the design and optimization of sequence models, which has the potential to lead to improved performance and better understanding of the underlying dynamics of sequence models. However, further research is needed to explore the practical implications of this work and to generalize the results to more complex scenarios. The use of subgroups of U(d) in the article's framework is an example of the application of group theory in machine learning, which is an active area of research. The results of this work may lead to improved performance in sequence models, particularly in the context of recurrent neural networks and transformers, which are widely used in natural language processing and other applications.
Recommendations
- ✓ Further research is needed to explore the practical implications of this work and to generalize the results to more complex scenarios.
- ✓ The authors should investigate the application of their framework to other areas of machine learning, such as image and speech processing.
