arXiv:2606.01765v1 Announce Type: cross Abstract: What formal languages can a recurrent neural language model recognize? Formal results in the literature conflict: some authors report Turing-completeness, while others show equivalence to regular languages. The reason for this discrepancy is that the underlying arithmetic model differs. The paper develops a unified algebraic account of the expressivity of recurrent neural networks, starting with a formal account of various arithmetic models. This account reduces expressivity to an algebraic question, e.g., whether a network's syntactic monoid d
This paper attempts to resolve conflicting formal results on the expressivity of recurrent neural language models, which is a foundational aspect of current AI systems research.
Understanding the fundamental computational limits and capabilities of recurrent neural networks is crucial for designing more robust, explainable, and powerful AI, impacting future model architectures and applications.
This theoretical work provides a unified algebraic framework for analyzing recurrent neural networks, potentially leading to more deliberate and theoretically grounded advancements in AI model development rather than purely empirical progress.
- · AI researchers
- · Deep learning framework developers
- · AI ethics and safety organizations
- · AI systems built on flawed theoretical assumptions
Clarified understanding of recurrent neural network expressivity.
Improved design principles for future recurrent and transformer-like architectures.
Enhanced ability to predict and control the capabilities and limitations of advanced AI models.
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