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When Does Tool Use Increase the Expressive Power of Finite-Precision Recurrent Models?

paperactiveprovisionalwhen-does-tool-use-increase-the-expressive-power-of-finite-precision-recurrent-models--7e2285f3·1 events·first seen Jul 8, 2026

Aliases: When Does Tool Use Increase the Expressive Power of Finite-Precision Recurrent Models?

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state space model

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6arXiv · cs.CL·Jul 8, 2026·source ↗

Formal theory of when tool use increases expressive power of finite-precision recurrent models

A new arXiv paper provides an exact, architecture-level characterization of when external tool access increases the computational expressivity of finite-precision recurrent sequence models, including SSMs. The key dichotomy: finite-state tools add essentially nothing (absorbable at logarithmic bit cost), while a single infinite-state tool (a read/write tape) makes the system Turing complete with only O(log|Q| + log|Γ|) bits of controller state. The paper further shows this construction is realized by a natural one-layer finite-precision selective affine SSM, with selectivity identified as essential.

Evaluation and Benchmarking Agent and Tool Ecosystem When Does Tool Use Increase the Expressive Power of Finite-Precision Recurrent Models?state space model