Interpretability for Turing Machines

Billy Snikkers; Rumi Salazar; Daniel Murfet; Will Troiani

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arXiv · 2609.04661

Interpretability for Turing Machines

Billy Snikkers·Rumi Salazar·Daniel Murfet·Will Troiani

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Abstract

We show that susceptibilities, an interpretability technique developed for neural networks, can identify the presence of algorithmic structure in Turing machines by probing the local loss landscape of a learning problem for noisy Turing machines introduced by Murfet and Troiani (arXiv:2504.08075). We prove that symmetries and path separation in the algorithm implemented by a Turing machine induce permutation symmetries and low-rank blocks in its susceptibility matrix. We study this empirically on a set of deterministic finite automata (DFAs) and demonstrate that algorithmic features can be recovered by principal component analysis and clustering methods in susceptibility space.

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BibTeX RIS

Billy Snikkers, Rumi Salazar, Daniel Murfet, Will Troiani. 2026-09-04. Interpretability for Turing Machines. https://arxiv.org/abs/2609.04661

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