# Interpretability for Turing Machines

arXiv: https://arxiv.org/abs/2609.04661 · HTML: https://mlsanity.com/paper/2609.04661/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 16 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Programs as Singularities](https://mlsanity.com/paper/2504.08075/) (2025)
- [Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning](https://mlsanity.com/paper/2605.07980/) (2026)
- [Geometry of Program Synthesis](https://mlsanity.com/paper/2103.16080/) (2021)

## Abstract (arXiv)

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.