Life sciences · Preprint

Interpretability for Turing Machines

arXiv · September 4, 2026

Hypothesis-Generating Why this matters to you Expert discussion

Raises a question worth testing. It does not answer one.

AI Summary

This preprint proposes and demonstrates that susceptibilities—an interpretability technique from neural networks—can identify algorithmic structure in Turing machines by detecting permutation symmetries and low-rank blocks in the susceptibility matrix. The work is theoretical and computational, proving that symmetries and path separation in algorithms induce specific matrix structures, and shows that algorithmic features can be recovered via dimensionality reduction.

What was studied

Theoretical analysis with empirical validation on finite automata. Deterministic finite automata and noisy Turing machines as defined by Murfet and Troiani.. Intervention: Application of susceptibilities (neural network interpretability technique) to probe local loss landscape of learning problems..

Key findings

Susceptibilities can identify presence of algorithmic structure in Turing machines by probing local loss landscape. Symmetries and path separation in algorithms induce permutation symmetries and low-rank blocks in susceptibility matrix. Algorithmic features can be recovered by principal component analysis and clustering methods in susceptibility space.

Safety

Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.

Who this may help

The source did not state who this applies to in practice.

Plain-language summary

This is a theoretical and computational study proposing that a neural network interpretability technique can detect algorithmic structure in Turing machines; it raises a mechanistic question rather than testing a clinical or translational claim.

Study design

As stated by the source record.

MethodsTheoretical proofs that algorithmic properties (symmetries, path separation) of Turing machines induce matrix structure in susceptibility matrices; empirical study applies principal component analysis and clustering to susceptibility space of deterministic finite automata.

DesignTheoretical analysis with empirical validation on finite automata

PopulationDeterministic finite automata and noisy Turing machines as defined by Murfet and Troiani.

InterventionApplication of susceptibilities (neural network interpretability technique) to probe local loss landscape of learning problems.

Caveats

This is a preprint and has not been peer reviewed.
No quantitative sample size or empirical metrics (e.g., accuracy, precision, recall) reported for DFA experiments.
No comparison to alternative interpretability or structure detection methods.
Findings are in abstract computational setting; generalization to practical machine learning or other domains is not demonstrated.

Evidence assessment

Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.

Study design

moderate

Combination of theoretical proofs and empirical demonstration on deterministic finite automata.

Directness

limited

Applies interpretability technique to abstract computational models; no direct biological, clinical, or applied endpoint.

Consistency

insufficient

Single study; no comparison to other interpretability methods or prior work on this specific mapping.

Risk of bias

moderate

Theoretical analysis and controlled empirical setting reduce bias; preprint status and lack of peer review noted.

Sample adequacy

insufficient

No sample size reported; empirical validation on 'a set of' DFAs without quantification.

What is missing. This record has no reported figures. That is a gap in the analysis, not a judgement about the study.

Source 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.

Follow from this

Taken from the source record, never inferred. Follow any of these and new work involving them reaches your briefing.

Daniel MurfetBilly SnikkersWill TroianiRumi Salazar