Skip to content
DraconiticResearch
Search Sources API
184,937 studies31 sourcesUpdated 46 min ago
PreprintCC BY 4.0arXiv

Interpretability for Turing Machines

  • Billy Snikkers
  • Rumi Salazar
  • Daniel Murfet
  • Will Troiani
Open at sourcePDFDOICite

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.

Related

  1. Order-preserving maps of the Turing degrees: regularity and consistency strength
    Liang Yu
    arXivPreprintCC0Full textLogic & foundationsarXiv
  2. Turing bifurcation, criticality, and multistability in a nonlocal advection-reaction-diffusion equation
    Yui Nagayama, Masaharu Nagayama, Hiroshi Ishii
    arXivPreprintarXiv licenceFull textAnalysis & PDEsStatistical & nonlinear physicsarXiv
  3. Pseudo-Hyperjump Inversion Fails for Turing Degrees
    Patrizio Cintioli
    arXivPreprintarXiv licenceFull textLogic & foundationsarXiv
  4. Who Wrote This? Turing, Total Variation, and the Mathematics of AI-Text Detection
    Santiago Schnell
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  5. From Turing Patterns to Spike Self-Replication and Nucleation in a Growing-Domain Tulip Breaking Virus Model
    Fanya Xia, Chunyi Gai
    arXivPreprintarXiv licenceFull textEvolutionary biologyAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{snikkers2026interpretability,
  title = {{Interpretability for Turing Machines}},
  author = {Billy Snikkers and Rumi Salazar and Daniel Murfet and Will Troiani},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04661},
  eprint = {2609.04661},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04661},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Interpretability for Turing Machines
AU  - Billy Snikkers
AU  - Rumi Salazar
AU  - Daniel Murfet
AU  - Will Troiani
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04661
UR  - https://arxiv.org/abs/2609.04661
AB  - 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.
ER  -