aiqbench analysis
This research bridges the gap between neural network interpretability and formal logic by demonstrating that susceptibility matrices can reveal algorithmic structures within Turing machines. By applying techniques like principal component analysis to noisy Turing machine loss landscapes, the study proves that symmetries in deterministic finite automata correspond to specific low-rank blocks in these matrices. This work advances the theoretical understanding of how to extract and analyze intrinsic computational patterns beyond standard deep learning architectures.
Interpretability for Turing Machines
arXiv:2609.04661v1 Announce Type: new 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.
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.
75 pages, 31 figures, 3 tables. Interactive companion: this https URL. Code and data: doi:https://doi.org/10.5281/zenodo.22205895
Machine Learning (cs.LG); Formal Languages and Automata Theory (cs.FL); Machine Learning (stat.ML)
arXiv:2609.04661 [cs.LG]
(or arXiv:2609.04661v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.04661 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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