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.
Viewing computing machines as symbolic dynamical systems is a powerful idea which has led to many important results. However, the standard setting of symbolic Turing dynamics is not well suited for studying questions of typicality, genericity, or robustness. Such natural questions, for example, as"what is the computati...
An important computational model studied in Formal Languages and Automata Theory is the Turing machine and its extensions, including the multitape Turing machine. Designing such machines is challenging because they operate at a low level of abstraction, making it difficult to understand why words in an unrestricted lan...
D. K. Fields, Sophia G. Turano, Andrés M. Garced et al.· Proceedings of the 2026 ACM...· 0 citations
Toric words have recently gained attention as a means to model the behaviour of dynamical systems such as linear loops. This work is concerned with describing when the toric model is precise enough to decide whether the trace of a system is contained in an omega-regular language. Our contributions are threefold. (i) We...
We investigate the computational complexity of analyzing the structural and behavioral properties of deterministic k-pebble automata, which represent a natural framework for studying minimal programmable machines. First, we provide an explicit construction of a three-pebble automaton U capable of simulating any determi...
In our book Why machines will never rule the world [13, 14] we argue that arti- ficial general intelligence is mathematically impossible. This is because the human beings and the processes which exhibit intelligence are complex systems whose be- haviour cannot be captured by the kinds of models that we can generate wit...
We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communica...
Antonin Callard, Andrei E. Romashchenko, V. Terrier et al.· 0 citations
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