arXiv:2611.13005v1 Announce Type: cross Abstract: Synthesizing programs from execution traces is a fundamental challenge in algorithmic interpretability and the reverse engineering of complex systems. We bring a rough-path-theoretic perspective to program induction, treating execution traces as high-dimensional rough paths and encoding them with the path signature transform, a tool from stochastic analysis whose expectation provably characterizes the distribution of traces a program induces. On three program-induction domains, Karel, List, and RASP, our log-signature trace encoder outperforms LSTM, Transformer, and Fourier baselines in almost every setting, with its largest margins when training data is scarce. We further observe that the trace-to-program pipeline is naturally contractive: it often produces valid programs that are shorter than the ground truth. We turn this into a bootstrapping procedure that exposes redundancy in the ground-truth supervision without any external oracle, which we demonstrate on redundancy-injected versions of our datasets. Finally, the log-signature encoder induces a markedly more interpretable latent geometry than the baselines, in which the nearest neighbors of every state lie on its own execution trace.