DiTTo: Decoupled Intrinsic Topology Tree Optimization for Neuro-Symbolic Discovery from Non-Stationary Signals

Abstract

Symbolic regression (SR) struggles with non-stationary time-series signals. Conventional methods rely on the absolute time coordinate t, making them vulnerable to stochastic phase jitter and distribution shifts. This leads to expression bloat and loss of interpretability, a fundamental limitation that we formalize as Temporal Shift Vulnerability, which manifests as severe manifold distortion under temporal misalignments.

To address this challenge, we propose DiTTo (Decoupled intrinsic Topology Tree Optimization), an end-to-end neuro-symbolic framework for symbolic discovery from non-stationary signals. DiTTo maps phase-shifted transients into a locally invariant topological manifold tau in [0,1), effectively reducing the search complexity by decoupling symbolic discovery from temporal misalignment. A lightweight Adaptive Neural Router then extracts morphological descriptors to generate probabilistic operator priors without manual annotation. These priors guide discrete search backends, instantiated via Monte Carlo Tree Search (MCTS) in this work, to efficiently discover physically plausible expressions. The proposed topological representation is solver-independent and serves as a plug-and-play frontend capable of enhancing downstream symbolic regression methods operating on non-stationary signals.

Evaluated across 190 datasets from four heterogeneous domains, DiTTo achieves comparable reconstruction fidelity to the leading baseline (p = 0.983) while requiring only 88% of its formula complexity. Furthermore, in the zero-shot ECG domain, the router autonomously identifies the Gaussian basis function without prior exposure. Stress tests demonstrate its robustness against phase jitter and background noise.