Abstract

Early stopping is a standard form of implicit regularization in neural sequence models, but criteria based solely on validation loss can become unstable or weakly informative in noisy, non-stationary, or weakly separated regimes. We propose Symbolic Early Stopping (SES), a representation-aware hybrid stopping criterion that monitors the evolution of validation hidden-state organization during training. At each epoch, SES constructs a Mapper-based symbolic abstraction of hidden representations extracted from a fixed monitored layer, transforms latent trajectories into symbol sequences, and summarizes them through a compact set of symbolic–dynamic descriptors capturing sequential complexity, transition uncertainty, and geometric dispersion. These descriptors are aggregated into a single symbolic stability score, which is combined with validation-loss monitoring to detect convergence of the learned representation. We evaluate SES on recurrent, bidirectional recurrent, and encoder-only Transformer architectures across multiple time-series regimes with different levels of structural regularity and noise. The results indicate that SES frequently terminates training substantially earlier than conservative loss-based baselines while preserving a competitive quality–efficiency trade-off relative to oracle validation-based stopping. Robustness experiments under additive input noise show that the symbolic monitoring signal remains informative under moderate perturbations, although its advantage is not uniform across all datasets and model classes. A layer-wise analysis further suggests that useful stopping signals may emerge before the final validation curve fully stabilizes, reflecting earlier organization of latent representations. Overall, SES provides an interpretable and computationally tractable framework for representation-level early stopping in neural sequence modeling.

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