τ-KL: Adaptive Time-Constant Divergence as a Distribution-Drift OOD Probe for Liquid Neural Networks (Bilingual Edition)

We propose τ-KL, a training-free, single-forward-pass out-of-distribution (OOD) probe that measures the per-layer Kullback-Leibler divergence over the adaptive time constants of a Liquid Neural Network (LNN). Across five real-world domains and a controlled noise-injection sweep, τ-KL monotonically rises with OOD severity (158× dynamic range from σ=0 to σ=10) without any auxiliary OOD labels or model retraining. This is the bilingual (English + Chinese) edition. The paper does not report ROC-AUROC head-to-head with MC-Dropout/Deep Ensembles; the empirical evidence is the monotonicity of τ-KL in noise-injection severity.