arXiv Machine Learning By Arman Kostanian, Armen Beklaryan

Identifiability of a dissipative knowledge-dynamics model: exact recovery under designed excitation, degeneration on observational data

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The paper presents a nonlinear dissipative dynamical model of human learning, featuring a concept‑transfer matrix, per‑concept forgetting rates, and a saturating practice‑response gain. It proves a structural identifiability theorem that guarantees exact parameter recovery under explicit excitation conditions, provides closed‑form recovery for the two‑concept case, and introduces a fast, L‑stable numerical scheme enabling estimation on large learner cohorts. Empirical results show exact recovery on synthetic data with designed excitation, but failure to recover on large observational benchmarks, illustrating a sharp boundary between identifiable and unidentifiable regimes and offering a validation protocol for interpretability claims.

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