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

Key points

• Human learning is a dissipative dynamical process: mastery accumulates through practice, decays through forgetting, and propagates across interdependent concepts.1
• We prove a structural identifiability theorem for the associated inverse problem under explicit excitation conditions, with constructive closed-form recovery for the two-concept case, together with monotonicity, robustness and L-stability results.1
• We derive a semi-implicit L-stable scheme for the dissipative subsystem and a batched solver numerically equivalent to the per-trajectory formulation (bit-exact predictions, gradients to $10^{-10}$) yet two orders of magnitude faster, making estimation feasible on cohorts of $10^5$ learners.1
• Under the theorem's excitation conditions, synthetic recovery is exact: parameters to machine precision, prerequisite structure at $F1 = 1.0$.1

Sources (1)

• [1]Identifiability of a dissipative knowledge-dynamics model: exact recovery under designed excitation, degeneration on observational data
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 11:50 AM

  We model it as a nonlinear dissipative system of ordinary differential equations whose parameters are mechanistically meaningful (a concept-transfer matrix encoding prerequisite coupling, per-concept forgetting rates, and a saturating practice-response gain), and we study when those parameters can actually be recovered from data.

  Human learning is a dissipative dynamical process: mastery accumulates through practice, decays through forgetting, and propagates across interdependent concepts.

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