Pole-Zero Geometry, Model Reduction, and Identifiability in Sensory Adaptation
arXiv:2609.01329
2026
Dynamics
2 ideas extracted · analyzed Sep 2, 2026
What the math gives to ML
The paper shows that pole geometry and latent-state properties can change under model reduction: the same higher-order system of real relaxation modes produces rho_moment = 4.50 under low-frequency moment matching and rho_window = 3.31 under finite-window fitting, crossing the reduced second-order boundary at rho = 4. This mechanism transfers to recurrent and state-space neural networks, where compression or finite-context fitting can create spurious oscillatory modes and degrade long-horizon prediction. The paper also shows that an observed scalar spectrum can be insensitive to hidden cross diffusion when the hidden state has no self-relaxation, even though path-space irreversibility changes. These results motivate protocol-robust pole regularization and latent irreversibility diagnostics.
Ideas from this paper
✗ Mechanism failed
2026
Train a latent state-space neural network so that its effective pole geometry remains consistent when identified by low-frequency moments and finite-window trajectories. Penalize disagreement between the two reductions, and penalize proximity to the oscillatory/non-oscillatory boundary, to reduce spurious ringing after distillation or context truncation.
Useful8/10
Difficulty5/10
Novelty7/10
✗ Failed on benchmark
2026
Use explicitly stochastic latent dynamics to detect hidden-state changes that are invisible in the observed output spectrum. Near the integral-memory regime, constrain or monitor cross diffusion with a forward-versus-reverse path statistic, preventing output-equivalent latent models from developing physically implausible irreversible dynamics.
Useful7/10
Difficulty6/10
Novelty8/10