Hidden-Diffusion Irreversibility Monitor
Implementation & benchmark of arXiv:2609.01329 — Pole-Zero Geometry, Model Reduction, and Identifiability in Sensory Adaptation
Source paper: Pole-Zero Geometry, Model Reduction, and Identifiability in Sensory Adaptation arXiv:2609.01329 ⓘ · analyzed Sep 2, 2026
AI-generated research hypothesis, automatically tested. Not peer-reviewed.
Idea description
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.
Formulas
Mathematical statement
For a two-dimensional Ornstein-Uhlenbeck latent process dX = -A X dt + B dW, with diffusion matrix D = B B^T / 2 and X = (x,y)^T, the paper identifies a blind spot: for nontrivial coupling, the scalar spectrum of x is insensitive to cross diffusion D_xy when the hidden state has no self-relaxation, A_yy = 0. This is the integral-memory limit associated with exact adaptation. The hidden diffusion can nevertheless change the Gaussian path-space irreversibility rate sigma. For a specified all-even reduced two-state drift with rho < 4, the paper gives sigma >= tau_x^(-1)(4/rho - 1), where tau_x is the observed-state relaxation time.
Implementation notes
Integrate this monitor into a stochastic RNN or latent world model with transition z_next = z + f_theta(z,u)*dt + L_theta(z,u)*sqrt(dt)*epsilon, where epsilon is standard Gaussian noise. Use a two-dimensional diagnostic latent subspace, or project a larger latent state onto its two slowest principal components. Estimate the local drift matrix A by regressing finite differences against the latent state. Estimate D from the covariance of residual increments, using D = residual_covariance/(2 dt). Estimate tau_x from exponential decay of the observed coordinate autocorrelation. Estimate irreversibility sigma using a forward-versus-time-reversed transition classifier or the difference between forward and reverse Gaussian transition log likelihoods. Pseudocode is: A,D = fit_OU(latents); rho = pole_coordinate(A); sigma = reverse_forward_loglik_gap(latents); bound = (4/rho - 1)/tau_x; loss = prediction_loss + lam*relu(bound-sigma)**2. The OU equations, the A_yy = 0 identifiability condition, and the irreversibility bound come from the paper; A, D, sigma, and estimation uncertainty are empirical. First test a synthetic two-state OU process with A_yy = 0, fixed observed spectrum, and several D_xy values, then use a noisy delayed-Copy task. The prediction is that output-spectrum error remains nearly constant as D_xy changes, while the forward/reverse likelihood gap changes. For rho < 4, measured sigma should satisfy the stated lower bound up to estimation error; violations should correlate with worse reverse-time prediction and poor long-horizon calibration.
Verification
Stage 1 · Toy mechanism gate: Not tested
Stage 2 · Mechanism transferred to benchmark: Not tested
Stage 2 · Practical benchmark result: Not run
Methodology: Toy-system gate first; the benchmark stage runs only after a pass. How verification works
Stage 1 — Mechanism check
Verdict computed by deterministic test code from paired-seed statistics — not by the language model.
Artifacts
Artifacts unavailable.