Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Information geometry — the geometry of statistical models — the Fisher information as a metric, natural gradient, curvature and its Kronecker and block structure, and the spectra of Fisher and Hessian matrices in learned models (ADR-026).
2 of 191 CASE documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| CASE-152 | Absent attempt or unresponsive receiver: with Y ∼ N(ab, 1), a the strength of an attempted influence and b the receiver’s responsiveness, the settings (a, b) = (0, 1) and (1, 0) give the same response distribution; K(a, b) = a²b²/2, the Fisher matrix has rank at most one and vanishes at the origin, and the real log canonical threshold is ½ with multiplicity 2, not the regular d/2 = 1, while changing b with a held fixed separates the two | The construction from the exchange of 2026-10-24 (workbench entry of 2026-10-24, U27), checked when filed. A two-parameter response model in which the observation depends on a product, the smallest singular model with a communicative reading. It shows a missing response failing to say whether nothing was attempted or nothing was taken up. | Active |
| CASE-159 | Authority geometry and response geometry: when an organization’s response is the authority-weighted mixture p_π(y | c) = Σ πᵢ pᵢ(y | c), the Fisher metric of its responses is the pullback JᵀD⁻¹J of the categorical (Shahshahani) metric on the shares π and never exceeds it; it vanishes along any redistribution between processes that respond alike under the probes used, so two specialists who both answer yes with probability 0.8 in routine contexts carry no information about their shares there, while a rare context in which they answer 0.9 and 0.1 carries 0.64/(p(1 − p)) per observation, p = 0.1 + 0.8π | From the continuation of the exchange of 2026-10-24 (U28–U31), where it appears in four replies (A28 §3, A29’s second priority, A30 §6A and A31’s probe diagnostic); checked when filed. The categorical metric on authority shares is the one in which the replicator is a gradient flow (CLAIM-444). What an evaluator sees is the response mixture, whose Fisher metric is that metric pulled back through the processes’ response profiles. Redistribution between processes that agree on the probes is invisible to them, and a probe on which they disagree restores it. The mixture counterpart of CASE-152’s product model. | Active |