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).
5 of 371 QUESTION documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| QUESTION-040 v4 | When the reification rule prices a candidate found in the same data, among many directions the data only partly determine, what must its Occam term count, and how far does the search inflate the candidate’s d’? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on CLAIM-154, CLAIM-188, CLAIM-152 and CLAIM-164. THEORY-080 and THEORY-028 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-051 v2 | What structure does training for one classification task leave in a network’s last layers, and what does that structure cost for decisions and distributions the network was not trained on? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on QUESTION-010 and CLAIM-164. THEORY-083, THEORY-104 and THEORY-085 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-127 v2 | Which diagnoses of frustration among a learner’s demands survive quotienting by function-preserving symmetries, which belong only to an update geometry, and which only to a particular training organization with its optimizer? | A34 §6G of the exchange of 2026-10-17: “When do two functionally equivalent parameterizations yield equivalent frustration diagnoses?” The owner, at U35: “interesting question, double click on this.” A35 answered the first-order coordinate case, filed as CLAIM-366: the common-descent test is chart-invariant, gradient cosines are not, and a budgeted test needs the metric pulled back. The rest is open: function- preserving symmetries, which are not charts of one space, and training trajectories, where “same current function ≠ same learning dynamics”. An answer sorts each diagnosis by what it is a property of. | Open |
| QUESTION-216 | Does the output Fisher–Rao geometry agreement across language models replicate with released code, and does it fall when models are fitted to different laws while their activation geometry stays as it was, with only a small part of the shared eigenvector structure exceeding a fair law-matched null? | The promotion condition formerly on THEORY-230. THEORY-230 was narrowed and promoted on 2026-10-20 (ADR-047 v2 and v3). Its identification is re-derived: the Fisher–Rao geometry of next-token laws is a function of the laws. Its measurement is one study read in full: mean rank agreement 0.88 against 0.62 in Picozzi’s ten models, and about 9% of the top eigenvector overlap beyond a displacement-matched null. Replication, and a test that varies the law, are open. | Open |
| QUESTION-286 | Under smooth invertible changes of the parameter coordinates, which first-order frustration diagnoses among a learner’s demands are invariant: pairwise Euclidean gradient angles, common strict first-order descent, or budgeted feasibility with the update geometry transported? | The coordinate part of QUESTION-127, split off by the status review of 2026-10-27 under ADR-049, because CLAIM-366 (Active) settles it in full. Common strict descent, 0 ∉ conv{g_i}, is invariant under smooth invertible reparameterization. The sign of a Euclidean gradient inner product is not, and a negative inner product does not exclude common descent. A budgeted test is invariant when the metric is pulled back. These are the first three rows of A35 §2’s table. | Answered |