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).
4 of 547 CLAIM documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| CLAIM-366 v3 | Whether several objectives share a strict first-order descent direction, 0 ∉ conv{g_i}, is invariant under smooth invertible reparameterization, while the sign of a Euclidean gradient inner product is not, and a negative inner product does not exclude common descent; a budgeted version is invariant only with the metric pulled back | A35 §2 of the exchange of 2026-10-17, at the owner’s U35 “double click” on whether functionally equivalent parameterizations give equivalent frustration diagnoses. Gradients transform as g′ = Jᵀg and directions as v′ = J⁻¹v, so directional derivatives, and with them the common-descent test 0 ∉ conv{g_i}, do not depend on coordinates. A Euclidean inner product does: g₁ = (1, 1), g₂ = (1, −½) have product ½, and under θ = diag(½, 2)ψ their transforms have −7/4, while d = (−1, 0) lowers both throughout. The sharp edge: it covers coordinate changes of one parameter space at first order, not function-preserving symmetries or training trajectories (QUESTION-127). The practice corollary, not to diagnose task conflict by gradient cosine, is the anthology’s. | Active |
| CLAIM-377 | For any differentiable model under squared loss with Gaussian noise of precision β, the model’s Fisher on n inputs is the Gauss–Newton matrix βJᵀJ, and its non-zero eigenvalues are exactly β times those of the empirical NTK Gram matrix JJᵀ, with the same multiplicities, its eigenvectors being Jᵀ applied to the Gram matrix’s, normalized | THEORY-084’s Step 1, stated as the record’s own and proved. Through the SVD J = UΣVᵀ, JᵀJ and JJᵀ share the non-zero eigenvalues σ_i² with equal multiplicities, and Jᵀu/σ is the eigenvector of JᵀJ for a unit eigenvector u of JJᵀ. Under y | x ~ N(f(x; θ), β⁻¹), the expected outer product of the score is β∇f∇fᵀ, which summed over inputs is βJᵀJ, the Gauss–Newton matrix. “Fisher” means the model’s Fisher, not the empirical Fisher of observed residuals. It holds at every width, in every regime and on any data. It says nothing about what the spectrum looks like, which is THEORY-084’s. | Active |
| CLAIM-391 | For any classes with weights π_c and per-class factor matrices H_c and Δ_c, the class-wise Kronecker product Σ_c π_c H_c ⊗ Δ_c exceeds the product of the weighted averages H̄ ⊗ Δ̄ by exactly the weighted between-class covariance Σ_c π_c (H_c − H̄) ⊗ (Δ_c − Δ̄), so the two agree when either factor is the same in every class | Active | |
| CLAIM-450 v5 | Three standards for a communicative distinction come apart: statistical distinguishability of an interpreter’s response profiles, measured locally by the Fisher metric and never raised by a parameter-independent garbling; usability by a bounded receiver, which a transformation can raise; and pragmatic efficacy in the act; and where response models are singular, as Watanabe’s theory treats, a missing response can come from an absent attempt or an unresponsive receiver alike, and only intervention or later dynamics separate them | The owner’s, 2026-10-24, after setting aside the belief–knowledge distinction: “forget about that distinction then and let’s connect back to the communicative act stuff and amari/watanabe theory”. Worked through the same day (workbench entry of 2026-10-24, U27). Amari’s geometry and Watanabe’s singular learning are given different jobs in one modelling architecture, alongside bounded legibility and the communicative-act account, rather than read as rival characterizations. | Active |