1.4 KiB
1.4 KiB
title, source, authors, affiliation, year, category, published, pages
| title | source | authors | affiliation | year | category | published | pages |
|---|---|---|---|---|---|---|---|
| Dead Directions: Geometric Singular Learning | arXiv:2606.05957v1 | Tejas Pradeep Shirodkar | IIIT Hyderabad | 2026 | cs.LG, stat.ML | 2026-06-04 | 139 |
Dead Directions: Geometric Singular Learning
Author: Tejas Pradeep Shirodkar (IIIT Hyderabad) arXiv: 2606.05957v1 [cs.LG, stat.ML] Published: 2026-06-04 | 139 pages
Abstract
Bridges singular learning theory and information geometry through one primitive: the dead direction — a unit vector where the Fisher metric degenerates, with KL order recoverable from directional Fisher curvature decay rate in original coordinates (no Hironaka resolution). Lifts to deep networks via K-FAC factorization, constructs DDCAdam optimizer, and enables readout of Watanabe's triple (lambda, m, nu) from a single checkpoint.
Key Concepts
- dead-direction — core primitive bridging SLT and info geometry
- singular-learning-theory — Watanabe's framework
- information-geometry — Amari's framework
- fisher-information-metric — the geometry object
- real-log-canonical-threshold — Watanabe's Bayesian invariant
- kl-order — the bridge invariant
- watanabe-triple — (lambda, m, nu)
- ddcadam — G-equivariant Adam-family preconditioner