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+---
+title: "Dead Directions: Geometric Singular Learning"
+source: "arXiv:2606.05957v1"
+authors: "Tejas Pradeep Shirodkar"
+affiliation: "IIIT Hyderabad"
+year: 2026
+category: "cs.LG, stat.ML"
+published: "2026-06-04"
+pages: 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|Dead Direction]] — core primitive bridging SLT and info geometry
+- [[singular-learning-theory|Singular Learning Theory]] — Watanabe's framework
+- [[information-geometry|Information Geometry]] — Amari's framework
+- [[fisher-information-metric|Fisher Information Metric]] — the geometry object
+- [[real-log-canonical-threshold|RLCT (lambda)]] — Watanabe's Bayesian invariant
+- [[kl-order|KL Order]] — the bridge invariant
+- [[watanabe-triple|Watanabe's Triple]] — (lambda, m, nu)
+- [[ddcadam|DDCAdam]] — G-equivariant Adam-family preconditioner