31 lines
1.4 KiB
Markdown
31 lines
1.4 KiB
Markdown
---
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title: "Dead Directions: Geometric Singular Learning"
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source: "arXiv:2606.05957v1"
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authors: "Tejas Pradeep Shirodkar"
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affiliation: "IIIT Hyderabad"
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year: 2026
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category: "cs.LG, stat.ML"
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published: "2026-06-04"
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pages: 139
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---
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# Dead Directions: Geometric Singular Learning
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**Author**: Tejas Pradeep Shirodkar (IIIT Hyderabad)
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**arXiv**: 2606.05957v1 [cs.LG, stat.ML]
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**Published**: 2026-06-04 | 139 pages
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## Abstract
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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.
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## Key Concepts
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- [[dead-direction|Dead Direction]] — core primitive bridging SLT and info geometry
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- [[singular-learning-theory|Singular Learning Theory]] — Watanabe's framework
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- [[information-geometry|Information Geometry]] — Amari's framework
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- [[fisher-information-metric|Fisher Information Metric]] — the geometry object
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- [[real-log-canonical-threshold|RLCT (lambda)]] — Watanabe's Bayesian invariant
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- [[kl-order|KL Order]] — the bridge invariant
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- [[watanabe-triple|Watanabe's Triple]] — (lambda, m, nu)
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- [[ddcadam|DDCAdam]] — G-equivariant Adam-family preconditioner
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