The information geometry of large language models is shared, learned, and controllable — Paper

Abstract

Large language models learn similar behaviours, yet it remains unclear what structure they share or how to change one behaviour without disturbing others. The Fisher-Rao geometry of next-token probabilities connects these questions: behaviour determines this geometry up to output-preserving symmetries, whereas activation geometry depends on coordinates. Across transformer, state-space and recurrent models, output geometries agree more strongly than activation geometries, and shared geometry supports semantic-category transfer. Agreement with human word choices increases with predictive accuracy, scale and training, and improves further after model-only calibration. Token probabilities and read-out geometry jointly predict the spectrum and its effective dimension. Controlled language assignments show that geometry follows the language law across architectures. Pretraining corpus statistics predict held-out fact acquisition without recalibration, while randomised experiments show that deeper evidence substantially delays acquisition across every tested architecture and evidence construction. Finally, the geometry prescribes minimum-disturbance local interventions, predicts their relative cost, and supports reusable control: updates learned on donor prompts transfer to unseen prompts while better preserving behaviour on reference prompts than Euclidean control. The same geometric correction improves steering, editing, attribution, dictionary learning and fine-tuning.

Authors 1

Dario Picozzi

Specification

Official page: arxiv.org/abs/2609.11063
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
arXiv id: 2609.11063
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Categories: cs.LG, cs.CL
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
PDF: arxiv.org/pdf/2609.11063
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh

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9

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T19

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34 min ago

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Authors: Dario Picozzi

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Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
Property changedPaperThe information geometry of large language models is shared, learned, and controllable
The information geometry of large language models is shared, learned, and controllable: arxiv announce type changed from new to cross
Arxiv announce typenew→crossarxiv
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11 Sept 2026
New paperPaperThe information geometry of large language models is shared, learned, and controllable
New paper: The information geometry of large language models is shared, learned, and controllable
arxiv
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.CL	feed	T1· Official	34 min ago	1
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	35 min ago	1

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.