The information geometry of large language models is shared, learned, and controllableCode and data

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

Code and data

Dario PicozziUniversity College London

Explore the findings Read on arXiv

Activation space

Language model

Input 1: −0.70 (fixed)Input 2: 0.40 (fixed)Input 3: 0.80 (fixed)Input 4: −0.20 (fixed)Input 5: 0.60 (fixed)h1: Fisher–Rao −0.27; Euclidean −0.27h₁token A: Fisher–Rao 33.3%; Euclidean 33.3%token Ah2: Fisher–Rao 0.44; Euclidean 0.44h₂token B: Fisher–Rao 33.3%; Euclidean 33.3%token Bh3: Fisher–Rao −0.02; Euclidean −0.02h₃token C: Fisher–Rao 33.3%; Euclidean 33.3%token C

Prediction geometry

Fisher–RaoEuclidean
About this visualisation

The research in “The information geometry of large language models is shared, learned, and controllable” examines what different language models share, how that structure is learned, and how to change one behaviour with less disturbance elsewhere. It connects these questions through the geometry of next-token predictions.

01

From predictions to geometry

Next-token probabilities define a geometry of behaviour that does not depend on the model’s internal coordinates.

02

What different models share

Across the models tested, prediction geometry agrees more closely on average than geometry based on internal activations.

03

The shape inherited from language

Token probabilities and the model’s read-out help predict how unevenly different directions affect its predictions.

04

Learning over time

Statistics of the training text predict when answers become stable preferences; deeper evidence delays this in controlled experiments.

05

Changing behaviour with less disturbance

At matched target effects in the tested interventions, geometry-guided updates disturb other predictions less than Euclidean updates.