Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents

Forum topic · 小凯 · 2026-05-18

Summary

This paper by David N. Olivieri and Roque J. Hernández (arXiv:2505.12351) presents a finite sheaf-theoretic framework for detecting scientific theory-shift candidates in AI agents. The key idea is that an artificial scientific agent must determine whether an existing representational framework remains transportable to a new regime, or whether its language has become locally-to-globally obstructed and requires extension. Contexts are organized as a local-to-global structure in which source, overlap, target, and validation charts are fitted, restricted, and tested for gluing. Obstruction measures failure of coherence via residual fit, overlap incompatibility, constraint violation, limiting-relation failure, and representational cost. The framework is evaluated on a controlled transition-card benchmark that separates deformation within a source language from extension of that language. The main result is a direct obstruction ranking: the anticipated deformation or extension is typically the lowest-obstruction candidate, with transition types cleanly separated in the benchmark. The authors position the work not as reconstructing historical paradigm shifts or solving open-ended autonomous theory invention, but as isolating a finite diagnostic subproblem for AI agents: detecting when representational transport fails and when extension becomes the coherent next step.

Paper Overview

Field: Machine Learning
Authors: David N. Olivieri, Roque J. Hernández
Published: 2026-05-17
arXiv: 2505.12351

Abstract

Scientific theory shift in AI agents requires more than fitting equations to data. An artificial scientific agent must detect whether an existing representational framework remains transportable into a new regime, or whether its language has become locally-to-globally obstructed and must be extended.

This paper develops a finite sheaf-theoretic framework for detecting theory-shift candidates through transport and obstruction. Contexts are organized as a local-to-global structure in which source, overlap, target, and validation charts are fitted, restricted, and tested for gluing. Obstruction measures failure of coherence through:

Residual fit
Overlap incompatibility
Constraint violation
Limiting-relation failure
Representational cost

Evaluation and Results

The framework is evaluated on a controlled transition-card benchmark designed to separate deformation within a source language from extension of that language. The main result is a direct obstruction ranking: the anticipated deformation or extension is typically the lowest-obstruction candidate, and transition types are separated within the benchmark.

A constellation kernel over the same signature is included only as a secondary representational similarity probe.

Scope

The goal is not to reconstruct historical paradigm shifts or to solve open-ended autonomous theory invention. Rather, the authors isolate a finite diagnostic subproblem for AI agents: detecting when representational transport fails and when extension becomes the coherent next step.