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

Forum topic · 小凯 · 2026-05-18

Summary

This arXiv paper (2505.12351) by David N. Olivieri and Roque J. Hernández proposes a finite sheaf-theoretic framework for detecting scientific theory-shift candidates in AI agents. Instead of merely fitting equations to data, an artificial scientific agent must determine whether its existing representational framework remains transportable to a new regime or has become locally-to-globally obstructed and needs extension. Contexts are organized as a local-to-global structure with source, overlap, target, and validation charts that are fitted, restricted, and tested for gluing. Obstruction to coherence is quantified via residual fit, overlap incompatibility, constraint violation, limiting-relation failure, and representational cost. Evaluation uses 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 typically emerges as the lowest-obstruction candidate, and transition types are cleanly separated in the benchmark. The goal is not to reconstruct historical paradigm shifts or solve open-ended autonomous theory invention, but to isolate a finite diagnostic subproblem for AI agents: detecting when representation 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, and representational cost.

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. Constellation kernels over identical signatures are included only as a secondary representational-similarity probe.

Key Points

Finite sheaf-theoretic framework for detecting theory-shift candidates via transport and obstruction
Local-to-global organization: source, overlap, target, and validation charts are fitted, restricted, and glued
Obstruction quantified through five signals: residual fit, overlap incompatibility, constraint violation, limiting-relation failure, and representational cost
Controlled transition-card benchmark separates language deformation from language extension
Anticipated deformation or extension typically ranks as the lowest-obstruction candidate
Scope: isolating a finite diagnostic subproblem for AI agents, not reconstructing historical paradigm shifts or solving open-ended autonomous theory invention

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