A Controlled Counterexample to Strong Proxy-Based Explanations of OOD Performance: in a Fixed Pretraining-and-Probing Setup

2026-05-12

AI Summary

This study investigates whether task-agnostic structural proxies reliably explain variations in out-of-distribution (OOD) transfer performance of pretrained models. Under fixed pretraining and probing conditions, the authors construct the first controlled counterexamples—through theoretical reasoning and synthetic sequence modeling experiments—that disentangle structural proxies from task-relevant structure. By integrating formal structural measures (e.g., epiplexity), operational proxy metrics, synthetic data, and multi-seed probing evaluations, they demonstrate a reversal in the ranking between structural proxies and OOD accuracy across two random seeds. This finding exposes fundamental limitations of structural proxies in analyzing OOD generalization and challenges their validity as universal explanatory tools for transfer performance.

Abstract

Task-agnostic structure proxies are often used to interpret why one pretraining corpus transfers better than another, but such explanations require the proxy to track the structure that matters for the downstream task. We test this requirement in a fixed pretraining-and-probing setup motivated by computationally bounded notions of learned structure, including epiplexity. The core question is whether a proxy ranking of two pretraining datasets must agree with their ranking by OOD probe accuracy. We show that it need not. First, we give a controlled construction in which a formal structure quantity, its operational proxy, and the task-relevant structure for a target family separate. We then instantiate the same mechanism in a synthetic sequence-model experiment: under the primary all-sample evaluation, the OOD accuracy ranking reverses the proxy ranking in two of three seeds, with auxiliary diagnostics and ablations supporting the same interpretation. The counterexample does not reject structure-based explanations in general; it identifies a boundary on strong proxy-based explanations. A proxy for total learned structure can fail to track the task-relevant structure that drives OOD performance, even in a controlled setting.

Problem

• out-of-distribution performance
• structure proxy
• pretraining corpus
• probe accuracy
• task-relevant structure

Innovation

• proxy-based explanation
• out-of-distribution (OOD) performance
• pretraining-and-probing
• learned structure
• epiplexity