Routing Probes Can Improve Without New Information: An Exact-Null Audit of Uncertainty Beyond Model Outputs

2026-09-30

AI Summary

This study addresses whether routing signals in Vision Transformers carry error information beyond model outputs, noting that prior research yielded spurious gain conclusions due to accuracy-based checkpoint selection. To resolve this, we propose an "exact null hypothesis" auditing framework that disentangles goodness-of-fit from incremental information. By systematically evaluating the sources of routing probe gains through generator-frozen label repainting, width-matched MLP comparisons, conditional permutation tests, and multi-model panel validation, this work reveals critical differences in noise sensitivity between conventional linear and MLP baselines. After correction, the detection rate drops from 27.5% to zero, demonstrating that most reported routing gains are statistical artifacts, with only weak evidence persisting under specific conditions. These findings establish a rigorous paradigm for evaluating routing mechanisms.

Abstract

Routing signals of modern vision transformers -- expert gates, attention-residual weights and halting scores -- often improve probes that predict whether the model is correct, and the improvement is commonly read as evidence that routing carries information about errors beyond the model's outputs. We test this inference directly: keeping real output-routing pairs, we redraw correctness labels from a frozen output-only generator fitted on disjoint data, so that routing is uninformative by construction. Under this exact label null, a width-matched MLP comparison still reports a routing gain in 51.3% of confidence-only evaluations (308/600), while a linear comparison reports none. Holding each training trajectory fixed on a six-model panel and selecting the checkpoint by validation log loss instead of validation accuracy removes the detections (50/120 to 0/120, and 83/120 to 0/120 in an independently implemented probe), identifying accuracy-based checkpoint selection as the cause; across all output views the raw detection rate falls from 27.5% (528/1,920) to zero observed detections. The repaired comparison is not sensitive, detecting an implanted signal of about 0.005 nats in 0/20 replicates in each of two matched settings, whereas a conditional permutation test built on an estimated routing law detects it in 11/20 and 10/20 and rejects rarely under the null. On real correctness labels, the conditional analysis yields model-relative evidence in five DeiT attention-residual families; in four it persists under two specified variants of the conditional law, and no family passes an additional noise criterion. Fitting a better probe and testing for incremental information are different problems, and each needs its own validation.

Problem

• routing probes
• vision transformers
• uncertainty estimation
• exact-null audit
• incremental information

Innovation

• exact-null audit
• routing probes
• conditional permutation test
• checkpoint selection
• uncertainty estimation