Information-Theoretic Requirements for Gradient-Based Task Affinity Estimation in Multi-Task Learning

TL;DR

This paper reveals that gradient-based task affinity estimation in multi-task learning requires significant sample overlap to be meaningful, explaining past inconsistent results and providing a new theoretical framework.

Contribution

It identifies a critical sample overlap threshold for gradient analysis validity and explains previous inconsistencies in multi-task learning outcomes.

Findings

Gradient-task correlations are indistinguishable from noise below 30% overlap.

Above 40% overlap, correlations reliably reflect biological structure.

Standard benchmarks operate far below the overlap threshold, invalidating gradient analysis.

Abstract

Multi-task learning shows strikingly inconsistent results -- sometimes joint training helps substantially, sometimes it actively harms performance -- yet the field lacks a principled framework for predicting these outcomes. We identify a fundamental but unstated assumption underlying gradient-based task analysis: tasks must share training instances for gradient conflicts to reveal genuine relationships. When tasks are measured on the same inputs, gradient alignment reflects shared mechanistic structure; when measured on disjoint inputs, any apparent signal conflates task relationships with distributional shift. We discover this sample overlap requirement exhibits a sharp phase transition: below 30% overlap, gradient-task correlations are statistically indistinguishable from noise; above 40%, they reliably recover known biological structure. Comprehensive validation across multiple datasets achieves strong correlations and recovers biological pathway organization. Standard benchmarks systematically violate this requirement -- MoleculeNet operates at <5% overlap, TDC at 8-14% -- far below the threshold where gradient analysis becomes meaningful. This provides the first principled explanation for seven years of inconsistent MTL results.