Task Relevance Is Not Local Replaceability: A Two-Axis View of Channel Information

2026-05-07

AI Summary

This work addresses a critical limitation in existing channel pruning methods, which conflate two orthogonal dimensions—task relevance and local substitutability—thereby constraining performance. For the first time, this study explicitly disentangles these concepts: task relevance quantifies a channel’s contribution to the target objective, while local substitutability measures whether its function can be compensated by other channels within the same layer. Theoretical analysis and empirical evidence demonstrate that these two properties rapidly decouple during training, with local substitutability emerging as a more reliable criterion for pruning. Through comprehensive validation—including input attribution, channel overlap analysis, task information metrics, residual gradient examination, and ablation studies—this approach consistently outperforms conventional pruning strategies across multiple architectures and benchmarks, including CIFAR-100 and ImageNet.

Abstract

Channel importance in vision networks is usually summarized by a single score. That summary hides two different questions: how much a channel is related to the task, and whether its function can be supplied by same-layer peers when the channel is removed. We call the second property local replaceability. We introduce a two-axis view that separates these questions. The local axis measures input capture and peer overlap, while the target axis measures task information and target-excess information. Across ResNet-18, VGG-16, and MobileNetV2 trained on CIFAR-100, the two axes are weakly aligned, induce different channel groupings, and separate rapidly during training despite being strongly coupled at random initialization. A Gaussian linear analysis accounts for how this separation can arise through residualized gradient directions, and lesion plus peer-replacement experiments show that peer support refines removability beyond input capture and task relevance alone. Under the fixed FLOPs-matched pruning protocol, local-axis metrics are more reliable predictors of removability than target-axis metrics across the three CIFAR-100 backbones, with the same direction preserved in stress tests on CIFAR-10, Tiny-ImageNet, ImageNet-100, and a ConvNeXt-T/ImageNet-100 pilot. These findings identify an axis-level distinction rather than a universal ranking of pruning scores: local replaceability is a more reliable guide to removability than target relevance, while norm-based baselines remain competitive in architectures such as VGG-16. Relevance-based scores ask what a channel says about the task; pruning asks whether the network still needs that channel when its peers remain available.

Problem

• channel importance
• task relevance
• local replaceability
• network pruning
• feature redundancy

Innovation

• local replaceability
• channel pruning
• two-axis analysis
• task relevance
• neural network interpretability