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

arXiv: https://arxiv.org/abs/2605.07086 · HTML: https://mlsanity.com/paper/2605.07086/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [CHIP: CHannel Independence-based Pruning for Compact Neural Networks](https://mlsanity.com/paper/2110.13981/) (2021)
- [Revisiting Random Channel Pruning for Neural Network Compression](https://mlsanity.com/paper/2205.05676/) (2022)
- [Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems](https://mlsanity.com/paper/1411.2832/) (2014)
- [Mutual Information Preserving Neural Network Pruning](https://mlsanity.com/paper/2411.00147/) (2024)
- [Partial Information Decomposition for Data Interpretability and Feature Selection](https://mlsanity.com/paper/2405.19212/) (2024)

## Abstract (arXiv)

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.