  Representations learned by pre-training a neural network on a large dataset
are increasingly used successfully to perform a variety of downstream tasks. In
this work, we take a closer look at how features are encoded in such
pre-trained representations. We find that learned representations in a given
layer exhibit a degree of diffuse redundancy, ie, any randomly chosen subset of
neurons in the layer that is larger than a threshold size shares a large degree
of similarity with the full layer and is able to perform similarly as the whole
layer on a variety of downstream tasks. For example, a linear probe trained on
$20\%$ of randomly picked neurons from the penultimate layer of a ResNet50
pre-trained on ImageNet1k achieves an accuracy within $5\%$ of a linear probe
trained on the full layer of neurons for downstream CIFAR10 classification. We
conduct experiments on different neural architectures (including CNNs and
Transformers) pre-trained on both ImageNet1k and ImageNet21k and evaluate a
variety of downstream tasks taken from the VTAB benchmark. We find that the
loss and dataset used during pre-training largely govern the degree of diffuse
redundancy and the "critical mass" of neurons needed often depends on the
downstream task, suggesting that there is a task-inherent
redundancy-performance Pareto frontier. Our findings shed light on the nature
of representations learned by pre-trained deep neural networks and suggest that
entire layers might not be necessary to perform many downstream tasks. We
investigate the potential for exploiting this redundancy to achieve efficient
generalization for downstream tasks and also draw caution to certain possible
unintended consequences. Our code is available at
\url{https://github.com/nvedant07/diffused-redundancy}.
