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In this study, we investigate whether the representations learned by neuralnetworks possess a privileged and convergent basis. Specifically, we examinethe significance of feature directions represented by individual neurons.First, we establish that arbitrary rotations of neural representations cannotbe inverted (unlike linear networks), indicating that they do not exhibitcomplete rotational invariance. Subsequently, we explore the possibility ofmultiple bases achieving identical performance. To do this, we compare thebases of networks trained with the same parameters but with varying randominitializations. Our study reveals two findings: (1) Even in wide networks suchas WideResNets, neural networks do not converge to a unique basis; (2) Basiscorrelation increases significantly when a few early layers of the network arefrozen identically.  Furthermore, we analyze Linear Mode Connectivity, which has been studied as ameasure of basis correlation. Our findings give evidence that while Linear ModeConnectivity improves with increased network width, this improvement is not dueto an increase in basis correlation.

On Privileged and Convergent Bases in Neural Network Representations