In this study, we investigate whether the representations learned by neural networks possess a privileged and convergent basis. Specifically, we examine the significance of feature directions represented by individual neurons. First, we establish that arbitrary rotations of neural representations cannot be inverted (unlike linear networks), indicating that they do not exhibit complete rotational invariance. Subsequently, we explore the possibility of multiple bases achieving identical performance. To do this, we compare the bases of networks trained with the same parameters but with varying random initializations. Our study reveals two findings: (1) Even in wide networks such as WideResNets, neural networks do not converge to a unique basis; (2) Basis correlation increases significantly when a few early layers of the network are frozen identically. Furthermore, we analyze Linear Mode Connectivity, which has been studied as a measure of basis correlation. Our findings give evidence that while Linear Mode Connectivity improves with increased network width, this improvement is not due to an increase in basis correlation.

翻译：本研究探讨神经网络所学表示是否具有特权基和收敛基。具体而言，我们考察由单个神经元表征的特征方向的重要性。首先，我们确定神经表示的任意旋转无法被反转（与线性网络不同），表明它们不具备完全的旋转不变性。随后，我们探索多种基实现相同性能的可能性。为此，我们比较了使用相同参数但不同随机初始化训练得到的网络的基。我们的研究揭示了两个发现：（1）即使在宽网络（如WideResNet）中，神经网络也不会收敛到唯一的基；（2）当网络的前几层被完全相同地冻结时，基的相关性显著增加。此外，我们分析了线性模式连通性（Linear Mode Connectivity），该指标已被研究作为基相关性的度量。我们的证据表明，虽然线性模式连通性随网络宽度增加而改善，但这种改善并非源于基相关性的提升。