Measuring the Representational Alignment of Neural Systems in Superposition

Comparing the internal representations of neural networks is a central goal in both neuroscience and machine learning. Standard alignment metrics operate on raw neural activations, implicitly assuming that similar representations produce similar activity patterns. However, neural systems frequently operate in superposition, encoding more features than they have neurons via linear compression. We derive closed-form expressions showing that superposition systematically deflates Representational Similarity Analysis, Centered Kernel Alignment, and linear regression, causing networks with identical feature content to appear dissimilar. The root cause is that these metrics are dependent on cross-similarity between two systems' respective superposition matrices, which under assumption of random projection usually differ significantly, not on the latent features themselves: alignment scores conflate what a system represents with how it represents it. Under partial feature overlap, this confound can invert the expected ordering, making systems sharing fewer features appear more aligned than systems sharing more. Crucially, the apparent misalignment need not reflect a loss of information; compressed sensing guarantees that the original features remain recoverable from the lower-dimensional activity, provided they are sparse. We therefore argue that comparing neural systems in superposition requires extracting and aligning the underlying features rather than comparing the raw neural mixtures.

Naturally Computed Scale Invariance in the Residual Stream of ResNet18

An important capacity in visual object recognition is invariance to image-altering variables which leave the identity of objects unchanged, such as lighting, rotation, and scale. How do neural networks achieve this? Prior mechanistic interpretability research has illuminated some invariance-building circuitry in InceptionV1, but the results are limited and networks with different architectures have remained largely unexplored. This work investigates ResNet18 with a particular focus on its residual stream, an architectural component which InceptionV1 lacks. We observe that many convolutional channels in intermediate blocks exhibit scale invariant properties, computed by the element-wise residual summation of scale equivariant representations: the block input's smaller-scale copy with the block pre-sum output's larger-scale copy. Through subsequent ablation experiments, we attempt to causally link these neural properties with scale-robust object recognition behavior. Our tentative findings suggest how the residual stream computes scale invariance and its possible role in behavior. Code is available at: https://github.com/cest-andre/residual-stream-interp

Interpreting the Residual Stream of ResNet18

A mechanistic understanding of the computations learned by deep neural networks (DNNs) is far from complete. In the domain of visual object recognition, prior research has illuminated inner workings of InceptionV1, but DNNs with different architectures have remained largely unexplored. This work investigates ResNet18 with a particular focus on its residual stream, an architectural mechanism which InceptionV1 lacks. We observe that for a given block, channel features of the stream are updated along a spectrum: either the input feature skips to the output, the block feature overwrites the output, or the output is some mixture between the input and block features. Furthermore, we show that many residual stream channels compute scale invariant representations through a mixture of the input's smaller-scale feature with the block's larger-scale feature. This not only mounts evidence for the universality of scale equivariance, but also presents how the residual stream further implements scale invariance. Collectively, our results begin an interpretation of the residual stream in visual object recognition, finding it to be a flexible feature manager and a medium to build scale invariant representations.