Similarity of Neural Network Representations in Superposition

Standard tools for comparing neural representations can produce misleading results when networks encode features in superposition, according to a paper submitted to ICLR 2026. The work shows that widely used linear alignment metrics measure how features are mixed across neurons rather than which features are present, creating what the authors call “mirages of misalignment.” [1][4] The study, led by Sunny Liu and colleagues, examines a problem that cuts across neuroscience and machine learning. Researchers in both fields routinely compare internal representations—the patterns of activity across neurons or artificial units—to understand how different brains or models process information. The most common methods include Representational Similarity Analysis, Centered Kernel Alignment, and linear regression. [1][2] These metrics are typically applied directly to neural activity coordinates. But the paper demonstrates through closed-form derivations that the scores depend on the Gram matrices of each system’s projection, not on the underlying features themselves. “Alignment thus combines what a system represents with how it is encoded,” the authors write. [2][3] The issue becomes acute when networks operate in superposition—a regime where a system encodes more features than it has neurons by compressing them linearly. In such cases, two networks can possess identical feature content yet appear more dissimilar than networks that share only partial feature overlap. [1][4] This finding carries implications for model selection and for efforts to map artificial networks onto biological brains. Deep learning architectures, from convolutional networks to transformers, are routinely compared using these metrics to assess whether different training runs or model sizes converge on similar solutions. [5][6] The new work suggests that lower alignment scores in smaller models may reflect compression artifacts rather than genuine representational divergence. [2] The authors do not leave the problem unresolved. They show that compressed sensing theory guarantees sparse features remain recoverable from compressed activity. By training supervised TopK sparse autoencoders—which realize solvable compressed sensing by construction—they demonstrate that alignment measured on recovered latent features is restored even when raw-activation alignment remains deflated. The result extends to unsupervised sparse autoencoders trained without ground-truth latents, and to autoencoders applied to pretrained vision and language models, where latent-feature alignment consistently exceeds raw-activation alignment. [1][3] The paper was first submitted on 31 March 2026 and revised on 22 June 2026. The initial submission was 2,474 KB; the revised version is 810 KB. [1] The work was submitted to ICLR 2026 under the title “Mirages of Misalignment: How Superposition Distorts Neural Representation Geometry.” [4]