# Similarity of Neural Network Representations in Superposition

arXiv: https://arxiv.org/abs/2604.00208 · HTML: https://mlsanity.com/paper/2604.00208/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 22 of 22)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Sparse Autoencoders Trained on the Same Data Learn Different Features](https://mlsanity.com/paper/2501.16615/) (2025)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [Deep Neural Networks Rival the Representation of Primate IT Cortex for Core Visual Object Recognition](https://mlsanity.com/paper/1406.3284/) (2014)
- [Revisiting the Platonic Representation Hypothesis: An Aristotelian View](https://mlsanity.com/paper/2602.14486/) (2026)
- [Mathematical Models of Computation in Superposition](https://mlsanity.com/paper/2408.05451/) (2024)
- [Cross-Entropy Is All You Need To Invert the Data Generating Process](https://mlsanity.com/paper/2410.21869/) (2024)
- [On the Complexity of Neural Computation in Superposition](https://mlsanity.com/paper/2409.15318/) (2024)
- [Compute Optimal Inference and Provable Amortisation Gap in Sparse Autoencoders](https://mlsanity.com/paper/2411.13117/) (2024)
- [From superposition to sparse codes: interpretable representations in neural networks](https://mlsanity.com/paper/2503.01824/) (2025)
- [How Many Features Can a Language Model Store Under the Linear Representation Hypothesis?](https://mlsanity.com/paper/2602.11246/) (2026)
- [Identifying Interpretable Visual Features in Artificial and Biological Neural Systems](https://mlsanity.com/paper/2310.11431/) (2023)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [Superposition disentanglement of neural representations reveals hidden alignment](https://mlsanity.com/paper/2510.03186/) (2025)

## Abstract (arXiv)

Comparing internal representations is a central goal in neuroscience and machine learning, but standard linear alignment metrics (Representational Similarity Analysis, Centered Kernel Alignment, and linear regression) are frequently applied to neural activity coordinates rather than on the underlying features. We show this matters when neural systems operate in superposition, encoding more features than they have neurons via linear compression. Closed-form derivations prove that these metrics depend on the Gram matrices of each system's projection, not on the latent features themselves: alignment thus combines what a system represents with how it is encoded. For those interested in what features two systems share, this is a problem: Two networks can have identical feature content yet appear more dissimilar than networks exhibiting partial feature overlap. This apparent misalignment need not reflect lost information as compressed sensing guarantees sparse features remain recoverable from the compressed activity. We confirm this by training supervised TopK sparse autoencoders that realize solvable compressed sensing by construction, finding alignment on recovered latents restored even when raw-activation alignment remains deflated. We extend the result to unsupervised SAEs trained without ground-truth latents, and to pretrained vision and language model SAEs, where SAE-latent alignment exceeds raw-activation alignment, consistent with superposition in real systems.