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This research establishes that classification accuracy in deep networks can be predicted by a sparse, universal geometry linking true-class and rival-centroid coordinates across vision, audio, and language modalities. The derived mean-field theory demonstrates that only a small subset of these geometric features is required to model performance gains as models scale, offering a parsimonious framework for interpreting high-dimensional neural representations without relying on random variability assumptions.
Sparse Prototype Code Underlies Classification and Prediction Across Modalities
arXiv:2608.15632v1 Announce Type: new Abstract: Neural representations have become a central tool for studying the internal mechanisms of modern AI models, yet their complex high-dimensional structure makes them difficult to interpret. We show that classification tasks give rise to a universal representational geometry, shared across state-of-the-art models in vision, audio, and language processing. The key structure is that within-class variability is not random in representation space. Instead, its classifier-relevant component has strong and structured correlations with the class's own centroid and with the centroids of its competing classes. Building on this observation, we derive an analytical mean-field theory governed mainly by the variability along true-class and rival-class centroid coordinates, together with a global renormalization of the class radius that compensates for the non-Gaussian statistics of real representations. The theory accurately predicts classification accuracy across architectures and modalities. The relevant geometric quantities improve systematically with model scale, mirroring the observed gains in accuracy. A striking feature of the theory is its sparsity: accurate prediction requires only a small set of centroid coordinates associated with the true class and its strongest rivals - connecting our framework to sparse-feature extraction approaches such as sparse autoencoders. Together, these results provide a parsimonious predictive theory of neural representations and suggest that classification in deep networks is governed by a sparse, centroid-aligned structure embedded within the full high-dimensional representation space.
Abstract:Neural representations have become a central tool for studying the internal mechanisms of modern AI models, yet their complex high-dimensional structure makes them difficult to interpret. We show that classification tasks give rise to a universal representational geometry, shared across state-of-the-art models in vision, audio, and language processing. The key structure is that within-class variability is not random in representation space. Instead, its classifier-relevant component has strong and structured correlations with the class's own centroid and with the centroids of its competing classes. Building on this observation, we derive an analytical mean-field theory governed mainly by the variability along true-class and rival-class centroid coordinates, together with a global renormalization of the class radius that compensates for the non-Gaussian statistics of real representations. The theory accurately predicts classification accuracy across architectures and modalities. The relevant geometric quantities improve systematically with model scale, mirroring the observed gains in accuracy. A striking feature of the theory is its sparsity: accurate prediction requires only a small set of centroid coordinates associated with the true class and its strongest rivals - connecting our framework to sparse-feature extraction approaches such as sparse autoencoders. Together, these results provide a parsimonious predictive theory of neural representations and suggest that classification in deep networks is governed by a sparse, centroid-aligned structure embedded within the full high-dimensional representation space.
Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
arXiv:2608.15632 [cs.LG]
(or arXiv:2608.15632v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.15632 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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