Sparse Prototype Code Underlies Classification and Prediction Across Modalities

• URL: http://arxiv.org/abs/2608.15632v1
• Date: Sun, 16 Aug 2026 08:53:21 GMT
• Title: Sparse Prototype Code Underlies Classification and Prediction Across Modalities
• Abstract summary: 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.<n>Key structure is that within-class variability is not random in representation space.<n>We derive an analytical mean-field theory governed mainly by the variability along true-class and rival-class centroid coordinates.
• Score: 9.027127884628092
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Hyperbolic Enhanced Representation Learning for Incomplete Multi-view Clustering [57.38215918201251]
  We propose HERL, a Hyperbolic Enhanced Representation Learning framework for Incomplete Multi-View Clustering.<n> operating within the Poincaré ball, HERL constructs a structure-aware latent space to enhance representation learning.<n>We show that HERL consistently outperforms state-of-the-art approaches.
  arXiv  Detail & Related papers  (2026-04-18T10:50:46Z)
• Local Intrinsic Dimension of Representations Predicts Alignment and Generalization in AI Models and Human Brain [14.072972213206524]
  Recent work has found that neural networks with stronger generalization tend to exhibit higher representational alignment with one another.<n>We show that models with stronger generalization also align more strongly with human neural activity.<n>These relationships can be explained by a single geometric property of learned representations: the local intrinsic dimension of embeddings.
  arXiv  Detail & Related papers  (2026-01-30T08:54:59Z)
• Scaling Laws and Representation Learning in Simple Hierarchical Languages: Transformers vs. Convolutional Architectures [49.19753720526998]
  We derive theoretical scaling laws for neural network performance on synthetic datasets.<n>We validate that convolutional networks, whose structure aligns with that of the generative process through locality and weight sharing, enjoy a faster scaling of performance.<n>This finding clarifies the architectural biases underlying neural scaling laws and highlights how representation learning is shaped by the interaction between model architecture and the statistical properties of data.
  arXiv  Detail & Related papers  (2025-05-11T17:44:14Z)
• Boosting of Classification Models with Human-in-the-Loop Computational Visual Knowledge Discovery [2.9465623430708905]
  This paper proposes moving boosting methodology from focusing on only misclassified cases to all cases in the class overlap areas.<n>A Divide and Classify process splits cases to simple and complex, classifying these individually through computational analysis and data visualization.<n>After finding pure and overlap class areas simple cases in pure areas are classified, generating interpretable sub-models like decision rules in Propositional and First-order Logics.
  arXiv  Detail & Related papers  (2025-02-10T21:09:19Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Understanding Imbalanced Semantic Segmentation Through Neural Collapse [81.89121711426951]
  We show that semantic segmentation naturally brings contextual correlation and imbalanced distribution among classes. We introduce a regularizer on feature centers to encourage the network to learn features closer to the appealing structure. Our method ranks 1st and sets a new record on the ScanNet200 test leaderboard.
  arXiv  Detail & Related papers  (2023-01-03T13:51:51Z)
• Isometric Representations in Neural Networks Improve Robustness [0.0]
  We train neural networks to perform classification while simultaneously maintaining within-class metric structure. We verify that isometric regularization improves the robustness to adversarial attacks on MNIST.
  arXiv  Detail & Related papers  (2022-11-02T16:18:18Z)
• Do We Really Need a Learnable Classifier at the End of Deep Neural Network? [118.18554882199676]
  We study the potential of learning a neural network for classification with the classifier randomly as an ETF and fixed during training. Our experimental results show that our method is able to achieve similar performances on image classification for balanced datasets.
  arXiv  Detail & Related papers  (2022-03-17T04:34:28Z)
• Generalized Shape Metrics on Neural Representations [26.78835065137714]
  We provide a family of metric spaces that quantify representational dissimilarity. We modify existing representational similarity measures based on canonical correlation analysis to satisfy the triangle inequality. We identify relationships between neural representations that are interpretable in terms of anatomical features and model performance.
  arXiv  Detail & Related papers  (2021-10-27T19:48:55Z)
• Embedding Graph Auto-Encoder for Graph Clustering [90.8576971748142]
  Graph auto-encoder (GAE) models are based on semi-supervised graph convolution networks (GCN) We design a specific GAE-based model for graph clustering to be consistent with the theory, namely Embedding Graph Auto-Encoder (EGAE) EGAE consists of one encoder and dual decoders.
  arXiv  Detail & Related papers  (2020-02-20T09:53:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.