mlsanityData to 14 Oct 2026

Linear Classification of Neural Manifolds with Correlated Variability

arXiv 2211.14961 ↗First posted 27 Nov 2022q-bio.NC cond-mat.dis-nn cond-mat.stat-mechcited by 9

Not on the map. Why?

Abstract (arXiv)

Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the axes effectively shrinks their radii, revealing a duality between correlations and geometry with respect to the problem of classification. We then apply our results to accurately estimate the capacity of deep network data.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 23 of its 57 references that are in the map. First posted on arXiv 27 Nov 2022.

Builds on

23 of 57 references.

References · 23

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 12,049
  3. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  4. 2019Momentum Contrast for Unsupervised Visual Representation Learningcited by 7,513
  5. 2021Convex optimizationcited by 2,515
  6. 2021Barlow Twins: Self-Supervised Learning via Redundancy Reductioncited by 1,838
  7. 2019Similarity of Neural Network Representations Revisitedcited by 1,755
  8. 2021VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learningcited by 1,057
  9. 2018Insights on representational similarity in neural networks with canonical correlationcited by 324
  10. 2018Towards a Definition of Disentangled Representationscited by 296
  11. 2019Intrinsic dimension of data representations in deep neural networkscited by 282
  12. 2018A mathematical theory of semantic development in deep neural networkscited by 186
11 more
  1. 2017Classification and Geometry of General Perceptual Manifoldscited by 62
  2. 2021Neural population geometry: An approach for understanding biological and artificial neural networkscited by 52
  3. 2015Linear Readout of Object Manifoldscited by 9
  4. 2020Efficiency of local learning rules in threshold-linear associative networkscited by 6
  5. 2020Quality of internal representation shapes learning performance in feedback neural networkscited by 4
  6. 2016Robust information propagation through noisy neural circuitscited by 2
  7. 2017Learning Data Manifolds with a Cutting Plane Methodcited by 2
  8. 2019Capacity of the covariance perceptroncited by 2
  9. 2020Geometric framework to predict structure from function in neural networkscited by 2
  10. 2021Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?cited by 2
  11. 2022Soft-margin classification of object manifoldscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 4; 2026: 2.

9 papers.

  1. 2025The Geometry of Prompting: Unveiling Distinct Mechanisms of Task Adaptation in Language Modelscited by 18
  2. 2024Neural population geometry and optimal coding of tasks with shared latent structurecited by 9
  3. 2025Feature Learning beyond the Lazy-Rich Dichotomy: Insights from Representational Geometrycited by 9
  4. 2023Inversion dynamics of class manifolds in deep learning reveals tradeoffs underlying generalisationcited by 6
  5. 2023Probing Biological and Artificial Neural Networks with Task-dependent Neural Manifoldscited by 4
  6. 2025A statistical physics framework for optimal learningcited by 3
  7. 2026Diagnosing Generalization Failures from Representational Geometry Markerscited by 2
  8. 2025Can Stationary Distributions of Scale-Invariant Neural Networks Be Described by the Thermodynamics of an Ideal Gas?cited by 0
  9. 2026Sparse Prototype Code Underlies Classification and Prediction Across Modalitiescited by 0