Neural Representation Geometry

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18 papers in the last four weeks, up 125% on the four weeks before. 0.2% of all new papers.

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Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks
May 1, 2026Akira TamamoriDynamical Systems Neural Representation Geometry
Faculty of Information Science, Aichi Institute of Technology 1247 Yachigusa, Yakusa-cho, Toyota-shi, Aichi 470-0392, Japan
Do Sparse Autoencoders Capture Concept Manifolds?
Apr 30, 2026Usha Bhalla, Thomas Fel, Can Rager +9Neural Representation Geometry Sparse Autoencoders
aHarvard University · bNortheastern University · cTechnion IIT +1
Semantic Structure of Feature Space in Large Language Models
Apr 29, 2026Austin C. Kozlowski, Andrei BoutylineNeural Representation Geometry LLM Interpretability
Knowledge Lab · University of Chicago · Department of Sociology +1
Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index
Apr 28, 2026Alexander KalinowskiRepresentation Collapse Neural Representation Geometry
SUNY Empire
Geometric Analysis of Self-Supervised Vision Representations for Semantic Image Retrieval
Apr 27, 2026Esteban Rodríguez-Betancourt, Edgar Casasola-MurilloNeural Representation Geometry Self-Supervised Visual Representation Learning
Posgrado en Computación e Informática Universidad de Costa Rica · Escuela de Ciencias de la Computación Universidad de Costa Rica
Representational Curvature Modulates Behavioral Uncertainty in Large Language Models
Apr 27, 2026Jack King, Evelina Fedorenko, Eghbal A. HosseiniNeural Representation Geometry Autoregressive Language Modeling
Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 · Google DeepMind
Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory
Apr 22, 2026Akira TamamoriNeural Representation Geometry Hopfield Networks
Faculty of Information Science, Aichi Institute of Technology 1247 Yachigusa, Yakusa-cho, Toyota-shi, Aichi 470-0392, Japan
Rethinking Intrinsic Dimension Estimation in Neural Representations
Apr 22, 2026Rickmer Schulte, David RügamerIntrinsic Dimensionality Neural Representation Geometry
LMU Munich, MCML
ILDR: Geometric Early Detection of Grokking
Apr 22, 2026Shreel GolwalaNeural Network Generalization Early Stopping
Virginia Tech
Geometric Decoupling: Diagnosing the Structural Instability of Latent
Apr 20, 2026Yuanbang Liang, Zhengwen Chen, Yu-Kun LaiNeural Representation Geometry Latent Diffusion Models
School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom
Semantic Step Prediction: Multi-Step Latent Forecasting in LLM Reasoning Trajectories via Step Sampling
Apr 20, 2026Yidi YuanNeural Representation Geometry Language Model Post-Training
Home Team Science and Technology Agency
The Umwelt Representation Hypothesis: Rethinking Universality
Apr 20, 2026Victoria Bosch, Rowan Sommers, Adrien Doerig +1Neural Representation Geometry
Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany. · Department of Psychology and Education, Freie Universität Berlin, Berlin, Germany. · Bernstein Center for Computational Neuroscience, Berlin, Germany
ATLAS: Constitution-Conditioned Latent Geometry and Redistribution Across Language Models and Neural Perturbation Data
Apr 19, 2026Gareth Seneque, Lap-Hang Ho, Nafise Erfanian Saeedi +2LLM Alignment Neural Representation Geometry
Australian Broadcasting Corporation
A Wasserstein Geometric Framework for Hebbian Plasticity
Apr 17, 2026Ulrich TanNeural Representation Geometry Hebbian Learning
Gating Enables Curvature: A Geometric Expressivity Gap in Attention
Apr 16, 2026Satwik Bathula, Anand A. JoshiInformation Geometry Neural Representation Geometry
Department of Electrical and Computer Engineering University of Southern California
A Complete Symmetry Classification of Shallow ReLU Networks
Apr 15, 2026Pranavkrishnan RamakrishnanShallow Neural Networks Neural Representation Geometry
Neural parametric representations for thin-shell shape optimisation
Apr 8, 2026Xiao Xiao, Fehmi CirakNeural Representation Geometry
School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. · Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, United Kingdom.
Understanding Latent Diffusability via Fisher Geometry
Apr 3, 2026Jing Gu, Morteza Mardani, Wonjun Lee +2Information Geometry Neural Representation Geometry
School of Mathematics, University of Minnesota · NVIDIA · Department of Mathematics, The Ohio State University +1
Similarity of Neural Network Representations in Superposition
Mar 31, 2026Sunny Liu, Habon Issa, André Longon +4Feature Superposition Representational Similarity Analysis
Cold Spring Harbor Laboratory · UC San Diego · Anthropic +2
Differential privacy representation geometry for medical image analysis
Mar 1, 2026Soroosh Tayebi Arasteh, Marziyeh Mohammadi, Sven Nebelung +1Neural Representation Geometry Healthcare
Lab for AI in Medicine, RWTH Aachen University, Aachen, Germany · Department of Diagnostic and Interventional Radiology, University Hospital RWTH Aachen, Aachen, Germany · INDA Institute, RWTH Aachen University, Aachen, Germany
Compositional Generalization Requires Linear, Orthogonal Representations in Vision Embedding Models
Feb 27, 2026Arnas Uselis, Andrea Dittadi, Seong Joon OhNeural Representation Geometry Visual Representation Learning
Tübingen AI Center, University of Tübingen · Helmholtz · Technical University of Munich
Disentangling Geometry, Performance, and Training in Language Models
Feb 24, 2026Atharva Kulkarni, Jacob Mitchell Springer, Arjun Subramonian +1LLM Evaluation Neural Representation Geometry
University of Southern California · 2Carnegie Mellon Univer · University of California, Los Angeles.
Symmetry in language statistics shapes the geometry of model representations
Feb 16, 2026Dhruva Karkada, Daniel J. Korchinski, Andres Nava +2Representation Learning Neural Representation Geometry
1UC Berkeley · 2EPFL · 3Johns Hopkins +1
Revisiting the Platonic Representation Hypothesis: An Aristotelian View
Feb 16, 2026Fabian Gröger, Shuo Wen, Maria BrbićRepresentational Similarity Analysis Neural Representation Geometry
1EPFL · University of Basel · 3HSLU
Multi-Way Representation Alignment
Feb 5, 2026Akshit Achara, Tatiana Gaintseva, Mateo Mahaut +5Neural Representation Geometry Latent Space Alignment
King’s College London, London, United Kingdom · Queen Mary University of London, London, United Kingdom · Universitat Pompeu Fabra, Barcelona, Spain +5
The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence
Jan 27, 2026Yichao Cai, Zhen Zhang, Yuhang Liu +1Cross-Modal Learning Contrastive Learning
Australian Institute for Machine Learning, Adelaide University · Responsible AI Research Centre
Geometric Stability: The Missing Axis of Representations
Jan 14, 2026Prashant C. RajuRepresentational Similarity Analysis Neural Representation Geometry
Output Embedding Centering for Stable LLM Pretraining
Jan 5, 2026Felix Stollenwerk, Anna Lokrantz, Niclas HertzbergLanguage Model Pretraining Neural Representation Geometry
AI Sweden
Probing Spectrum-Like Organization of States of Mind in Transformer Representation Spaces
Dec 23, 2025Sophie ZhaoTransformer Interpretability Neural Representation Geometry
School of Computer Science Georgia Institute of Technology
TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid
Nov 20, 2025Seonghun Oh, Youngjung Uh, Jin-Hwa Kim3D Mesh Generation Neural Representation Geometry
Yonsei University, Republic of Korea · NAVER AI Lab, Republic of Korea · Seoul National University, Republic of Korea

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Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks

Akira Tamamori

Faculty of Information Science, Aichi Institute of Technology 1247 Yachigusa, Yakusa-cho, Toyota-shi, Aichi 470-0392, Japan

Dynamical Systems Neural Representation Geometry Hopfield Networks Associative Memory

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High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit strong storage capabilities, but the dynamical and geometric mechanisms underlying their stability remain poorly understood. This paper investigates the global geometry of attractor basins and the mechanisms governing the storage limit in KLR-trained Hopfield networks. We combine empirical evaluations using random sequences and real-world image embeddings (CIFAR-10) with morphing experiments and statistical Signal-to-Noise Ratio (SNR) analysis. Our experiments show that the network achieves a storage capacity for random sequences up to

P/N \approx 16

, while maintaining stable retrieval for structured data at effective loads near

P/N \approx 20

. Morphing analysis indicates that attractors on the "Ridge of Optimization" are separated by sharp, phase-transition-like boundaries, characterized by steep effective potential barriers and critical slowing down. Furthermore, by comparing an SNR analysis with a geometric reference point inspired by Cover's theorem, we show that the practical storage limit is governed primarily not by a lack of geometric separability in the feature space, but by the loss of dynamical stability against crosstalk noise. These findings suggest that KLR networks function as highly localized exemplar-based memories that operate near the onset of dynamical collapse, providing a useful perspective on the design of robust, large-scale retrieval systems.

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