Bound by semanticity: universal laws governing the generalization-identification tradeoff

• URL: http://arxiv.org/abs/2506.14797v1
• Date: Sun, 01 Jun 2025 15:56:26 GMT
• Title: Bound by semanticity: universal laws governing the generalization-identification tradeoff
• Authors: Marco Nurisso, Jesseba Fernando, Raj Deshpande, Alan Perotti, Raja Marjieh, Steven M. Frankland, Richard L. Lewis, Taylor W. Webb, Declan Campbell, Francesco Vaccarino, Jonathan D. Cohen, Giovanni Petri,
• Abstract summary: We show that finite-resolution similarity is a fundamental emergent informational constraint, not merely a toy-model artifact.<n>These results provide an exact theory of the generalization-identification trade-off and clarify how semantic resolution shapes the representational capacity of deep networks and brains alike.
• Score: 8.437463955457423
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Intelligent systems must deploy internal representations that are simultaneously structured -- to support broad generalization -- and selective -- to preserve input identity. We expose a fundamental limit on this tradeoff. For any model whose representational similarity between inputs decays with finite semantic resolution $\varepsilon$, we derive closed-form expressions that pin its probability of correct generalization $p_S$ and identification $p_I$ to a universal Pareto front independent of input space geometry. Extending the analysis to noisy, heterogeneous spaces and to $n>2$ inputs predicts a sharp $1/n$ collapse of multi-input processing capacity and a non-monotonic optimum for $p_S$. A minimal ReLU network trained end-to-end reproduces these laws: during learning a resolution boundary self-organizes and empirical $(p_S,p_I)$ trajectories closely follow theoretical curves for linearly decaying similarity. Finally, we demonstrate that the same limits persist in two markedly more complex settings -- a convolutional neural network and state-of-the-art vision-language models -- confirming that finite-resolution similarity is a fundamental emergent informational constraint, not merely a toy-model artifact. Together, these results provide an exact theory of the generalization-identification trade-off and clarify how semantic resolution shapes the representational capacity of deep networks and brains alike.

Related papers

• Neural Expectation Operators [2.1756081703276]
  This paper introduces textbfMeasure Learning, a paradigm for modeling ambiguity via non-linear expectations.<n>We define Neural Expectation Operators as solutions to Backward Differential Equations (BSDEs) whose drivers are parameterized by neural networks.<n>We provide constructive methods for enforcing key axiomatic properties, such as convexity, by architectural design.
  arXiv  Detail & Related papers  (2025-07-13T06:19:28Z)
• Deep Generative Models: Complexity, Dimensionality, and Approximation [18.530164193967945]
  We show that generative networks can generate high-dimensional data from lower-dimensional inputs.<n>Our findings challenge the belief on the relationship between input dimensionality and the ability of generative networks to model data distributions.<n>This novel insight not only corroborates the practical effectiveness of generative networks in handling complex data structures, but also underscores a critical trade-off between approximation error, dimensionality, and model complexity.
  arXiv  Detail & Related papers  (2025-04-01T14:07:02Z)
• Interaction Asymmetry: A General Principle for Learning Composable Abstractions [27.749478197803256]
  We show that interaction asymmetry enables both disentanglement and compositional generalization. We propose an implementation of these criteria using a flexible Transformer-based VAE, with a novel regularizer on the attention weights of the decoder.
  arXiv  Detail & Related papers  (2024-11-12T13:33:26Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• PAC-Chernoff Bounds: Understanding Generalization in the Interpolation Regime [6.645111950779666]
  This paper introduces a distribution-dependent PAC-Chernoff bound that exhibits perfect tightness for interpolators.<n>We present a unified theoretical framework revealing why certain interpolators show an exceptional generalization, while others falter.
  arXiv  Detail & Related papers  (2023-06-19T14:07:10Z)
• A Robustness Analysis of Blind Source Separation [91.3755431537592]
  Blind source separation (BSS) aims to recover an unobserved signal from its mixture $X=f(S)$ under the condition that the transformation $f$ is invertible but unknown. We present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$. We show that a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees.
  arXiv  Detail & Related papers  (2023-03-17T16:30:51Z)
• 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)
• Self-Ensembling GAN for Cross-Domain Semantic Segmentation [107.27377745720243]
  This paper proposes a self-ensembling generative adversarial network (SE-GAN) exploiting cross-domain data for semantic segmentation. In SE-GAN, a teacher network and a student network constitute a self-ensembling model for generating semantic segmentation maps, which together with a discriminator, forms a GAN. Despite its simplicity, we find SE-GAN can significantly boost the performance of adversarial training and enhance the stability of the model.
  arXiv  Detail & Related papers  (2021-12-15T09:50:25Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations. We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• Convex Geometry and Duality of Over-parameterized Neural Networks [70.15611146583068]
  We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We show that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set. In higher dimensions, we show that the training problem can be cast as a finite dimensional convex problem with infinitely many constraints.
  arXiv  Detail & Related papers  (2020-02-25T23:05:33Z)
• A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-$\ell_1$-Norm Interpolated Classifiers [3.167685495996986]
  This paper establishes a precise high-dimensional theory for boosting on separable data. Under a class of statistical models, we provide an exact analysis of the universality error of boosting. We also explicitly pin down the relation between the boosting test error and the optimal Bayes error.
  arXiv  Detail & Related papers  (2020-02-05T00:24:53Z)

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.