The Universality Lens: Why Even Highly Over-Parametrized Models Learn Well

• URL: http://arxiv.org/abs/2506.07661v1
• Date: Mon, 09 Jun 2025 11:32:31 GMT
• Title: The Universality Lens: Why Even Highly Over-Parametrized Models Learn Well
• Authors: Meir Feder, Ruediger Urbanke, Yaniv Fogel,
• Abstract summary: We study a Bayesian mixture with log-loss and (almost) uniform prior over an expansive hypothesis class.<n>Key result shows that the learner's regret is not determined by the overall size of the hypothesis class.<n>Results apply broadly across online, batch, and supervised learning settings.
• Score: 4.2466572124752995
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

Related papers

• StepVAR: Structure-Texture Guided Pruning for Visual Autoregressive Models [98.72926158261937]
  We propose a training-free token pruning framework for Visual AutoRegressive models.<n>We employ a lightweight high-pass filter to capture local texture details, while leveraging Principal Component Analysis (PCA) to preserve global structural information.<n>To maintain valid next-scale prediction under sparse tokens, we introduce a nearest neighbor feature propagation strategy.
  arXiv  Detail & Related papers  (2026-03-02T11:35:05Z)
• Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting [63.8116386935854]
  We demonstrate that state-of-the-art probabilistic skill requires neither intricate architectural constraints nor specialized trainings.<n>We introduce a scalable framework for learning multi-scale atmospheric dynamics by combining a directly downsampled latent space with a history-conditioned local projector.<n>We find that our framework design is robust to the choice of probabilistic estimators, seamlessly supporting interpolants, diffusion models, and CRPS-based ensemble training.
  arXiv  Detail & Related papers  (2026-01-26T03:52:16Z)
• Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models [51.03144354630136]
  Generalization in natural data domains is progressively achieved during training before the onset of memorization.<n>Generalization vs. memorization is then best understood as a competition between time scales.<n>We show that this phenomenology is recovered in diffusion models learning a simple probabilistic context-free grammar with random rules.
  arXiv  Detail & Related papers  (2025-05-22T17:40:08Z)
• A Classical View on Benign Overfitting: The Role of Sample Size [14.36840959836957]
  We focus on almost benign overfitting, where models simultaneously achieve both arbitrarily small training and test errors.<n>This behavior is characteristic of neural networks, which often achieve low (but non-zero) training error while still generalizing well.
  arXiv  Detail & Related papers  (2025-05-16T18:37:51Z)
• 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)
• Generalized Factor Neural Network Model for High-dimensional Regression [50.554377879576066]
  We tackle the challenges of modeling high-dimensional data sets with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships.<n>Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression.
  arXiv  Detail & Related papers  (2025-02-16T23:13:55Z)
• Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond [61.18736646013446]
  In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena.
  arXiv  Detail & Related papers  (2024-10-31T22:54:34Z)
• Enhanced Transformer architecture for in-context learning of dynamical systems [0.3749861135832073]
  In this paper, we enhance the original meta-modeling framework through three key innovations. The efficacy of these modifications is demonstrated through a numerical example focusing on the Wiener-Hammerstein system class.
  arXiv  Detail & Related papers  (2024-10-04T10:05:15Z)
• Revisiting Optimism and Model Complexity in the Wake of Overparameterized Machine Learning [6.278498348219108]
  We revisit model complexity from first principles, by first reinterpreting and then extending the classical statistical concept of (effective) degrees of freedom. We demonstrate the utility of our proposed complexity measures through a mix of conceptual arguments, theory, and experiments.
  arXiv  Detail & Related papers  (2024-10-02T06:09:57Z)
• Understanding the Double Descent Phenomenon in Deep Learning [49.1574468325115]
  This tutorial sets the classical statistical learning framework and introduces the double descent phenomenon. By looking at a number of examples, section 2 introduces inductive biases that appear to have a key role in double descent by selecting. section 3 explores the double descent with two linear models, and gives other points of view from recent related works.
  arXiv  Detail & Related papers  (2024-03-15T16:51:24Z)
• The No Free Lunch Theorem, Kolmogorov Complexity, and the Role of Inductive Biases in Machine Learning [80.1018596899899]
  We argue that neural network models share this same preference, formalized using Kolmogorov complexity. Our experiments show that pre-trained and even randomly language models prefer to generate low-complexity sequences. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.
  arXiv  Detail & Related papers  (2023-04-11T17:22:22Z)
• The Neural Race Reduction: Dynamics of Abstraction in Gated Networks [12.130628846129973]
  We introduce the Gated Deep Linear Network framework that schematizes how pathways of information flow impact learning dynamics. We derive an exact reduction and, for certain cases, exact solutions to the dynamics of learning. Our work gives rise to general hypotheses relating neural architecture to learning and provides a mathematical approach towards understanding the design of more complex architectures.
  arXiv  Detail & Related papers  (2022-07-21T12:01:03Z)
• More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize [94.70343385404203]
  We find that most theoretical analyses fall short of capturing qualitative phenomena even for kernel regression. We prove that the classical GCV estimator converges to the generalization risk whenever a local random matrix law holds. Our findings suggest that random matrix theory may be central to understanding the properties of neural representations in practice.
  arXiv  Detail & Related papers  (2022-03-11T18:59:01Z)
• A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning [37.01683478234978]
  The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of over parameterized models.
  arXiv  Detail & Related papers  (2021-09-06T10:48:40Z)
• Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalization [93.8373619657239]
  Neural networks trained with SGD were recently shown to rely preferentially on linearly-predictive features. This simplicity bias can explain their lack of robustness out of distribution (OOD) We demonstrate that the simplicity bias can be mitigated and OOD generalization improved.
  arXiv  Detail & Related papers  (2021-05-12T12:12:24Z)
• XY Neural Networks [0.0]
  We show how to build complex structures for machine learning based on the XY model's nonlinear blocks. The final target is to reproduce the deep learning architectures, which can perform complicated tasks.
  arXiv  Detail & Related papers  (2021-03-31T17:47:10Z)
• Provable Benefits of Overparameterization in Model Compression: From Double Descent to Pruning Neural Networks [38.153825455980645]
  Recent empirical evidence indicates that the practice of overization not only benefits training large models, but also assists - perhaps counterintuitively - building lightweight models. This paper sheds light on these empirical findings by theoretically characterizing the high-dimensional toolsets of model pruning. We analytically identify regimes in which, even if the location of the most informative features is known, we are better off fitting a large model and then pruning.
  arXiv  Detail & Related papers  (2020-12-16T05:13:30Z)
• Generalization and Memorization: The Bias Potential Model [9.975163460952045]
  generative models and density estimators behave quite differently from models for learning functions. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted. In the long term, the model either memorizes the samples or diverges.
  arXiv  Detail & Related papers  (2020-11-29T04:04:54Z)
• S2RMs: Spatially Structured Recurrent Modules [105.0377129434636]
  We take a step towards exploiting dynamic structure that are capable of simultaneously exploiting both modular andtemporal structures. We find our models to be robust to the number of available views and better capable of generalization to novel tasks without additional training.
  arXiv  Detail & Related papers  (2020-07-13T17:44:30Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)

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.