New theory challenges traditional machine learning assumptions.
problem Traditional machine learning theories are critiqued.
method A new theory is proposed and discussed.
result Learning true probabilities is not equivalent to other learning goals.
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48 results for “Learning theory”
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a the…
Machine learning explores symmetries in field theory and algebra.
problem Understanding symmetries in field theory and algebra.
method Using neural networks to analyze conformal field theory and Lie algebra representation theory.
result Recent advances in machine learning have uncovered new symmetries.
Survey on learning Boolean functions in computational theory.
problem Learning Boolean function classes in computational theory.
method Overview of known results in PAC and related models.
result Discussion of various learning results for Boolean functions.
Theory explains how deep nets learn features from data.
problem Understanding how deep neural networks learn features from data.
method Developed a noise-nonlinearity phase diagram and a mechanical theory.
result Links feature learning across layers to generalization.
Statistical field theory aids in understanding deep learning complexities.
problem Complexity and lack of theoretical understanding in deep learning.
method Statistical field theory as a theoretical framework.
result Field theory provides insights into generalization, bias, and feature learning.
Abstract: Surveying connections between ML and Control Theory.
problem Addressing the intersection of Machine Learning and Control Theory.
method Develops connections through reinforcement learning, supervised learning, deep learning, and stochastic gradient descent.
result Machine Learning and Control Theory are interconnected, with ML solving large control problems and Control Theory providing tools for ML.
New theory uses probability sets for data variability, improving machine learning.
problem Variability in data distribution causes learning issues.
method Uses convex sets of probabilities (credal sets) to model data variability.
result Derives bounds for risk of models learned from multiple training sets.
Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here. I show that, under some conditions, the theory of PAC Learnable provides a way to solve the Applied learning problem. However, the theory requires t…
(K)not machine learninghep-th
Machine learning knot invariants with physics applications.
problem Understanding relations between knot invariants in physics.
method Machine learning and theoretical physics (Chern-Simons theory, gauge theories).
result New analytic results from Big Data experiments.
This paper applies AMP theory to improve learning tasks.
problem Improving learning efficiency by optimizing task-specific models.
method Uses aggregated Markov processes to reduce model complexity and enhance learning.
result Demonstrates how AMP theory can be effectively applied to stochastic learning.
Lectures on deep learning from a learning theory perspective.
problem Understanding how deep learning architectures lead to inductive bias.
method Statistical learning theory and stochastic optimization.
result Gradient descent on linear diagonal networks can lead to various forms of implicit bias.
We propose using category theory to unify deep learning architectures.
problem Lack of a coherent bridge between model constraints and implementations.
method Apply category theory to unify neural network design.
result Theory recovers constraints from geometric deep learning and encodes standard constructs.
Unified theory of deep learning from approximation to emergence.
problem Understanding the mechanisms behind deep learning.
method Unified, proof-oriented approach tracing from classical foundations to contemporary mechanisms.
result Unified theory explaining deep learning from approximation to emergence.
A theory of deep learning is emerging, focusing on training dynamics and statistics.
problem Develop a scientific theory to understand deep learning.
method Synthesize research into five areas: idealized settings, tractable limits, mathematical laws, hyperparameters, and universal behaviors.
result The emerging theory is a mechanics of the learning process, named learning mechanics.
Survey on statistical learning theory for control, focusing on linear systems.
problem Applying machine learning techniques to control systems, especially linear ones.
method Adapting tools from modern high-dimensional statistics and learning theory.
result Recent advances in statistical learning theory for control, particularly for linear systems.
Lecture Notes on Linear Neural Networks: A Tale of Optimization and Generalization in Deep Learningcs.LG
Lecture notes on linear neural networks for deep learning optimization and generalization.
problem Understanding optimization and generalization in deep learning models.
method Mathematical tools and dynamical systems theory.
result Potential of mathematical tools to enhance understanding of deep learning.
Learning-rate schedules for large models match optimization theory closely, leading to better training.
problem Improving training of large models with optimal learning rates.
method Used a bound from non-smooth convex optimization theory to match learning-rate schedules with practical benefits.
result Extending the learning-rate schedule with optimal learning-rate and transferring it across schedules improves model training.
This paper develops a federated EM algorithm for unsupervised learning of mixture models.
problem Theoretical foundations of unsupervised federated learning are lacking.
method Introduces a federated gradient EM algorithm (FedGrEM) for unsupervised learning of mixture models.
result Theoretical analysis shows FedGrEM outperforms local single-task learning.
Federated learning linked to mean-field games for large-scale learning.
problem Large-scale distributed and privacy-preserving learning algorithms.
method Established a connection between federated learning and mean-field games, presenting federated learning as a differential game.
result Properties of the equilibrium of the federated learning game were discussed.
New theory improves understanding of ensemble learning systems.
problem Improving the effectiveness of ensemble learning systems.
method Generalized Fano's inequality to account for information loss in model combination.
result Reveals strengths and weaknesses of ensemble systems on accuracy and diversity.
Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theorycond-mat.stat-mech
Paper reviews algebraic research in machine learning theory.
problem Understanding phase transitions in machine learning models.
method Algebraic approaches in statistical mechanics.
result Algebraic methods are essential for analyzing machine learning models with singularities.
The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover's theory (BC theory), which gives a mathematical justification of the MDL principle. The original BC theory, however, can be applied to supervised learning only …
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. Thi…
Extreme value theory enhances statistical learning extrapolation for rare events.
problem Challenges in traditional machine learning methods for extreme data.
method Asymptotic theory and statistical tools for tail behavior.
result Effective extrapolation methods for extreme quantiles and anomalies.
Theory of learning with weight-distribution constraints.
problem Understanding how structure influences function in neural networks.
method Statistical mechanical theory and optimal transport.
result Reduction in capacity due to constrained weight-distribution is related to Wasserstein distance.
Much attention has been devoted recently to the generalization puzzle in deep learning: large, deep networks can generalize well, but existing theories bounding generalization error are exceedingly loose, and thus cannot explain this striking performance. Furthermore, a major hope is that knowledge may transfer across …
SLT explains neural network success by closing theory-practice gap.
problem Failure of classical inference and learning theory in modern neural networks.
method Physics-inspired Singular Learning Theory (SLT) applied to neural networks.
result SLT recovers known and novel scaling laws for neural network phase transitions.
With this positional paper we present a representation learning view on predicate invention. The intention of this proposal is to bridge the relational and deep learning communities on the problem of predicate invention. We propose a theory reconstruction approach, a formalism that extends autoencoder approach to repre…
Simplified neural network EFTs reveal a single critical condition.
problem Understanding neuron statistics in neural networks at initialization.
method Diagrammatic approach to effective field theories (EFTs).
result A single condition governs criticality of all neuron preactivations.
GQML uses symmetries from representation theory to improve quantum machine learning.
problem Creating quantum models with symmetries to improve performance.
method Introduction to representation theory for quantum learning, focusing on group actions and symmetries.
result Effective implementation of GQML requires knowledge of group representation theory.
The main goal of statistical learning theory is to provide a fundamental framework for the problem of decision making and model construction based on sets of data. Here, we present a brief introduction to the fundamentals of statistical learning theory, in particular the difference between empirical and structural risk…
New learnability criteria for non-iid processes equivalent to online learning.
problem Statistical learning under non-iid stochastic processes is underdeveloped.
method Defined two learnability notions and showed their equivalence to online learning.
result Learnability criteria for non-iid processes are equivalent to online learning.
SSL theory improves representation learning from raw data.
problem Challenges in SSL, including instability and collapse.
method Precise analysis of generalization performance with a theory-friendly setup.
result Insights for SSL practitioners on data augmentation, network architecture, and training algorithm.
New PAC-Bayesian bounds explain few-shot learning performance gaps.
problem Gap between PAC-Bayesian theory and practice in few-shot learning.
method Developed new PAC-Bayesian bounds for few-shot learning, derived MAML and Reptile from these bounds, and introduced a new PACMAML algorithm.
result PAC-Bayesian bounds explain performance of MAML and Reptile, and outperform existing algorithms.
GNNs learn graph representations, with new theory on their power and limitations.
problem Understanding the capabilities and limitations of GNNs.
method Theoretical analysis of GNNs, focusing on approximation and learning properties.
result New insights into the representation, generalization, and extrapolation of GNNs.
Paper analyzes error exponent in agnostic PAC learning.
problem Analyzing performance of agnostic PAC learning.
method Using error exponent from Information Theory to analyze PAC learning.
result Improved distribution-dependent error exponent for agnostic learning.
The paper outlines future work in random sets theory.
problem Developing a theory of statistical reasoning with random sets.
method Generalizing logistic regression, probability laws, and geometric uncertainty.
result A new geometric approach to uncertainty with general random sets.
Information Theory in Open-world Machine Learning Foundations, Frameworks, and Future Directionstat.ML
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
Improved learning theory for kernel distribution regression with two-stage sampling.
problem Distribution regression problem and two-stage sampling setting.
method Kernel methods, near-unbiased condition, new error bounds, convergence rates.
result Strictly improved convergence rates for three important classes of kernels.
The interpretation of Large Hadron Collider (LHC) data in the framework of Beyond the Standard Model (BSM) theories is hampered by the need to run computationally expensive event generators and detector simulators. Performing statistically convergent scans of high-dimensional BSM theories is consequently challenging, a…
Deep ReLU networks can approximate matrix-vector products with error bounds.
problem Can deep ReLU networks accurately approximate matrix-vector products?
method Derived error bounds in Lebesgue and Sobolev norms for deep ReLU FNNs.
result Developed deep approximation theory with successful applications.
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and …
A theoretical framework for deep learning is proposed to explain its effectiveness.
problem Lack of a comprehensive theory explaining deep learning's effectiveness.
method Integrates three characteristics into a graphical model called neurashed.
result Explains common empirical patterns in deep learning and provides insights into regularization and elasticity.
Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theorystat.ML
Study shows LLC correlates with neural network compressibility.
problem Evaluating limits of neural network compression.
method Extended minimum description length principle using singular learning theory.
result Complexity estimates based on LLC are linearly correlated with compressibility.
Improves few-shot learning using multi-task representation learning theory.
problem Few-shot learning with limited data.
method Multi-task representation learning theory and spectral-based regularization.
result Improved performance of meta-learning methods through new spectral regularization.
A novel model combines deep learning and extreme value theory for multivariate cyber risk prediction.
problem High dimensionality and heavy tails in multivariate cyber risk patterns.
method Combines deep learning for point predictions and extreme value theory for quantile predictions.
result The model provides satisfactory high quantile predictions and accurate point predictions.