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Two papers analyze theoretical limits of empirical risk minimization in ML

By PulseAugur Editorial · [2 sources] ·

Two new research papers explore the theoretical underpinnings of empirical risk minimization (ERM) in machine learning. The first paper, "Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model," introduces an incremental approximate message passing (IAMP) algorithm to analyze ERM performance in high-dimensional settings, aiming to characterize the optimal performance achievable by polynomial-time algorithms. The second paper, "Universality of empirical risk minimization," proves general universality results for train and test errors in ERM, demonstrating that under certain conditions, the minimum value depends only on the asymptotic mean and covariance of the data distribution, extending previous findings beyond strongly convex loss functions. AI

IMPACT These theoretical analyses could lead to more efficient and robust machine learning algorithms by better understanding the optimization landscape.

RANK_REASON Two academic papers published on arXiv discussing theoretical aspects of machine learning algorithms.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Two papers analyze theoretical limits of empirical risk minimization in ML

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Andrea Montanari, Kangjie Zhou ·

    Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model

    arXiv:2606.28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions. Such cost functions can have a multitude of local optima and yet, gradient-based optimization appears to converge to near…

  2. arXiv stat.ML TIER_1 English(EN) · Andrea Montanari, Basil Saeed ·

    Universality of empirical risk minimization

    arXiv:2202.08832v3 Announce Type: replace-cross Abstract: We study a general class of optimization problems with decision variable $\boldsymbol{\Theta} \in \mathbb{R}^{p \times k}$ and cost function which is the sum of $n$ terms, each dependent on $\boldsymbol{\Theta}$ through th…

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