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Optimization of machine learning models is commonly performed through stochastic gradient updates on randomly ordered training examples. This practice means that sub-epochs comprise of independent random samples of the training data that…

Machine Learning · Computer Science 2019-06-20 Eliav Buchnik , Edith Cohen , Avinatan Hassidim , Yossi Matias

Inspired by human learning, researchers have proposed ordering examples during training based on their difficulty. Both curriculum learning, exposing a network to easier examples early in training, and anti-curriculum learning, showing the…

Machine Learning · Computer Science 2021-02-10 Xiaoxia Wu , Ethan Dyer , Behnam Neyshabur

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is \emph{asymptotically} equivalent to a stochastic…

Machine Learning · Computer Science 2025-10-06 Martino Bernasconi , Andrea Celli , Riccardo Colini-Baldeschi , Federico Fusco , Stefano Leonardi , Matteo Russo

Generalization remains a central yet unresolved challenge in deep learning, particularly the ability to predict a model's performance beyond its training distribution using quantities available prior to test-time evaluation. Building on the…

A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…

Machine Learning · Statistics 2016-06-14 Jonathan Rosenblatt , Boaz Nadler

As large language models (LLMs) become integral to diverse applications, ensuring their reliability under varying input conditions is crucial. One key issue affecting this reliability is order sensitivity, wherein slight variations in the…

Computation and Language · Computer Science 2025-05-12 Bryan Guan , Tanya Roosta , Peyman Passban , Mehdi Rezagholizadeh

Not all instances in a data set are equally beneficial for inferring a model of the data. Some instances (such as outliers) are detrimental to inferring a model of the data. Several machine learning techniques treat instances in a data set…

Machine Learning · Computer Science 2013-12-19 Michael R. Smith , Tony Martinez

Sequential computation via autoregressive generation can make difficult tasks learnable, but the generation order of intermediate states strongly affects whether training succeeds. We address the problem of discovering a learning-friendly…

Machine Learning · Computer Science 2026-05-11 Yuta Sato , Kazuhiko Kawamoto , Hiroshi Kera

Despite exceptional achievements, training neural networks remains computationally expensive and is often plagued by instabilities that can degrade convergence. While learning rate schedules can help mitigate these issues, finding optimal…

Machine Learning · Computer Science 2026-03-30 Benoit Dherin , Benny Avelin , Anders Karlsson , Hanna Mazzawi , Javier Gonzalvo , Michael Munn

This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…

Statistics Theory · Mathematics 2007-06-13 Antoine Chambaz

Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a…

Information Theory · Computer Science 2016-11-17 Cihan Tepedelenlioglu , Adithya Rajan , Yuan Zhang

In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…

Computation and Language · Computer Science 2025-11-14 Warren Li , Yiqian Wang , Zihan Wang , Jingbo Shang

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking…

Machine Learning · Computer Science 2023-09-06 Vikrant Varma , Rohin Shah , Zachary Kenton , János Kramár , Ramana Kumar

Building on insights from the grokking literature, we study character-level Transformers trained to compute modular addition from text, and focus on robustness under input-format variation rather than only in-distribution accuracy. We…

Machine Learning · Computer Science 2026-01-09 Nikolay Yudin

We show that language models' activations linearly encode when information was learned during training. Our setup involves creating a model with a known training order by sequentially fine-tuning Llama-3.2-1B on six disjoint but otherwise…

Machine Learning · Computer Science 2025-09-23 Dmitrii Krasheninnikov , Richard E. Turner , David Krueger

The phenomenon of grokking in over-parameterized neural networks has garnered significant interest. It involves the neural network initially memorizing the training set with zero training error and near-random test error. Subsequent…

Machine Learning · Computer Science 2024-12-17 Hu Qiye , Zhou Hao , Yu RuoXi

We consider a system of multiple sources, a single communication channel, and a single monitoring station. Each source measures a time-varying quantity with varying levels of accuracy and one of them sends its update to the monitoring…

Artificial Intelligence · Computer Science 2023-10-25 Hitesh Gudwani

Grokking, or delayed generalization, is an intriguing learning phenomenon where test set loss decreases sharply only after a model's training set loss has converged. This challenges conventional understanding of the training dynamics in…

Machine Learning · Computer Science 2025-02-05 Breno W. Carvalho , Artur S. d'Avila Garcez , Luís C. Lamb , Emílio Vital Brazil

A range of approaches have been proposed for estimating the accuracy or robustness of the measured performance of IR methods. One is to use bootstrapping of test sets, which, as we confirm, provides an estimate of variation in performance.…

Information Retrieval · Computer Science 2025-09-26 Meng Yuan , Justin Zobel

Grokking typically achieves similar loss to ordinary, "steady", learning. We ask whether these different learning paths - grokking versus ordinary training - lead to fundamental differences in the learned models. To do so we compare the…

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