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Experimental neuroscience increasingly requires tractable models for analyzing and predicting the behavior of neurons and networks. The generalized linear model (GLM) is an increasingly popular statistical framework for analyzing neural…

Neural and Evolutionary Computing · Computer Science 2014-04-09 Jonathon Shlens

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These…

Computation and Language · Computer Science 2022-11-15 Cem Anil , Yuhuai Wu , Anders Andreassen , Aitor Lewkowycz , Vedant Misra , Vinay Ramasesh , Ambrose Slone , Guy Gur-Ari , Ethan Dyer , Behnam Neyshabur

Systematic Generalization refers to a learning algorithm's ability to extrapolate learned behavior to unseen situations that are distinct but semantically similar to its training data. As shown in recent work, state-of-the-art deep learning…

Artificial Intelligence · Computer Science 2020-10-06 Tong Gao , Qi Huang , Raymond J. Mooney

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training…

Machine Learning · Computer Science 2026-02-20 Jianliang He , Leda Wang , Siyu Chen , Zhuoran Yang

We study the dynamics of gradient flow with small weight decay on general training losses $F: \mathbb{R}^d \to \mathbb{R}$. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the…

Machine Learning · Computer Science 2025-11-06 Etienne Boursier , Scott Pesme , Radu-Alexandru Dragomir

This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in…

Machine Learning · Computer Science 2019-08-28 Hrushikesh Mhaskar , Tomaso Poggio

Early in training, LMs can behave like n-gram models, but eventually they often learn tree-based syntactic rules and generalize hierarchically out of distribution (OOD). We study this shift using controlled grammar-learning tasks: question…

Machine Learning · Computer Science 2025-09-30 Tian Qin , Naomi Saphra , David Alvarez-Melis

Training dynamics during grokking concentrate along a small number of dominant update directions -- the spectral edge -- which reliably distinguishes grokking from non-grokking regimes. We show that standard mechanistic interpretability…

Machine Learning · Computer Science 2026-04-09 Yongzhong Xu

Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…

Statistics Theory · Mathematics 2024-05-13 Karthik Duraisamy

In this paper we study the generalization capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being…

Machine Learning · Statistics 2019-07-30 Anastasia Borovykh , Cornelis W. Oosterlee , Sander M. Bohte

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve…

In the framework of on-line learning, a learning machine might move around a teacher due to the differences in structures or output functions between the teacher and the learning machine or due to noises. The generalization performance of a…

Physics and Society · Physics 2009-11-11 Seiji Miyoshi , Masato Okada

We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is…

Machine Learning · Computer Science 2021-07-07 Petr Taborsky , Lars Kai Hansen

The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that…

Machine Learning · Computer Science 2020-04-14 Andrzej Banburski , Qianli Liao , Brando Miranda , Lorenzo Rosasco , Fernanda De La Torre , Jack Hidary , Tomaso Poggio

Recent empirical studies have explored the idea of continuing to train a model at test-time for a given task, known as test-time training (TTT), and have found it to yield significant performance improvements. However, there is limited…

Machine Learning · Computer Science 2026-02-10 Jonas Hübotter , Patrik Wolf , Alexander Shevchenko , Dennis Jüni , Andreas Krause , Gil Kur

In imitation learning, imitators and demonstrators are policies for picking actions given past interactions with the environment. If we run an imitator, we probably want events to unfold similarly to the way they would have if the…

Machine Learning · Computer Science 2022-10-05 Michael K. Cohen , Marcus Hutter , Neel Nanda

Regularization is a well recognized powerful strategy to improve the performance of a learning machine and $l^q$ regularization schemes with $0<q<\infty$ are central in use. It is known that different $q$ leads to different properties of…

Machine Learning · Computer Science 2014-09-26 Shaobo Lin , Jinshan Zeng , Jian Fang , Zongben Xu

World models have recently emerged as a promising approach to reinforcement learning (RL), achieving state-of-the-art performance across a wide range of visual control tasks. This work aims to obtain a deep understanding of the robustness…

Machine Learning · Computer Science 2025-01-03 Qiaoyi Fang , Weiyu Du , Hang Wang , Junshan Zhang

We derive a differential equation that governs the evolution of the generalization gap when a deep network is trained by gradient descent. This differential equation is controlled by two quantities, a contraction factor that brings together…

Machine Learning · Computer Science 2025-10-14 Rubing Yang , Pratik Chaudhari

Transformers trained on natural language data have been shown to learn its hierarchical structure and generalize to sentences with unseen syntactic structures without explicitly encoding any structural bias. In this work, we investigate…

Computation and Language · Computer Science 2025-03-18 Kabir Ahuja , Vidhisha Balachandran , Madhur Panwar , Tianxing He , Noah A. Smith , Navin Goyal , Yulia Tsvetkov