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This paper introduces a new technique to measure the feature dependency of neural network models. The motivation is to better understand a model by querying whether it is using information from human-understandable features, e.g.,…

Machine Learning · Computer Science 2024-10-10 Yinzhu Jin , Matthew B. Dwyer , P. Thomas Fletcher

Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data.…

Machine Learning · Computer Science 2016-05-27 Sander Dieleman , Jeffrey De Fauw , Koray Kavukcuoglu

In this paper, we study the dynamics of gradient descent in learning neural networks for classification problems. Unlike in existing works, we consider the linearly non-separable case where the training data of different classes lie in…

Machine Learning · Computer Science 2020-12-11 Ziang Long , Penghang Yin , Jack Xin

The \emph{strong collapse} of a simplicial complex, proposed by Barmak and Minian (\emph{Disc. Comp. Geom. 2012}), is a combinatorial collapse of a complex onto its sub-complex. Recently, it has received attention from computational…

Computational Geometry · Computer Science 2023-01-10 Jean-Daniel Boissonnat , Kunal Dutta , Soumik Dutta , Siddharth Pritam

The double descent phenomenon, which deviates from the traditional bias-variance trade-off theory, attracts considerable research attention; however, the mechanism of its occurrence is not fully understood. On the other hand, in the study…

Computer Vision and Pattern Recognition · Computer Science 2025-03-05 Shun Iwase , Shuya Takahashi , Nakamasa Inoue , Rio Yokota , Ryo Nakamura , Hirokatsu Kataoka

We propose a simple modification to standard ResNet architectures--L2 normalization over feature space--that substantially improves out-of-distribution (OoD) performance on the previously proposed Deep Deterministic Uncertainty (DDU)…

Machine Learning · Computer Science 2023-01-13 Jarrod Haas , William Yolland , Bernhard Rabus

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

Machine Learning · Computer Science 2023-11-17 Ilya Kaufman , Omri Azencot

Prototypical self-supervised learning methods consistently suffer from partial prototype collapse, where multiple prototypes converge to nearly identical representations. This undermines their central purpose -- providing diverse and…

We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal…

Machine Learning · Computer Science 2021-05-18 Christoph D. Hofer , Florian Graf , Marc Niethammer , Roland Kwitt

The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works…

Machine Learning · Computer Science 2024-11-06 Mo Zhou , Rong Ge

Neural networks with a large number of parameters often do not overfit, owing to implicit regularization that favors \lq good\rq{} networks. Other related and puzzling phenomena include properties of flat minima, saddle-to-saddle dynamics,…

Artificial Intelligence · Computer Science 2026-01-06 Joachim Bona-Pellissier , François Malgouyres , François Bachoc

We analyze the topological properties of the set of functions that can be implemented by neural networks of a fixed size. Surprisingly, this set has many undesirable properties. It is highly non-convex, except possibly for a few exotic…

General Topology · Mathematics 2020-01-24 Philipp Petersen , Mones Raslan , Felix Voigtlaender

Neural networks have attracted a lot of attention due to its success in applications such as natural language processing and computer vision. For large scale data, due to the tremendous number of parameters in neural networks, overfitting…

Machine Learning · Statistics 2022-07-05 Xiaoxi Shen , Jinghang Lin

We prove that training neural networks on 1-D data is equivalent to solving convex Lasso problems with discrete, explicitly defined dictionary matrices. We consider neural networks with piecewise linear activations and depths ranging from 2…

Machine Learning · Computer Science 2024-07-25 Emi Zeger , Yifei Wang , Aaron Mishkin , Tolga Ergen , Emmanuel Candès , Mert Pilanci

Dropout as a common regularizer to prevent overfitting in deep neural networks has been less effective in convolutional layers than in fully connected layers. This is because Dropout drops features randomly, without considering local…

Machine Learning · Computer Science 2025-06-05 Liyan Chen , Philippos Mordohai , Sergul Aydore

The local geometry of high dimensional neural network loss landscapes can both challenge our cherished theoretical intuitions as well as dramatically impact the practical success of neural network training. Indeed recent works have observed…

Machine Learning · Computer Science 2019-10-15 Stanislav Fort , Surya Ganguli

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they…

Machine Learning · Statistics 2022-06-10 Andrea Montanari , Yiqiao Zhong

Graph neural networks (GNNs) have received tremendous attention due to their superiority in learning node representations. These models rely on message passing and feature transformation functions to encode the structural and feature…

Machine Learning · Computer Science 2021-12-02 Kai Guo , Kaixiong Zhou , Xia Hu , Yu Li , Yi Chang , Xin Wang

In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…

Machine Learning · Computer Science 2024-02-22 Daniel LeJeune , Sina Alemohammad