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We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying assumptions, while…

Machine Learning · Computer Science 2026-03-03 Guy Smorodinsky , Sveta Gimpleson , Itay Safran

We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks. The key ingredient is a new smoothness condition derived from practical neural network training examples. We observe that…

Optimization and Control · Mathematics 2020-02-12 Jingzhao Zhang , Tianxing He , Suvrit Sra , Ali Jadbabaie

When discriminating dynamic noisy sensory signals, human and primate subjects achieve higher accuracy when they take more time to decide, an effect attributed to accumulation of evidence over time to overcome neural noise. We measured the…

Neurons and Cognition · Quantitative Biology 2015-06-05 Pamela Reinagel , Robert E Clark

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of…

Machine Learning · Computer Science 2026-04-29 Hugo Ninou , Jonathan Kadmon , N. Alex Cayco-Gajic

Contrastive learning has emerged as a powerful framework for learning generalizable representations, yet its theoretical understanding remains limited, particularly under imbalanced data distributions that are prevalent in real-world…

Machine Learning · Computer Science 2026-02-12 Haixu Liao , Yating Zhou , Songyang Zhang , Meng Wang , Shuai Zhang

Deep learning neural network models must be large enough to adapt to their problem domain, while small enough to avoid overfitting training data during gradient descent. To balance these competing demands, over-provisioned deep learning…

Machine Learning · Computer Science 2025-09-04 B. N. Kausik

Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number…

Machine Learning · Statistics 2019-02-05 Zhuoning Yuan , Yan Yan , Rong Jin , Tianbao Yang

This article exposes the failure of some big neural networks to leverage added capacity to reduce underfitting. Past research suggest diminishing returns when increasing the size of neural networks. Our experiments on ImageNet LSVRC-2010…

Machine Learning · Computer Science 2013-03-18 Yann N. Dauphin , Yoshua Bengio

In the modern knowledge economy, success demands sustained focus and high cognitive performance. Research suggests that human cognition is linked to a finite resource, and upon its depletion, cognitive functions such as self-control and…

Computers and Society · Computer Science 2018-09-11 Nathan O. Hodas , Jacob Hunter , Stephen J. Young , Kristina Lerman

One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value…

Machine Learning · Computer Science 2021-01-08 Kaustubh Yadav

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting…

Machine Learning · Computer Science 2018-04-25 Leslie N. Smith

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its…

Machine Learning · Computer Science 2020-10-28 Clare Lyle , Lisa Schut , Binxin Ru , Yarin Gal , Mark van der Wilk

One of the well-known challenges in computer vision tasks is the visual diversity of images, which could result in an agreement or disagreement between the learned knowledge and the visual content exhibited by the current observation. In…

Machine Learning · Computer Science 2020-01-03 Yan Luo , Yongkang Wong , Mohan S. Kankanhalli , Qi Zhao

Deep Neural Networks (DNNs) rely on inherent fluctuations in their internal parameters (weights and biases) to effectively navigate the complex optimization landscape and achieve robust performance. While these fluctuations are recognized…

Machine Learning · Computer Science 2025-11-14 Darsh Pareek , Umesh Kumar , Ruthu Rao , Ravi Janjam

Recent advancements in data-to-text generation largely take on the form of neural end-to-end systems. Efforts have been dedicated to improving text generation systems by changing the order of training samples in a process known as…

Computation and Language · Computer Science 2021-02-09 Ernie Chang , Hui-Syuan Yeh , Vera Demberg

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

This paper studies how neural network architecture affects the speed of training. We introduce a simple concept called gradient confusion to help formally analyze this. When gradient confusion is high, stochastic gradients produced by…

Machine Learning · Computer Science 2020-07-08 Karthik A. Sankararaman , Soham De , Zheng Xu , W. Ronny Huang , Tom Goldstein

Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate…

Machine Learning · Computer Science 2021-07-28 Zhiyong Hao , Yixuan Jiang , Huihua Yu , Hsiao-Dong Chiang

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike…

Machine Learning · Computer Science 2017-08-04 Chuan Guo , Geoff Pleiss , Yu Sun , Kilian Q. Weinberger

Despite achieving remarkable performance on many image classification tasks, state-of-the-art machine learning (ML) classifiers remain vulnerable to small input perturbations. Especially, the existence of adversarial examples raises…

Machine Learning · Computer Science 2020-02-06 David Mickisch , Felix Assion , Florens Greßner , Wiebke Günther , Mariele Motta