Publication

Generalized Gradient Norm Clipping & Non-Euclidean (L 0 , L 1 )-Smoothness

2025

Abstract

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of (L 0 ,L 1)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal O(n −1/4) convergence rate by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning, which we dub Clipped Scion, and demonstrate their properties on image classification and language modeling. The code is available at https://github.com/LIONS-EPFL/ClippedScion. * Equal contribution. 2 By conditional gradient based methods, we mean those methods which leverage a linear minimization oracle lmo(d) = arg min x∈D ⟨d, x⟩ when updating their parameters with an open-loop stepsize.

Official source

https://infoscience.epfl.ch/entities/publication/a8ca1660-049a-4122-a239-5938ff0d6012

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a8ca1660-049a-4122-a239-5938ff0d6012

About this result

Related concepts (32)

Gradient descent

In mathematics, gradient descent (also often called steepest descent) is a iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent.

Language model

A language model is a probabilistic model of a natural language that can generate probabilities of a series of words, based on text corpora in one or multiple languages it was trained on. Large language models, as their most advanced form, are a combination of feedforward neural networks and transformers. They have superseded recurrent neural network-based models, which had previously superseded the pure statistical models, such as word n-gram language model.

Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. What kind of graph is used depends on the application.