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We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's…

Machine Learning · Computer Science 2020-06-09 James Martens , Roger Grosse

The core components of many modern neural network architectures, such as transformers, convolutional, or graph neural networks, can be expressed as linear layers with $\textit{weight-sharing}$. Kronecker-Factored Approximate Curvature…

Machine Learning · Computer Science 2024-01-12 Runa Eschenhagen , Alexander Immer , Richard E. Turner , Frank Schneider , Philipp Hennig

This paper advances the computational efficiency of Deep Hedging frameworks through the novel integration of Kronecker-Factored Approximate Curvature (K-FAC) optimization. While recent literature has established Deep Hedging as a…

Statistical Finance · Quantitative Finance 2024-11-25 Tsogt-Ochir Enkhbayar

Existing methods of pruning deep neural networks focus on removing unnecessary parameters of the trained network and fine tuning the model afterwards to find a good solution that recovers the initial performance of the trained model. Unlike…

Machine Learning · Computer Science 2021-11-17 Abdolghani Ebrahimi , Diego Klabjan

Training neural networks with many processors can reduce time-to-solution; however, it is challenging to maintain convergence and efficiency at large scales. The Kronecker-factored Approximate Curvature (K-FAC) was recently proposed as an…

Machine Learning · Computer Science 2020-07-03 J. Gregory Pauloski , Zhao Zhang , Lei Huang , Weijia Xu , Ian T. Foster

Physics-informed neural networks (PINNs) are infamous for being hard to train. Recently, second-order methods based on natural gradient and Gauss-Newton methods have shown promising performance, improving the accuracy achieved by…

Machine Learning · Computer Science 2024-10-31 Felix Dangel , Johannes Müller , Marius Zeinhofer

Kronecker-factored approximate curvature (KFAC) is arguably one of the most prominent curvature approximations in deep learning. Its applications range from optimization to Bayesian deep learning, training data attribution with influence…

Machine Learning · Computer Science 2025-07-08 Felix Dangel , Bálint Mucsányi , Tobias Weber , Runa Eschenhagen

We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after…

Machine Learning · Statistics 2018-05-22 Hippolyt Ritter , Aleksandar Botev , David Barber

Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to…

Machine Learning · Statistics 2016-05-25 Roger Grosse , James Martens

We consider the development of practical stochastic quasi-Newton, and in particular Kronecker-factored block-diagonal BFGS and L-BFGS methods, for training deep neural networks (DNNs). In DNN training, the number of variables and components…

Machine Learning · Computer Science 2021-01-11 Donald Goldfarb , Yi Ren , Achraf Bahamou

Kronecker-factored Approximate Curvature (K-FAC) method is a high efficiency second order optimizer for the deep learning. Its training time is less than SGD(or other first-order method) with same accuracy in many large-scale problems. The…

Machine Learning · Computer Science 2021-01-05 Yingshi Chen

In stochastic optimization, using large batch sizes during training can leverage parallel resources to produce faster wall-clock training times per training epoch. However, for both training loss and testing error, recent results analyzing…

Machine Learning · Computer Science 2021-04-21 Linjian Ma , Gabe Montague , Jiayu Ye , Zhewei Yao , Amir Gholami , Kurt Keutzer , Michael W. Mahoney

Hyperbolic neural networks (HNNs) have demonstrated notable efficacy in representing real-world data with hierarchical structures via exploiting the geometric properties of hyperbolic spaces characterized by negative curvatures. Curvature…

Machine Learning · Computer Science 2025-08-27 Xiaomeng Fan , Yuwei Wu , Zhi Gao , Mehrtash Harandi , Yunde Jia

Reducing the test time resource requirements of a neural network while preserving test accuracy is crucial for running inference on resource-constrained devices. To achieve this goal, we introduce a novel network reparameterization based on…

Machine Learning · Computer Science 2019-05-16 Chaoqi Wang , Roger Grosse , Sanja Fidler , Guodong Zhang

Second-order methods have the capability of accelerating optimization by using much richer curvature information than first-order methods. However, most are impractical for deep learning, where the number of training parameters is huge. In…

Machine Learning · Computer Science 2022-02-22 Yi Ren , Achraf Bahamou , Donald Goldfarb

Neural networks have achieved remarkable success in many cognitive tasks. However, when they are trained sequentially on multiple tasks without access to old data, their performance on early tasks tend to drop significantly. This problem is…

Machine Learning · Computer Science 2021-02-10 Dong Yin , Mehrdad Farajtabar , Ang Li , Nir Levine , Alex Mott

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…

Machine Learning · Computer Science 2019-10-24 Han Zhao , Yao-Hung Hubert Tsai , Ruslan Salakhutdinov , Geoffrey J. Gordon

Second-order optimizers are thought to hold the potential to speed up neural network training, but due to the enormous size of the curvature matrix, they typically require approximations to be computationally tractable. The most successful…

Machine Learning · Computer Science 2022-06-13 Frederik Benzing

Catastrophic forgetting remains a major challenge when neural networks learn tasks sequentially. Elastic Weight Consolidation (EWC) attempts to address this problem by introducing a Bayesian-inspired regularization loss to preserve…

Machine Learning · Computer Science 2025-03-27 Steven Vander Eeckt , Hugo Van hamme

Multi-task learning is useful in NLP because it is often practically desirable to have a single model that works across a range of tasks. In the medical domain, sequential training on tasks may sometimes be the only way to train models,…

Computation and Language · Computer Science 2021-11-12 Denis Jered McInerney , Luyang Kong , Kristjan Arumae , Byron Wallace , Parminder Bhatia
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