Fisher-Orthogonal Projected Natural Gradient Descent for Continual Learning

Fuente: arXiv
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Main Authors: Garg, Ishir, Kolhe, Neel, Peng, Andy, Gopalam, Rohan
Format: Preprint
Published: 2026
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author Garg, Ishir
Kolhe, Neel
Peng, Andy
Gopalam, Rohan
author_facet Garg, Ishir
Kolhe, Neel
Peng, Andy
Gopalam, Rohan
contents Continual learning aims to enable neural networks to acquire new knowledge on sequential tasks. However, the key challenge in such settings is to learn new tasks without catastrophically forgetting previously learned tasks. We propose the Fisher-Orthogonal Projected Natural Gradient Descent (FOPNG) optimizer, which enforces Fisher-orthogonal constraints on parameter updates to preserve old task performance while learning new tasks. Unlike existing methods that operate in Euclidean parameter space, FOPNG projects gradients onto the Fisher-orthogonal complement of previous task gradients. This approach unifies natural gradient descent with orthogonal gradient methods within an information-geometric framework. We provide theoretical analysis deriving the projected update, describe efficient and practical implementations using the diagonal Fisher, and demonstrate strong results on standard continual learning benchmarks such as Permuted-MNIST, Split-MNIST, Rotated-MNIST, Split-CIFAR10, and Split-CIFAR100. Our code is available at https://github.com/ishirgarg/FOPNG.
format Preprint
id arxiv_https___arxiv_org_abs_2601_12816
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Fisher-Orthogonal Projected Natural Gradient Descent for Continual Learning
Garg, Ishir
Kolhe, Neel
Peng, Andy
Gopalam, Rohan
Machine Learning
Artificial Intelligence
Continual learning aims to enable neural networks to acquire new knowledge on sequential tasks. However, the key challenge in such settings is to learn new tasks without catastrophically forgetting previously learned tasks. We propose the Fisher-Orthogonal Projected Natural Gradient Descent (FOPNG) optimizer, which enforces Fisher-orthogonal constraints on parameter updates to preserve old task performance while learning new tasks. Unlike existing methods that operate in Euclidean parameter space, FOPNG projects gradients onto the Fisher-orthogonal complement of previous task gradients. This approach unifies natural gradient descent with orthogonal gradient methods within an information-geometric framework. We provide theoretical analysis deriving the projected update, describe efficient and practical implementations using the diagonal Fisher, and demonstrate strong results on standard continual learning benchmarks such as Permuted-MNIST, Split-MNIST, Rotated-MNIST, Split-CIFAR10, and Split-CIFAR100. Our code is available at https://github.com/ishirgarg/FOPNG.
title Fisher-Orthogonal Projected Natural Gradient Descent for Continual Learning
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2601.12816