Symmetric Rank-One Quasi-Newton Methods for Deep Learning Using Cubic Regularization Article Swipe
Aditya Ranganath
,
Mukesh Singhal
,
Roummel F. Marcia
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.12298
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.12298
Stochastic gradient descent and other first-order variants, such as Adam and AdaGrad, are commonly used in the field of deep learning due to their computational efficiency and low-storage memory requirements. However, these methods do not exploit curvature information. Consequently, iterates can converge to saddle points or poor local minima. On the other hand, Quasi-Newton methods compute Hessian approximations which exploit this information with a comparable computational budget. Quasi-Newton methods re-use previously computed iterates and gradients to compute a low-rank structured update. The most widely used quasi-Newton update is the L-BFGS, which guarantees a positive semi-definite Hessian approximation, making it suitable in a line search setting. However, the loss functions in DNNs are non-convex, where the Hessian is potentially non-positive definite. In this paper, we propose using a limited-memory symmetric rank-one quasi-Newton approach which allows for indefinite Hessian approximations, enabling directions of negative curvature to be exploited. Furthermore, we use a modified adaptive regularized cubics approach, which generates a sequence of cubic subproblems that have closed-form solutions with suitable regularization choices. We investigate the performance of our proposed method on autoencoders and feed-forward neural network models and compare our approach to state-of-the-art first-order adaptive stochastic methods as well as other quasi-Newton methods.x
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2502.12298
- https://arxiv.org/pdf/2502.12298
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4407759309
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https://openalex.org/W4407759309Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2502.12298Digital Object Identifier
- Title
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Symmetric Rank-One Quasi-Newton Methods for Deep Learning Using Cubic RegularizationWork title
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preprintOpenAlex work type
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enPrimary language
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2025Year of publication
- Publication date
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2025-02-17Full publication date if available
- Authors
-
Aditya Ranganath, Mukesh Singhal, Roummel F. MarciaList of authors in order
- Landing page
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https://arxiv.org/abs/2502.12298Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2502.12298Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2502.12298Direct OA link when available
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Regularization (linguistics), Rank (graph theory), Mathematics, Applied mathematics, Combinatorics, Computer science, Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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