A general-purpose toolbox for efficient Kronecker-based learning

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The Open Journal

Reference7 articles.

1. Effective Extensible Programming: Unleashing Julia on GPUs

2. Scientific computing is increasingly incorporating the advancements in machine learning and the ability to work with large amounts of data. At the same time, machine learning models are becoming increasingly sophisticated and exhibit many features often seen in scientific computing, stressing the capabilities of machine learning frameworks. Just as the disciplines of scientific computing and machine learning have shared common underlying infrastructure in the form of numerical linear algebra, we now have the opportunity to further share new computational infrastructure, and thus ideas, in the form of Differentiable Programming. We describe Zygote, a Differentiable Programming system that is able to take gradients of general program structures. We implement this system in the Julia programming language. Our system supports almost all language constructs (control flow, recursion, mutation, etc.) and compiles high-performance code without requiring any user intervention or refactoring to stage computations. This enables an expressive programming model for deep learning, but more importantly, it enables us to incorporate a large ecosystem of libraries in our models in a straightforward way. We discuss our approach to automatic differentiation, including its support for advanced techniques such as mixed-mode, complex and checkpointed differentiation, and present several examples of differentiating programs., arXiv, 1907.07587, Innes, Mike and Edelman, Alan and Fischer, Keno and Rackauckas, Chris and Saba, Elliot and Shah, Viral B and Tebbutt, Will, 1907.07587, :Users/michielstock/Library/Application Support/Mendeley Desktop/Downloaded/Innes et al. - Unknown - ∂P A Differentiable Programming System to Bridge Machine Learning and Scientific Computing.pdf:pdf, A differentiable programming system to bridge machine learning and scientific computing, https://arxiv.org/pdf/1907.07587.pdf http://arxiv.org/abs/1907.07587, 2019

3. In this paper, we review basic properties of the Kronecker product, and give an overview of its history and applications. We then move on to introducing the symmetric Kronecker product, and we derive sev- eral of its properties. Furthermore, we show its application in finding search directions in semidefinite programming., Schäcke, Kathrin, :Users/michielstock/Library/Application Support/Mendeley Desktop/Downloaded/Schäcke - 2013 - On the Kronecker Product.pdf:pdf, 1–35, On the Kronecker Product, https://www.math.uwaterloo.ca/ hwolkowi/henry/reports/kronthesisschaecke04.pdf, 2013

4. A Comparative Study of Pairwise Learning Methods Based on Kernel Ridge Regression

5. Fast Kronecker Product Kernel Methods via Generalized Vec Trick

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