Tensor Methods in Computer Vision and Deep Learning
- URL: http://arxiv.org/abs/2107.03436v1
- Date: Wed, 7 Jul 2021 18:42:45 GMT
- Title: Tensor Methods in Computer Vision and Deep Learning
- Authors: Yannis Panagakis, Jean Kossaifi, Grigorios G. Chrysos, James Oldfield,
Mihalis A. Nicolaou, Anima Anandkumar, Stefanos Zafeiriou
- Abstract summary: tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions.
With the advent of the deep learning paradigm shift in computer vision, tensors have become even more fundamental.
This article provides an in-depth and practical review of tensors and tensor methods in the context of representation learning and deep learning.
- Score: 120.3881619902096
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Tensors, or multidimensional arrays, are data structures that can naturally
represent visual data of multiple dimensions. Inherently able to efficiently
capture structured, latent semantic spaces and high-order interactions, tensors
have a long history of applications in a wide span of computer vision problems.
With the advent of the deep learning paradigm shift in computer vision, tensors
have become even more fundamental. Indeed, essential ingredients in modern deep
learning architectures, such as convolutions and attention mechanisms, can
readily be considered as tensor mappings. In effect, tensor methods are
increasingly finding significant applications in deep learning, including the
design of memory and compute efficient network architectures, improving
robustness to random noise and adversarial attacks, and aiding the theoretical
understanding of deep networks.
This article provides an in-depth and practical review of tensors and tensor
methods in the context of representation learning and deep learning, with a
particular focus on visual data analysis and computer vision applications.
Concretely, besides fundamental work in tensor-based visual data analysis
methods, we focus on recent developments that have brought on a gradual
increase of tensor methods, especially in deep learning architectures, and
their implications in computer vision applications. To further enable the
newcomer to grasp such concepts quickly, we provide companion Python notebooks,
covering key aspects of the paper and implementing them, step-by-step with
TensorLy.
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