Tensor Regression Networks

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on flattened activation vectors. Despite empirical success, this approach has notable drawbacks. Flattening followed by fully connected layers discards multilinear structure in the activations and requires many parameters. We address these problems by incorporating tensor algebraic operations that preserve multilinear structure at every layer. First, we introduce Tensor Contraction Layers (TCLs) that reduce the dimensionality of their input while preserving their multilinear structure using tensor contraction. Next, we introduce Tensor Regression Layers (TRLs), which express outputs through a low-rank multilinear mapping from a high-order activation tensor to an output tensor of arbitrary order. We learn the contraction and regression factors end-to-end, and produce accurate nets with fewer parameters. Additionally, our layers regularize networks by imposing low-rank constraints on the activations (TCL) and regression weights (TRL). Experiments on ImageNet show that, applied to VGG and ResNet architectures, TCLs and TRLs reduce the number of parameters compared to fully connected layers by more than 65% while maintaining or increasing accuracy. In addition to the space savings, our approach's ability to leverage topological structure can be crucial for structured data such as MRI. In particular, we demonstrate significant performance improvements over comparable architectures on three tasks associated with the UK Biobank dataset

The Damaging Effects of Intersectionality and Layers of Oppression on United States Female Soccer Players

Black athletes face structural and overt racism in all sports across the country, in which the majority of White Americans either chooses to ignore or sometimes even use to victimize certain athletes. They are discriminated against because of the color of their skin, despite achieving the same levels of success and fame as their white competitors. Black athletes must work harder than white athletes for the same end goal, not because of any sort of athletic disadvantage, but because of racial injustice and intolerance. Soccer is a prime example of how Black athletes face racism in sport. Black female soccer players, however, face many more layers of oppression compared to not only Black male soccer players, but also their female counterparts. The lack of representation and involvement of Black female athlete in the sport of soccer shows the repercussions of these layers of oppression. The sport of soccer favors male athletes and their success, caters to middle- and upper-class families and individuals, and structural racism within athletics prefers white athletes