Advanced structural matrix approximations can be employed as a technique to reduce the high parametrization and computational cost of fully connected layers in deep learning models.

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The high computational cost of transforming $$d$$ inputs into $$q$$ outputs in a fully connected layer can be mitigated through various approximation and compression techniques. These methods generally trade a small degree of accuracy for significant improvements in computational and storage efficiency.

Reducing Computational Cost of Fully Connected Layers

Dive into Deep Learning

Deep Fried Convnets are a neural network architecture approach that reduces the computational cost of fully connected layers from quadratic to log-linear. This is achieved by using a combination of permutations, Fourier transforms, and scaling.

Deep Fried Convnets

Structural Matrix Approximations for Neural Networks

Quaternion-like decompositions can be used to compress fully connected layers, reducing their computational cost from $$\mathcal{O}(dq)$$ to $$\mathcal{O}(\frac{dq}{n})$$. This technique relies on a compression factor $$n$$, allowing models to trade off a minor amount of accuracy for improved computational and storage efficiency.

Quaternion-like Decompositions for Cost Reduction

When designing techniques to reduce the computational cost of neural network layers, a major challenge is that the most compact mathematical representation or the smallest number of floating-point operations does not always translate to the best performance. Instead, research focuses on finding solutions that can be executed most efficiently on modern GPU hardware.

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