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

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.

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.

GPU Efficiency in Neural Network Cost Reduction

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.

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For any fully connected neural network layer with $$d$$ inputs and $$q$$ outputs, the parametrization and computational cost is quadratic, specifically $$\mathcal{O}(dq)$$. This high cost can become prohibitive in practical deep learning applications.

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