Kronecker Neural Network Weight Segmentation for Resource Reduction
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Solution Overview
Problem
As neural networks (NNs) become larger and more complex, they require significant computational resources and memory, making them costly and difficult to deploy on resource-constrained hardware devices for inference tasks.
Innovation Solution
The method involves training a Kronecker neural network (KNN) using knowledge distillation, which includes one or more Kronecker layers that perform matrix multiplications using Kronecker product values, reducing the computational resources needed while maintaining similar performance to the original NN.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a neural network is made larger and more complex to improve performance, then inference accuracy is improved, but computational resources and memory requirements increase
Solution Approach 1:
The patent segments the weight matrix W into two smaller matrices A and B such that W ≈ A ⊗ B (Kronecker product). This segmentation reduces the storage requirements from O(n²) to O(n√n) while maintaining approximate inference accuracy, directly resolving the contradiction between model size and resource consumption.
Solution Approach 2:
The patent changes the parameter representation from a dense n×n weight matrix to two √n×√n matrices with Kronecker product structure. This parameter transformation maintains the functional capability of the neural network while significantly reducing the number of parameters that need to be stored and computed, thereby reducing computational resources.
2Measurement precision
If a neural network is made larger and more complex to improve performance, then inference accuracy is improved, but memory requirements increase
Solution Approach 1:
The weight matrix is segmented into two smaller matrices whose Kronecker product approximates the original matrix. This segmentation reduces memory requirements from storing n² values to storing 2n values (for two √n×√n matrices), enabling deployment on memory-constrained devices while preserving inference accuracy.
Solution Approach 2:
The patent transforms the storage dimensionality from a 2D n×n matrix to two separate √n×√n matrices. This dimensional reorganization allows the same information to be represented with fewer elements, reducing memory requirements while maintaining the network's computational capability.
3Ease of operation
If traditional matrix multiplication is used in neural network layers, then computation is straightforward, but computational efficiency decreases
Solution Approach 1:
The patent changes the computation from standard matrix multiplication using a dense weight matrix to Kronecker product-based multiplication using two smaller matrices. This parameter change reduces the computational complexity from O(n²m) to O(n√n·m) while maintaining computational simplicity through the structured factorization.
Data Source
AI summary
Methods and systems for compressing a neural network (NN) which performs an inference task and for performing computations of a Kronecker layer of a Kronecker NN are described. Data samples are obtained from a training dataset. The input data of the data samples are inputted into a trained NN to generate NN predictions for the input data. Further, the input data are inputted into a Kronecker NN to generate Kronecker NN predictions for the input data. Two losses are computed: a knowledge distillation loss, based on outputs generated by a layer of the NN and a corresponding Kronecker layer of the Kronecker NN and a loss for Kronecker layer, based on the Kronecker NN predictions and ground-truth labels of the data samples. The two losses are combined into a total loss, which is propagated through the Kronecker NN to adjust values of learnable parameters of the Kronecker NN.