Neural Network Training via Batched Orthogonal Matrices
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Solution Overview
Problem
Neural networks with increasing complexity face challenges in environments with low storage and computational power, as they require significant memory and computations, hindering their usage in resource-constrained settings, and orthogonal parameterizations are underutilized due to sequential transformations in vectorized compute architectures.
Innovation Solution
A method for training neural networks using vectorized compute architectures by processing orthogonal weight matrices in parallel through batched computations, employing Singular Value Decomposition (SVD) and Tensor Train Decomposition (TTD) for parameterization, and utilizing Householder transformations to enhance efficiency and scalability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If orthogonal parameterizations are used to improve training stability, then training stability is improved, but the sequential nature of transformations reduces computational efficiency in vectorized architectures
Solution Approach 1:
The patent combines multiple orthogonal parameterization transformations into a single batched operation that processes multiple weight matrices simultaneously. By merging the sequential transformations into a unified batched computation, the system maintains the stability benefits of orthogonal parameterizations while achieving parallel execution compatible with vectorized compute architectures.
Solution Approach 2:
The patent introduces a batch dimension to the transformation process, transitioning from processing single weight matrices sequentially to processing batches of weight matrices in parallel. This dimensional extension enables the use of vectorized compute architectures while preserving the orthogonal parameterization properties that ensure training stability.
2Adaptability or versatility
If neural network complexity increases to solve more complex problems, then problem-solving capability is improved, but memory and computational requirements increase, hindering usage in resource-constrained environments
Solution Approach 1:
The patent segments the neural network weight matrices into batches that can be processed independently and in parallel. This segmentation allows the system to handle large-scale neural networks by dividing them into manageable chunks, reducing the memory footprint and computational burden on resource-constrained devices while maintaining the ability to solve complex problems.
Solution Approach 2:
The patent changes the parameterization approach from standard weight matrices to orthogonal parameterizations with batched transformations. This parameter change enables more efficient memory utilization and computation, allowing complex neural networks to run in resource-constrained environments by reducing the effective resource requirements through mathematical reparameterization.
3Productivity
If batched computations are used to improve vectorized architecture efficiency, then computational efficiency is improved, but the complexity of implementing batched orthogonal transformations increases
Solution Approach 1:
The patent develops a universal batched transformation framework that handles multiple orthogonal parameterization types (such as QR decomposition, singular value decomposition, and Jacobi rotations) through a single unified implementation. This multi-functional approach enables efficient batched processing while reducing implementation complexity by providing a general-purpose solution that works across different orthogonal transformation methods.
Data Source
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AI summary
A computer-implemented method for training a neural network using a vectorized compute architecture, the neural network having a plurality of layers associated with a respective plurality of weight matrices, comprising: obtaining a data sample from a dataset, the data sample including an input and an expected output of the neural network; and computing a predicted output by applying the neural network, as parameterized by parameterization configurations resulting from processing the plurality of weight matrices, to the data sample, wherein computing the predicted output comprises: reading a batch of parameterization configurations from memory, the read batch comprising parameterization configurations of a plurality of orthogonal matrices; and executing a function expression associated with the read batch to compute simultaneously the plurality of orthogonal matrices.