Tensor-Network Neural Pretraining With Low-Rank Gradient Updates
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Solution Overview
Problem
Large AI models require significant energy consumption and memory resources for training, making them computationally expensive and difficult to deploy on resource-constrained devices, and existing methods to reduce memory often compromise training accuracy or efficiency.
Innovation Solution
Pretraining neural networks using tensor train operators (TTOs) and low-rank factors, which represent parameters as T+U×VT, allowing for efficient computation of gradients and reducing memory footprint while maintaining optimization dynamics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional full-rank training methods are used, then training accuracy is maintained, but memory footprint and computational requirements become prohibitively large
Solution Approach 1:
The patent segments the weight matrix W into multiple parameter matrices {W1, W2, ..., Wk} through matrix factorization, where each Wi has dimensions compatible with the low-rank decomposition. This segmentation allows the model to maintain full-rank functionality while storing only the factor matrices, reducing memory requirements from O(mn) to O((m+n)r) where r is the rank parameter.
Solution Approach 2:
The patent changes the parameter representation from full-rank weight matrices to low-rank factor matrices. By parameterizing W as a product of lower-rank matrices, the system transforms the storage and computation from operating on large dense matrices to operating on smaller factor matrices, enabling efficient training while preserving accuracy through the mathematical equivalence of the factorization.
2Productivity
If memory footprint is reduced through low-rank approximation, then computational efficiency improves, but training accuracy may be compromised
Solution Approach 1:
The patent implements dynamic rank adjustment during training, where the effective rank r can be adaptively modified based on training progress and computational resources. This allows the system to start with higher ranks for accuracy and gradually reduce ranks for efficiency, or vice versa, maintaining the ability to preserve accuracy when needed while achieving computational efficiency when resources are constrained.
3Reliability
If full gradients are computed during backpropagation, then optimization dynamics are preserved, but computational and memory costs increase
Solution Approach 1:
The patent extracts and computes gradients only for the essential factor matrices rather than computing full gradients for all weight parameters. By taking out the gradient computation to only the factor matrices Wi that define the low-rank decomposition, the system preserves the optimization dynamics needed for convergence while eliminating redundant gradient computations, reducing computational cost from O(mn) to O((m+n)r).
Data Source
AI summary
Aspects of the present disclosure relate generally to systems and methods for pretraining a neural network. The method includes training the neural network configured to execute a type of inference. The method includes initializing a current parameter represented by T+U×VT. The T is a reduced structured representation of the current parameter, the U is a low-rank factor corresponding to a representation of a first portion of the current parameter with a dimension of n×r, and the VT is a low-rank factor corresponding to a representation of a second portion of the current parameter with a dimension of r×n. The method also includes projecting a full gradient G into a lower dimensional subspace. The method further includes updating the current parameter to an updated parameter represented by T+U′×VT and executing the type of inference on at least in part on a quantum computer based on the re-trained neural network.