Fixed Recurrent Matrices for Neural Network Dimensionality
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Solution Overview
Problem
The high computational cost of running neural networks due to the large number of learned parameters in weight matrices, which complicates the process of high-dimensional vector-matrix multiplications during inference and training.
Innovation Solution
A neural network configuration involving an input layer, a hidden layer with sparse connections, and an output layer, where a subset of hidden nodes are not connected to the input layer, using a fixed recurrent matrix Wrec for matrix vector multiplications to increase dimensionality without additional training costs, allowing for efficient matrix operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of learned parameters in weight matrices is increased to improve network performance, then the computational cost and complexity of vector-matrix multiplications increases
Solution Approach 1:
The patent segments the weight matrix into two distinct parts: a fixed matrix Wfix that remains unchanged during training, and a learned matrix Wlearn that contains the trainable parameters. This segmentation allows the network to achieve high-dimensional transformations without requiring all parameters to be learned, thereby reducing computational complexity while maintaining performance.
Solution Approach 2:
The patent extracts the recurrent connection weights from the set of trainable parameters and designates them as a fixed matrix Wfix. By taking out these weights from the learning process and keeping them fixed, the system reduces the number of parameters that need to be optimized during training,从而降低 computational burden while still providing dimensional expansion functionality.
2Reliability
If the dimensionality of the hidden layer is increased to improve network performance, then the number of parameters and training cost increases
Solution Approach 1:
The fixed matrix Wfix serves multiple functions simultaneously: it acts as the recurrent connection matrix for temporal dependencies, serves as a dimensional expansion mechanism, and provides a structured prior that guides learning. This multi-functionality allows the system to achieve high dimensionality without proportionally increasing the number of trainable parameters.
Solution Approach 2:
The patent changes the status of certain parameters from trainable to fixed. By designating Wfix as a fixed matrix with predetermined values (often initialized randomly but kept constant), the system transforms what would normally be high-dimensional trainable parameters into a fixed transformation structure, thereby reducing the quantity of parameters that need to be learned.
3Productivity
If fixed weights are used in the recurrent matrix to reduce training costs, then the adaptability of the network may be reduced
Solution Approach 1:
The patent merges the recurrent connection mechanism with a fixed transformation matrix. By combining these two functions into a single fixed matrix Wfix, the system achieves both temporal recurrence and dimensional expansion without requiring separate learned parameters for each function, thereby maintaining training efficiency while preserving adaptability through the learned matrix Wlearn.
Solution Approach 2:
The fixed matrix Wfix acts as an intermediary that bridges the input space and hidden state space with a predetermined transformation. This intermediary structure provides a stable, reusable transformation that does not require relearning at each training step, while the learned matrix Wlearn adapts to specific tasks, thus balancing efficiency and adaptability.
Data Source
AI summary
A method of operating a neural network. The input layer of the network may have n input nodes connected to output nodes via a hidden layer. The hidden layer may include m hidden nodes. The n input nodes may connect to a subset of k nodes of the m hidden nodes via respective synaptic connections, to which training weights are associated, which form an n×k input matrix Win, whereas a subset of m−k nodes of the hidden layer are not connected by any node of the input layer. Running the network may include performing a first matrix vector multiplication between the input matrix Win and a vector of values obtained in output of the input nodes and a second matrix vector multiplication between a fixed matrix Wrec of fixed weights and a vector of values obtained in output of the m nodes of the hidden layer.