Volume-Preserving Neural Network Layers for Stable Deep Training
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Solution Overview
Problem
Deep neural networks face significant challenges with vanishing and exploding gradients, particularly in deep networks, which hinder effective training and performance in tasks like image recognition and natural language processing.
Innovation Solution
A volume-preserving artificial neural network (VPNN) architecture is introduced, utilizing rotation, permutation, and diagonal sublayers, along with coupled activation functions, to maintain gradient equilibrium and prevent vanishing or exploding gradients, ensuring consistent learning rates across layers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional deep neural networks are used with multiple layers, then the network can address complex machine learning problems, but gradient instability (vanishing and exploding gradients) occurs
Solution Approach 1:
The patent changes the parameters of the transformation layers from general linear transformations to volume-preserving transformations with specific structural constraints (rotation, permutation, diagonal components). This parameter change ensures that the determinant of the transformation matrix remains 1, preserving gradient magnitude and preventing vanishing or exploding gradients while maintaining the network's ability to learn complex functions
Solution Approach 2:
The patent segments the linear transformation layer into distinct sublayers: rotation sublayers, permutation sublayers, and diagonal sublayers. Each sublayer performs a specific function (rotation for feature mixing, permutation for reordering, diagonal for scaling) while collectively maintaining volume preservation. This segmentation allows independent optimization of each component while ensuring overall gradient stability
2Productivity
If the number of layers is increased to improve performance, then deeper networks can be built, but training reliability deteriorates due to gradient issues
Solution Approach 1:
The volume-preserving transformation ensures continuous and stable gradient flow through all layers during backpropagation. By maintaining determinant = 1, the gradient magnitude remains consistent across layers, enabling reliable training of deep networks without the degradation typically seen in traditional deep networks
3Reliability
If volume-preserving transformations are used, then gradient stability is improved, but the complexity of the transformation structure increases
Solution Approach 1:
The complex volume-preserving transformation is segmented into simpler, interpretable sublayers (rotation, permutation, diagonal). Each sublayer has a clear mathematical form and physical interpretation, making the overall complex transformation more manageable and easier to train while maintaining gradient stability
Solution Approach 2:
The patent introduces trainable parameters within the volume-preserving structure, allowing the network to dynamically adapt the rotation angles, permutation patterns, and diagonal scaling factors during training. This dynamic capability enables the network to learn optimal transformations for different tasks while maintaining the volume-preserving constraint
Data Source
AI summary
There is provided a volume preserving trainable artificial neural network and a system and a method for building a volume preserving trainable artificial neural network. In an aspect, an artificial neural network including: an input layer to receive input data; one or more sequentially connected hidden layers, the first hidden layer connected to the input layer, to perform operations on the input data, each hidden layer including: one or more volume-preserving rotation sublayers; one or more volume-preserving permutation sublayers; one or more volume-preserving diagonal sublayers; and an activation sublayer; and a downsizing output layer connected to the activation sublayer of the last hidden layer. In some cases, the activation sublayer includes a grouped activation function acting on a grouping of input variables to the activation sublayer.