Revisiting Gradient Descent: A Dual-Weight Method for Improved Learning

• URL: http://arxiv.org/abs/2503.11965v2
• Date: Tue, 18 Mar 2025 03:34:27 GMT
• Title: Revisiting Gradient Descent: A Dual-Weight Method for Improved Learning
• Authors: Xi Wang,
• Abstract summary: We introduce a novel framework for learning in neural networks by decomposing each neuron's weight vector into two distinct parts.<n>We show that this decomposition enhances generalization and resists overfitting, especially when training data are sparse or noisy.
• Score: 4.751362812627724
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a novel framework for learning in neural networks by decomposing each neuron's weight vector into two distinct parts, $W_1$ and $W_2$, thereby modeling contrastive information directly at the neuron level. Traditional gradient descent stores both positive (target) and negative (non-target) feature information in a single weight vector, often obscuring fine-grained distinctions. Our approach, by contrast, maintains separate updates for target and non-target features, ultimately forming a single effective weight $W = W_1 - W_2$ that is more robust to noise and class imbalance. Experimental results on both regression (California Housing, Wine Quality) and classification (MNIST, Fashion-MNIST, CIFAR-10) tasks suggest that this decomposition enhances generalization and resists overfitting, especially when training data are sparse or noisy. Crucially, the inference complexity remains the same as in the standard $WX + \text{bias}$ setup, offering a practical solution for improved learning without additional inference-time overhead.

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