"Reconstructing Deep Neural Networks: Unleashing the Optimization Potential of Natural Gradient Descent"

Smart network reconstruction makes advanced optimization accessible for deep learning.

Natural Gradient Descent training is now faster and more efficient through a novel network reconstruction approach that breaks down complex calculations into simpler local computations.

https://arxiv.org/abs/2412.07441v1

🤔 Original Problem:

Natural Gradient Descent (NGD) offers superior optimization but calculating inverse Fisher matrices makes it computationally expensive for deep neural networks.

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🔧 Solution in this Paper:

→ Introduces Structured Natural Gradient Descent (SNGD) that reconstructs networks with local Fisher layers

→ Decomposes global Fisher matrix calculations into efficient local computations

→ Transforms parameter matrices using G^(-1/2) normalization sub-layers

→ Optimizes new weight parameters using traditional gradient descent

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💡 Key Insights:

→ NGD optimization equals fast gradient descent on reconstructed networks

→ Local Fisher layers provide curvature signals and regularization effects

→ Method universally applies across MLP, CNN, LSTM architectures

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📊 Results:

→ MNIST: 97.6% test accuracy vs 96.3% for KFAC and 94.8% for SGD

→ CIFAR-10: ResNet-18 achieves 94.44% vs SGD (93.02%) and Adam (92.93%)

→ ImageNet: 73.41% top-1 accuracy, beating SGD (70.23%) and Adam (63.79%)

→ Comparable training time to first-order optimizers despite better performance