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A Mean Field Theory of Quantized Deep Networks: The Quantization-Depth Trade-Off
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use theory-derived initialization with optimized normalized activation spacing | Quantized fully connected networks · MNIST | trainable depth | Helped |
| Increase the number of activation states | Quantized feed-forward networks · MNIST | maximal trainable depth: L_{\max}\sim3\left(N+1\right)^{1.82} | Helped |
| Set the bias variance to zero (ablation) | Quantized activation networks · Signal propagation | depth scale | Helped |
| Add stochastic rounding noise to sign activations (ablation) | Sign activation networks · Signal propagation | fixed-point slope | Hurt |
| Replace constant-spaced activations with tested linear-spacing activations (ablation) | Quantized activation networks · Signal propagation | depth scale | No clear effect |
| Use a critical initialization that maximizes signal propagation | Wide, deep neural networks · Early-stage training | generalization error | Helped |
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