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A Mean Field Theory of Quantized Deep Networks: The Quantization-Depth Trade-Off
Yaniv Blumenfeld · Dar Gilboa · Daniel Soudry

Thu Dec 12 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #154
Reducing the precision of weights and activation functions in neural network training, with minimal impact on performance, is essential for the deployment of these models in resource-constrained environments. We apply mean field techniques to networks with quantized activations in order to evaluate the degree to which quantization degrades signal propagation at initialization. We derive initialization schemes which maximize signal propagation in such networks, and suggest why this is helpful for generalization. Building on these results, we obtain a closed form implicit equation for $L_{\max}$, the maximal trainable depth (and hence model capacity), given $N$, the number of quantization levels in the activation function. Solving this equation numerically, we obtain asymptotically: $L_{\max}\propto N^{1.82}$.

Author Information

Yaniv Blumenfeld (Technion)
Dar Gilboa (Columbia University)
Daniel Soudry (Technion)

I am an assistant professor in the Department of Electrical Engineering at the Technion, working in the areas of Machine learning and theoretical neuroscience. I am especially interested in all aspects of neural networks and deep learning. I did my post-doc (as a Gruss Lipper fellow) working with Prof. Liam Paninski in the Department of Statistics, the Center for Theoretical Neuroscience the Grossman Center for Statistics of the Mind, the Kavli Institute for Brain Science, and the NeuroTechnology Center at Columbia University. I did my Ph.D. (2008-2013, direct track) in the Network Biology Research Laboratory in the Department of Electrical Engineering at the Technion, Israel Institute of technology, under the guidance of Prof. Ron Meir. In 2008 I graduated summa cum laude with a B.Sc. in Electrical Engineering and a B.Sc. in Physics, after studying in the Technion since 2004.

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