Optimal Architectures in a Solvable Model of Deep Networks

Authors: Jonathan Kadmon, Haim Sompolinsky

NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Figure 2: Overlap dynamics. (A) Trajectory of overlaps across layers from eq (8)-(11) (solid lines) and simulations (circles). Dashed red line show the predicted separatrix m . The deviation from the theoretical prediction near the separatrix are due to final size effects of the simulations ( = 0.4, f = 0.1). (B) Basin of attraction for two values of f as a function of . Line show theoretical prediction and shaded area simulations. (C) Convergence time (number of layers) of the m = 1 attractor. Near the unstable fixed point (dashed vertical lines) convergence time diverges and rapidly decreases for larger initial conditions, m0 > m . In figure 4, two networks were trained as autoencoders on a set of templates composed of 3-digit numbers (See experimental procedures in the supplementary material). Both networks have the same number of neurons. In the first, all processing neurons are placed in a single wide layer, while in the other neurons were divided into 10 equally-sized layers. As the theory predicts, the deep structure is able to reproduce the original templates for a wide range of initial noise, while the single layer typically reduces the noise but fails to reproduce the original image.
Researcher Affiliation Academia Jonathan Kadmon The Racah Institute of Physics and ELSC The Hebrew University, Israel jonathan.kadmon@mail.huji.ac.il Haim Sompolinsky The Racah Institute of Physics and ELSC The Hebrew University, Israel and Center for Brain Science Harvard University
Pseudocode No The paper describes the mathematical model and equations (8)-(11) but does not provide any explicitly labeled pseudocode or algorithm blocks.
Open Source Code No In figure 4, two networks were trained as autoencoders on a set of templates composed of 3-digit numbers (See experimental procedures in the supplementary material).
Open Datasets Yes In figure 4, two networks were trained as autoencoders on a set of templates composed of 3-digit numbers (See experimental procedures in the supplementary material). Input data was prepared using the MNIST handwritten digit database.
Dataset Splits No Input data was prepared using the MNIST handwritten digit database.
Hardware Specification No The paper does not provide any specific hardware details such as GPU models, CPU types, or memory specifications used for running the experiments or simulations.
Software Dependencies No The paper does not specify any software dependencies with version numbers (e.g., programming languages, libraries, or frameworks with their respective versions) that would be needed to replicate the experiments.
Experiment Setup No In figure 4, two networks were trained as autoencoders on a set of templates composed of 3-digit numbers (See experimental procedures in the supplementary material).