Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with depth separation:
TR18-062 | 7th April 2018
Suryajith Chillara, Christian Engels, Nutan Limaye, Srikanth Srinivasan

A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits

We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting.

We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log n),$ there is an explicit multilinear polynomial $P^{(\Delta)}$ on $n$ variables that ... more >>>

TR20-085 | 5th June 2020
Gal Vardi, Ohad Shamir

Neural Networks with Small Weights and Depth-Separation Barriers

In studying the expressiveness of neural networks, an important question is whether there are functions which can only be approximated by sufficiently deep networks, assuming their size is bounded. However, for constant depths, existing results are limited to depths $2$ and $3$, and achieving results for higher depths has been ... more >>>

ISSN 1433-8092 | Imprint