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Technical Program

Paper Detail

Paper IDD3-S1-T3.2
Paper Title Neural Network Computations with DOMINATION Functions
Authors Kordag Mehmet Kilic, Jehoshua Bruck, California Institute of Technology, United States
Session D3-S1-T3: Neural Estimation
Chaired Session: Wednesday, 14 July, 22:00 - 22:20
Engagement Session: Wednesday, 14 July, 22:20 - 22:40
Abstract We study a new representation of neural networks based on DOMINATION functions. Specifically, we show that a threshold function can be computed by its variables connected via an unweighted bipartite graph to a universal gate computing a DOMINATION function. The DOMINATION function consists of fixed weights that are ascending powers of 2. We derive circuit-size upper and lower bounds for circuits with small weights that compute DOMINATION functions. Interestingly,the circuit-size bounds are dependent on the sparsity of the bipartite graph. In particular, functions with sparsity 1 (like the EQUALITY function) can be implemented by small-size constant-weight circuits.