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The perceptron strikes back
Abstract: "We show that circuits composed of a symmetric gate at the root with AND-OR subcircuits of constant depth can be simulated by probabilistic depth-2 circuits with essentially the same symmetric gate at the root and AND gates of small fanin at the bottom. In particular, every language recognized by a depth-d AC⁰ circuit is decidable by a probabilistic perceptron of size 2[superscript O(log 5d n)] and order O(log[superscript 5d] n) that uses O(log³n) probabilistic bits. As a corollary, we present a new proof that depth-d AND-OR circuits computing the parity of n binary inputs require size 2[superscript n omega](1/d)]."
- "Abstract: "We show that circuits composed of a symmetric gate at the root with AND-OR subcircuits of constant depth can be simulated by probabilistic depth-2 circuits with essentially the same symmetric gate at the root and AND gates of small fanin at the bottom. In particular, every language recognized by a depth-d AC⁰ circuit is decidable by a probabilistic perceptron of size 2[superscript O(log 5d n)] and order O(log[superscript 5d] n) that uses O(log³n) probabilistic bits. As a corollary, we present a new proof that depth-d AND-OR circuits computing the parity of n binary inputs require size 2[superscript n omega](1/d)].""@en
- "The perceptron strikes back"@en
- "The perceptron strikes back"