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On the implementation of frontier-to-root tree automata in recursive neural networks

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3 Author(s)
Gori, M. ; Dipt. di Ingegneria dell''Inf., Siena Univ., Italy ; Kuchler, A. ; Sperduti, A.

We explore the node complexity of recursive neural network implementations of frontier-to-root tree automata (FRA). Specifically, we show that an FRAO (Mealy version) with m states, l input-output labels, and maximum rank N can be implemented by a recursive neural network with O(√(log l+log m)lmN/log l+N log m) units and four computational layers, i.e., without counting the input layer. A lower bound is derived which is tight when no restrictions are placed on the number of layers. Moreover, we present a construction with three computational layers having node complexity of O((log l+log m)√lm N) and O((log l+log m)lmN) connections. A construction with two computational layers is given that implements any given FRAO with a node complexity of O(lmN) and O((log l+log m)lmN) connections. As a corollary we also get a new upper bound for the implementation of finite-state automata into recurrent neural networks with three computational layers

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Neural Networks, IEEE Transactions on  (Volume:10 ,  Issue: 6 )