One Analog Neuron Cannot Recognize Deterministic Context-Free Languages

0505945 - ÚI 2020 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
Šíma, Jiří - Plátek, Martin
One Analog Neuron Cannot Recognize Deterministic Context-Free Languages.
Neural Information Processing. Proceedings, Part III. Heidelberg: Springer, 2019 - (Gedeon, T.; Wong, K.; Lee, M.), s. 77-89. Lecture Notes on Computer Science, 11955. ISBN 978-3-030-36717-6.
[ICONIP 2019. International Conference on Neural Information Processing of the Asia-Pacific Neural Network /26./. Sydney (AU), 12.12.2019-15.12.2019]
Grant CEP: GA ČR(CZ) GA19-05704S
Institucionální podpora: RVO:67985807
Klíčová slova: Neural computing * Analog neuron hierarchy * Deterministic context-free language * Restart automaton * Chomsky hierarchy
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
https://www.springer.com/gp/book/9783030367176

We analyze the computational power of discrete-time recurrent neural networks (NNs) with the saturated-linear activation function within the Chomsky hierarchy. This model restricted to integer weights coincides with binary-state NNs with the Heaviside activation function, which are equivalent to finite automata (Chomsky level 3), while rational weights make this model Turing complete even for three analog-state units (Chomsky level 0). For an intermediate model alphaANN of a binary-state NN that is extended with alpha>=0 extra analog-state neurons with rational weights, we have established the analog neuron hierarchy 0ANNs subset 1ANNs subset 2ANNs subseteq 3ANNs. The separation 1ANNs subsetneq 2ANNs has been witnessed by the deterministic context-free language (DCFL) L_#={0^n1^n|n>=1} which cannot be recognized by any 1ANN even with real weights, while any DCFL (Chomsky level 2) is accepted by a 2ANN with rational weights. In this paper, we generalize this result by showing that any non-regular DCFL cannot be recognized by 1ANNs with real weights, which means (DCFLs-REG) subset (2ANNs-1ANNs), implying 0ANNs = 1ANNs cap DCFLs. For this purpose, we show that L_# is the simplest non-regular DCFL by reducing L_# to any language in this class, which is by itself an interesting achievement in computability theory.
Trvalý link: http://hdl.handle.net/11104/0297270