Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

Dimensions of Neural-symbolic Integration - A Structured Survey

Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. We present a comprehensive survey of the field of neural-symbolic integration, including a new classification of system according to their architectures and abilities.Comment: 28 page

AI Methods in Algorithmic Composition: A Comprehensive Survey

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.This study was partially supported by a grant for the MELOMICS project (IPT-300000-2010-010) from the Spanish Ministerio de Ciencia e Innovación, and a grant for the CAUCE project (TSI-090302-2011-8) from the Spanish Ministerio de Industria, Turismo y Comercio. The first author was supported by a grant for the GENEX project (P09-TIC- 5123) from the Consejería de Innovación y Ciencia de Andalucía

A modular architecture for transparent computation in recurrent neural networks

publisher: Elsevier articletitle: A modular architecture for transparent computation in recurrent neural networks journaltitle: Neural Networks articlelink: http://dx.doi.org/10.1016/j.neunet.2016.09.001 content_type: article copyright: © 2016 Elsevier Ltd. All rights reserved

Non-Direct Encoding Method Based on Cellular Automata to Design Neural Network Architectures

Architecture design is a fundamental step in the successful application of Feed forward Neural Networks. In most cases a large number of neural networks architectures suitable to solve a problem exist and the architecture design is, unfortunately, still a human expert’s job. It depends heavily on the expert and on a tedious trial-and-error process. In the last years, many works have been focused on automatic resolution of the design of neural network architectures. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability; thus, for representing large architectures very large structures are required. More interesting alternatives are represented by indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is proposed. This scheme is based on cellular automata representations and is inspired by the idea that only a few seeds for the initial configuration of a cellular automaton can produce a wide variety of feed forward neural networks architectures. The cellular approach is experimentally validated in different domains and compared with a direct codification scheme.Publicad