João Pedro Neto

Symbolic processing in neural networks

In this paper we show that programming languages can be translated into recurrent (analog, rational weighted) neural nets. Implementation of programming languages in neural nets turns to be not only theoretical exciting, but has also some practical implications in the recent efforts to merge symbolic and sub symbolic computation. To be of some use, it should be carried in a context of bounded resources. Herein, we show how to use resource bounds to speed up computations over neural nets, through suitable data type coding like in the usual programming languages. We introduce data types and show how to code and keep them inside the information flow of neural nets. Data types and control structures are part of a suitable programming language called NETDEF. Each NETDEF program has a specific neural net that computes it. These nets have a strong modular structure and a synchronization mechanism allowing sequential or parallel execution of subnets, despite the massive parallel feature of neural nets. Each instruction denotes an independent neural net. There are constructors for assignment, conditional and loop instructions. Besides the language core, many other features are possible using the same method.

Turing Universality of Neural Nets (Revisited)

We show how to use recursive function theory to prove Turing universality of finite analog recurrent neural nets, with a piecewise linear sigmoid function as activation function. We emphasize the modular construction of nets within nets, a relevant issue from the software engineering point of view.

Multi-agent learning: how to interact to improve collective results

The evolution from individual to collective learning opens a new dimension of solutions to address problems that appeal for gradual adaptation in dynamic and unpredictable environments. A team of individuals has the potential to outperform any sum of isolated efforts, and that potential is materialized when a good system of interaction is considered. In this paper, we describe two forms of cooperation that allow multi-agent learning: the sharing of partial results obtained during the learning activity, and the social adaptation to the stages of collective learning. We consider different ways of sharing information and different options for social reconfiguration, and apply them to the same learning problem. The results show the effects of cooperation and help to put in perspective important properties of the collective learning activity.

A virtual machine for neural computers

Neural Networks are mainly seen as algorithmic solutions for optimization and learning tasks where the ability to spread the acquired knowledge into several neurons, i.e., the use of sub-symbolic computation, is the key. We have shown in previous works that neural networks can perform other types of computation, namely symbolic and chaotic computations. Here in, we show how these nets can be decomposed into tuples which can be efficient calculated by software or hardware simpler than previous neural solutions.

ON COMPUTATION OVER CHAOS USING NEURAL NETWORKS: APPLICATION TO BLIND SEARCH AND RANDOM NUMBER GENERATION

This paper deals with computation over dynamical analog systems, exploring applications of chaos. The dynamical system used is an artificial neural network model that can code any symbolic algorithm. Herein, we propose the integration of chaotic dynamics onto this model, to implement computational tasks, namely, a blind search algorithm and a pseudo-random number generator.

Enhancing Modularity and Feedback in Computer Aided Assessment

We present a model of a computer aided assessment system - CATS (computer assessable task system) - for mathematics, which is both modular and has rich feedback. Modular in the sense that elaborated tasks need not be built from scratch but, instead, from already existing tasks. Modules are made general enough to be reusable in many different contexts. As a consequence, the construction and management of multiple-step problems with complex system-user interaction, is facilitated for non-expert users. By rich feedback we mean that the system automatically generates messages explaining errors, whenever students make algebraic manipulation and logical mistakes. This contrasts with current assessment software where feedback must be hard coded by the teacher, therefore constraining feedback richness by the teacher programming skills

Ordinal sums of impartial games

Abstract In an ordinal sum of two combinatorial games G and H , denoted by G : H , a player may move in either G (base) or H (subordinate), with the additional constraint that any move on G completely annihilates the component H . It is well-known that the ordinal sum does not depend on the form of its subordinate, but depends on the form of its base. In this work, we analyze G ( G : H ) where G and H are impartial forms, observing that the G -values are related to the concept of minimum excluded value of order k . As a case study, we introduce the ruleset oak , a generalization of green hackenbush . By defining the operation gin sum, it is possible to determine the literal forms of the bases in polynomial time.

A method for regularization of evolutionary polynomial regression

Display Omitted A regularization term is proposed to control complexity in polynomial regression using genetic algorithms.Regularization reduces out-of-sample error with respect to polynomials found by non-regularized methods.Regularization improves convergence speed.Error performance is empirically evaluated on some common datasets versus standard regression methods. While many applications require models that have no acceptable linear approximation, the simpler nonlinear models are defined by polynomials. The use of genetic algorithms to find polynomial models from data is known as evolutionary polynomial regression (EPR). This paper introduces evolutionary polynomial regression with regularization, an algorithm extending EPR with a regularization term to control polynomial complexity. The article also describes a set of experiences to compare both flavors of EPR against other methods including linear regression, regression trees and support vector regression. These experiments show that evolutionary polynomial regression with regularization is able to achieve better fitting and needs less computation time than plain EPR.

A recursive process related to a partisan variation of Wythoff

Abstract. Wythoff Queens is a classical combinatorial game related to very interesting mathematical results. An amazing one is the fact that the -positions are given by and where . In this paper, we analyze a different version where one player (Left) plays with a chess bishop and the other (Right) plays with a chess knight. The new game (call it Chessfights) lacks a Beatty sequence structure in the -positions as in Wythoff Queens. However, it is possible to formulate and prove some general results of a general recursive law which is a particular case of a Partizan Subtraction game.

Parallelization of algorithms with recurrent neural networks

Neural networks can be used to describe symbolic algorithms like those specified in high-level programming languages. This article shows how to translate these network description of algorithms into a more suitable format in order to feed an arbitrary number of parallel processors to speed-up the computation of sequential and parallel algorithms.