Optical computing by injection-locked lasers

A programmable optical computer has remained an elusive concept. To construct a practical computing primitive equivalent to an electronic Boolean logic, one should find a nonlinear phenomenon that overcomes weaknesses present in many optical processing schemes. Ideally, the nonlinearity should provide a functionally complete set of logic operations, enable ultrafast all-optical programmability, and allow cascaded operations without a change in the operating wavelength or in the signal encoding format. Here we demonstrate a programmable logic gate using an injection-locked Vertical-Cavity Surface-Emitting Laser (VCSEL). The gate program is switched between the AND and the OR operations at the rate of 1 GHz with Bit Error Ratio (BER) of 10e-6 without changes in the wavelength or in the signal encoding format. The scheme is based on nonlinearity of normalization operations, which can be used to construct any continuous complex function or operation, Boolean or otherwise.Comment: 47 pages, 7 figures in total, 2 tables. Intended for submission to Nature Physics within the next two week

Provably Stable Interpretable Encodings of Context Free Grammars in RNNs with a Differentiable Stack

Given a collection of strings belonging to a context free grammar (CFG) and another collection of strings not belonging to the CFG, how might one infer the grammar? This is the problem of grammatical inference. Since CFGs are the languages recognized by pushdown automata (PDA), it suffices to determine the state transition rules and stack action rules of the corresponding PDA. An approach would be to train a recurrent neural network (RNN) to classify the sample data and attempt to extract these PDA rules. But neural networks are not a priori aware of the structure of a PDA and would likely require many samples to infer this structure. Furthermore, extracting the PDA rules from the RNN is nontrivial. We build a RNN specifically structured like a PDA, where weights correspond directly to the PDA rules. This requires a stack architecture that is somehow differentiable (to enable gradient-based learning) and stable (an unstable stack will show deteriorating performance with longer strings). We propose a stack architecture that is differentiable and that provably exhibits orbital stability. Using this stack, we construct a neural network that provably approximates a PDA for strings of arbitrary length. Moreover, our model and method of proof can easily be generalized to other state machines, such as a Turing Machine.Comment: 20 pages, 2 figure

The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases

We briefly survey the basic concepts and results concerning the computational power of neural net-orks which basically depends on the information content of eight parameters. In particular, recurrent neural networks with integer, rational, and arbitrary real weights are classi ed within the Chomsky and finer complexity hierarchies. Then we re ne the analysis between integer and rational weights by investigating an intermediate model of integer-weight neural networks with an extra analog rational-weight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using so-called cut languages. Our analysis reveals an interesting link to an active research field on non-standard positional numeral systems with non-integer bases. Within this framework, we introduce a new concept of quasi-periodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy

Descrição de comportamentos robóticos utilizando uma abordagem gramatical e sua implementação através de redes neurais artificiais

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Ciência da Computação.A Robótica Baseada em Comportamentos (RBC) se baseia na emergência de comportamentos robóticos de modo a garantir inteligência e autonomia nas ações que um agente deve descrever para alcançar seus objetivos. Desta forma, surge a necessidade de se achar uma maneira formal de representar estes comportamentos robóticos, mantendo características como complexidade, concisão e compactação na representação. Neste trabalho se afirma que as linguagens contidas na hierarquia de Chomsky são capazes de representar esta variada gama de comportamentos robóticos

Estudio de la dinámica de una red neural recurrente discreta y su aplicación a la detección de patrones en señales biomédicas e identificación de sistemas

En esta tesis se plantea el objetivo de hacer menos opaca la representación interna de una clase particular de redes neuronales dinámicas, mediante el análisis de las dinámicas no lineales posibles. Dada la capacidad de representación de una red de este tipo, capaz de emular casi cualquier sistema dinámico, el llevar a cabo esta tarea por completo resulta imposible. Por ello, se han fijado como objeto de análisis sistemas sencillos de una y dos neuronas (espacios de estados de una y dos dimensiones). Aun así, en el sistema de dos neuronas se encuentran dinámicas tan complejas como caos, órbitas cuasiperiódicas y configuraciones con múltiples puntos fijos. Cada una de estas dinámicas, así como las transiciones entre ellas (bifurcaciones) han sido objeto de estudio. Además de hacer explícito el funcionamiento de las redes, se pretendía también utilizar ese conocimiento en el problema del entrenamiento, que en este tipo de sistemas es muy complejo y constituye uno de los problemas prácticos fundamentales. Se intenta elaborar un catálogo con las bifurcaciones presentes en el sistema, tarea necesariamente incompleta debido a su complejidad, salvo en el caso simple de una sola neurona. Aquí la herramienta fundamental es la forma normal, que permite determinar las condiciones para la aparición de cada bifurcación. Se han interpretado las dinámicas en términos de la forma de las trayectorias más comunes, así como los de los dominios de atracción de los conjuntos invariantes que las determinan. Se ha prestado especial atención a las trayectorias cuasiperiódicas y las bifurcaciones que las originan, estableciendo condiciones sobre su estabilidad. Las configuraciones caóticas también han sido objeto de estudio especial, intentando caracterizar la aparición y forma de los atractores