On probabilistic analog automata

We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy environment suggested by Maass and Orponen, and Maass and Sontag. Our main result is a generalization of Rabin's reduction theorem that implies that under very mild conditions, the computational power of the automaton is limited to regular languages

Forward Signal Propagation Learning

We propose a new learning algorithm for propagating a learning signal and updating neural network parameters via a forward pass, as an alternative to backpropagation. In forward signal propagation learning (sigprop), there is only the forward path for learning and inference, so there are no additional structural or computational constraints on learning, such as feedback connectivity, weight transport, or a backward pass, which exist under backpropagation. Sigprop enables global supervised learning with only a forward path. This is ideal for parallel training of layers or modules. In biology, this explains how neurons without feedback connections can still receive a global learning signal. In hardware, this provides an approach for global supervised learning without backward connectivity. Sigprop by design has better compatibility with models of learning in the brain and in hardware than backpropagation and alternative approaches to relaxing learning constraints. We also demonstrate that sigprop is more efficient in time and memory than they are. To further explain the behavior of sigprop, we provide evidence that sigprop provides useful learning signals in context to backpropagation. To further support relevance to biological and hardware learning, we use sigprop to train continuous time neural networks with Hebbian updates and train spiking neural networks without surrogate functions

Automating Vehicles by Deep Reinforcement Learning using Task Separation with Hill Climbing

Within the context of autonomous driving a model-based reinforcement learning algorithm is proposed for the design of neural network-parameterized controllers. Classical model-based control methods, which include sampling- and lattice-based algorithms and model predictive control, suffer from the trade-off between model complexity and computational burden required for the online solution of expensive optimization or search problems at every short sampling time. To circumvent this trade-off, a 2-step procedure is motivated: first learning of a controller during offline training based on an arbitrarily complicated mathematical system model, before online fast feedforward evaluation of the trained controller. The contribution of this paper is the proposition of a simple gradient-free and model-based algorithm for deep reinforcement learning using task separation with hill climbing (TSHC). In particular, (i) simultaneous training on separate deterministic tasks with the purpose of encoding many motion primitives in a neural network, and (ii) the employment of maximally sparse rewards in combination with virtual velocity constraints (VVCs) in setpoint proximity are advocated.Comment: 10 pages, 6 figures, 1 tabl

Using the Gibbs Function as a Measure of Human Brain Development Trends from Fetal Stage to Advanced Age

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions

Using the gibbs function as a measure of human brain development trends from fetal stage to advanced age

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions

Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis