A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware

An analog feedback associative memory

A method for the storage of analog vectors, i.e., vectors whose components are real-valued, is developed for the Hopfield continuous-time network. An important requirement is that each memory vector has to be an asymptotically stable (i.e. attractive) equilibrium of the network. Some of the limitations imposed by the continuous Hopfield model on the set of vectors that can be stored are pointed out. These limitations can be relieved by choosing a network containing visible as well as hidden units. An architecture consisting of several hidden layers and a visible layer, connected in a circular fashion, is considered. It is proved that the two-layer case is guaranteed to store any number of given analog vectors provided their number does not exceed 1 + the number of neurons in the hidden layer. A learning algorithm that correctly adjusts the locations of the equilibria and guarantees their asymptotic stability is developed. Simulation results confirm the effectiveness of the approach

NASA JSC neural network survey results

A survey of Artificial Neural Systems in support of NASA's (Johnson Space Center) Automatic Perception for Mission Planning and Flight Control Research Program was conducted. Several of the world's leading researchers contributed papers containing their most recent results on artificial neural systems. These papers were broken into categories and descriptive accounts of the results make up a large part of this report. Also included is material on sources of information on artificial neural systems such as books, technical reports, software tools, etc

Artificial Neural Network Representations for Hierarchical Preference Structures

In this paper, we introduce two artificial neural network formulations that can be used to predict the preference ratings from the pairwise comparison matrices of the Analytic Hierarchy Process (AHP). First, we introduce a modified Hopfield network that can be used to exactly determine the vector of preference ratings associated with a positive reciprocal comparison matrix. The dynamics of this network are mathematically equivalent to the power method, a widely used numerical method for computing the principal eigenvectors of square matrices. However, we show that the Hopfield network representation is incapable of generalizing the preference patterns, and consequently is not suitable for approximating the preference ratings if the preference information is imprecise. Then we present a feed-forward neural network formulation that does have the ability to accurately approximate the preference ratings. A simulation experiment is used to verify the robustness of the feed-forward neural network formulation with respect to imprecise pairwise judgments. From the results of this experiment, we conclude that the feed-forward neural network formulation appears to be a powerful tool for analyzing discrete alternative multicriteria decision problems with imprecise or fuzzy ratio-scale preference judgments

Neural networks: from the perceptron to deep nets

Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming data is generated by a teacher model, asymptotic generalisation predictions were originally derived using the replica method and the online learning dynamics has been described in the large system limit. In this chapter, we review the key original ideas of this literature along with their heritage in the ongoing quest to understand the efficiency of modern deep learning algorithms. One goal of current and future research is to characterize the bias of the learning algorithms toward well-generalising minima in a complex overparametrized loss landscapes with many solutions perfectly interpolating the training data. Works on perceptrons, two-layer committee machines and kernel-like learning machines shed light on these benefits of overparametrization. Another goal is to understand the advantage of depth while models now commonly feature tens or hundreds of layers. If replica computations apparently fall short in describing general deep neural networks learning, studies of simplified linear or untrained models, as well as the derivation of scaling laws provide the first elements of answers.Comment: Contribution to the book Spin Glass Theory and Far Beyond: Replica Symmetry Breaking after 40 Years; Chap. 2