An Online Algorithm for Contrastive Principal Component Analysis

An important problem encountered by both natural and engineered signal processing systems is blind source separation. In many instances of the problem, the sources are bounded by their nature and known to be so, even though the particular bound may not be known. To separate such bounded sources from their mixtures, we propose a new optimization problem, Bounded Similarity Matching (BSM). A principled derivation of an adaptive BSM algorithm leads to a recurrent neural network with a clipping nonlinearity. The network adapts by local learning rules, satisfying an important constraint for both biological plausibility and implementability in neuromorphic hardware.

A biologically inspired controller for sound and vibration applications

With the rapid increase of data in many areas, clustering on large datasets has become an important problem in data analysis. Since cluster is a highly iterative process, cluster on large datasets prefers short iteration on a relatively small representative set. Thus, a two-phase framework sampling/summarization - iterative cluster analysis is often applied in practice. Since the clustering result only labels the small representative set, there are problems with extending the result to the entire large dataset, which are almost ignored by the traditional clustering research. This extending is often named as labeling process. Labeling irregular shaped clusters, distinguishing outliers and extending cluster boundary are the main problems in this stage. We address these problems and propose a visualization-based approach to dealing with them precisely. This approach partially involves human into the process of defining and refining the structure ClusterMap. Based on this structure, the ClusterMap algorithm scans the large dataset to adapt the boundary extension and generate the cluster labels for the entire dataset. Experimental result shows that ClusterMap can preserve cluster quality considerably with low computational cost, compared to the distance-comparison-based labeling algorithms.

The purpose of this paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons).

A biologically inspired control approach for reducing radiated sound power from distributed elastic systems has been experimentally verified for harmonic, narrowband excitation. The control paradigm approximates natural biological systems for initiating movement, hi that a small number of signals are sent from an advanced, centralized controller (analogous to the brain) and are then distributed by local rules and actions to multiple actuators (analogous to muscle fiber). The controller was applied to attenuate radiated sound power from a plate. Experimental investigations of two different local learning rules, the phase variation and optimal methods, were carried out. Performance of the various methods decreased radiated sound power from a clamped plate by up to 16 dB for harmonic off-resonance excitation and up to 22 dB for on-resonance excitation. In general the results have demonstrated that the biological control approach has the potential to control multimodal response in distributed elastic systems using an array of many actuators with a reduced-order main controller. Thus significant reductions in control system computational complexity have been realized by this approach. Nomenclature / = cost function M = number of microphones v = error sensor voltage y = slave actuator complex gains \JL = convergence parameter I. Introduction R ECENT work has demonstrated the potential of active control of distributed elastic systems using multiple, independent actuators and sensors. In work concerned with the control of sound radiation from vibrating panels, the importance of number of channels of control and optimization of the transducer position and shape has been demonstrated.1 However, these investigations were carried out for a fixed frequency, and it is apparent that for good control over a bandwidth of frequencies the control actuators and sensors need to be adaptive in shape. At first sight this problem could be solved using an overall transducer broken up into many individual small elements, each connected by an individual control channel. In this situation the control transducer would effectively reoptimize its configuration for different conditions by adaptively weighting each transducer segment. Meirovitch and Norris2 have demonstrated the advantage of such an approach by considering fully distributed control in reducing control spillover. The disadvantage of this approach is that, for systems with a high modal density, the number of actuators and sensors required becomes extremely large. A high number of control channels has a number of problems mainly associated with memory requirements and computational time in the hardware systems used to implement the control. In addition, collinearity of transducer transfer functions (i.e., the transducer transfer functions are not fully linear independent) causes stability problems in systems with a high number of transducers. A new approach of controlling distributed elastic systems is presented. The approach is inspired by the action of biological natural systems where a small number of main signals are transmitted from the brain to a large area of muscle tissue to activate many independent segments of muscle. The signals then stimulate local action that is governed by, for example, chemical interaction of locally

Equilibrium Propagation is a biologically-inspired algorithm that trains convergent recurrent neural networks with a local learning rule. This approach constitutes a major lead to allow learning-capable neuromophic systems and comes with strong theoretical guarantees. Equilibrium propagation operates in two phases, during which the network is let to evolve freely and then “nudged” toward a target; the weights of the network are then updated based solely on the states of the neurons that they connect. The weight updates of Equilibrium Propagation have been shown mathematically to approach those provided by Backpropagation Through Time (BPTT), the mainstream approach to train recurrent neural networks, when nudging is performed with infinitely small strength. In practice, however, the standard implementation of Equilibrium Propagation does not scale to visual tasks harder than MNIST. In this work, we show that a bias in the gradient estimate of equilibrium propagation, inherent in the use of finite nudging, is responsible for this phenomenon and that canceling it allows training deep convolutional neural networks. We show that this bias can be greatly reduced by using symmetric nudging (a positive nudging and a negative one). We also generalize Equilibrium Propagation to the case of cross-entropy loss (by opposition to squared error). As a result of these advances, we are able to achieve a test error of 11.7% on CIFAR-10, which approaches the one achieved by BPTT and provides a major improvement with respect to the standard Equilibrium Propagation that gives 86% test error. We also apply these techniques to train an architecture with unidirectional forward and backward connections, yielding a 13.2% test error. These results highlight equilibrium propagation as a compelling biologically-plausible approach to compute error gradients in deep neuromorphic systems.

One of the biggest stakes in nanoelectronics today is to meet the needs of Artificial Intelligence by designing hardware neural networks which, by fusing computation and memory, process and learn from data with limited energy. For this purpose, memristive devices are excellent candidates to emulate synapses. A challenge, however, is to map existing learning algorithms onto a chip: for a physical implementation, a learning rule should ideally be tolerant to the typical intrinsic imperfections of such memristive devices, and local. Restricted Boltzmann Machines (RBM), for their local learning rule and inherent tolerance to stochasticity, comply with both of these constraints and constitute a highly attractive algorithm towards achieving memristor-based Deep Learning. On simulation grounds, this work gives insights into designing simple memristive devices programming protocols to train on chip Boltzmann Machines. Among other RBM-based neural networks, we advocate using a Discriminative RBM, with two hardware-oriented adaptations. We propose a pulse width selection scheme based on the sign of two successive weight updates, and show that it removes the constraint to precisely tune the initial programming pulse width as a hyperparameter. We also propose to evaluate the weight update requested by the algorithm across several samples and stochastic realizations. We show that this strategy brings a partial immunity against the most severe memristive device imperfections such as the non-linearity and the stochasticity of the conductance updates, as well as device-to-device variability.

Associative storage and retrieval of binary random patterns in various neural net models with one-step threshold-detection retrieval and local learning rules are the subject of this chapter. For different heteroas-sociation and autoassociation memory tasks specified by the properties of the pattern sets to be stored and upper bounds on the retrieval errors, we compare the performance of various models of finite as well as asymptotically infinite sizes. In infinite models, we consider the case of asymptotically sparse patterns, where the mean activity in a pattern vanishes, and study two asymptotic fidelity requirements: constant error probabilities and vanishing error probabilities. A signal-to-noise ratio analysis is carried out for one retrieval step where the calculations are comparatively straightforward and easy. As performance measures we propose and evaluate information capacities in bits/synapse which also take into account the important property of fault tolerance. For autoassociation we compare one-step and fixed-point retrieval that is analyzed in the literature by methods of statistical mechanics.

Lower bound for connectivity in local-learning neural networks

Genetic algorithms and neural networks for the quantitative analysis of ternary mixtures using surface plasmon resonance

A fundamental aspect of learning in biological neural networks is the plasticity property which allows them to modify their configurations during their lifetime. Hebbian learning is a biologically plausible mechanism for modeling the plasticity property in artificial neural networks (ANNs), based on the local interactions of neurons. However, the emergence of a coherent global learning behavior from local Hebbian plasticity rules is not very well understood. The goal of this work is to discover interpretable local Hebbian learning rules that can provide autonomous global learning. To achieve this, we use a discrete representation to encode the learning rules in a finite search space. These rules are then used to perform synaptic changes, based on the local interactions of the neurons. We employ genetic algorithms to optimize these rules to allow learning on two separate tasks (a foraging and a prey-predator scenario) in online lifetime learning settings. The resulting evolved rules converged into a set of well-defined interpretable types, that are thoroughly discussed. Notably, the performance of these rules, while adapting the ANNs during the learning tasks, is comparable to that of offline learning methods such as hill climbing.

Handwritten digit recognition is the intelligence of computers to recognize digits written by humans. But it becomes one of the most challenging tasks for machines as handwritten digits are not perfect and can be made with many different: flavors, size, thickness. Thus, as a solution to this problem, Handwriting digit recognition model comes into picture. Many machine learning techniques have been employed to solve the handwritten digit recognition problem. This paper focuses on Neural Network (NN) approaches. Among the three famous NN approaches: deep neural network (DNN), deep belief network (DBN) and convolutional neural network (CNN), the specialization of CNN as compared to other NN of being able to detect pattern is what makes it so useful for recognizing handwritten digits. Humans can very easily see, read & write any handwritten digits, when written in proper format. Even if the digits are not written in proper format we can use our logic and predict what digit it could be. But It is a hard task for the machine to recognize handwritten digits as these are not perfect and can be made with many different flavors. Thus handwritten digit recognition is the solution to this problem which uses the image of a digit and recognizes the digit present in the image. The handwritten digit recognition is the ability of computers to recognize human handwritten digits. The goal is to build a model that can efficiently and reliably recognize the digits and output the proper result. Amongst all the other neural networks, working and implementing a model using Convolution Neural Network gives out the most precise results. It is most popularly used for analyzing images as well as for other data analysis or classification problems. CNN has hidden layers called convolutional layers. These layers work the same way as other layers do but here we need to specify the no of filters each layer should have These filters are actually what detects the pattern. Patterns could be edges, corners, circles or any complex other objects like eyes, ears or even deeper full dogs, cats, etc. Thus, the specialization of CNN as compared to other NN of being able to detect patterns is what makes it so useful for recognizing handwritten digits Key Word: Neural Networks; Convolutional Neural Networks (CNN); Image Processing; Optical Character Recognition (OCR); MNIST Dataset

Online algorithms are an important branch in algorithm design. Designing online algorithms with a bounded competitive ratio (in terms of worst-case performance) can be hard and usually relies on problem-specific assumptions. Inspired by adversarial training from Generative Adversarial Net and the fact that the competitive ratio of an online algorithm is based on worst-case input, we adopt deep neural networks (NNs) to learn an online algorithm for a resource allocation and pricing problem from scratch, with the goal that the performance gap between offline optimum and the learned online algorithm can be minimized for worst-case input. Specifically, we leverage two NNs as the algorithm and the adversary, respectively, and let them play a zero sum game, with the adversary being responsible for generating worst-case input while the algorithm learns the best strategy based on the input provided by the adversary. To ensure better convergence of the algorithm network (to the desired online algorithm), we propose a novel per-round update method to handle sequential decision making to break complex dependency among different rounds so that update can be done for every possible action instead of only sampled actions. To the best of our knowledge, our work is the first using deep NNs to design an online algorithm from the perspective of worst-case performance guarantee. Empirical studies show that our updating methods ensure convergence to Nash equilibrium and the learned algorithm outperforms state-of-the-art online algorithms under various settings.

We introduce an information maximizing neural network that employs only local learning rules, simple activation functions, and feedback in its functioning. The network consists of an input layer, an output layer that can be overcomplete, and a set of auxiliary layers comprising feed-forward, lateral, and feedback connecwtions. The auxiliary layers implement a novel ”neural multigrid,” and each computes a Fourier mode of a key infomax learning vector. Initially, a partial multigrid computes only low frequency modes of this learning vector, resulting in a spatially correlated topographic map. As higher frequency modes of the learning vector are gradually added, an infomax solution emerges, maximizing the entropy of the output without disrupting the map’s topographic order. When feed-forward and feedback connections to the neural multigrid are passed through a nonlinear activation function, infomax emerges in a phase-independent topographic map. Information rates estimated by Principal Components Analysis (PCA) are comparable to those of standard infomax, indicating the neural multigrid successfully imposes a topographic order on the optimal infomax-derived bases.KeywordsMutual InformationCoarse GridMultigrid MethodFourier ModeNeural ComputationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Networks based on coordinated spike coding can encode information with high efficiency in the spike trains of individual neurons. These networks exhibit single-neuron variability and tuning curves as typically observed in cortex, but paradoxically coincide with a precise, non-redundant spike-based population code. However, it has remained unclear whether the specific synaptic connectivities required in these networks can be learnt with local learning rules. Here, we show how to learn the required architecture. Using coding efficiency as an objective, we derive spike-timing-dependent learning rules for a recurrent neural network, and we provide exact solutions for the networks’ convergence to an optimal state. As a result, we deduce an entire network from its input distribution and a firing cost. After learning, basic biophysical quantities such as voltages, firing thresholds, excitation, inhibition, or spikes acquire precise functional interpretations.