scholarly journals Learning Precise Spike Train–to–Spike Train Transformations in Multilayer Feedforward Neuronal Networks

2016 ◽  
Vol 28 (5) ◽  
pp. 826-848 ◽  
Author(s):  
Arunava Banerjee
Keyword(s):  
Spike Train ◽  
Gradient Descent ◽  
Probabilistic Models ◽  
Spike Timing ◽  
Inhibitory Neurons ◽  
Closed Form Solutions ◽  
Learning Framework ◽  
Error Functional ◽  
The Error Functional ◽  
Quantities Of Interest

We derive a synaptic weight update rule for learning temporally precise spike train–to–spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation to the deterministic spiking neuron setting, is based strictly on spike timing and avoids invoking concepts pertaining to spike rates or probabilistic models of spiking. The derivation is founded on two innovations. First, an error functional is proposed that compares the spike train emitted by the output neuron of the network to the desired spike train by way of their putative impact on a virtual postsynaptic neuron. This formulation sidesteps the need for spike alignment and leads to closed-form solutions for all quantities of interest. Second, virtual assignment of weights to spikes rather than synapses enables a perturbation analysis of individual spike times and synaptic weights of the output, as well as all intermediate neurons in the network, which yields the gradients of the error functional with respect to the said entities. Learning proceeds via a gradient descent mechanism that leverages these quantities. Simulation experiments demonstrate the efficacy of the proposed learning framework. The experiments also highlight asymmetries between synapses on excitatory and inhibitory neurons.

scholarly journals A Reinforcement Learning Framework for Spiking Networks with Dynamic Synapses

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Karim El-Laithy ◽  
Martin Bogdan
Keyword(s):  
Reinforcement Learning ◽  
Spike Timing ◽  
Neural Representation ◽  
Model Parameters ◽  
Learning Framework ◽  
Reference Target ◽  
Wide Range ◽  
Spiking Network ◽  
Dynamic Synapses ◽  
Exclusive Or

An integration of both the Hebbian-based and reinforcement learning (RL) rules is presented for dynamic synapses. The proposed framework permits the Hebbian rule to update the hidden synaptic model parameters regulating the synaptic response rather than the synaptic weights. This is performed using both the value and the sign of the temporal difference in the reward signal after each trial. Applying this framework, a spiking network with spike-timing-dependent synapses is tested to learn the exclusive-OR computation on a temporally coded basis. Reward values are calculated with the distance between the output spike train of the network and a reference target one. Results show that the network is able to capture the required dynamics and that the proposed framework can reveal indeed an integrated version of Hebbian and RL. The proposed framework is tractable and less computationally expensive. The framework is applicable to a wide class of synaptic models and is not restricted to the used neural representation. This generality, along with the reported results, supports adopting the introduced approach to benefit from the biologically plausible synaptic models in a wide range of intuitive signal processing.

scholarly journals Learning tractable probabilistic models for moral responsibility and blame

2021 ◽  
Vol 35 (2) ◽  
pp. 621-659
Author(s):  
Lewis Hammond ◽  
Vaishak Belle
Keyword(s):  
Moral Responsibility ◽  
Probabilistic Models ◽  
Autonomous Systems ◽  
Cancer Staging ◽  
Data Driven ◽  
Probabilistic Learning ◽  
Learning Framework ◽  
Decision Points ◽  
Self Driving Cars ◽  
Trolley Problems

AbstractMoral responsibility is a major concern in autonomous systems, with applications ranging from self-driving cars to kidney exchanges. Although there have been recent attempts to formalise responsibility and blame, among similar notions, the problem of learning within these formalisms has been unaddressed. From the viewpoint of such systems, the urgent questions are: (a) How can models of moral scenarios and blameworthiness be extracted and learnt automatically from data? (b) How can judgements be computed effectively and efficiently, given the split-second decision points faced by some systems? By building on constrained tractable probabilistic learning, we propose and implement a hybrid (between data-driven and rule-based methods) learning framework for inducing models of such scenarios automatically from data and reasoning tractably from them. We report on experiments that compare our system with human judgement in three illustrative domains: lung cancer staging, teamwork management, and trolley problems.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

Fast Inhibition Alters First Spike Timing in Auditory Brainstem Neurons

2004 ◽  
Vol 92 (4) ◽  
pp. 2615-2621 ◽  
Author(s):  
Antonio G. Paolini ◽  
Janine C. Clarey ◽  
Karina Needham ◽  
Graeme M. Clark
Keyword(s):  
Lateral Inhibition ◽  
Cochlear Nucleus ◽  
Stellate Cell ◽  
Discharge Rate ◽  
Stellate Cells ◽  
Auditory Pathway ◽  
Auditory Brainstem ◽  
Spike Timing ◽  
Inhibitory Neurons

Within the first processing site of the central auditory pathway, inhibitory neurons (D stellate cells) broadly tuned to tonal frequency project on narrowly tuned, excitatory output neurons (T stellate cells). The latter is thought to provide a topographic representation of sound spectrum, whereas the former is thought to provide lateral inhibition that improves spectral contrast, particularly in noise. In response to pure tones, the overall discharge rate in T stellate cells is unlikely to be suppressed dramatically by D stellate cells because they respond primarily to stimulus onset and provide fast, short-duration inhibition. In vivo intracellular recordings from the ventral cochlear nucleus (VCN) showed that, when tones were presented above or below the characteristic frequency (CF) of a T stellate neuron, they were inhibited during depolarization. This resulted in a delay in the initial action potential produced by T stellate cells. This ability of fast inhibition to alter the first spike timing of a T stellate neuron was confirmed by electrically activating the D stellate cell pathway that arises in the contralateral cochlear nucleus. Delay was also induced when two tones were presented: one at CF and one outside the frequency response area of the T stellate neuron. These findings suggest that the traditional view of lateral inhibition within the VCN should incorporate delay as one of its principle outcomes.

Improving the Generalization Properties of Radial Basis Function Neural Networks

1991 ◽  
Vol 3 (4) ◽  
pp. 579-588 ◽  
Author(s):  
Chris Bishop
Keyword(s):  
Neural Networks ◽  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Error Functional ◽  
Radial Basis ◽  
The Error Functional ◽  
Network Mapping ◽  
Nonlinear Mappings

An important feature of radial basis function neural networks is the existence of a fast, linear learning algorithm in a network capable of representing complex nonlinear mappings. Satisfactory generalization in these networks requires that the network mapping be sufficiently smooth. We show that a modification to the error functional allows smoothing to be introduced explicitly without significantly affecting the speed of training. A simple example is used to demonstrate the resulting improvement in the generalization properties of the network.

Spatial Phase and the Temporal Structure of the Response to Gratings in V1

1998 ◽  
Vol 80 (2) ◽  
pp. 554-571 ◽  
Author(s):  
Jonathan D. Victor ◽  
Keith P. Purpura
Keyword(s):  
Spatial Frequency ◽  
Spike Train ◽  
Temporal Structure ◽  
Spike Timing ◽  
Dependent Manner ◽  
Data Set ◽  
Simple Cells ◽  
Complex Cells ◽  
Spatial Phase ◽  
Contrast Information

Victor, Jonathan D. and Keith P. Purpura. Spatial phase and the temporal structure of the response to gratings in V1. J. Neurophysiol. 80: 554–571, 1998. We recorded single-unit activity of 25 units in the parafoveal representation of macaque V1 to transient appearance of sinusoidal gratings. Gratings were systematically varied in spatial phase and in one or two of the following: contrast, spatial frequency, and orientation. Individual responses were compared based on spike counts, and also according to metrics sensitive to spike timing. For each metric, the extent of stimulus-dependent clustering of individual responses was assessed via the transmitted information, H. In nearly all data sets, stimulus-dependent clustering was maximal for metrics sensitive to the temporal pattern of spikes, typically with a precision of 25–50 ms. To focus on the interaction of spatial phase with other stimulus attributes, each data set was analyzed in two ways. In the “pooled phases” approach, the phase of the stimulus was ignored in the assessment of clustering, to yield an index H pooled. In the “individual phases” approach, clustering was calculated separately for each spatial phase and then averaged across spatial phases to yield an index H indiv. H pooled expresses the extent to which a spike train represents contrast, spatial frequency, or orientation in a manner which is not confounded by spatial phase (phase-independent representation), whereas H indiv expresses the extent to which a spike train represents one of these attributes, provided spatial phase is fixed (phase-dependent representation). Here, representation means that a stimulus attribute has a reproducible and systematic influence on individual responses, not a neural mechanism for decoding this influence. During the initial 100 ms of the response, contrast was represented in a phase-dependent manner by simple cells but primarily in a phase-independent manner by complex cells. As the response evolved, simple cell responses acquired phase-independent contrast information, whereas complex cells acquired phase-dependent contrast information. Simple cells represented orientation and spatial frequency in a primarily phase-dependent manner, but also they contained some phase-independent information in their initial response segment. Complex cells showed primarily phase-independent representation of orientation but primarily phase-dependent representation of spatial frequency. Joint representation of two attributes (contrast and spatial frequency, contrast and orientation, spatial frequency and orientation) was primarily phase dependent for simple cells, and primarily phase independent for complex cells. In simple and complex cells, the variability in the number of spikes elicited on each response was substantially greater than the expectations of a Poisson process. Although some of this variation could be attributed to the dependence of the response on the spatial phase of the grating, variability was still markedly greater than Poisson when the contribution of spatial phase to response variance was removed.

scholarly journals Regularized Instance Embedding for Deep Multi-Instance Learning

2019 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Yi Lin ◽  
Honggang Zhang
Keyword(s):  
Neural Network ◽  
Big Data ◽  
Supervised Learning ◽  
Regularization Method ◽  
Gradient Descent ◽  
State Of The Art ◽  
Stochastic Gradient Descent ◽  
Learning Framework ◽  
Weakly Supervised ◽  
The Cost

In the era of Big Data, multi-instance learning, as a weakly supervised learning framework, has various applications since it is helpful to reduce the cost of the data-labeling process. Due to this weakly supervised setting, learning effective instance representation/embedding is challenging. To address this issue, we propose an instance-embedding regularizer that can boost the performance of both instance- and bag-embedding learning in a unified fashion. Specifically, the crux of the instance-embedding regularizer is to maximize correlation between instance-embedding and underlying instance-label similarities. The embedding-learning framework was implemented using a neural network and optimized in an end-to-end manner using stochastic gradient descent. In experiments, various applications were studied, and the results show that the proposed instance-embedding-regularization method is highly effective, having state-of-the-art performance.

scholarly journals Facial Action Unit Intensity Estimation via Semantic Correspondence Learning with Dynamic Graph Convolution

2020 ◽  
Vol 34 (07) ◽  
pp. 12701-12708
Author(s):  
Yingruo Fan ◽  
Jacqueline Lam ◽  
Victor Li
Keyword(s):  
Probabilistic Models ◽  
Superior Performance ◽  
Feature Maps ◽  
Dynamic Graph ◽  
Intensity Estimation ◽  
Facial Action ◽  
Learning Framework ◽  
Benchmark Datasets ◽  
Relationship Of ◽  
Semantic Correspondence

The intensity estimation of facial action units (AUs) is challenging due to subtle changes in the person's facial appearance. Previous approaches mainly rely on probabilistic models or predefined rules for modeling co-occurrence relationships among AUs, leading to limited generalization. In contrast, we present a new learning framework that automatically learns the latent relationships of AUs via establishing semantic correspondences between feature maps. In the heatmap regression-based network, feature maps preserve rich semantic information associated with AU intensities and locations. Moreover, the AU co-occurring pattern can be reflected by activating a set of feature channels, where each channel encodes a specific visual pattern of AU. This motivates us to model the correlation among feature channels, which implicitly represents the co-occurrence relationship of AU intensity levels. Specifically, we introduce a semantic correspondence convolution (SCC) module to dynamically compute the correspondences from deep and low resolution feature maps, and thus enhancing the discriminability of features. The experimental results demonstrate the effectiveness and the superior performance of our method on two benchmark datasets.

scholarly journals Self-Adversarially Learned Bayesian Sampling

2019 ◽  
Vol 33 ◽  
pp. 5893-5900
Author(s):  
Yang Zhao ◽  
Jianyi Zhang ◽  
Changyou Chen
Keyword(s):  
Gradient Descent ◽  
Training Data ◽  
Transition Kernel ◽  
Adversarial Learning ◽  
Bayesian Sampling ◽  
Learning Framework ◽  
Unsupervised Deep Learning ◽  
Highly Correlated ◽  
Self Learning ◽  
Modern Machine

Scalable Bayesian sampling is playing an important role in modern machine learning, especially in the fast-developed unsupervised-(deep)-learning models. While tremendous progresses have been achieved via scalable Bayesian sampling such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD), the generated samples are typically highly correlated. Moreover, their sample-generation processes are often criticized to be inefficient. In this paper, we propose a novel self-adversarial learning framework that automatically learns a conditional generator to mimic the behavior of a Markov kernel (transition kernel). High-quality samples can be efficiently generated by direct forward passes though a learned generator. Most importantly, the learning process adopts a self-learning paradigm, requiring no information on existing Markov kernels, e.g., knowledge of how to draw samples from them. Specifically, our framework learns to use current samples, either from the generator or pre-provided training data, to update the generator such that the generated samples progressively approach a target distribution, thus it is called self-learning. Experiments on both synthetic and real datasets verify advantages of our framework, outperforming related methods in terms of both sampling efficiency and sample quality.

STDP Provides the Substrate for Igniting Synfire Chains by Spatiotemporal Input Patterns

2008 ◽  
Vol 20 (2) ◽  
pp. 415-435 ◽  
Author(s):  
Ryosuke Hosaka ◽  
Osamu Araki ◽  
Tohru Ikeguchi
Keyword(s):  
Neural Network ◽  
Experimental Studies ◽  
Spike Timing ◽  
Inhibitory Neurons ◽  
Spatiotemporal Pattern ◽  
Spiking Neural Network ◽  
Synfire Chains ◽  
The Neural Network ◽  
Stdp Rule ◽  
Neural Network Structure

Spike-timing-dependent synaptic plasticity (STDP), which depends on the temporal difference between pre- and postsynaptic action potentials, is observed in the cortices and hippocampus. Although several theoretical and experimental studies have revealed its fundamental aspects, its functional role remains unclear. To examine how an input spatiotemporal spike pattern is altered by STDP, we observed the output spike patterns of a spiking neural network model with an asymmetrical STDP rule when the input spatiotemporal pattern is repeatedly applied. The spiking neural network comprises excitatory and inhibitory neurons that exhibit local interactions. Numerical experiments show that the spiking neural network generates a single global synchrony whose relative timing depends on the input spatiotemporal pattern and the neural network structure. This result implies that the spiking neural network learns the transformation from spatiotemporal to temporal information. In the literature, the origin of the synfire chain has not been sufficiently focused on. Our results indicate that spiking neural networks with STDP can ignite synfire chains in the cortices.

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