Multilayer neural networks have led to remarkable performance on many kinds of benchmark tasks in text, speech, and image processing. Nonlinear parameter estimation in hierarchical models is known to be subject to overfitting and misspecification. One approach to these estimation and related problems (e.g., saddle points, colinearity, feature discovery) is called Dropout. The Dropout algorithm removes hidden units according to a binomial random variable with probability p prior to each update, creating random “shocks” to the network that are averaged over updates (thus creating weight sharing). In this letter, we reestablish an older parameter search method and show that Dropout is a special case of this more general model, stochastic delta rule (SDR), published originally in 1990. Unlike Dropout, SDR redefines each weight in the network as a random variable with mean μ w i j and standard deviation σ w i j . Each weight random variable is sampled on each forward activation, consequently creating an exponential number of potential networks with shared weights (accumulated in the mean values). Both parameters are updated according to prediction error, thus resulting in weight noise injections that reflect a local history of prediction error and local model averaging. SDR therefore implements a more sensitive local gradient-dependent simulated annealing per weight converging in the limit to a Bayes optimal network. We run tests on standard benchmarks (CIFAR and ImageNet) using a modified version of DenseNet and show that SDR outperforms standard Dropout in top-5 validation error by approximately 13% with DenseNet-BC 121 on ImageNet and find various validation error improvements in smaller networks. We also show that SDR reaches the same accuracy that Dropout attains in 100 epochs in as few as 40 epochs, as well as improvements in training error by as much as 80%.

The ability to move fast and accurately track moving objects is fundamentally constrained by the biophysics of neurons and dynamics of the muscles involved. Yet the corresponding trade-offs between these factors and tracking motor commands have not been rigorously quantified. We use feedback control principles to quantify performance limitations of the sensorimotor control system (SCS) to track fast periodic movements. We show that (1) linear models of the SCS fail to predict known undesirable phenomena, including skipped cycles, overshoot and undershoot, produced when tracking signals in the “fast regime,” while nonlinear pulsatile control models can predict such undesirable phenomena, and (2) tools from nonlinear control theory allow us to characterize fundamental limitations in this fast regime. Using a validated and tractable nonlinear model of the SCS, we derive an analytical upper bound on frequencies that the SCS model can reliably track before producing such undesirable phenomena as a function of the neurons' biophysical constraints and muscle dynamics. The performance limitations derived here have important implications in sensorimotor control. For example, if the primary motor cortex is compromised due to disease or damage, the theory suggests ways to manipulate muscle dynamics by adding the necessary compensatory forces using an assistive neuroprosthetic device to restore motor performance and, more important, fast and agile movements. Just how one should compensate can be informed by our SCS model and the theory developed here.

The Kalman filter provides a simple and efficient algorithm to compute the posterior distribution for state-space models where both the latent state and measurement models are linear and gaussian. Extensions to the Kalman filter, including the extended and unscented Kalman filters, incorporate linearizations for models where the observation model p ( observation | state ) is nonlinear. We argue that in many cases, a model for p ( state | observation ) proves both easier to learn and more accurate for latent state estimation. Approximating p ( state | observation ) as gaussian leads to a new filtering algorithm, the discriminative Kalman filter (DKF), which can perform well even when p ( observation | state ) is highly nonlinear and/or nongaussian. The approximation, motivated by the Bernstein–von Mises theorem, improves as the dimensionality of the observations increases. The DKF has computational complexity similar to the Kalman filter, allowing it in some cases to perform much faster than particle filters with similar precision, while better accounting for nonlinear and nongaussian observation models than Kalman-based extensions. When the observation model must be learned from training data prior to filtering, off-the-shelf nonlinear and nonparametric regression techniques can provide a gaussian model for p ( observation | state ) that cleanly integrates with the DKF. As part of the BrainGate2 clinical trial, we successfully implemented gaussian process regression with the DKF framework in a brain-computer interface to provide real-time, closed-loop cursor control to a person with a complete spinal cord injury. In this letter, we explore the theory underlying the DKF, exhibit some illustrative examples, and outline potential extensions.

Stimulus equivalence (SE) and projective simulation (PS) study complex behavior, the former in human subjects and the latter in artificial agents. We apply the PS learning framework for modeling the formation of equivalence classes. For this purpose, we first modify the PS model to accommodate imitating the emergence of equivalence relations. Later, we formulate the SE formation through the matching-to-sample (MTS) procedure. The proposed version of PS model, called the equivalence projective simulation (EPS) model, is able to act within a varying action set and derive new relations without receiving feedback from the environment. To the best of our knowledge, it is the first time that the field of equivalence theory in behavior analysis has been linked to an artificial agent in a machine learning context. This model has many advantages over existing neural network models. Briefly, our EPS model is not a black box model, but rather a model with the capability of easy interpretation and flexibility for further modifications. To validate the model, some experimental results performed by prominent behavior analysts are simulated. The results confirm that the EPS model is able to reliably simulate and replicate the same behavior as real experiments in various settings, including formation of equivalence relations in typical participants, nonformation of equivalence relations in language-disabled children, and nodal effect in a linear series with nodal distance five. Moreover, through a hypothetical experiment, we discuss the possibility of applying EPS in further equivalence theory research.

As synchronized activity is associated with basic brain functions and pathological states, spike train synchrony has become an important measure to analyze experimental neuronal data. Many measures of spike train synchrony have been proposed, but there is no gold standard allowing for comparison of results from different experiments. This work aims to provide guidance on which synchrony measure is best suited to quantify the effect of epileptiform-inducing substances (e.g., bicuculline, BIC) in in vitro neuronal spike train data. Spike train data from recordings are likely to suffer from erroneous spike detection, such as missed spikes (false negative) or noise (false positive). Therefore, different timescale-dependent (cross-correlation, mutual information, spike time tiling coefficient) and timescale-independent (Spike-contrast, phase synchronization (PS), A-SPIKE-synchronization, A-ISI-distance, ARI-SPIKE-distance) synchrony measures were compared in terms of their robustness to erroneous spike trains. For this purpose, erroneous spike trains were generated by randomly adding (false positive) or deleting (false negative) spikes (in silico manipulated data) from experimental data. In addition, experimental data were analyzed using different spike detection threshold factors in order to confirm the robustness of the synchrony measures. All experimental data were recorded from cortical neuronal networks on microelectrode array chips, which show epileptiform activity induced by the substance BIC. As a result of the in silico manipulated data, Spike-contrast was the only measure that was robust to false-negative as well as false-positive spikes. Analyzing the experimental data set revealed that all measures were able to capture the effect of BIC in a statistically significant way, with Spike-contrast showing the highest statistical significance even at low spike detection thresholds. In summary, we suggest using Spike-contrast to complement established synchrony measures because it is timescale independent and robust to erroneous spike trains.

The synchronous firing of neurons in a pulse-coupled neural network composed of excitatory and inhibitory neurons is analyzed. The neurons are connected by both chemical synapses and electrical synapses among the inhibitory neurons. When electrical synapses are introduced, periodically synchronized firing as well as chaotically synchronized firing is widely observed. Moreover, we find stochastic synchrony where the ensemble-averaged dynamics shows synchronization in the network but each neuron has a low firing rate and the firing of the neurons seems to be stochastic. Stochastic synchrony of chaos corresponding to a chaotic attractor is also found.

We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory.