Sparse code formation in the primary visual cortex (V1) has been inspiration for many state-of-the-art visual recognition systems. To stimulate this behavior, networks are trained networks under mathematical constraint of sparsity or selectivity. In this paper, the authors exploit another approach which uses lateral interconnections in feature learning networks. However, instead of adding direct lateral interconnections among neurons, we introduce an inhibitory layer placed right after normal encoding layer. This idea overcomes the challenge of computational cost and complexity on lateral networks while preserving crucial objective of sparse code formation. To demonstrate this idea, we use sparse autoencoder as normal encoding layer and apply inhibitory layer. Early experiments in visual recognition show relative improvements over traditional approach on CIFAR-10 dataset. Moreover, simple installment and training process using Hebbian rule allow inhibitory layer to be integrated into existing networks, which enables further analysis in the future.
Lateral connections have been widely used in models in neuroscience. Our work is loosely based on E-I net @cite_4 . In E-I net, simple cells are divided into two types of neurons, excitatory neurons and inhibitory neurons. One inhibitory cell sends an amount of inhibitory current directly to all excitotary simple cells and other inhibitory cells. Inhibitory cells predict the redundant part of the network activity, thus decorrelate the activity of the excitatory cells by suppressing redundant spiking activity. In our networks, relationship between encoding cells is stored in connections between two layers. Inhibitory cells only do the computation based on encoding signals and the corresponding weights. In one recent work that shares the idea of local computation @cite_0 , spiking signal is chosen using winter-take-all rule while the rest is grounded to 0. Moreover, the competition range is predefined. In other works aiming at learning structural features such as structural sparse coding @cite_10 and topographical ICA @cite_1 , structural order emerges through regularization. Meanwhile, with inhibitory layer, neighborhood rather than order is obtained through ad hoc optimization.
@cite_0 @cite_10 @cite_1 @cite_4
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Sparse coding models of natural scenes can account for several physiological properties of primary visual cortex (V1), including the shapes of simple cell receptive fields (RFs) and the highly kurtotic firing rates of V1 neurons. Current spiking network models of pattern learning and sparse coding require direct inhibitory connections between the excitatory simple cells, in conflict with the physiological distinction between excitatory (glutamatergic) and inhibitory (GABAergic) neurons (Dale9s Law). At the same time, the computational role of inhibitory neurons in cortical microcircuit function has yet to be fully explained. Here we show that adding a separate population of inhibitory neurons to a spiking model of V1 provides conformance to Dale9s Law, proposes a computational role for at least one class of interneurons, and accounts for certain observed physiological properties in V1. When trained on natural images, this excitatory–inhibitory spiking circuit learns a sparse code with Gabor-like RFs as found in V1 using only local synaptic plasticity rules. The inhibitory neurons enable sparse code formation by suppressing predictable spikes, which actively decorrelates the excitatory population. The model predicts that only a small number of inhibitory cells is required relative to excitatory cells and that excitatory and inhibitory input should be correlated, in agreement with experimental findings in visual cortex. We also introduce a novel local learning rule that measures stimulus-dependent correlations between neurons to support “explaining away” mechanisms in neural coding. This article initiates a rigorous theoretical analysis of the computational power of circuits that employ modules for computing winner-take-all. Computational models that involve competitive stages have so far been neglected in computational complexity theory, although they are widely used in computational brain models, artificial neural networks, and analog VLSI. Our theoretical analysis shows that winner-take-all is a surprisingly powerful computational module in comparison with threshold gates (also referred to as McCulloch-Pitts neurons) and sigmoidal gates. We prove an optimal quadratic lower bound for computing winner-take-all in any feedforward circuit consisting of threshold gates. In addition we show that arbitrary continuous functions can be approximated by circuits employing a single soft winner-take-all gate as their only nonlinear operation. Our theoretical analysis also provides answers to two basic questions raised by neurophysiologists in view of the well-known asymmetry between excitatory and inhibitory connections in cortical circuits: how much computational power of neural networks is lost if only positive weights are employed in weighted sums and how much adaptive capability is lost if only the positive weights are subject to plasticity. The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex. The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper.