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Register a new userA biologically plausible neural network for multi-channel Canonical Correlation Analysis
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Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement Canonical Correlation Analysis (CCA), an unsupervised learning method that projects the inputs onto a common subspace so as to maximize the correlations between the projections. To this end, we seek a multi-channel CCA algorithm that can be implemented in a biologically plausible neural network. For biological plausibility, we require that the network operates in the online setting and its synaptic update rules are local. Starting from a novel CCA objective function, we derive an online optimization algorithm whose optimization steps can be implemented in a single-layer neural network with multi-compartmental neurons and local non-Hebbian learning rules. We also derive an extension of our online CCA algorithm with adaptive output rank and output whitening. Interestingly, the extension maps onto a neural network whose neural architecture and synaptic updates resemble neural circuitry and synaptic plasticity observed experimentally in cortical pyramidal neurons.
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Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is currently no SFA algorithm with a biologically plausible neural network implementation, by which we mean an algorithm operates in the online setting and can be mapped onto a neural network with local synaptic updates. In this work, starting from an SFA objective, we derive an SFA algorithm, called Bio-SFA, with a biologically plausible neural network implementation. We validate Bio-SFA on naturalistic stimuli.
The quest for biologically plausible deep learning is driven, not just by the desire to explain experimentally-observed properties of biological neural networks, but also by the hope of discovering more efficient methods for training artificial networks. In this paper, we propose a new algorithm named Variational Probably Flow (VPF), an extension of minimum probability flow for training binary Deep Boltzmann Machines (DBMs). We show that weight updates in VPF are local, depending only on the states and firing rates of the adjacent neurons. Unlike contrastive divergence, there is no need for Gibbs confabulations; and unlike backpropagation, alternating feedforward and feedback phases are not required. Moreover, the learning algorithm is effective for training DBMs with intra-layer connections between the hidden nodes. Experiments with MNIST and Fashion MNIST demonstrate that VPF learns reasonable features quickly, reconstructs corrupted images more accurately, and generates samples with a high estimated log-likelihood. Lastly, we note that, interestingly, if an asymmetric version of VPF exists, the weight updates directly explain experimental results in Spike-Timing-Dependent Plasticity (STDP).
A companion paper introduces a nonlinear network with Hebbian excitatory (E) neurons that are reciprocally coupled with anti-Hebbian inhibitory (I) neurons and also receive Hebbian feedforward excitation from sensory (S) afferents. The present paper derives the network from two normative principles that are mathematically equivalent but conceptually different. The first principle formulates unsupervised learning as a constrained optimization problem: maximization of S-E correlations subject to a copositivity constraint on E-E correlations. A combination of Legendre and Lagrangian duality yields a zero-sum continuous game between excitatory and inhibitory connections that is solved by the neural network. The second principle defines a zero-sum game between E and I cells. E cells want to maximize S-E correlations and minimize E-I correlations, while I cells want to maximize I-E correlations and minimize power. The conflict between I and E objectives effectively forces the E cells to decorrelate from each other, although only incompletely. Legendre duality yields the neural network.
The estimation of causal network architectures in the brain is fundamental for understanding cognitive information processes. However, access to the dynamic processes underlying cognition is limited to indirect measurements of the hidden neuronal activity, for instance through fMRI data. Thus, estimating the network structure of the underlying process is challenging. In this article, we embed an adaptive importance sampler called Adaptive Path Integral Smoother (APIS) into the Expectation-Maximization algorithm to obtain point estimates of causal connectivity. We demonstrate on synthetic data that this procedure finds not only the correct network structure but also the direction of effective connections from random initializations of the connectivity matrix. In addition--motivated by contradictory claims in the literature--we examine the effect of the neuronal timescale on the sensitivity of the BOLD signal to changes in the connectivity and on the maximum likelihood solutions of the connectivity. We conclude with two warnings: First, the connectivity estimates under the assumption of slow dynamics can be extremely biased if the data was generated by fast neuronal processes. Second, the faster the time scale, the less sensitive the BOLD signal is to changes in the incoming connections to a node. Hence, connectivity estimation using realistic neural dynamics timescale requires extremely high-quality data and seems infeasible in many practical data sets.
Throughout this paper, we focus on the improvement of the direct feedback alignment (DFA) algorithm and extend the usage of the DFA to convolutional and recurrent neural networks (CNNs and RNNs). Even though the DFA algorithm is biologically plausible and has a potential of high-speed training, it has not been considered as the substitute for back-propagation (BP) due to the low accuracy in the CNN and RNN training. In this work, we propose a new DFA algorithm for BP-level accurate CNN and RNN training. Firstly, we divide the network into several modules and apply the DFA algorithm within the module. Second, the DFA with the sparse backward weight is applied. It comes with a form of dilated convolution in the CNN case, and in a form of sparse matrix multiplication in the RNN case. Additionally, the error propagation method of CNN becomes simpler through the group convolution. Finally, hybrid DFA increases the accuracy of the CNN and RNN training to the BP-level while taking advantage of the parallelism and hardware efficiency of the DFA algorithm.
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