Deep Gated Hebbian Predictive Coding Accounts for Emergence of Complex Neural Response Properties Along the Visual Cortical Hierarchy

Predictive coding provides a computational paradigm for modeling perceptual processing as the construction of representations accounting for causes of sensory inputs. Here, we developed a scalable, deep network architecture for predictive coding that is trained using a gated Hebbian learning rule and mimics the feedforward and feedback connectivity of the cortex. After training on image datasets, the models formed latent representations in higher areas that allowed reconstruction of the original images. We analyzed low- and high-level properties such as orientation selectivity, object selectivity and sparseness of neuronal populations in the model. As reported experimentally, image selectivity increased systematically across ascending areas in the model hierarchy. Depending on the strength of regularization factors, sparseness also increased from lower to higher areas. The results suggest a rationale as to why experimental results on sparseness across the cortical hierarchy have been inconsistent. Finally, representations for different object classes became more distinguishable from lower to higher areas. Thus, deep neural networks trained using a gated Hebbian formulation of predictive coding can reproduce several properties associated with neuronal responses along the visual cortical hierarchy.

A Novel Muscle Synergy Extraction Method Used for Motor Function Evaluation of Stroke Patients: A Pilot Study

In this paper, we present a novel muscle synergy extraction method based on multivariate curve resolution–alternating least squares (MCR-ALS) to overcome the limitation of the nonnegative matrix factorization (NMF) method for extracting non-sparse muscle synergy, and we study its potential application for evaluating motor function of stroke survivors. Nonnegative matrix factorization (NMF) is the most widely used method for muscle synergy extraction. However, NMF is susceptible to components’ sparseness and usually provides inferior reliability, which significantly limits the promotion of muscle synergy. In this study, MCR-ALS was employed to extract muscle synergy from electromyography (EMG) data. Its performance was compared with two other matrix factorization algorithms, NMF and self-modeling mixture analysis (SMMA). Simulated data sets were utilized to explore the influences of the sparseness and noise on the extracted synergies. As a result, the synergies estimated by MCR-ALS were the most similar to true synergies as compared with SMMA and NMF. MCR-ALS was used to analyze the muscle synergy characteristics of upper limb movements performed by healthy (n = 11) and stroke (n = 5) subjects. The repeatability and intra-subject consistency were used to evaluate the performance of MCR-ALS. As a result, MCR-ALS provided much higher repeatability and intra-subject consistency as compared with NMF, which were important for the reliability of the motor function evaluation. The stroke subjects had lower intra-subject consistency and seemingly had more synergies as compared with the healthy subjects. Thus, MCR-ALS is a promising muscle synergy analysis method for motor function evaluation of stroke patients.

Sparseness and Smoothness Regularized Imaging for improving the resolution of Cryo-EM single-particle reconstruction

Three-dimensional refinement is a critical component of cryo-EM single-particle reconstruction. In this paper, we report the development of a computational method, OPUS-SSRI, and its application to seven real cryo-EM datasets. Our data clearly demonstrated that OPUS-SSRI can improve the final resolutions and structural details in cryo-EM single-particle analysis.

In this paper, we present a refinement method for cryo-electron microscopy (cryo-EM) single-particle reconstruction, termed as OPUS-SSRI (Sparseness and Smoothness Regularized Imaging). In OPUS-SSRI, spatially varying sparseness and smoothness priors are incorporated to improve the regularity of electron density map, and a type of real space penalty function is designed. Moreover, we define the back-projection step as a local kernel regression and propose a first-order method to solve the resulting optimization problem. On the seven cryo-EM datasets that we tested, the average improvement in resolution by OPUS-SSRI over that from RELION 3.0, the commonly used image-processing software for single-particle cryo-EM, was 0.64 Å, with the largest improvement being 1.25 Å. We expect OPUS-SSRI to be an invaluable tool to the broad field of cryo-EM single-particle analysis. The implementation of OPUS-SSRI can be found at https://github.com/alncat/cryoem.

Effect of Circuit Structure on Odor Representation in the Insect Olfactory System

In neuroscience, the structure of a circuit has often been used to intuit function—an inversion of Louis Kahn’s famous dictum, “Form follows function” (Kristan and Katz, 2006). However, different brain networks may use different network architectures to solve the same problem. The olfactory circuits of two insects, the locust, Schistocerca americana, and the fruit fly, Drosophila melanogaster, serve the same function—to identify and discriminate odors. The neural circuitry that achieves this shows marked structural differences. Projection neurons (PNs) in the antennal lobe innervate Kenyon cells (KCs) of the mushroom body. In locust, each KC receives inputs from ∼50% of PNs, a scheme that maximizes the difference between inputs to any two of ∼50,000 KCs. In contrast, in Drosophila, this number is only 5% and appears suboptimal. Using a computational model of the olfactory system, we show that the activity of KCs is sufficiently high-dimensional that it can separate similar odors regardless of the divergence of PN–KC connections. However, when temporal patterning encodes odor attributes, dense connectivity outperforms sparse connections. Increased separability comes at the cost of reliability. The disadvantage of sparse connectivity can be mitigated by incorporating other aspects of circuit architecture seen in Drosophila. Our simulations predict that Drosophila and locust circuits lie at different ends of a continuum where the Drosophila gives up on the ability to resolve similar odors to generalize across varying environments, while the locust separates odor representations but risks misclassifying noisy variants of the same odor.

An Adaptive Homeostatic Algorithm for the Unsupervised Learning of Visual Features

The formation of structure in the visual system, that is, of the connections between cells within neural populations, is by and large an unsupervised learning process. In the primary visual cortex of mammals, for example, one can observe during development the formation of cells selective to localized, oriented features, which results in the development of a representation in area V1 of images’ edges. This can be modeled using a sparse Hebbian learning algorithms which alternate a coding step to encode the information with a learning step to find the proper encoder. A major difficulty of such algorithms is the joint problem of finding a good representation while knowing immature encoders, and to learn good encoders with a nonoptimal representation. To solve this problem, this work introduces a new regulation process between learning and coding which is motivated by the homeostasis processes observed in biology. Such an optimal homeostasis rule is implemented by including an adaptation mechanism based on nonlinear functions that balance the antagonistic processes that occur at the coding and learning time scales. It is compatible with a neuromimetic architecture and allows for a more efficient emergence of localized filters sensitive to orientation. In addition, this homeostasis rule is simplified by implementing a simple heuristic on the probability of activation of neurons. Compared to the optimal homeostasis rule, numerical simulations show that this heuristic allows to implement a faster unsupervised learning algorithm while retaining much of its effectiveness. These results demonstrate the potential application of such a strategy in machine learning and this is illustrated by showing the effect of homeostasis in the emergence of edge-like filters for a convolutional neural network.

Back-Propagation Learning in Deep Spike-By-Spike Networks

Artificial neural networks (ANNs) are important building blocks in technical applications. They rely on noiseless continuous signals in stark contrast to the discrete action potentials stochastically exchanged among the neurons in real brains. We propose to bridge this gap with Spike-by-Spike (SbS) networks which represent a compromise between non-spiking and spiking versions of generative models. What is missing, however, are algorithms for finding weight sets that would optimize the output performances of deep SbS networks with many layers. Here, a learning rule for feed-forward SbS networks is derived. The properties of this approach are investigated and its functionality is demonstrated by simulations. In particular, a Deep Convolutional SbS network for classifying handwritten digits achieves a classification performance of roughly 99.3% on the MNIST test data when the learning rule is applied together with an optimizer. Thereby it approaches the benchmark results of ANNs without extensive parameter optimization. We envision this learning rule for SBS networks to provide a new basis for research in neuroscience and for technical applications, especially when they become implemented on specialized computational hardware.

Task-Related Synaptic Changes Localized to Small Neuronal Population in Recurrent Neural Network Cortical Models

Humans have flexible control over cognitive functions depending on the context. Several studies suggest that the prefrontal cortex (PFC) controls this cognitive flexibility, but the detailed underlying mechanisms remain unclear. Recent developments in machine learning techniques allow simple PFC models written as a recurrent neural network to perform various behavioral tasks like humans and animals. Computational modeling allows the estimation of neuronal parameters that are crucial for performing the tasks, which cannot be observed by biologic experiments. To identify salient neural-network features for flexible cognition tasks, we compared four PFC models using a context-dependent integration task. After training the neural networks with the task, we observed highly plastic synapses localized to a small neuronal population in all models. In three of the models, the neuronal units containing these highly plastic synapses contributed most to the performance. No common tendencies were observed in the distribution of synaptic strengths among the four models. These results suggest that task-dependent plastic synaptic changes are more important for accomplishing flexible cognitive tasks than the structures of the constructed synaptic networks.

Sparse Ordinal Logistic Regression and Its Application to Brain Decoding

Brain decoding with multivariate classification and regression has provided a powerful framework for characterizing information encoded in population neural activity. Classification and regression models are respectively used to predict discrete and continuous variables of interest. However, cognitive and behavioral parameters that we wish to decode are often ordinal variables whose values are discrete but ordered, such as subjective ratings. To date, there is no established method of predicting ordinal variables in brain decoding. In this study, we present a new algorithm, sparse ordinal logistic regression (SOLR), that combines ordinal logistic regression with Bayesian sparse weight estimation. We found that, in both simulation and analyses using real functional magnetic resonance imaging (fMRI) data, SOLR outperformed ordinal logistic regression with non-sparse regularization, indicating that sparseness leads to better decoding performance. SOLR also outperformed classification and linear regression models with the same type of sparseness, indicating the advantage of the modeling tailored to ordinal outputs. Our results suggest that SOLR provides a principled and effective method of decoding ordinal variables.

Different latent class models were used and evaluated for assessing the accuracy of campylobacter diagnostic tests: overcoming imperfect reference standards?

In the absence of perfect reference standard, classical techniques result in biased diagnostic accuracy and prevalence estimates. By statistically defining the true disease status, latent class models (LCM) constitute a promising alternative. However, LCM is a complex method which relies on parametric assumptions, including usually a conditional independence between tests and might suffer from data sparseness. We carefully applied LCMs to assess new campylobacter infection detection tests for which bacteriological culture is an imperfect reference standard. Five diagnostic tests (culture, polymerase chain reaction and three immunoenzymatic tests) of campylobacter infection were collected in 623 patients from Bordeaux and Lyon Hospitals, France. Their diagnostic accuracy were estimated with standard and extended LCMs with a thorough examination of models goodness-of-fit. The model including a residual dependence specific to the immunoenzymatic tests best complied with LCM assumptions. Asymptotic results of goodness-of-fit statistics were substantially impaired by data sparseness and empirical distributions were preferred. Results confirmed moderate sensitivity of the culture and high performances of immunoenzymatic tests. LCMs can be used to estimate diagnostic tests accuracy in the absence of perfect reference standard. However, their implementation and assessment require specific attention due to data sparseness and limitations of existing software.

Simulation-based evaluation of the linear-mixed model in the presence of an increasing proportion of singletons

Data in medical sciences often have a hierarchical structure with lower level units (e.g. children) nested in higher level units (e.g. departments). Several specific but frequently studied settings, mainly in longitudinal and family research, involve a large number of units that tend to be quite small, with units containing only one element referred to as singletons. Regardless of sparseness, hierarchical data should be analyzed with appropriate methodology such as, for example linear-mixed models. Using a simulation study, based on the structure of a data example on Ceftriaxone consumption in hospitalized children, we assess the impact of an increasing proportion of singletons (0-95%), in data with a low, medium, or high intracluster correlation, on the stability of linear-mixed models parameter estimates, confidence interval coverage and F test performance. Some techniques that are frequently used in the presence of singletons include ignoring clustering, dropping the singletons from the analysis and grouping the singletons into an artificial unit. We show that both the fixed and random effects estimates and their standard errors are stable in the presence of an increasing proportion of singletons. We demonstrate that ignoring clustering and dropping singletons should be avoided as they come with biased standard error estimates. Grouping the singletons into an artificial unit might be considered, although the linear-mixed model performs better even when the proportion of singletons is high. We conclude that the linear-mixed model is stable in the presence of singletons when both lower- and higher level sample sizes are fixed. In this setting, the use of remedial measures, such as ignoring clustering and grouping or removing singletons, should be dissuaded.

The Role of Architectural and Learning Constraints in Neural Network Models: A Case Study on Visual Space Coding

The recent "deep learning revolution" in artificial neural networks had strong impact and widespread deployment for engineering applications, but the use of deep learning for neurocomputational modeling has been so far limited. In this article we argue that unsupervised deep learning represents an important step forward for improving neurocomputational models of perception and cognition, because it emphasizes the role of generative learning as opposed to discriminative (supervised) learning. As a case study, we present a series of simulations investigating the emergence of neural coding of visual space for sensorimotor transformations. We compare different network architectures commonly used as building blocks for unsupervised deep learning by systematically testing the type of receptive fields and gain modulation developed by the hidden neurons. In particular, we compare Restricted Boltzmann Machines (RBMs), which are stochastic, generative networks with bidirectional connections trained using contrastive divergence, with autoencoders, which are deterministic networks trained using error backpropagation. For both learning architectures we also explore the role of sparse coding, which has been identified as a fundamental principle of neural computation. The unsupervised models are then compared with supervised, feed-forward networks that learn an explicit mapping between different spatial reference frames. Our simulations show that both architectural and learning constraints strongly influenced the emergent coding of visual space in terms of distribution of tuning functions at the level of single neurons. Unsupervised models, and particularly RBMs, were found to more closely adhere to neurophysiological data from single-cell recordings in the primate parietal cortex. These results provide new insights into how basic properties of artificial neural networks might be relevant for modeling neural information processing in biological systems.

Central auditory neurons have composite receptive fields

High-level neurons processing complex, behaviorally relevant signals are sensitive to conjunctions of features. Characterizing the receptive fields of such neurons is difficult with standard statistical tools, however, and the principles governing their organization remain poorly understood. Here, we demonstrate multiple distinct receptive-field features in individual high-level auditory neurons in a songbird, European starling, in response to natural vocal signals (songs). We then show that receptive fields with similar characteristics can be reproduced by an unsupervised neural network trained to represent starling songs with a single learning rule that enforces sparseness and divisive normalization. We conclude that central auditory neurons have composite receptive fields that can arise through a combination of sparseness and normalization in neural circuits. Our results, along with descriptions of random, discontinuous receptive fields in the central olfactory neurons in mammals and insects, suggest general principles of neural computation across sensory systems and animal classes.

Adult hippocampal neurogenesis and pattern separation in DG: a role for feedback inhibition in modulating sparseness to govern population-based coding

The dentate gyrus (DG) of mammals harbors neural stem cells that generate new dentate granule cells (DGCs) throughout life. Behavioral studies using the contextual fear discrimination paradigm have found that selectively augmenting or blocking adult hippocampal neurogenesis enhances or impairs discrimination under conditions of high, but not low, interference suggestive of a role in pattern separation. Although contextual discrimination engages population-based coding mechanisms underlying pattern separation such as global remapping in the DG and CA3, how adult hippocampal neurogenesis modulates pattern separation in the DG is poorly understood. Here, we propose a role for adult-born DGCs in re-activation coupled modulation of sparseness through feed-back inhibition to govern global remapping in the DG.

A unifying theory of synaptic long-term plasticity based on a sparse distribution of synaptic strength

Long-term synaptic plasticity is fundamental to learning and network function. It has been studied under various induction protocols and depends on firing rates, membrane voltage, and precise timing of action potentials. These protocols show different facets of a common underlying mechanism but they are mostly modeled as distinct phenomena. Here, we show that all of these different dependencies can be explained from a single computational principle. The objective is a sparse distribution of excitatory synaptic strength, which may help to reduce metabolic costs associated with synaptic transmission. Based on this objective we derive a stochastic gradient ascent learning rule which is of differential-Hebbian type. It is formulated in biophysical quantities and can be related to current mechanistic theories of synaptic plasticity. The learning rule accounts for experimental findings from all major induction protocols and explains a classic phenomenon of metaplasticity. Furthermore, our model predicts the existence of metaplasticity for spike-timing-dependent plasticity Thus, we provide a theory of long-term synaptic plasticity that unifies different induction protocols and provides a connection between functional and mechanistic levels of description.

Network architecture underlying maximal separation of neuronal representations

One of the most basic and general tasks faced by all nervous systems is extracting relevant information from the organism's surrounding world. While physical signals available to sensory systems are often continuous, variable, overlapping, and noisy, high-level neuronal representations used for decision-making tend to be discrete, specific, invariant, and highly separable. This study addresses the question of how neuronal specificity is generated. Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties. For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated. In particular, connection probability ½, as found in the locust antennal-lobe-mushroom-body circuit, serves to maximize separation of neuronal representations across the target Kenyon cells (KCs), and explains their specific and reliable responses. This analysis yields a function expressing response specificity in terms of lower network parameters; together with appropriate gain control this leads to a simple neuronal algorithm for generating arbitrarily sparse and selective codes and linking network architecture and neural coding. I suggest a straightforward way to construct ecologically meaningful representations from this code.