Armen Stepanyants

Sparse connectivity is a hallmark of the brain and a desired property of artificial neural networks. It promotes energy efficiency, simplifies training, and enhances the robustness of network function. Thus, a detailed understanding of how to achieve sparsity without jeopardizing network performance is beneficial for neuroscience, deep learning, and neuromorphic computing applications. We used an exactly solvable model of associative learning to evaluate the effects of various sparsity-inducing constraints on connectivity and function. We determine the optimal level of sparsity achieved by the ℓ_{0} norm constraint and find that nearly the same efficiency can be obtained by eliminating weak connections. We show that this method of achieving sparsity can be implemented online, making it compatible with neuroscience and machine learning applications.

Fully automated registration algorithms are prone to getting trapped in solutions corresponding to local minima of their objective functions, leading to errors that are easy to detect but challenging to correct. Traditional solutions often involve iterative parameter tuning, data preprocessing and preregistering, and multiple algorithm reruns—an approach that is both time-consuming and does not guarantee satisfactory results. Therefore, for tasks where registration accuracy is more important than speed, it is appropriate to explore alternative, user-assisted registration strategies. In such tasks, finding and correcting errors in automated registration is often more time-consuming than directly integrating user input during the registration process. Therefore, this study evaluates a user-assisted approach for accurate nonrigid registration of images and traces. By leveraging the corresponding sets of fiducial points provided by the user to guide the registration, the algorithm computes an optimal nonrigid transformation that combines linear and nonlinear components. Our findings demonstrate that the registration accuracy of this approach improves consistently with the increased complexity of the linear transformation and as more fiducial points are provided. As a result, accuracy sufficient for many biomedical applications can be achieved within minutes, requiring only a small number of user-provided fiducial points.

Analyses of biomedical images often rely on accurate segmentation of structures of interest. Traditional segmentation methods based on thresholding, watershed, fast marching, and level set perform well in high-contrast images containing structures of similar intensities. However, such methods can under-segment or miss entirely low-intensity objects on noisy backgrounds. Machine learning segmentation methods promise superior performance but require large training datasets of labeled images which are difficult to create, particularly in 3D. Here, we propose an algorithm based on the Local Binary Fitting (LBF) level set method, specifically designed to improve the segmentation of low-contrast structures.

Neural networks in the brain can function reliably despite various sources of errors and noise present at every step of signal transmission. These sources include errors in the presynaptic inputs to the neurons, noise in synaptic transmission, and fluctuations in the neurons’ postsynaptic potentials. Collectively they lead to errors in the neurons’ outputs which are, in turn, injected into the network. Does unreliable network activity hinder fundamental functions of the brain, such as learning and memory retrieval? To explore this question, this article examines the effects of errors and noise on the properties of model networks of inhibitory and excitatory neurons involved in associative sequence learning. The associative learning problem is solved analytically and numerically, and it is also shown how memory sequences can be loaded into the network with a biologically more plausible perceptron-type learning rule. Interestingly, the results reveal that errors and noise during learning increase the probability of memory recall. There is a tradeoff between the capacity and reliability of stored memories, and, noise during learning is required for optimal retrieval of stored information. What is more, networks loaded with associative memories to capacity display many structural and dynamical features observed in local cortical circuits in mammals. Based on the similarities between the associative and cortical networks, this article predicts that connections originating from more unreliable neurons or neuron classes in the cortex are more likely to be depressed or eliminated during learning, while connections onto noisier neurons or neuron classes have lower probabilities and higher weights. SIGNIFICANCE STATEMENT Signal transmission in the brain is accompanied by many sources of errors and noise, and yet, neural networks can reliably store memories. This article argues that noise should not be viewed as a nuisance, but that it is an essential component of the reliable learning mechanism implemented by the brain. The article describes a network model of associative sequence learning, showing that for optimal retrieval of stored information learning must be carried out in the presence of noise. To validate the model, it is shown that associative memories can be loaded into the network with an online perceptron-type learning rule and that networks loaded to capacity develop many structural and dynamical properties observed in the brain.

The ability of neural networks to associate successive states of network activity lies at the basis of many cognitive functions. Hence, we hypothesized that many ubiquitous structural and dynamical properties of local cortical networks result from associative learning. To test this hypothesis, we trained recurrent networks of excitatory and inhibitory neurons on memories composed of varying numbers of associations and compared the resulting network properties with those observed experimentally. We show that, when the network is robustly loaded with near-maximum amount of associations it can support, it develops properties that are consistent with the observed probabilities of excitatory and inhibitory connections, shapes of connection weight distributions, overexpression of specific 2- and 3-neuron motifs, distributions of connection numbers in clusters of 3–8 neurons, sustained, irregular, and asynchronous firing activity, and balance of excitation and inhibition. In addition, memories loaded into the network can be retrieved, even in the presence of noise that is comparable with the baseline variations in the postsynaptic potential. The confluence of these results suggests that many structural and dynamical properties of local cortical networks are simply a byproduct of associative learning. We predict that overexpression of excitatory–excitatory bidirectional connections observed in many cortical systems must be accompanied with underexpression of bidirectionally connected inhibitory–excitatory neuron pairs. SIGNIFICANCE STATEMENT Many structural and dynamical properties of local cortical networks are ubiquitously present across areas and species. Because synaptic connectivity is shaped by experience, we wondered whether continual learning, rather than genetic control, is responsible for producing such features. To answer this question, we developed a biologically constrained recurrent network of excitatory and inhibitory neurons capable of learning predefined sequences of network states. Embedding such associative memories into the network revealed that, when individual neurons are robustly loaded with a near-maximum amount of memories they can support, the network develops many properties that are consistent with experimental observations. Our findings suggest that basic structural and dynamical properties of local networks in the brain are simply a byproduct of learning and memory storage.

In vivo imaging experiments often require automated detection and tracking of changes in the specimen. These tasks can be hindered by variations in the position and orientation of the specimen relative to the microscope, as well as by linear and nonlinear tissue deformations. We propose a feature-based registration method, coupled with optimal transformations, designed to address these problems in 3D time-lapse microscopy images. Features are detected as local regions of maximum intensity in source and target image stacks, and their bipartite intensity dissimilarity matrix is used as an input to the Hungarian algorithm to establish initial correspondences. A random sampling refinement method is employed to eliminate outliers, and the resulting set of corresponding features is used to determine an optimal translation, rigid, affine, or B-spline transformation for the registration of the source and target images. Accuracy of the proposed algorithm was tested on fluorescently labeled axons imaged over a 68-day period with a two-photon laser scanning microscope. To that end, multiple axons in individual stacks of images were traced semi-manually and optimized in 3D, and the distances between the corresponding traces were measured before and after the registration. The results show that there is a progressive improvement in the registration accuracy with increasing complexity of the transformations. In particular, sub-micrometer accuracy (2-3 voxels) was achieved with the regularized affine and Bspline transformations.

The ability to extract accurate morphology of labeled neurons from microscopy images is crucial for mapping brain connectivity and for understanding changes in connectivity that underlie learning and neurological disorders. There are, however, two problems, specific to optical microscopy imaging of neurons, which make accurate neuron tracing exceedingly challenging: (i) neurites can appear broken due to inhomogeneous labeling and (ii) neurites can appear fused in 3D due to limited resolution. Here, we propose and evaluate several artificial neural network (ANN) architectures and conventional image enhancement filters with the aim of alleviating both problems. We developed four image quality metrics to evaluate the effects of the proposed filters: normalized intensity in the cross-over regions between neurites, effective radius of neurites, coefficient of variation of intensity along neurites, and local background to neurite intensity ratio. Our results show that ANN-based filters, trained on optimized semi-manual traces of neurites, can significantly outperform conventional filters. In particular, U-Net based filtering can virtually eliminate background intensity, while also reducing the effective radius of neurites to nearly 1 voxel. In addition, this filter significantly decreases intensity in the cross-over regions between neurites and reduces fluctuations of intensity on neurites’ centerlines. These results suggest that including an ANN-based filtering step, which does not require substantial extra time or computing power, can be beneficial for automated neuron tracing projects.

The ability to extract accurate morphology of labeled neurons from microscopy images is crucial for mapping brain connectivity and for understanding changes in connectivity that underlie learning and memory formation. There are, however, two problems, specific to optical microscopy imaging of neurons, which make accurate neuron tracing exceedingly challenging: ( i ) neurites can appear broken due to inhomogeneous labeling and ( ii ) neurites can appear fused in 3D due to limited resolution. Here, we propose and evaluate several artificial neural network (NN) architectures and conventional image enhancement filters with the aim of solving both problems. To evaluate the effects of filtering, we examine the following four image quality metrics: normalized intensity in the cross-over regions between neurites, radius of neurites, coefficient of variation of intensity along neurites, and local background to neurite intensity ratio. Our results show that NN filters, trained on optimized semi-manual traces of neurites, can significantly outperform conventional filters. In particular, U-Net based filtering can virtually eliminate background intensity, while also reducing radius of neurites by 23% to nearly 1 voxel, decreasing intensity in the cross-over regions between neurites by 22%, and reducing variations in intensity along neurites by 26%. These results suggest that including a NN filtering step, which does not require much extra time or computing power, can be beneficial for neuron tracing projects.

In vivo imaging experiments often require automated detection and tracking of changes in the specimen. This problem, however, can be hindered by variations in the position and orientation of the specimen relative to the microscope, as well as by linear and nonlinear deformations. Here, we present a feature-based registration method, coupled with translation, rigid, affine, and B-spline transformations, designed to address these issues in 3D time-lapse microscopy images. In this method, features are detected as local intensity maxima in the source and target image stacks, and their similarity matrix is used as an input to the Hungarian algorithm to establish initial correspondences. Random Sampling Consensus algorithm is then employed to eliminate outliers. The resulting set of corresponding features is used to determine the optimal transformations. Accuracy of the proposed algorithm was tested on fluorescently labeled axons imaged over a 48- day period with a two-photon laser scanning microscope. For this, multiple axons in individual stacks of images were traced semi-manually in 3D, and the distances between the corresponding traces were measured before and after the registration. The results show that there is a progressive improvement in the registration accuracy with increasing complexity of the transformations. In particular, an accuracy of less than 1 voxel (0.26 μm) was achieved with a regularized B-spline transformation. To illustrate the utility of the proposed method, registered images were used to automatically track synaptic boutons on axons over the entire duration of the experiment, yielding 99% precision and recall.

The ability of neural networks to associate successive states of network activity lies at the basis of many cognitive functions. Hence, we hypothesized that many ubiquitous structural and dynamical properties of local cortical networks result from associative learning. To test this hypothesis, we trained recurrent networks of excitatory and inhibitory neurons on memory sequences of varying lengths and compared network properties to those observed experimentally. We show that when the network is robustly loaded with near-maximum amount of associations it can support, it develops properties that are consistent with the observed probabilities of excitatory and inhibitory connections, shapes of connection weight distributions, overrepresentations of specific 3-neuron motifs, distributions of connection numbers in clusters of 3–8 neurons, sustained, irregular, and asynchronous firing activity, and balance of excitation and inhibition. What is more, memories loaded into the network can be retrieved even in the presence of noise comparable to the baseline variations in the postsynaptic potential. Confluence of these results suggests that many structural and dynamical properties of local cortical networks are simply a byproduct of associative learning.