Dmitri B. Chklovskii

Lyndon R. Duong, Eero P. Simoncelli, Dmitri B. Chklovskii et al.

Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed as an adaptive form of statistical whitening. Existing mechanistic models of adaptive whitening exclusively use either synaptic plasticity or gain modulation as the biological substrate for adaptation; however, on their own, each of these models has significant limitations. In this work, we unify these approaches in a normative multi-timescale mechanistic model that adaptively whitens its responses with complementary computational roles for synaptic plasticity and gain modulation. Gains are modified on a fast timescale to adapt to the current statistical context, whereas synapses are modified on a slow timescale to match structural properties of the input statistics that are invariant across contexts. Our model is derived from a novel multi-timescale whitening objective that factorizes the inverse whitening matrix into basis vectors, which correspond to synaptic weights, and a diagonal matrix, which corresponds to neuronal gains. We test our model on synthetic and natural datasets and find that the synapses learn optimal configurations over long timescales that enable adaptive whitening on short timescales using gain modulation.

Lyndon R. Duong, David Lipshutz, David J. Heeger et al.

Statistical whitening transformations play a fundamental role in many computational systems, and may also play an important role in biological sensory systems. Existing neural circuit models of adaptive whitening operate by modifying synaptic interactions; however, such modifications would seem both too slow and insufficiently reversible. Motivated by the extensive neuroscience literature on gain modulation, we propose an alternative model that adaptively whitens its responses by modulating the gains of individual neurons. Starting from a novel whitening objective, we derive an online algorithm that whitens its outputs by adjusting the marginal variances of an overcomplete set of projections. We map the algorithm onto a recurrent neural network with fixed synaptic weights and gain-modulating interneurons. We demonstrate numerically that sign-constraining the gains improves robustness of the network to ill-conditioned inputs, and a generalization of the circuit achieves a form of local whitening in convolutional populations, such as those found throughout the visual or auditory systems.

David Lipshutz, Cengiz Pehlevan, Dmitri B. Chklovskii

Early sensory systems in the brain rapidly adapt to fluctuating input statistics, which requires recurrent communication between neurons. Mechanistically, such recurrent communication is often indirect and mediated by local interneurons. In this work, we explore the computational benefits of mediating recurrent communication via interneurons compared with direct recurrent connections. To this end, we consider two mathematically tractable recurrent linear neural networks that statistically whiten their inputs -- one with direct recurrent connections and the other with interneurons that mediate recurrent communication. By analyzing the corresponding continuous synaptic dynamics and numerically simulating the networks, we show that the network with interneurons is more robust to initialization than the network with direct recurrent connections in the sense that the convergence time for the synaptic dynamics in the network with interneurons (resp. direct recurrent connections) scales logarithmically (resp. linearly) with the spectrum of their initialization. Our results suggest that interneurons are computationally useful for rapid adaptation to changing input statistics. Interestingly, the network with interneurons is an overparameterized solution of the whitening objective for the network with direct recurrent connections, so our results can be viewed as a recurrent linear neural network analogue of the implicit acceleration phenomenon observed in overparameterized feedforward linear neural networks.

Siavash Golkar, David Lipshutz, Tiberiu Tesileanu et al.

Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a more informative generalization of PCA that takes advantage of contrastive learning. However, the performance of cPCA is sensitive to hyper-parameter choice and there is currently no online algorithm for implementing cPCA. Here, we introduce a modified cPCA method, which we denote cPCA*, that is more interpretable and less sensitive to the choice of hyper-parameter. We derive an online algorithm for cPCA* and show that it maps onto a neural network with local learning rules, so it can potentially be implemented in energy efficient neuromorphic hardware. We evaluate the performance of our online algorithm on real datasets and highlight the differences and similarities with the original formulation.

Yanis Bahroun, Dmitri B. Chklovskii, Anirvan M. Sengupta

A normative approach called Similarity Matching was recently introduced for deriving and understanding the algorithmic basis of neural computation focused on unsupervised problems. It involves deriving algorithms from computational objectives and evaluating their compatibility with anatomical and physiological observations. In particular, it introduces neural architectures by considering dual alternatives instead of primal formulations of popular models such as PCA. However, its connection to the Representer theorem remains unexplored. In this work, we propose to use teachings from this approach to explore supervised learning algorithms and clarify the notion of Hebbian learning. We examine regularized supervised learning and elucidate the emergence of neural architecture and additive versus multiplicative update rules. In this work, we focus not on developing new algorithms but on showing that the Representer theorem offers the perfect lens to study biologically plausible learning algorithms. We argue that many past and current advancements in the field rely on some form of dual formulation to introduce biological plausibility. In short, as long as a dual formulation exists, it is possible to derive biologically plausible algorithms. Our work sheds light on the pivotal role of the Representer theorem in advancing our comprehension of neural computation.

Yanis Bahroun, Shagesh Sridharan, Atithi Acharya et al.

While effective, the backpropagation (BP) algorithm exhibits limitations in terms of biological plausibility, computational cost, and suitability for online learning. As a result, there has been a growing interest in developing alternative biologically plausible learning approaches that rely on local learning rules. This study focuses on the primarily unsupervised similarity matching (SM) framework, which aligns with observed mechanisms in biological systems and offers online, localized, and biologically plausible algorithms. i) To scale SM to large datasets, we propose an implementation of Convolutional Nonnegative SM using PyTorch. ii) We introduce a localized supervised SM objective reminiscent of canonical correlation analysis, facilitating stacking SM layers. iii) We leverage the PyTorch implementation for pre-training architectures such as LeNet and compare the evaluation of features against BP-trained models. This work combines biologically plausible algorithms with computational efficiency opening multiple avenues for further explorations.

Jason Moore, Alexander Genkin, Magnus Tournoy et al.

In the quest to model neuronal function amidst gaps in physiological data, a promising strategy is to develop a normative theory that interprets neuronal physiology as optimizing a computational objective. This study extends the current normative models, which primarily optimize prediction, by conceptualizing neurons as optimal feedback controllers. We posit that neurons, especially those beyond early sensory areas, act as controllers, steering their environment towards a specific desired state through their output. This environment comprises both synaptically interlinked neurons and external motor sensory feedback loops, enabling neurons to evaluate the effectiveness of their control via synaptic feedback. Utilizing the novel Direct Data-Driven Control (DD-DC) framework, we model neurons as biologically feasible controllers which implicitly identify loop dynamics, infer latent states and optimize control. Our DD-DC neuron model explains various neurophysiological phenomena: the shift from potentiation to depression in Spike-Timing-Dependent Plasticity (STDP) with its asymmetry, the duration and adaptive nature of feedforward and feedback neuronal filters, the imprecision in spike generation under constant stimulation, and the characteristic operational variability and noise in the brain. Our model presents a significant departure from the traditional, feedforward, instant-response McCulloch-Pitts-Rosenblatt neuron, offering a novel and biologically-informed fundamental unit for constructing neural networks.

Jules Berman, Dmitri B. Chklovskii, Jingpeng Wu

In the field of Connectomics, a primary problem is that of 3D neuron segmentation. Although deep learning-based methods have achieved remarkable accuracy, errors still exist, especially in regions with image defects. One common type of defect is that of consecutive missing image sections. Here, data is lost along some axis, and the resulting neuron segmentations are split across the gap. To address this problem, we propose a novel method based on point cloud representations of neurons. We formulate the problem as a classification problem and train CurveNet, a state-of-the-art point cloud classification model, to identify which neurons should be merged. We show that our method not only performs strongly but also scales reasonably to gaps well beyond what other methods have attempted to address. Additionally, our point cloud representations are highly efficient in terms of data, maintaining high performance with an amount of data that would be unfeasible for other methods. We believe that this is an indicator of the viability of using point cloud representations for other proofreading tasks.

Johannes Friedrich, Siavash Golkar, Shiva Farashahi et al.

A major problem in motor control is understanding how the brain plans and executes proper movements in the face of delayed and noisy stimuli. A prominent framework for addressing such control problems is Optimal Feedback Control (OFC). OFC generates control actions that optimize behaviorally relevant criteria by integrating noisy sensory stimuli and the predictions of an internal model using the Kalman filter or its extensions. However, a satisfactory neural model of Kalman filtering and control is lacking because existing proposals have the following limitations: not considering the delay of sensory feedback, training in alternating phases, and requiring knowledge of the noise covariance matrices, as well as that of systems dynamics. Moreover, the majority of these studies considered Kalman filtering in isolation, and not jointly with control. To address these shortcomings, we introduce a novel online algorithm which combines adaptive Kalman filtering with a model free control approach (i.e., policy gradient algorithm). We implement this algorithm in a biologically plausible neural network with local synaptic plasticity rules. This network performs system identification and Kalman filtering, without the need for multiple phases with distinct update rules or the knowledge of the noise covariances. It can perform state estimation with delayed sensory feedback, with the help of an internal model. It learns the control policy without requiring any knowledge of the dynamics, thus avoiding the need for weight transport. In this way, our implementation of OFC solves the credit assignment problem needed to produce the appropriate sensory-motor control in the presence of stimulus delay.

Yanis Bahroun, Anirvan M. Sengupta, Dmitri B. Chklovskii

Learning to detect content-independent transformations from data is one of the central problems in biological and artificial intelligence. An example of such problem is unsupervised learning of a visual motion detector from pairs of consecutive video frames. Rao and Ruderman formulated this problem in terms of learning infinitesimal transformation operators (Lie group generators) via minimizing image reconstruction error. Unfortunately, it is difficult to map their model onto a biologically plausible neural network (NN) with local learning rules. Here we propose a biologically plausible model of motion detection. We also adopt the transformation-operator approach but, instead of reconstruction-error minimization, start with a similarity-preserving objective function. An online algorithm that optimizes such an objective function naturally maps onto an NN with biologically plausible learning rules. The trained NN recapitulates major features of the well-studied motion detector in the fly. In particular, it is consistent with the experimental observation that local motion detectors combine information from at least three adjacent pixels, something that contradicts the celebrated Hassenstein-Reichardt model.

Yanis Bahroun, Dmitri B. Chklovskii

The development of neuromorphic hardware and modeling of biological neural networks requires algorithms with local learning rules. Artificial neural networks using local learning rules to perform principal subspace analysis (PSA) and clustering have recently been derived from principled objective functions. However, no biologically plausible networks exist for minor subspace analysis (MSA), a fundamental signal processing task. MSA extracts the lowest-variance subspace of the input signal covariance matrix. Here, we introduce a novel similarity matching objective for extracting the minor subspace, Minor Subspace Similarity Matching (MSSM). Moreover, we derive an adaptive MSSM algorithm that naturally maps onto a novel neural network with local learning rules and gives numerical results showing that our method converges at a competitive rate.

Siavash Golkar, David Lipshutz, Yanis Bahroun et al.

The backpropagation algorithm is an invaluable tool for training artificial neural networks; however, because of a weight sharing requirement, it does not provide a plausible model of brain function. Here, in the context of a two-layer network, we derive an algorithm for training a neural network which avoids this problem by not requiring explicit error computation and backpropagation. Furthermore, our algorithm maps onto a neural network that bears a remarkable resemblance to the connectivity structure and learning rules of the cortex. We find that our algorithm empirically performs comparably to backprop on a number of datasets.

Siavash Golkar, David Lipshutz, Yanis Bahroun et al.

To guide behavior, the brain extracts relevant features from high-dimensional data streamed by sensory organs. Neuroscience experiments demonstrate that the processing of sensory inputs by cortical neurons is modulated by instructive signals which provide context and task-relevant information. Here, adopting a normative approach, we model these instructive signals as supervisory inputs guiding the projection of the feedforward data. Mathematically, we start with a family of Reduced-Rank Regression (RRR) objective functions which include Reduced Rank (minimum) Mean Square Error (RRMSE) and Canonical Correlation Analysis (CCA), and derive novel offline and online optimization algorithms, which we call Bio-RRR. The online algorithms can be implemented by neural networks whose synaptic learning rules resemble calcium plateau potential dependent plasticity observed in the cortex. We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal. We demonstrate that, despite relying exclusively on biologically plausible local learning rules, our algorithms perform competitively with existing implementations of RRMSE and CCA.

David Lipshutz, Charlie Windolf, Siavash Golkar et al.

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.

David Lipshutz, Cengiz Pehlevan, Dmitri B. Chklovskii

An important problem in neuroscience is to understand how brains extract relevant signals from mixtures of unknown sources, i.e., perform blind source separation. To model how the brain performs this task, we seek a biologically plausible single-layer neural network implementation of a blind source separation algorithm. For biological plausibility, we require the network to satisfy the following three basic properties of neuronal circuits: (i) the network operates in the online setting; (ii) synaptic learning rules are local; (iii) neuronal outputs are nonnegative. Closest is the work by Pehlevan et al. [Neural Computation, 29, 2925--2954 (2017)], which considers Nonnegative Independent Component Analysis (NICA), a special case of blind source separation that assumes the mixture is a linear combination of uncorrelated, nonnegative sources. They derive an algorithm with a biologically plausible 2-layer network implementation. In this work, we improve upon their result by deriving 2 algorithms for NICA, each with a biologically plausible single-layer network implementation. The first algorithm maps onto a network with indirect lateral connections mediated by interneurons. The second algorithm maps onto a network with direct lateral connections and multi-compartmental output neurons.

David Lipshutz, Yanis Bahroun, Siavash Golkar et al.

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.

Cengiz Pehlevan, Dmitri B. Chklovskii

Although the currently popular deep learning networks achieve unprecedented performance on some tasks, the human brain still has a monopoly on general intelligence. Motivated by this and biological implausibility of deep learning networks, we developed a family of biologically plausible artificial neural networks (NNs) for unsupervised learning. Our approach is based on optimizing principled objective functions containing a term that matches the pairwise similarity of outputs to the similarity of inputs, hence the name - similarity-based. Gradient-based online optimization of such similarity-based objective functions can be implemented by NNs with biologically plausible local learning rules. Similarity-based cost functions and associated NNs solve unsupervised learning tasks such as linear dimensionality reduction, sparse and/or nonnegative feature extraction, blind nonnegative source separation, clustering and manifold learning.

Andrea Giovannucci, Victor Minden, Cengiz Pehlevan et al.

Big data problems frequently require processing datasets in a streaming fashion, either because all data are available at once but collectively are larger than available memory or because the data intrinsically arrive one data point at a time and must be processed online. Here, we introduce a computationally efficient version of similarity matching, a framework for online dimensionality reduction that incrementally estimates the top K-dimensional principal subspace of streamed data while keeping in memory only the last sample and the current iterate. To assess the performance of our approach, we construct and make public a test suite containing both a synthetic data generator and the infrastructure to test online dimensionality reduction algorithms on real datasets, as well as performant implementations of our algorithm and competing algorithms with similar aims. Among the algorithms considered we find our approach to be competitive, performing among the best on both synthetic and real data.

Cengiz Pehlevan, Sreyas Mohan, Dmitri B. Chklovskii

Blind source separation, i.e. extraction of independent sources from a mixture, is an important problem for both artificial and natural signal processing. Here, we address a special case of this problem when sources (but not the mixing matrix) are known to be nonnegative, for example, due to the physical nature of the sources. We search for the solution to this problem that can be implemented using biologically plausible neural networks. Specifically, we consider the online setting where the dataset is streamed to a neural network. The novelty of our approach is that we formulate blind nonnegative source separation as a similarity matching problem and derive neural networks from the similarity matching objective. Importantly, synaptic weights in our networks are updated according to biologically plausible local learning rules.

Cengiz Pehlevan, Anirvan Sengupta, Dmitri B. Chklovskii

Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet, derivations of single-layer networks with such local learning rules from principled optimization objectives became possible only recently, with the introduction of similarity matching objectives. What explains the success of similarity matching objectives in deriving neural networks with local learning rules? Here, using dimensionality reduction as an example, we introduce several variable substitutions that illuminate the success of similarity matching. We show that the full network objective may be optimized separately for each synapse using local learning rules both in the offline and online settings. We formalize the long-standing intuition of the rivalry between Hebbian and anti-Hebbian rules by formulating a min-max optimization problem. We introduce a novel dimensionality reduction objective using fractional matrix exponents. To illustrate the generality of our approach, we apply it to a novel formulation of dimensionality reduction combined with whitening. We confirm numerically that the networks with learning rules derived from principled objectives perform better than those with heuristic learning rules.

Yuansi Chen, Cengiz Pehlevan, Dmitri B. Chklovskii

Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be determined adaptively by thresholding the singular values of the input data matrix. However, setting such threshold requires knowing the magnitude of the desired singular values in advance. Here we propose online algorithms where the threshold is self-calibrating based on the singular values computed from the existing observations. To derive these algorithms from the similarity matching cost function we propose novel regularizers. As before, these online algorithms can be implemented by Hebbian/anti-Hebbian neural networks in which the learning rule depends on the chosen regularizer. We demonstrate both mathematically and via simulation the effectiveness of these online algorithms in various settings.

Cengiz Pehlevan, Dmitri B. Chklovskii

In analyzing information streamed by sensory organs, our brains face challenges similar to those solved in statistical signal processing. This suggests that biologically plausible implementations of online signal processing algorithms may model neural computation. Here, we focus on such workhorses of signal processing as Principal Component Analysis (PCA) and whitening which maximize information transmission in the presence of noise. We adopt the similarity matching framework, recently developed for principal subspace extraction, but modify the existing objective functions by adding a decorrelating term. From the modified objective functions, we derive online PCA and whitening algorithms which are implementable by neural networks with local learning rules, i.e. synaptic weight updates that depend on the activity of only pre- and postsynaptic neurons. Our theory offers a principled model of neural computations and makes testable predictions such as the dropout of underutilized neurons.

Cengiz Pehlevan, Dmitri B. Chklovskii

To make sense of the world our brains must analyze high-dimensional datasets streamed by our sensory organs. Because such analysis begins with dimensionality reduction, modelling early sensory processing requires biologically plausible online dimensionality reduction algorithms. Recently, we derived such an algorithm, termed similarity matching, from a Multidimensional Scaling (MDS) objective function. However, in the existing algorithm, the number of output dimensions is set a priori by the number of output neurons and cannot be changed. Because the number of informative dimensions in sensory inputs is variable there is a need for adaptive dimensionality reduction. Here, we derive biologically plausible dimensionality reduction algorithms which adapt the number of output dimensions to the eigenspectrum of the input covariance matrix. We formulate three objective functions which, in the offline setting, are optimized by the projections of the input dataset onto its principal subspace scaled by the eigenvalues of the output covariance matrix. In turn, the output eigenvalues are computed as i) soft-thresholded, ii) hard-thresholded, iii) equalized thresholded eigenvalues of the input covariance matrix. In the online setting, we derive the three corresponding adaptive algorithms and map them onto the dynamics of neuronal activity in networks with biologically plausible local learning rules. Remarkably, in the last two networks, neurons are divided into two classes which we identify with principal neurons and interneurons in biological circuits.

Tao Hu, Cengiz Pehlevan, Dmitri B. Chklovskii

Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modeled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor-filter receptive fields from a natural image ensemble in agreement with physiological experiments. Whereas the OF algorithm can be mapped onto the dynamics and synaptic plasticity in a single-layer neural network, the derived learning rule is nonlocal - the synaptic weight update depends on the activity of neurons other than just pre- and postsynaptic ones - and hence biologically implausible. Here, to overcome this problem, we derive sparse dictionary learning from a novel cost-function - a regularized error of the symmetric factorization of the input's similarity matrix. Our algorithm maps onto a neural network of the same architecture as OF but using only biologically plausible local learning rules. When trained on natural images our network learns Gabor-filter receptive fields and reproduces the correlation among synaptic weights hard-wired in the OF network. Therefore, online symmetric matrix factorization may serve as an algorithmic theory of neural computation.

Cengiz Pehlevan, Dmitri B. Chklovskii

Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of the streamed data. By starting with the SNMF cost function we derive an online algorithm, which can be implemented by a biologically plausible network with local learning rules. We demonstrate that such network performs soft clustering of the data as well as sparse feature discovery. The derived algorithm replicates many known aspects of sensory anatomy and biophysical properties of neurons including unipolar nature of neuronal activity and synaptic weights, local synaptic plasticity rules and the dependence of learning rate on cumulative neuronal activity. Thus, we make a step towards an algorithmic theory of neuronal function, which should facilitate large-scale neural circuit simulations and biologically inspired artificial intelligence.

Cengiz Pehlevan, Tao Hu, Dmitri B. Chklovskii

Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost function these rules are nonlocal and hence biologically implausible. At the same time, biologically plausible local rules have been postulated rather than derived from a principled cost function. Here, to bridge this gap, we derive a biologically plausible network for subspace learning on streaming data by minimizing a principled cost function. In a departure from previous work, where cost was quantified by the representation, or reconstruction, error, we adopt a multidimensional scaling (MDS) cost function for streaming data. The resulting algorithm relies only on biologically plausible Hebbian and anti-Hebbian local learning rules. In a stochastic setting, synaptic weights converge to a stationary state which projects the input data onto the principal subspace. If the data are generated by a nonstationary distribution, the network can track the principal subspace. Thus, our result makes a step towards an algorithmic theory of neural computation.

Tao Hu, Zaid J. Towfic, Cengiz Pehlevan et al.

A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of synaptic weights scaled by an outgoing sparse activity vector. Formally, a neuron minimizes a cost function comprising a cumulative squared representation error and regularization terms. We derive an online algorithm that minimizes such cost function by alternating between the minimization with respect to activity and with respect to synaptic weights. The steps of this algorithm reproduce well-known physiological properties of a neuron, such as weighted summation and leaky integration of synaptic inputs, as well as an Oja-like, but parameter-free, synaptic learning rule. Our theoretical framework makes several predictions, some of which can be verified by the existing data, others require further experiments. Such framework should allow modeling the function of neuronal circuits without necessarily measuring all the microscopic biophysical parameters, as well as facilitate the design of neuromorphic electronics.

Juan Nunez-Iglesias, Ryan Kennedy, Toufiq Parag et al.

We aim to improve segmentation through the use of machine learning tools during region agglomeration. We propose an active learning approach for performing hierarchical agglomerative segmentation from superpixels. Our method combines multiple features at all scales of the agglomerative process, works for data with an arbitrary number of dimensions, and scales to very large datasets. We advocate the use of variation of information to measure segmentation accuracy, particularly in 3D electron microscopy (EM) images of neural tissue, and using this metric demonstrate an improvement over competing algorithms in EM and natural images.

Tao Hu, Dmitri B. Chklovskii

Natural stimuli are highly redundant, possessing significant spatial and temporal correlations. While sparse coding has been proposed as an efficient strategy employed by neural systems to encode sensory stimuli, the underlying mechanisms are still not well understood. Most previous approaches model the neural dynamics by the sparse representation dictionary itself and compute the representation coefficients offline. In reality, faced with the challenge of constantly changing stimuli, neurons must compute the sparse representations dynamically in an online fashion. Here, we describe a leaky linearized Bregman iteration (LLBI) algorithm which computes the time varying sparse representations using a biologically motivated network of leaky rectifying neurons. Compared to previous attempt of dynamic sparse coding, LLBI exploits the temporal correlation of stimuli and demonstrate better performance both in representation error and the smoothness of temporal evolution of sparse coefficients.

Tao Hu, Alexander Genkin, Dmitri B. Chklovskii

Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating via low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, such operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise, specifically, the representation error decays as 1/sqrt(t) for Gaussian white noise.

Tao Hu, Dmitri B. Chklovskii

We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI is bias free and compare its operation with existing sparse LMS algorithms by rederiving them in the online convex optimization framework. We perform convergence analysis of OLBI for white input signals and derive theoretical expressions for both the steady state and instantaneous mean square deviations (MSD). We demonstrate numerically that OLBI improves the performance of LMS type algorithms for signals generated from sparse tap weights.