Functional specificity of recurrent inhibition in visual cortex.

In the neocortex, neural activity is shaped by the interaction of excitatory and inhibitory neurons, defined by the organization of their synaptic connections. Although connections among excitatory pyramidal neurons are sparse and functionally tuned, inhibitory connectivity is thought to be dense and largely unstructured. By measuring in vivo visual responses and synaptic connectivity of parvalbumin-expressing (PV+) inhibitory cells in mouse primary visual cortex, we show that the synaptic weights of their connections to nearby pyramidal neurons are specifically tuned according to the similarity of the cells' responses. Individual PV+ cells strongly inhibit those pyramidal cells that provide them with strong excitation and share their visual selectivity. This structured organization of inhibitory synaptic weights provides a circuit mechanism for tuned inhibition onto pyramidal cells despite dense connectivity, stabilizing activity within feature-specific excitatory ensembles while supporting competition between them.

Supervised training of spiking neural networks for robust deployment on mixed-signal neuromorphic processors.

Mixed-signal analog/digital circuits emulate spiking neurons and synapses with extremely high energy efficiency, an approach known as "neuromorphic engineering". However, analog circuits are sensitive to process-induced variation among transistors in a chip ("device mismatch"). For neuromorphic implementation of Spiking Neural Networks (SNNs), mismatch causes parameter variation between identically-configured neurons and synapses. Each chip exhibits a different distribution of neural parameters, causing deployed networks to respond differently between chips. Current solutions to mitigate mismatch based on per-chip calibration or on-chip learning entail increased design complexity, area and cost, making deployment of neuromorphic devices expensive and difficult. Here we present a supervised learning approach that produces SNNs with high robustness to mismatch and other common sources of noise. Our method trains SNNs to perform temporal classification tasks by mimicking a pre-trained dynamical system, using a local learning rule from non-linear control theory. We demonstrate our method on two tasks requiring temporal memory, and measure the robustness of our approach to several forms of noise and mismatch. We show that our approach is more robust than common alternatives for training SNNs. Our method provides robust deployment of pre-trained networks on mixed-signal neuromorphic hardware, without requiring per-device training or calibration.

Feedforward Approximations to Dynamic Recurrent Network Architectures.

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solving systems of differential equations, and the number of evaluations required to determine their response to a given input can vary with the input or can be indeterminate altogether in the case of oscillations or instability. In feedforward networks, by contrast, only a single pass through the network is needed to determine the response to a given input. Modern machine learning systems are designed to operate efficiently on feedforward architectures. We hypothesized that two-layer feedforward architectures with simple, deterministic dynamics could approximate the responses of single-layer recurrent network architectures. By identifying the fixed-point responses of a given recurrent network, we trained two-layer networks to directly approximate the fixed-point response to a given input. These feedforward networks then embodied useful computations, including competitive interactions, information transformations, and noise rejection. Our approach was able to find useful approximations to recurrent networks, which can then be evaluated in linear and deterministic time complexity.

Specific excitatory connectivity for feature integration in mouse primary visual cortex.

Local excitatory connections in mouse primary visual cortex (V1) are stronger and more prevalent between neurons that share similar functional response features. However, the details of how functional rules for local connectivity shape neuronal responses in V1 remain unknown. We hypothesised that complex responses to visual stimuli may arise as a consequence of rules for selective excitatory connectivity within the local network in the superficial layers of mouse V1. In mouse V1 many neurons respond to overlapping grating stimuli (plaid stimuli) with highly selective and facilitatory responses, which are not simply predicted by responses to single gratings presented alone. This complexity is surprising, since excitatory neurons in V1 are considered to be mainly tuned to single preferred orientations. Here we examined the consequences for visual processing of two alternative connectivity schemes: in the first case, local connections are aligned with visual properties inherited from feedforward input (a 'like-to-like' scheme specifically connecting neurons that share similar preferred orientations); in the second case, local connections group neurons into excitatory subnetworks that combine and amplify multiple feedforward visual properties (a 'feature binding' scheme). By comparing predictions from large scale computational models with in vivo recordings of visual representations in mouse V1, we found that responses to plaid stimuli were best explained by assuming feature binding connectivity. Unlike under the like-to-like scheme, selective amplification within feature-binding excitatory subnetworks replicated experimentally observed facilitatory responses to plaid stimuli; explained selective plaid responses not predicted by grating selectivity; and was consistent with broad anatomical selectivity observed in mouse V1. Our results show that visual feature binding can occur through local recurrent mechanisms without requiring feedforward convergence, and that such a mechanism is consistent with visual responses and cortical anatomy in mouse V1.

Thalamic nuclei convey diverse contextual information to layer 1 of visual cortex.

Sensory perception depends on the context in which a stimulus occurs. Prevailing models emphasize cortical feedback as the source of contextual modulation. However, higher order thalamic nuclei, such as the pulvinar, interconnect with many cortical and subcortical areas, suggesting a role for the thalamus in providing sensory and behavioral context. Yet the nature of the signals conveyed to cortex by higher order thalamus remains poorly understood. Here we use axonal calcium imaging to measure information provided to visual cortex by the pulvinar equivalent in mice, the lateral posterior nucleus (LP), as well as the dorsolateral geniculate nucleus (dLGN). We found that dLGN conveys retinotopically precise visual signals, while LP provides distributed information from the visual scene. Both LP and dLGN projections carry locomotion signals. However, while dLGN inputs often respond to positive combinations of running and visual flow speed, LP signals discrepancies between self-generated and external visual motion. This higher order thalamic nucleus therefore conveys diverse contextual signals that inform visual cortex about visual scene changes not predicted by the animal's own actions.

Model-based analysis of pattern motion processing in mouse primary visual cortex.

Neurons in sensory areas of neocortex exhibit responses tuned to specific features of the environment. In visual cortex, information about features such as edges or textures with particular orientations must be integrated to recognize a visual scene or object. Connectivity studies in rodent cortex have revealed that neurons make specific connections within sub-networks sharing common input tuning. In principle, this sub-network architecture enables local cortical circuits to integrate sensory information. However, whether feature integration indeed occurs locally in rodent primary sensory areas has not been examined directly. We studied local integration of sensory features in primary visual cortex (V1) of the mouse by presenting drifting grating and plaid stimuli, while recording the activity of neuronal populations with two-photon calcium imaging. Using a Bayesian model-based analysis framework, we classified single-cell responses as being selective for either individual grating components or for moving plaid patterns. Rather than relying on trial-averaged responses, our model-based framework takes into account single-trial responses and can easily be extended to consider any number of arbitrary predictive models. Our analysis method was able to successfully classify significantly more responses than traditional partial correlation (PC) analysis, and provides a rigorous statistical framework to rank any number of models and reject poorly performing models. We also found a large proportion of cells that respond strongly to only one stimulus class. In addition, a quarter of selectively responding neurons had more complex responses that could not be explained by any simple integration model. Our results show that a broad range of pattern integration processes already take place at the level of V1. This diversity of integration is consistent with processing of visual inputs by local sub-networks within V1 that are tuned to combinations of sensory features.

Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks.

The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection weighting modulated by physical proximity (i.e., asymmetric Euclidean random matrices), modular network partitioning, and functional specificity within the excitatory population. We present a set of analytical constraints that apply to the eigenvalue spectra of associated weight matrices, highlighting the relationship between connectivity rules and classes of network dynamics.

Functional organization of excitatory synaptic strength in primary visual cortex.

The strength of synaptic connections fundamentally determines how neurons influence each other's firing. Excitatory connection amplitudes between pairs of cortical neurons vary over two orders of magnitude, comprising only very few strong connections among many weaker ones. Although this highly skewed distribution of connection strengths is observed in diverse cortical areas, its functional significance remains unknown: it is not clear how connection strength relates to neuronal response properties, nor how strong and weak inputs contribute to information processing in local microcircuits. Here we reveal that the strength of connections between layer 2/3 (L2/3) pyramidal neurons in mouse primary visual cortex (V1) obeys a simple rule--the few strong connections occur between neurons with most correlated responses, while only weak connections link neurons with uncorrelated responses. Moreover, we show that strong and reciprocal connections occur between cells with similar spatial receptive field structure. Although weak connections far outnumber strong connections, each neuron receives the majority of its local excitation from a small number of strong inputs provided by the few neurons with similar responses to visual features. By dominating recurrent excitation, these infrequent yet powerful inputs disproportionately contribute to feature preference and selectivity. Therefore, our results show that the apparently complex organization of excitatory connection strength reflects the similarity of neuronal responses, and suggest that rare, strong connections mediate stimulus-specific response amplification in cortical microcircuits.

Developmental self-construction and -configuration of functional neocortical neuronal networks.

The prenatal development of neural circuits must provide sufficient configuration to support at least a set of core postnatal behaviors. Although knowledge of various genetic and cellular aspects of development is accumulating rapidly, there is less systematic understanding of how these various processes play together in order to construct such functional networks. Here we make some steps toward such understanding by demonstrating through detailed simulations how a competitive co-operative ('winner-take-all', WTA) network architecture can arise by development from a single precursor cell. This precursor is granted a simplified gene regulatory network that directs cell mitosis, differentiation, migration, neurite outgrowth and synaptogenesis. Once initial axonal connection patterns are established, their synaptic weights undergo homeostatic unsupervised learning that is shaped by wave-like input patterns. We demonstrate how this autonomous genetically directed developmental sequence can give rise to self-calibrated WTA networks, and compare our simulation results with biological data.

Anatomical constraints on lateral competition in columnar cortical architectures.

Competition is a well-studied and powerful mechanism for information processing in neuronal networks, providing noise rejection, signal restoration, decision making and associative memory properties, with relatively simple requirements for network architecture. Models based on competitive interactions have been used to describe the shaping of functional properties in visual cortex, as well as the development of functional maps in columnar cortex. These models require competition within a cortical area to occur on a wider spatial scale than cooperation, usually implemented by lateral inhibitory connections having a longer range than local excitatory connections. However, measurements of cortical anatomy reveal that the spatial extent of inhibition is in fact more restricted than that of excitation. Relatively few models reflect this, and it is unknown whether lateral competition can occur in cortical-like networks that have a realistic spatial relationship between excitation and inhibition. Here we analyze simple models for cortical columns and perform simulations of larger models to show how the spatial scales of excitation and inhibition can interact to produce competition through disynaptic inhibition. Our findings give strong support to the direct coupling effect-that the presence of competition across the cortical surface is predicted well by the anatomy of direct excitatory and inhibitory coupling and that multisynaptic network effects are negligible. This implies that for networks with short-range inhibition and longer-range excitation, the spatial extent of competition is even narrower than the range of inhibitory connections. Our results suggest the presence of network mechanisms that focus on intra-rather than intercolumn competition in neocortex, highlighting the need for both new models and direct experimental characterizations of lateral inhibition and competition in columnar cortex.

Developmental origin of patchy axonal connectivity in the neocortex: a computational model.

Injections of neural tracers into many mammalian neocortical areas reveal a common patchy motif of clustered axonal projections. We studied in simulation a mathematical model for neuronal development in order to investigate how this patchy connectivity could arise in layer II/III of the neocortex. In our model, individual neurons of this layer expressed the activator-inhibitor components of a Gierer-Meinhardt reaction-diffusion system. The resultant steady-state reaction-diffusion pattern across the neuronal population was approximately hexagonal. Growth cones at the tips of extending axons used the various morphogens secreted by intrapatch neurons as guidance cues to direct their growth and invoke axonal arborization, so yielding a patchy distribution of arborization across the entire layer II/III. We found that adjustment of a single parameter yields the intriguing linear relationship between average patch diameter and interpatch spacing that has been observed experimentally over many cortical areas and species. We conclude that a simple Gierer-Meinhardt system expressed by the neurons of the developing neocortex is sufficient to explain the patterns of clustered connectivity observed experimentally.

FocusStack and StimServer: a new open source MATLAB toolchain for visual stimulation and analysis of two-photon calcium neuronal imaging data.

Two-photon calcium imaging of neuronal responses is an increasingly accessible technology for probing population responses in cortex at single cell resolution, and with reasonable and improving temporal resolution. However, analysis of two-photon data is usually performed using ad-hoc solutions. To date, no publicly available software exists for straightforward analysis of stimulus-triggered two-photon imaging experiments. In addition, the increasing data rates of two-photon acquisition systems imply increasing cost of computing hardware required for in-memory analysis. Here we present a Matlab toolbox, FocusStack, for simple and efficient analysis of two-photon calcium imaging stacks on consumer-level hardware, with minimal memory footprint. We also present a Matlab toolbox, StimServer, for generation and sequencing of visual stimuli, designed to be triggered over a network link from a two-photon acquisition system. FocusStack is compatible out of the box with several existing two-photon acquisition systems, and is simple to adapt to arbitrary binary file formats. Analysis tools such as stack alignment for movement correction, automated cell detection and peri-stimulus time histograms are already provided, and further tools can be easily incorporated. Both packages are available as publicly-accessible source-code repositories.

From neural arbors to daisies.

Pyramidal neurons in layers 2 and 3 of the neocortex collectively form an horizontal lattice of long-range, periodic axonal projections, known as the superficial patch system. The precise pattern of projections varies between cortical areas, but the patch system has nevertheless been observed in every area of cortex in which it has been sought, in many higher mammals. Although the clustered axonal arbors of single pyramidal cells have been examined in detail, the precise rules by which these neurons collectively merge their arbors remain unknown. To discover these rules, we generated models of clustered axonal arbors following simple geometric patterns. We found that models assuming spatially aligned but independent formation of each axonal arbor do not produce patchy labeling patterns for large simulated injections into populations of generated axonal arbors. In contrast, a model that used information distributed across the cortical sheet to generate axonal projections reproduced every observed quality of cortical labeling patterns. We conclude that the patch system cannot be built during development using only information intrinsic to single neurons. Information shared across the population of patch-projecting neurons is required for the patch system to reach its adult state.