### Publications by lab

 Larry Abbott Google Scholar PubMed Lab Homepage Ken Miller Google Scholar PubMed Lab Homepage John Cunningham Google Scholar PubMed Lab Homepage Sean Escola Google Scholar PubMed Lab Homepage Stefano Fusi Google Scholar PubMed Lab Homepage Liam Paninski Google Scholar PubMed Lab Homepage Ning Qian Google Scholar PubMed Lab Homepage Misha Tsodyks Google Scholar PubMed Lab Homepage

### Publications by year

#### 2016

 Reorganization between preparatory and movement population responses in motor cortex Gamaleldin F Elsayed, Antonio H Lara, Matthew T Kaufman, Mark M Churchland, John P Cunningham (2016) Nature Communications [ABSTRACT] Simultaneous Denoising, Deconvolution, and Demixing of Calcium Imaging Data E. A. Pnevmatikakis, D. Soudry, Y. Gao, T. A. Machado, J. Merel, D. Pfau,T. Reardon,Y. Mu, C. Lacefield, W. Yang, M. Ahrens, R. Bruno, T. M. Jessell, D. S. Peterka, R. Yuste, L. Paninski, (2016) Neuron [ABSTRACT] Computational principles of synaptic memory consolidation MK Benna, S Fusi (2016) Nature Neuroscience [ABSTRACT] Partition Functions from Rao-Blackwellized Tempered Sampling David Carlson*, Patrick Stinson*, Ari Pakman*, and Liam Paninski (2016) ICML [ABSTRACT] Parallel processing by cortical inhibition enables context-dependent behavior. " Kishore V Kuchibhotla, Jonathan V Gill, Grace W Lindsay, Eleni S Papadoyannis, Rachel E Field, Tom A Hindmarsh Sten, Kenneth D Miller, Robert C Froemke (2016) Nature Neuroscience [ABSTRACT] Energy-Efficient Neuromorphic Classifiers Daniel Martí, Mattia Rigotti, Mingoo Soek, Stefano Fusi (2016) Neural Computation [ABSTRACT] Computational principles of synaptic plasticity Stefano Fusi (2016) Banff International Research Station for Mathematical Innovation and Discovery [ABSTRACT] Estimating the dimensionality of neural responses with fMRI repetition suppression Mattia Rigotti, Stefano Fusi (2016) arXiv [ABSTRACT] Why neurons mix: high dimensionality for higher cognition Stefano Fusi, Earl K Miller, Mattia Rigotti (2016) Current Opinion in Neurobiology [ABSTRACT] Strength in More Than Numbers Sawtell, N. and Abbott, L.F. (2016) Nature Neuroscience [ABSTRACT] Activity Regulates the Incidence of Heteronymous Sensory-Motor Connections Mendelsohn, A., Simon, C.M., Abbott, L.F., Mentis, G.Z. and Jessell, T.M. (2016) Neuron [ABSTRACT] Random Walk Initialization for Training Very Deep Feedforward Networks Sussillo, D. and Abbott, L.F. (2016) arXiv [ABSTRACT] Conceptual and technical advances define a key moment for theoretical neuroscience Churchland AK, Abbott LF (2016) Nat Neuroscience [ABSTRACT] Building functional networks of spiking model neurons Abbott LF, DePasquale B, Memmesheimer RM (2016) Nat Neuroscience [ABSTRACT] Bayesian Sparse Regression Analysis Documents the Diversity of Spinal Inhibitory Interneurons Gabitto MI, Pakman A, Bikoff JB, Abbott LF, Jessell TM, Paninski L (2016) Cell [ABSTRACT] Stability and Competition in Multi-spike Models of Spike-Timing Dependent Plasticity Babadi B, Abbott LF (2016) PLoS Comput. Biol. [ABSTRACT] Tuning Curves for Arm Posture Control in Motor Cortex Are Consistent with Random Connectivity Hagai Lalazar , L. F. Abbott, Eilon Vaadia (2016) PLoS Comput. Biol. [ABSTRACT] LFADS - Latent Factor Analysis via Dynamical Systems Sussillo, D., Jozefowicz, R., Abbott, L.F. and Pandarinath, C. (2016) arXiv [ABSTRACT] Why neurons mix: high dimensionality for higher cognition Fusi, S., Miller, E.K., Rigotti, M. (2016) Current Opinion in Neurobiology 37:66-74. Neurons often respond to diverse combinations of task-relevant variables. This form of mixed selectivity plays an important computational role which is related to the dimensionality of the neural representations: high-dimensional representations with mixed selectivity allow a simple linear readout to generate a huge number of different potential responses. In contrast, neural representations based on highly specialized neurons are low dimensional and they preclude a linear readout from generating several responses that depend on multiple task-relevant variables. Here we review the conceptual and theoretical framework that explains the importance of mixed selectivity and the experimental evidence that recorded neural representations are high-dimensional. We end by discussing the implications for the design of future experiments. Canonical computations of cerebral cortex. Miller, K.D. (2016) Current Opinion in Neurobiology 37:75-84. The idea that there is a fundamental cortical circuit that performs canonical computations remains compelling though far from proven. Here we review evidence for two canonical operations within sensory cortical areas: a feedforward computation of selectivity; and a recurrent computation of gain in which, given sufficiently strong external input, perhaps from multiple sources, intracortical input largely, but not completely, cancels this external input. This operation leads to many characteristic cortical nonlinearities in integrating multiple stimuli. The cortical computation must combine such local processing with hierarchical processing across areas. We point to important changes in moving from sensory cortex to motor and frontal cortex and the possibility of substantial differences between cortex in rodents vs. species with columnar organization of selectivity.

#### 2015

 Feature-based Attention in Convolutional Neural Networks. Lindsay, GW (2015) arxiv Convolutional neural networks (CNNs) have proven effective for image processing tasks, such as object recognition and classification. Recently, CNNs have been enhanced with concepts of attention, similar to those found in biology. Much of this work on attention has focused on effective serial spatial processing. In this paper, I introduce a simple procedure for applying feature-based attention (FBA) to CNNs and compare multiple implementation options. FBA is a top-down signal applied globally to an input image which aides in detecting chosen objects in cluttered or noisy settings. The concept of FBA and the implementation details tested here were derived from what is known (and debated) about biological object- and feature-based attention. The implementations of FBA described here increase performance on challenging object detection tasks using a procedure that is simple, fast, and does not require additional iterative training. Furthermore, the comparisons performed here suggest that a proposed model of biological FBA (the "feature similarity gain model") is effective in increasing performance. Mapping nonlinear receptive field structure in primate retina at single cone resolution. Freeman, J., Field, G., Li, P., Greschner, M., Gunning, D., Mathieson, K., Sher, A., Litke, A., Paninski, L., Simoncelli, E. & Chichilnisky, E.J (2015) eLife 2015;4:e05241 The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits. Efficient shotgun" inference of neural connectivity from highly sub-sampled activity data. Soudry, D., Keshri, S., Stinson, P., Oh, M.-W., Iyengar, G. & Paninski, L. (2015). PLoS Comput Biol Oct 14;11(10):e1004464 Inferring connectivity in neuronal networks remains a key challenge in statistical neuroscience. The "common input" problem presents a major roadblock: it is difficult to reliably distinguish causal connections between pairs of observed neurons versus correlations induced by common input from unobserved neurons. Available techniques allow us to simultaneously record, with sufficient temporal resolution, only a small fraction of the network. Consequently, naive connectivity estimators that neglect these common input effects are highly biased. This work proposes a "shotgun" experimental design, in which we observe multiple sub-networks briefly, in a serial manner. Thus, while the full network cannot be observed simultaneously at any given time, we may be able to observe much larger subsets of the network over the course of the entire experiment, thus ameliorating the common input problem. Using a generalized linear model for a spiking recurrent neural network, we develop a scalable approximate expected loglikelihood-based Bayesian method to perform network inference given this type of data, in which only a small fraction of the network is observed in each time bin. We demonstrate in simulation that the shotgun experimental design can eliminate the biases induced by common input effects. Networks with thousands of neurons, in which only a small fraction of the neurons is observed in each time bin, can be quickly and accurately estimated, achieving orders of magnitude speed up over previous approaches. Primacy of flexor locomotor pattern revealed by ancestral reversion of motor neuron identity. Machado, T., Miri, A., Pnevmatikakis, E., Paninski, L. & Jessell, T (2015). Cell 162: 338-350 Spinal circuits can generate locomotor output in the absence of sensory or descending input, but the principles of locomotor circuit organization remain unclear. We sought insight into these principles by considering the elaboration of locomotor circuits across evolution. The identity of limb-innervating motor neurons was reverted to a state resembling that of motor neurons that direct undulatory swimming in primitive aquatic vertebrates, permitting assessment of the role of motor neuron identity in determining locomotor pattern. Two-photon imaging was coupled with spike inference to measure locomotor firing in hundreds of motor neurons in isolated mouse spinal cords. In wild-type preparations, we observed sequential recruitment of motor neurons innervating flexor muscles controlling progressively more distal joints. Strikingly, after reversion of motor neuron identity, virtually all firing patterns became distinctly flexor like. Our findings show that motor neuron identity directs locomotor circuit wiring and indicate the evolutionary primacy of flexor pattern generation. Encoder-decoder optimization for brain-computer interfaces. Merel, J., Pianto, D., Cunningham, J. & Paninski, L. (2015). PLoS Comput Biol Jun 1;11(6):e1004288 Neuroprosthetic brain-computer interfaces are systems that decode neural activity into useful control signals for effectors, such as a cursor on a computer screen. It has long been recognized that both the user and decoding system can adapt to increase the accuracy of the end effector. Co-adaptation is the process whereby a user learns to control the system in conjunction with the decoder adapting to learn the user's neural patterns. We provide a mathematical framework for co-adaptation and relate co-adaptation to the joint optimization of the user's control scheme ("encoding model") and the decoding algorithm's parameters. When the assumptions of that framework are respected, co-adaptation cannot yield better performance than that obtainable by an optimal initial choice of fixed decoder, coupled with optimal user learning. For a specific case, we provide numerical methods to obtain such an optimized decoder. We demonstrate our approach in a model brain-computer interface system using an online prosthesis simulator, a simple human-in-the-loop pyschophysics setup which provides a non-invasive simulation of the BCI setting. These experiments support two claims: that users can learn encoders matched to fixed, optimal decoders and that, once learned, our approach yields expected performance advantages. Abstract Context Representations in Primate Amygdala and Prefrontal Cortex. A. Saez, M. Rigotti, S. Ostojic, S. Fusi, and C.D. Salzman (2015) NeuronVolume 87, Issue 4, 869-881 Neurons in prefrontal cortex (PFC) encode rules, goals, and other abstract information thought to underlie cognitive, emotional, and behavioral flexibility. Here we show that the amygdala, a brain area traditionally thought to mediate emotions, also encodes abstract information that could underlie this flexibility. Monkeys performed a task in which stimulus-reinforcement contingencies varied between two sets of associations, each defining a context. Reinforcement prediction required identifying a stimulus and knowing the current context. Behavioral evidence indicated that monkeys utilized this information to perform inference and adjust their behavior. Neural representations in both amygdala and PFC reflected the linked sets of associations implicitly defining each context, a process requiring a level of abstraction characteristic of cognitive operations. Surprisingly, when errors were made, the context signal weakened substantially in the amygdala. These data emphasize the importance of maintaining abstract cognitive information in the amygdala to support flexible behavior. Computational principles of biological memory. Marcus Benna and Stefano Fusi (2015) arXiv5:1507.07580 Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of synaptic models that efficiently harnesses biological complexity to preserve numerous memories. The memory capacity scales almost linearly with the number of synapses, which is a substantial improvement over the square root scaling of previous models. This was achieved by combining multiple dynamical processes that initially store memories in fast variables and then progressively transfer them to slower variables. Importantly, the interactions between fast and slow variables are bidirectional. The proposed models are robust to parameter perturbations and can explain several properties of biological memory, including delayed expression of synaptic modifications, metaplasticity, and spacing effects. Energy-efficient neuromorphic classifiers. Daniel Marti, Mattia Rigotti, Mingoo Seok, Stefano Fusi (2015) arXiv5:1507.0023 Neuromorphic engineering combines the architectural and computational principles of systems neuroscience with semiconductor electronics, with the aim of building efficient and compact devices that mimic the synaptic and neural machinery of the brain. Neuromorphic engineering promises extremely low energy consumptions, comparable to those of the nervous system. However, until now the neuromorphic approach has been restricted to relatively simple circuits and specialized functions, rendering elusive a direct comparison of their energy consumption to that used by conventional von Neumann digital machines solving real-world tasks. Here we show that a recent technology developed by IBM can be leveraged to realize neuromorphic circuits that operate as classifiers of complex real-world stimuli. These circuits emulate enough neurons to compete with state-of-the-art classifiers. We also show that the energy consumption of the IBM chip is typically 2 or more orders of magnitude lower than that of conventional digital machines when implementing classifiers with comparable performance. Moreover, the spike-based dynamics display a trade-off between integration time and accuracy, which naturally translates into algorithms that can be flexibly deployed for either fast and approximate classifications, or more accurate classifications at the mere expense of longer running times and higher energy costs. This work finally proves that the neuromorphic approach can be efficiently used in real-world applications and it has significant advantages over conventional digital devices when energy consumption is considered. Hippocampal-prefrontal input supports spatial encoding in working memory. Timothy Spellman, Mattia Rigotti, Susanne E. Ahmari, Stefano Fusi, Joseph A. Gogos & Joshua A. Gordon (2015) Nature522, 309-314 Spatial working memory, the caching of behaviourally relevant spatial cues on a timescale of seconds, is a fundamental constituent of cognition. Although the prefrontal cortex and hippocampus are known to contribute jointly to successful spatial working memory, the anatomical pathway and temporal window for the interaction of these structures critical to spatial working memory has not yet been established. Here we find that direct hippocampal-prefrontal afferents are critical for encoding, but not for maintenance or retrieval, of spatial cues in mice. These cues are represented by the activity of individual prefrontal units in a manner that is dependent on hippocampal input only during the cue-encoding phase of a spatial working memory task. Successful encoding of these cues appears to be mediated by gamma-frequency synchrony between the two structures. These findings indicate a critical role for the direct hippocampal-prefrontal afferent pathway in the continuous updating of task-related spatial information during spatial working memory. The stabilized supralinear network: A unifying circuit motif underlying multi-input integration in sensory cortex. Rubin, D.B., S.D. Van Hooser and K.D. Miller (2015) Neuron85:402-417. Neurons in sensory cortex integrate multiple influences to parse objects and support perception. Across multiple cortical areas, integration is characterized by two neuronal response properties: (1) surround suppression-modulatory contextual stimuli suppress responses to driving stimuli; and (2) "normalization"-responses to multiple driving stimuli add sublinearly. These depend on input strength: for weak driving stimuli, contextual influences facilitate or more weakly suppress and summation becomes linear or supralinear. Understanding the circuit operations underlying integration is critical to understanding cortical function and disease. We present a simple, general theory. A wealth of integrative properties, including the above, emerge robustly from four cortical circuit properties: (1) supralinear neuronal input/output functions; (2) sufficiently strong recurrent excitation; (3) feedback inhibition; and (4) simple spatial properties of intracortical connections. Integrative properties emerge dynamically as circuit properties, with excitatory and inhibitory neurons showing similar behaviors. In new recordings in visual cortex, we confirm key model predictions. Neurons in cat V1 show significant clustering by degree of turning. Ziskind, A.J., A.A. Emondi, A.V. Kurgansky, S.P. Rebrik and K.D. Miller (2015) Journal of NeurophysiologyFeb 2015, DOI: 10.1152/jn.00646.2014 Neighboring neurons in cat primary visual cortex (V1) have similar preferred orientation, direction, and spatial frequency. How diverse is their degree of tuning for these properties? To address this, we used single-tetrode recordings to simultaneously isolate multiple cells at single recording sites and record their responses to flashed and drifting gratings of multiple orientations, spatial frequencies and, for drifting gratings, directions. Orientation tuning width, spatial frequency tuning width and direction selectivity index (DSI) all showed significant clustering: pairs of neuron recorded at a single site were significantly more similar in each of these properties than pairs of neurons from different recording sites. The strength of the clustering was generally modest. The percentage decrease in the median difference between pairs from the same site, relative to pairs from different sites, was: for different measures of orientation tuning width, 29-35% (drifting gratings) or 15-25% (flashed gratings); for DSI, 24%; and for spatial frequency tuning width measured in octaves, 8% (drifting gratings). The clusterings of all of these measures were much weaker than for preferred orientation (68% decrease), but comparable to that seen for preferred spatial frequency in response to drifting gratings (26%). For the above properties, little difference in clustering was seen between simple and complex cells. In studies of spatial frequency tuning to flashed gratings, strong clustering was seen among simple-cell pairs for tuning width (70% decrease) and preferred frequency (71% decrease), whereas no clustering was seen for simple/complex or complex/complex cell pairs. Transition to Chaos in Random Networks with Cell-Type-Specific Connectivity. Aljadeff, J., Stern, M., Sharpee, T. (2015) Phys. Rev. Lett. 114, 088101. In neural circuits, statistical connectivity rules strongly depend on cell-type identity. We study dynamics of neural networks with cell-type-specific connectivity by extending the dynamic mean-field method and find that these networks exhibit a phase transition between silent and chaotic activity. By analyzing the locus of this transition, we derive a new result in random matrix theory: the spectral radius of a random connectivity matrix with block-structured variances. We apply our results to show how a small group of hyperexcitable neurons within the network can significantly increase the network's computational capacity by bringing it into the chaotic regime. Effects of long-term representations on free recall of unrelated words. Katkov, M., Romani, S., & Tsodyks, M. (2015) Learning & Memory 22(2), 101-108. Human memory stores vast amounts of information. Yet recalling this information is often challenging when specific cues are lacking. Here we consider an associative model of retrieval where each recalled item triggers the recall of the next item based on the similarity between their long-term neuronal representations. The model predicts that different items stored in memory have different probability to be recalled depending on the size of their representation. Moreover, items with high recall probability tend to be recalled earlier and suppress other items. We performed an analysis of a large data set on free recall and found a highly specific pattern of statistical dependencies predicted by the model, in particular negative correlations between the number of words recalled and their average recall probability. Taken together, experimental and modeling results presented here reveal complex interactions between memory items during recall that severely constrain recall capacity.

#### 2012

 Efficient coding of spatial information in the primate retina Doi, E., Gauthier, J.L., Field, G.D., Shlens, J., She, A., Greschner, M., Machado, T.A., Jepson, L.H., Mathieson, K., Gunning, D.E., Litke, A.M., Paninski, L., Chichilnisky, E.J., and Simoncelli, E.P. (2012) J. Neurosci. 32: 16256-16264. Sensory neurons have been hypothesized to efficiently encode signals from the natural environment subject to resource constraints. The predictions of this efficient coding hypothesis regarding the spatial filtering properties of the visual system have been found consistent with human perception, but they have not been compared directly with neural responses. Here, we analyze the information that retinal ganglion cells transmit to the brain about the spatial information in natural images subject to three resource constraints: the number of retinal ganglion cells, their total response variances, and their total synaptic strengths. We derive a model that optimizes the transmitted information and compare it directly with measurements of complete functional connectivity between cone photoreceptors and the four major types of ganglion cells in the primate retina, obtained at single-cell resolution. We find that the ganglion cell population exhibited 80% efficiency in transmitting spatial information relative to the model. Both the retina and the model exhibited high redundancy (.30%) among ganglion cells of the same cell type. A novel and unique prediction of efficient coding, the relationships between projection patterns of individual cones to all ganglion cells, was consistent with the observed projection patterns in the retina. These results indicate a high level of efficiency with near-optimal redundancy in visual signaling by the retina. Suppression of cortical neural variability is stimulus- and state-dependent White, B., Abbott, L. F., and Fiser, J. (2012) J. Neurophysiol. 108:2383-2392. Internally generated, spontaneous activity is ubiquitous in the cortex, yet it does not appear to have a signi?cant negative impact on sensory processing. Various studies have found that stimulus onset reduces the variability of cortical responses, but the characteristics of this suppression remained unexplored. By recording multiunit activity from awake and anesthetized rats, we investigated whether and how this noise suppression depends on properties of the stimulus and on the state of the cortex. In agreement with theoretical predictions, we found that the degree of noise suppression in awake rats has a nonmonotonic dependence on the temporal frequency of a flickering visual stimulus with an optimal frequency for noise suppression ~2 Hz. This effect cannot be explained by features of the power spectrum of the spontaneous neural activity. The nonmonotonic frequency dependence of the suppression of variability gradually disappears under increasing levels of anesthesia and shifts to a monotonic pattern of increasing suppression with decreasing frequency. Signal-to-noise ratios show a similar, although inverted, dependence on cortical state and frequency. These results suggest the existence of an active noise suppression mechanism in the awake cortical system that is tuned to support signal propagation and coding. Two layers of neural variability (news and views) Churchland, M. M. and Abbott, L. F. (2012) Nature Neurosci. 15:1472-1474. Variability in neuronal firing rates and spike timing can be modeled as doubly stochastic. A study now suggests that these phenomena could arise from a network built of deterministic neurons with balanced excitation and inhibition. Fast nonnegative spatiotemporal calcium smoothing in dendritic trees Pnevmatikakis, E., Kelleher, K., Chen, R., Josic, K., Saggau, P. & Paninski, L. (2012) PLoS Comp. Bio., 8(6):e1002569 We discuss methods for fast spatiotemporal smoothing of calcium signals in dendritic trees, given spatially localized imaging data obtained via multi-photon microscopy. By analyzing the dynamics of calcium binding to probe molecules and the e ects of the imaging procedure, we show that calcium con- centration can be estimated up to an ane transformation, i.e., an additive and multiplicative constant. To obtain a full spatiotemporal estimate, we model calcium dynamics within the cell using a functional approach. The evolution of calcium concentration is represented through a smaller set of hidden vari- ables that incorporate fast transients due to backpropagating action potentials (bAPs), or other forms of stimulation. Because of the resulting state space structure, inference can be done in linear time using forward-backward maximum-a-posteriori methods. Non-negativity constraints on the calcium concentra- tion can also be incorporated using a log-barrier method that does not a ect the computational scaling. Moreover, by exploiting the neuronal tree structure we show that the cost of the algorithm is also linear in the size of the dendritic tree, making the approach applicable to arbitrarily large trees. We apply this algorithm to data obtained from hippocampal CA1 pyramidal cells with experimentally evoked bAPs, some of which were paired with excitatory postsynaptic potentials (EPSPs). The algorithm recovers the timing of the bAPs and provides an estimate of the induced calcium transient throughout the tree. The proposed methods could be used to further understand the interplay between bAPs and EPSPs in synaptic strength modi cation. More generally, this approach allows us to infer the concentration on intracellular calcium across the dendritic tree from noisy observations at a discrete set of points in space. Robust particle filters via sequential pairwise reparameterized Gibbs sampling Paninski, L., Rahnama Rad, K. & Vidne, M. (2012) CISS '12. Sequential Monte Carlo (“particle filtering”) methods provide a powerful set of tools for recursive optimal Bayesian filtering in state-space models. However, these methods are based on importance sampling, which is known to be nonrobust in several key scenarios, and therefore standard particle fitering methods can fail in these settings. We present a filtering method which solves the key forward recursion using a reparameterized Gibbs sampling method, thus sidestepping the need for importance sampling. In many cases the resulting filter is much more robust and efficient than standard importance sampling particle filter implementations. We illustrate the method with an application to a nonlinear, non-Gaussian model from neuroscience. Bayesian compressed sensing approach to reconstructing neural connectivity from subsampled anatomical data. Mishchenko, Y. & Paninski, L. (2012) J. Comput. Neuro., 33: 371-388. In recent years, the problem of reconstructing the connectivity in large neural circuits ("connectomics") has re-emerged as one of the main objectives of neuroscience. Classically, reconstructions of neural connectivity have been approached anatomically, using electron or light microscopy and histological tracing methods. This paper describes a statistical approach for connectivity reconstruction that relies on measurements of relatively easy-to-obtain ï¬‚uorescent probes such as synaptic markers, cytoplasmic dyes, transsynaptic tracers, or activity-dependent dyes. We describe the possible design of these experiments and develop a Bayesian framework for extracting neural connectivity from compilations of such data. We show that the statistical reconstruction problem can be formulated naturally as a tractable L1-regularized quadratic optimization. As a concrete example, we consider a realistic hypothetical connectivity reconstruction experiment in C. elegans, a popular neuroscience model where a complete wiring diagram has been previously obtained based on long-term electron microscopy work. We show that the new statistical approach could lead to an orders of magnitude reduction in experimental eï¬€ort in reconstructing the connectivity in this circuit. We further demonstrate that the spatial heterogeneity and biological variability in the connectivity matrixâ€”not just the "average" connectivityâ€”can also be estimated using the same method. Mathematical Equivalence of Two Common Forms of Firing Rate Models of Neural Networks Fumarola, F. and Miller K.D. (2012) Neural Computation 24:25-31 We demonstrate the mathematical equivalence of two commonly used forms of ring rate model equations for neural networks. In addition, we show that what is commonly interpreted as the ring rate in one form of model may be better interpreted as a low-pass-ltered ring rate, and we point out a conductance-based ring rate model. Transferring Learning from External to Internal Weights in Echo-State Networks with Sparse Connectivity Sussillo, D. and Abbott, L.F. (2012) PLoS One7:e37372 Modifying weights within a recurrent network to improve performance on a task has proven to be difficult. Echo-state networks in which modification is restricted to the weights of connections onto network outputs provide an easier alternative, but at the expense of modifying the typically sparse architecture of the network by including feedback from the output back into the network. We derive methods for using the values of the output weights from a trained echo-state network to set recurrent weights within the network. The result of this “transfer of learning” is a recurrent network that performs the task without requiring the output feedback present in the original network. We also discuss a hybrid version in which online learning is applied to both output and recurrent weights. Both approaches provide efficient ways of training recurrent networks to perform complex tasks. Through an analysis of the conditions required to make transfer of learning work, we define the concept of a “self-sensing” network state, and we compare and contrast this with compressed sensing. Fast interior-point inference in high-dimensional sparse, penalized state-space models. Pnevmatikakis & Paninski, L. (2012) AISTATS '12. Low rank continuous-space graphical models. Smith, C., Wood, F. & Paninski, L. (2012) AISTATS '12. A Computational Approach Enhances Learning in Aplysia (news and views) Abbott, L.F. and Kandel, E.R. (2012) Nature Neurosci.15:178-179 A mathematical model based on the dynamics of molecular signaling pathways predicts an optimal training regimen that enhances learning and memory. The impact of common noise on the activity of a large network of retinal ganglion cells Vidne, M. et al (2012) J. Comput. Neuro., in press. Inferring synaptic inputs given a noisy voltage trace Paninski, L., Vidne, M., DePasquale, B., & Ferreira, D. (2012) J. Comput. Neuro., in press. We discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques (“par- ticle ltering”). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. De- pending on the observation noise level, no averaging over multiple trials may be required. However, excitatory inputs are consistently inferred more accurately than inhibitory in- puts at physiological resting potentials, due to the stronger driving force associated with excitatory conductances. Once these synaptic input time courses are recovered, it be- comes possible to t (via tractable convex optimization techniques) models describing the relationship between the sensory stimulus and the observed synaptic input. We develop both parametric and nonparametric expectation-maximization (EM) algorithms that con- sist of alternating iterations between these synaptic recovery and model estimation steps. We employ a fast, robust convex optimization-based method to e ectively initialize the lter; these fast methods may be of independent interest. The proposed methods could be applied to better understand the balance between excitation and inhibition in sensory processing in vivo. Optimal experimental design for sampling voltage on dendritic trees Huggins, J. & Paninski, L. (2012) J Comput. Neuro., in press. Due to the limitations of current voltage sensing techniques, optimal ltering of noisy, undersampled voltage signals on dendritic trees is a key problem in computational cellular neuroscience. These limitations lead to voltage data that is incomplete (in the sense of only capturing a small portion of the full spatiotemporal signal) and often highly noisy. In this paper we use a Kalman ltering framework to develop optimal experimental design methods for voltage sampling. Our approach is to use a simple greedy algorithm with lazy evaluation to minimize the expected square error of the estimated spatiotemporal voltage signal. We take advantage of some particular features of the dendritic ltering problem to eciently calculate the Kalman estimators covariance. We test our framework with simulations of real dendritic branching structures and compare the quality of both time-invariant and time-varying sampling schemes. While the benet of using the experimental design methods was modest in the time-invariant case, improvements of 25-100% over more na¨ve methods were found when the observation locations were allowed to change with time. We also present a heuristic approximation to the greedy algorithm that is an order of magnitude faster while still providing comparable results.

#### 2010

 Functional connectivity in the retina at the resolution of photoreceptors Field, G., Gauthier, J., Sher, A. et al. (2010) Nature, 467:673-677. To understand a neural circuit requires knowledge of its connectivity. Here we report measurements of functional connectivity between the input and ouput layers of the macaque retina at single-cell resolution and the implications of these for colour vision. Multi-electrode technology was used to record simultaneously from complete populations of the retinal ganglion cell types (midget, parasol and small bistratified) that transmit high-resolution visual signals to the brain. Fine-grained visual stimulation was used to identify the location, type and strength of the functional input of each cone photoreceptor to each ganglion cell. The populations of ON and OFF midget and parasol cells each sampled the complete population of long- and middle-wavelength-sensitive cones. However, only OFF midget cells frequently received strong input from short-wavelength-sensitive cones. ON and OFF midget cells showed a small non-random tendency to selectively sample from either long- or middle-wavelength-sensitive cones to a degree not explained by clumping in the cone mosaic. These measurements reveal computations in a neural circuit at the elementary resolution of individual neurons. Efficient estimation of two-dimensional firing rate surfaces via Gaussian process methods Rahnama Rad, K. & Paninski, L. (2010) Network: Computation in Neural Systems 21: 142-68. Estimating two-dimensional ring rate maps is a common problem, arising in a number of contexts: the estimation of place elds in hippocampus, the analysis of temporally nonstationary tuning curves in sensory and motor areas, the estimation of ring rates following spike-triggered covariance analyses, etc. Here we introduce methods based on Gaussian process nonparametric Bayesian techniques for estimating these two-dimensional rate maps. These techniques oer a number of advantages: the estimates may be computed eciently, come equipped with natural errorbars, adapt their smoothness automatically to the local density and informativeness of the observed data, and permit direct tting of the model hyperparameters (e.g., the prior smoothness of the rate map) via maximum marginal likelihood. We illustrate the exibility and performance of the new techniques on a variety of simulated and real data. Inferring Stimulus Selectivity from the Spatial Structure of Neural Network Dynamics Rajan, K., Abbott, L.F., and Sompolinsky, H. (2010) Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S. and Culotta, A. eds. Advances in Neural Information Processing Systems 23. How are the spatial patterns of spontaneous and evoked population responses re-lated? We study the impact of connectivity on the spatial pattern of fluctuations in the input-generated response, by comparing the distribution of evoked and intrinsically generated activity across the different units of a neural network. We develop a complementary approach to principal component analysis in which separate high-variance directions are derived for each input condition. We analyze subspace angles to compute the difference between the shapes of trajectories corresponding to different network states, and the orientation of the low-dimensional subspaces that driven trajectories occupy within the full space of neuronal activity. In addition to revealing how the spatiotemporal structure of spontaneous activity affects input-evoked responses, these methods can be used to infer input selectivity induced by network dynamics from experimentally accessible measures of spontaneous activity (e.g. from voltage- or calcium-sensitive optical imaging experiments). We conclude that the absence of a detailed spatial map of afferent inputs and cortical connectivity does not limit our ability to design spatially extended stimuli that evoke strong responses. π = Visual Cortex (News and Views). Miller, K.D. (2010) Science, 330(6007):1059-60. Three distantly-related mammals share a brain architecture characterized by a density of π. Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity Babadi, B. and Abbott, L.F. (2010) PLoS Comput. Biol. 11:e1000961 Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent "triplet" model of STDP. Our results indicate that the detailed shape of the STDPwindow function near the transition fromdepression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study. Stimulus-dependent suppression of chaos in recurrent neural networks Rajan, K., Abbott, L.F., and Sompolinsky, H. (2010) Phys. Rev. E 82:011903 Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a “resonant” frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate. Emotion, cognition, and mental state representation in amygdala and prefrontal cortex Salzman, C.D. and Fusi, S. (2010) Annu Rev Neurosci. 33:173-202 Neuroscientists have often described cognition and emotion as separable processes implemented by different regions of the brain, such as the amygdala for emotion and the prefrontal cortex for cognition. In this framework, functional interactions between the amygdala and prefrontal cortex mediate emotional influences on cognitive processes such as decision-making, as well as the cognitive regulation of emotion. However, neurons in these structures often have entangled representations, whereby single neurons encode multiple cognitive and emotional variables. Here we review studies using anatomical, lesion, and neurophysiological approaches to investigate the representation and utilization of cognitive and emotional parameters. We propose that these mental state parameters are inextricably linked and represented in dynamic neural networks composed of interconnected prefrontal and limbic brain structures. Future theoretical and experimental work is required to understand how these mental state representations form and how shifts between mental states occur, a critical feature of adaptive cognitive and emotional behavior. Attractor concretion as a mechanism for the formation of context representations Rigotti, M., Ben Dayan Rubin, D., Morrison, S.E., Salzman, C.D., and Fusi, S. (2010) Neuroimage. 52:833-847 Complex tasks often require the memory of recent events, the knowledge about the context in which they occur, and the goals we intend to reach. All this information is stored in our mental states. Given a set of mental states, reinforcement learning (RL) algorithms predict the optimal policy that maximizes future reward. RL algorithms assign a value to each already-known state so that discovering the optimal policy reduces to selecting the action leading to the state with the highest value. But how does the brain create representations of these mental states in the first place? We propose a mechanism for the creation of mental states that contain information about the temporal statistics of the events in a particular context. We suggest that the mental states are represented by stable patterns of reverberating activity, which are attractors of the neural dynamics. These representations are built from neurons that are selective to specific combinations of external events (e.g. sensory stimuli) and pre-existent mental states. Consistent with this notion, we find that neurons in the amygdala and in orbitofrontal cortex (OFC) often exhibit this form of mixed selectivity. We propose that activating different mixed selectivity neurons in a fixed temporal order modifies synaptic connections so that conjunctions of events and mental states merge into a single pattern of reverberating activity. This process corresponds to the birth of a new, different mental state that encodes a different temporal context. The concretion process depends on temporal contiguity, i.e. on the probability that a combination of an event and mental states follows or precedes the events and states that define a certain context. The information contained in the context thereby allows an animal to assign unambiguously a value to the events that initially appeared in different situations with different meanings. Internal representation of task rules by recurrent dynamics: the importance of the diversity of neural responses Rigotti, M., Ben Dayan Rubin, D., Wang, X-J., and Fusi, S. (2010) Front. Comput. Neurosci., doi:10.3389/fncom.2010.00024 Neural activity of behaving animals, especially in the prefrontal cortex, is highly heterogeneous, with selective responses to diverse aspects of the executed task. We propose a general model of recurrent neural networks that perform complex rule-based tasks, and we show that the diversity of neuronal responses plays a fundamental role when the behavioral responses are context dependent. Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states. Such mixed selectivity is easily obtained by neurons that connect with random synaptic strengths both to the recurrent network and to neurons encoding sensory inputs. The number of randomly connected neurons needed to solve a task is on average only three times as large as the number of neurons needed in a network designed ad hoc. Moreover, the number of needed neurons grows only linearly with the number of task-relevant events and mental states, provided that each neuron responds to a large proportion of events (dense/distributed coding). A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context dependent tasks. Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation. Fast Kalman filtering on quasilinear dendritic trees Paninski, L. (2010) J. Comp. Neurosci. 28:211-228 Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem --- the vector of voltages at every compartment --- is very high-dimensional: typical realistic multicompartmental models have on the order of $N=10^4$ compartments. Standard implementations of the Kalman filter require $O(N^3)$ time and $O(N^2)$ space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in $O(N)$ time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in $O(N)$ time using methods that exploit the sparse tree structure of dendritic dynamics. The resulting methods give a very good approximation to the exact Kalman solution, but only require $O(N)$ time and space. We illustrate the method with applications to real and simulated dendritic branching structures, and describe how to extend the techniques to incorporate spatially subsampled, temporally filtered, and nonlinearly transformed observations. Fast non-negative deconvolution for spike train inference from population calcium imaging Vogelstein, J., Packer, A., Machado, T., Sippy, T. Babadi, B., Yuste, R. and Paninski, L. (2010) J. Neurophys. In press Fluorescent calcium indicators are becoming increasingly popular as a means for observing the spiking activity of large neuronal populations. Unfortunately, extracting the spike train of each neuron from a raw fluorescence movie is a nontrivial problem. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train of each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm runs in linear time, like the Wiener filter, and is fast enough that even when imaging over 100 neurons simultaneously, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the inferred spike train estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments. Efficient Markov chain Monte Carlo methods for decoding neural spike trains Ahmadian, Y., Pillow, J., and Paninski, L. (2010) Neural Computation In press Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log-concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly non-Gaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for Gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the "hit-and-run" algorithm performed better than other MCMC methods. Using these algorithms we show that for this latter class of priors the posterior mean estimate can have a considerably lower average error than MAP, whereas for Gaussian priors the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting non-marginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for Gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators. Model-based decoding, information estimation, and change-point detection techniques for multi-neuron spike trains Pillow, J., Ahmadian, Y., and Paninski, L. (2010) Neural Computation In press One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or "forward" models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow for efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding-model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a Gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (e.g. the time at which the stimulus undergoes a change in mean or variance), by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data. Automating the design of informative sequences of sensory stimuli Lewi, J., Schneider, D., Woolley, S., and Paninski, L. (2010) J. Comput. Neuro. In press Adaptive stimulus design methods can potentially improve the efficiency of sensory neurophysiology experiments significantly; however, designing optimal stimulus sequences in real time remains a serious technical challenge. Here we describe two approximate methods for generating informative stimulus sequences: the first approach provides a fast method for scoring the informativeness of a batch of specific potential stimulus sequences, while the second method attempts to compute an optimal stimulus distribution from which the experimenter may easily sample. We apply these methods to single-neuron spike train data recorded from the auditory midbrain of zebra finches, and demonstrate that the resulting stimulus sequences do in fact provide more information about neuronal tuning in a shorter amount of time than do more standard experimental designs. Population decoding of motor cortical activity using a generalized linear model with hidden states Lawhern, V., Wu, W., Hatsopoulos, N.G., and Paninski, L. (2010) J. Neurosci. Meth. In press Generalized linear models (GLMs) have been developed for modeling and decod- ing population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject's level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation-Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (lowering the Mean Square Error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications. A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data Mishchencko, Y., Vogelstein, J., and Paninski, L. (2010) Annals of applied statistics In press Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work, we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation- Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L1 penalization methods. A new look at state-space models for neural data Paninski, L., Ahmadian, Y., Ferreira, D.G., Koyama, S, Rahnama Rad, K., Vidne, M., Vogelstein, J., and Wu, W. (2010) J. Comput. Neuro. (special issue on statistical analysis of neural data) In press State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in state-space models with non-Gaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way, we point out connections to some related standard statistical methods, including spline smoothing and isotonic regression. Finally, we note that the computational methods reviewed here do not in fact depend on the state-space setting at all; instead, the key property we are exploiting involves the bandedness of certain matrices. We close by discussing some applications of this more general point of view, including Markov chain Monte Carlo methods for neural decoding and efficient estimation of spatially-varying firing rates. Neuropeptide feedback modifies odor-evoked dynamics in C. elegans olfactory neurons Chalasani, S., Kato, S., Albrecht, D., Nakagawa, T., Abbott, L.F. and Bargmann, C. (2010) Nature Neurosci. 13:615-621 Many neurons release classical transmitters together with neuropeptide co-transmitters whose functions are incompletely understood. Here we define the relationship between two transmitters in the olfactory system of C. elegans, showing that a neuropeptide-to-neuropeptide feedback loop alters sensory dynamics in primary olfactory neurons. The AWC olfactory neuron is glutamatergic and also expresses the peptide NLP-1. Worms with nlp-1 mutations show increased AWC-dependent behaviors, suggesting that NLP-1 limits the normal response. The receptor for NLP-1 is the G protein-coupled receptor NPR-11, which acts in postsynaptic AIA interneurons. Feedback from AIA interneurons modulates odor-evoked calcium dynamics in AWC olfactory neurons and requires INS-1, a neuropeptide released from AIA. The neuropeptide feedback loop dampens behavioral responses to odors on short and long timescales. Our results point to neuronal dynamics as a site of behavioral regulation and reveal the ability of neuropeptide feedback to remodel sensory networks on multiple timescales. Generating sparse and selective third-order responses in the olfactory system of the fly Luo, S., Axel, R. and Abbott, L.F. (2010) Proc. Natl. Acad. Sci. USA 107:10713–10718 In the antennal lobe of Drosophila, information about odors is transferred from olfactory receptor neurons (ORNs) to projection neurons (PNs), which then send axons to neurons in the lateral horn of the protocerebrum (LHNs) and to Kenyon cells (KCs) in the mushroom body. The transformation from ORN to PN responses can be described by a normalization model similar to what has been used in modeling visually responsive neurons. We study the implications of this transformation for the generation of LHN and KC responses under the hypothesis that LHN responses are highly selective and therefore suitable for driving innate behaviors, whereas KCs provide a more general sparse representation of odors suitable for forming learned behavioral associations. Our results indicate that the transformation from ORN to PN !ring rates in the antennal lobe equalizes the magnitudes of and decorrelates responses to different odors through feedforward nonlinearities and lateral suppression within the circuitry of the antennal lobe, and we study how these two components affect LHN and KC responses.

#### 2008

 Theoretical Neuroscience Rising Abbott, L.F. (2008) Neuron, 60:489-495 Theoretical neuroscience has experienced explosive growth over the past 20 years. In addition to bringing new researchers into the field with backgrounds in physics, mathematics, computer science, and engineering, theoretical approaches have helped to introduce new ideas and shape directions of neuroscience research. This review presents some of the developments that have occurred and the lessons they have taught us. Simulating In Vivo Background Activity in a Slice with the Dynamic Clamp Chance, F.C. and Abbott, L.F. (2008) In T. Bal and A. Destexhe, eds. Dynamic-Clamp: From Principles To Applications (Springer Science, New York) pp. 73-87 Neurons in vivo receive a large amount of internally generated "background" activity in addition to synaptic input directly driven by an external stimulus. Stimulus-driven and background synaptic inputs interact, through the nonlinearities of neuronal integration, in interesting ways. The dynamic clamp can be used in vitro to duplicate background input, allowing the experimenter to take advantage of the accessibility of neurons in vitro while still studying them under in vivo conditions. In this chapter we discuss some results from experiments in which a neuron is driven by current injection that simulates a stimulusdriven input as well as dynamic-clamp-generated background activity. One of the effects uncovered in this way is multiplicative gain modulation, achieved by varying the level of background synaptic input. We discuss how the dynamic clamp was used to discover this effect and also how to choose parameters to simulate in vivo background synaptic input in slice neurons. Designing neurophysiology experiments to optimally constrain receptive field models along parametric submanifolds Jeremy Lewi, Robert Butera, David Schneider, Sarah Woolley, and Liam Paninski (2008) NIPS 2008 Sequential optimal design methods hold great promise for improving the efficiency of neurophysiology experiments. However, previous methods for optimal experimental design have incorporated only weak prior information about the underlying neural system (e.g., the sparseness or smoothness of the receptive field). Here we describe how to use stronger prior information, in the form of parametric models of the receptive field, in order to construct optimal stimuli and further improve the efficiency of our experiments. For example, if we believe that the receptive field is well-approximated by a Gabor function, then our method constructs stimuli that optimally constrain the Gabor parameters (orientation, spatial frequency, etc.) using as few experimental trials as possible. More generally, we may believe a priori that the receptive field lies near a known sub-manifold of the full parameter space; in this case, our method chooses stimuli in order to reduce the uncertainty along the tangent space of this sub-manifold as rapidly as possible. Applications to simulated and real data indicate that these methods may in many cases improve the experimental efficiency by an order of magnitude. Memory traces in dynamical systems Surya Ganguli, Dongsung Huh, and Haim Sompolinsky (2008) PNAS 105:18970-18975 To perform nontrivial, real-time computations on a sensory input stream, biological systems must retain a short-term memory trace of their recent inputs. It has been proposed that generic highdimensional dynamical systems could retain a memory trace for past inputs in their current state. This raises important questions about the fundamental limits of such memory traces and the properties required of dynamical systems to achieve these limits. We address these issues by applying Fisher information theory to dynamical systems driven by time-dependent signals corrupted by noise. We introduce the Fisher Memory Curve (FMC) as a measure of the signal-to-noise ratio (SNR) embedded in the dynamical state relative to the input SNR. The integrated FMC indicates the total memory capacity. We apply this theory to linear neuronal networks and show that the capacity of networks with normal connectivity matrices is exactly 1 and that of any network of N neurons is, at most, N. A nonnormal network achieving this bound is subject to stringent design constraints: It must have a hidden feedforward architecture that superlinearly amplifies its input for a time of order N, and the input connectivity must optimally match this architecture. The memory capacity of networks subject to saturating nonlinearities is further limited, and cannot exceed N. This limit can be realized by feedforward structures with divergent fan out that distributes the signal across neurons, thereby avoiding saturation. We illustrate the generality of the theory by showing that memory in fluid systems can be sustained by transient nonnormal amplification due to convective instability or the onset of turbulence. Cell groups reveal structure of stimulus space C. Curto and V. Itskov (2008) PLoS Computational Biology 4(10) An important task of the brain is to represent the outside world. It is unclear how the brain may do this, however, as it can only rely on neural responses and has no independent access to external stimuli in order to ?decode? what those responses mean. We investigate what can be learned about a space of stimuli using only the action potentials (spikes) of cells with stereotyped?but unknown?receptive fields. Using hippocampal place cells as a model system, we show that one can (1) extract global features of the environment and (2) construct an accurate representation of space, up to an overall scale factor, that can be used to track the animal's position. Unlike previous approaches to reconstructing position from place cell activity, this information is derived without knowing place fields or any other functions relating neural responses to position. We find that simply knowing which groups of cells fire together reveals a surprising amount of structure in the underlying stimulus space; this may enable the brain to construct its own internal representations. Internally Generated Cell Assembly Sequences in the Rat Hippocampus E. Pastalkova, V. Itskov, A. Amarasingham, G. Buzsaki (2008) Science 321(5894) :1322-1327 A long-standing conjecture in neuroscience is that aspects of cognition depend on the brain's ability to self-generate sequential neuronal activity. We found that reliably and continually changing cell assemblies in the rat hippocampus appeared not only during spatial navigation but also in the absence of changing environmental or body-derived inputs. During the delay period of a memory task, each moment in time was characterized by the activity of a particular assembly of neurons. Identical initial conditions triggered a similar assembly sequence, whereas different conditions gave rise to different sequences, thereby predicting behavioral choices, including errors. Such sequences were not formed in control (nonmemory) tasks. We hypothesize that neuronal representations, evolved for encoding distance in spatial navigation, also support episodic recall and the planning of action sequences. Theta-mediated dynamics of spatial information in hippocampus V. Itskov, E. Pastalkova, K. Mizuseki, G. Buzsaki, K.D. Harris (2008) Journal of Neuroscience 28(23) In rodent hippocampus, neuronal activity is organized by a 6-10 Hz theta oscillation. The spike timing of hippocampal pyramidal cells with respect to the theta rhythm correlates with an animal's position in space. This correlation has been suggested to indicate an explicit temporal code for position. Alternatively, it may be interpreted as a byproduct of theta-dependent dynamics of spatial information flow in hippocampus. Here we show that place cell activity on different phases of theta reflects positions shifted into the future or past along the animal's trajectory in a two-dimensional environment. The phases encoding future and past positions are consistent across recorded CA1 place cells, indicating a coherent representation at the network level. Consistent theta-dependent time offsets are not simply a consequence of phase-position correlation (phase precession), because they are no longer seen after data randomization that preserves the phase-position relationship. The scale of these time offsets, 100?300 ms, is similar to the latencies of hippocampal activity after sensory input and before motor output, suggesting that offset activity may maintain coherent brain activity in the face of information processing delays. Gating Deficits in Model Networks:A Path to Schizophrenia Vogels,T.P and Abbott, L.F. (2008) Pharmacopsychiatry 40:S73-S77 Gating deficits and hallucinatory sensations are prominent symptoms of schizophrenia. Comparing these abnormalities with the failure modes of network models is an interesting way to explore how they arise. We present a network model that can both propagate and gate signals. The model exhibits effects reminiscent of clinically observed pathologies when the balance between excitation and inhibition that it requires is not properly maintained. Perceptron for Sparse Discrimination Itskov, V. and Abbott, L.F. (2008) Phys. Rev. Lett 101018101 We evaluate the capacity and performance of a perceptron discriminator operating in a highly sparse regime where classic perceptron results do not apply. The perceptron is constructed to respond to a specified set of q stimuli, with only statistical information provided about other stimuli to which it is not supposed to respond. We compute the probability of both false-positive and false-negative errors and determine the capacity of the system for not responding to nonselected stimuli and for responding to selected stimuli in the presence of noise. If q is a sublinear function of N, the number of inputs to the perceptron, these capacities are exponential in N=q. Mean-field approximations for coupled populations of generalized linear model spiking neurons with Markov refractoriness Taro Toyoizumi, Kamiar Rahnama Rad, and Liam Paninski (2008) Neural Computation, 21(5):1203-1243 There has recently been a great deal of interest in inferring network connectivity from the spike trains in populations of neurons. One class of useful models which can be fit easily to spiking data is based on generalized linear point process models from statistics. Once the parameters for these models are fit, the analyst is left with a nonlinear spiking network model with delays, which in general may be very difficult to understand analytically. Here we develop mean-field methods for approximating the stimulus-driven firing rates (both in the time-varying and steady-state case), auto- and cross-correlations, and stimulus-dependent filtering properties of these networks. These approximations are valid when the contributions of individual network coupling terms are small and, hence, the total input to a neuron is approximately Gaussian. These approximations lead to deterministic ordinary differential equations that are much easier to solve and analyze than direct Monte Carlo simulation of the network activity. These approximations also provide analytical way to evaluate the linear input-output filter of neurons and how the filters are modulated by network interactions and some stimulus feature. Finally, in the case of strong refractory effects, the mean-field approximations in the generalized linear model become inaccurate; therefore we introduce a model that captures strong refractoriness, retains all of the easy fitting properties of the standard generalized linear model, and leads to much more accurate approximations of mean firing rates and cross-correlations that retain fine temporal behaviors. Statistical models of spike trains Liam Paninski, Emery Brown, Satish Iyengar, and Rob Kass (2008) Book chapter in Stochastic Methods in Neuroscience, Oxford University Press, ed. Laing, C. and Lord, G. Spiking neurons make inviting targets for analytical methods based on stochastic processes: spike trains carry information in their temporal patterning, yet they are often highly irregular across time and across experimental replications. The bulk of this volume is devoted to mathematical and biophysical models useful in understanding neurophysiological processes. In this chapter we consider statistical models for analyzing spike train data. Strictly speaking, what we would call a statistical model for spike trains is simply a probabilistic description of the sequence of spikes. But it is somewhat misleading to ignore the data-analytical context of these models. In particular, we want to make use of these probabilistic tools for the purpose of scientific inference. The leap from simple descriptive uses of probability to inferential applications is worth emphasizing for two reasons. First, this leap was one of the great conceptual advances in science, taking roughly two hundred years. It was not until the late 1700s that there emerged any clear notion of inductive (or what we would now call statistical) reasoning; it was not until the first half of the twentieth century that modern methods began to be developed systematically; and it was only in the second half of the twentieth century that these methods became well understood in terms of both theory and practice. Second, the focus on inference changes the way one goes about the modeling process. It is this change in perspective we want to highlight here, and we will do so by discussing one of the most important models in neuroscience, the stochastic integrate-and-fire (IF) model for spike trains. The stochastic IF model has a long history (Gerstein and Mandelbrot, 1964; Stein, 1965; Knight, 1972; Burkitt, 2006): it is the simplest dynamical model that captures the basic properties of neurons, including the temporal integration of noisy subthreshold inputs, all- or-none spiking, and refractoriness. Of course, the IF model is a caricature of true neural dynamics (see, e.g., (Ermentrout and Kopell, 1986; Brunel and Latham, 2003; Izhikevich, 2007) for more elaborate models) but, as demonstrated in this book and others (Ricciardi, 1977; Tuckwell, 1989; Gerstner and Kistler, 2002), it has provided much insight into the behavior of single neurons and neural populations. In this chapter we explore some of the key statistical questions that arise when we use this model to perform inference with real neuronal spike train data. How can we efficiently fit the model to spike train data? Once we have estimated the model parameters, what can the model tell us about the encoding properties of the observed neuron? We also briefly consider some more general approaches to statistical modeling of spike train data. We begin, in section 1, by discussing three distinct useful ways of approaching the IF model, via the language of stochastic (diffusion) processes, hidden Markov models, and point processes, respectively. Each of these viewpoints comes equipped with its own specialized analytical tools, and the power of the IF model is most evident when all of these tools may be brought to bear simultaneously. We discuss three applications of these methods in section 2, and then close in 3 by indicating the scope of the general point process framework of which the IF model is a part, and the possibilities for solving some key outstanding data-analytic problems in systems neuroscience. A coincidence-based test for uniformity given very sparsely-sampled discrete data Paninski, L. (2008) IEEE Transactions on Information Theory, 54(10):4750-4755 How many independent samples N do we need from a distribution p to decide that p is epsilon-distant from uniform in an L1 sense, Sigma(i=1 to m) |p(i) - 1/m| > epsilon? (Here m is the number of bins on which the distribution is supported, and is assumed known a priori.) Somewhat surprisingly, we only need N*epsilon^2 >> m^1/2 to make this decision reliably (this condition is both sufficient and necessary). The test for uniformity introduced here is based on the number of observed "coincidences" (samples that fall into the same bin), the mean and variance of which may be computed explicitly for the uniform distribution and bounded nonparametrically for any distribution that is known to be epsilon-distant from uniform. Some connections to the classical birthday problem are noted. Spatio-temporal correlations and visual signaling in a complete neuronal population Pillow, J., Shlens, J., Paninski, L.,Sher, A., Litke, A., Chichilnisky, E., Simoncelli, E. (2008) Nature, 454(7206):995-999 Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons. Undersmoothed kernel entropy estimator Paninski, L. and Yajima, M. (2008) IEEE Transactions on Information Theory, (in press) We develop a "plug-in" kernel estimator for the differential entropy that is consistent even if the kernel width tends to zero as quickly as 1/N, where N is the number of independent and identically distributed (i.i.d.) samples. Thus, accurate density estimates are not required for accurate kernel entropy estimates; in fact, it is a good idea when estimating entropy to sacrifice some accuracy in the quality of the corresponding density estimate. State-space decoding of goal-directed movement Kulkarni, J. and Paninski, L. (2008) IEEE Signal Processing Magazine (special issue on brain-computer interfaces), 25:78-86 This article reviews an earlier recursive approach for computing such reach trajectories and presents a new nonrecursive approach, with computations that may be performed analytically for the most part, leading to a significant gain in the accuracy of the inferred trajectory while imposing a very small computational burden. Extensions of the approach are discussed including the incorporation of multiple target observations at different times, and multiple possible target locations. Inferring input nonlinearities in neural encoding model Ahrens, M., Paninski, L. and Sahani, M. (2008) Network: Computation in Neural Systems 19:35-67 We describe a class of models that predict how the instantaneous firing rate of a neuron depends on a dynamic stimulus. The models utilize a learnt pointwise nonlinear transform of the stimulus, followed by a linear filter that acts on the sequence of transformed inputs. In one case, the nonlinear transform is the same at all filter lag-times. Thus, this "input nonlinearity" converts the initial numerical representation of stimulus value to a new representation that provides optimal input to the subsequent linear model. We describe algorithms that estimate both the input nonlinearity and the linear weights simultaneously; and present techniques to regularise and quantify uncertainty in the estimates. In a second approach, the model is generalized to allow a different nonlinear transform of the stimulus value at each lag-time. Although more general, this model is algorithmically more straightforward to fit. However, it has many more degrees of freedom than the first approach, thus requiring more data for accurate estimation. We test the feasibility of these methods on synthetic data, and on responses from a neuron in rodent barrel cortex. The models are shown to predict responses to novel data accurately, and to recover several important neuronal response properties. Spike inference from calcium imaging using sequential Monte Carlo method Joshua Vogelstein, Brendon Watson, Adam Packer, Bruno Jedynak, Rafael Yuste, and Liam Paninski (2008) Biophysical Journal, 97(2):636-655 As recent advances in calcium sensing technologies enable us to simultaneously image many neurons, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. While the observations here are fluorescence images, the signals of interest - spike trains and/or time varying intracellular calcium concentrations - are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing a family of particle filters based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing errorbars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation-maximization with only a very limited amount of data, without the requirement of any simultaneous electrophysiology and imaging experiments. One-dimensional dynamics of attention and decision making in LIP Ganguli, S., Bisley, J.W., Roitman, J.D., Shadlen, M.N., Goldberg, M.E., Miller, K.D. (2008) Neuron 58:15-25 Where we allocate our visual spatial attention depends upon a continual competition between internally gen- erated goals and external distractions. Recently it was shown that single neurons in the macaque lateral intraparietal area (LIP) can predict the amount of time a distractor can shift the locus of spatial attention away from a goal. We propose that this remarkable dy- namical correspondence between single neurons and attention can be explained by a network model in which generically high-dimensional firing-rate vectors rapidly decay to a single mode. We find direct experi- mental evidence for this model, not only in the original attentional task, but also in a very different task involv- ing perceptual decision making. These results confirm a theoretical prediction that slowly varying activity pat- terns are proportional to spontaneous activity, pose constraints on models of persistent activity, and sug- gest a network mechanism for the emergence of ro- bust behavioral timing from heterogeneous neuronal populations. On the importance of the static nonlinearity in estimating spatiotemporal neural filters with natural stimuli Sharpee, T.O,. Miller, K.D., Stryker, M.P. (2008) J Neurophysiol. 99(5):2496-2509 Understanding neural responses with natural stimuli has increasingly become an essential part of characterizing neural coding. Neural responses are commonly characterized by a linear-nonlinear (LN) model, in which the output of a linear filter applied to the stimulus is transformed by a static nonlinearity to determine neural response. To estimate the linear filter in the LN model, studies of responses to natural stimuli commonly use methods that are unbiased only for a linear model (in which there is no static nonlinearity): spike-triggered averages with correction for stimulus power spectrum, with or without regularization. While these methods work well for artificial stimuli, such as Gaussian white noise, we show here that they estimate neural filters of LN models from responses to natural stimuli much more poorly. We studied simple cells in cat primary visual cortex. We demonstrate that the filters computed by directly taking the nonlinearity into account have better predictive power and depend less on the stimulus than those computed under the linear model. With noise stimuli, filters computed using the linear and LN models were similar, as predicted theoretically. With natural stimuli, filters of the two models can differ profoundly. Noise and natural stimulus filters differed significantly in spatial properties, but these differences were exaggerated when filters were computed using the linear rather that the LN model. While regularization of filters computed under the linear model improved their predictive power, it also led to systematic distortions of their spatial frequency profiles, especially at low spatial and temporal frequencies. Statistical models for neural encoding, decoding, and optimal stimulus design Liam Paninski, Jonathan Pillow, Jeremy Lewi (2008) Book chapter in Computational Neuroscience: Progress in Brain Research, eds. Cisek, P., Drew, T. and Kalaska, J. pp 493-507 There are two basic problems in the statistical analysis of neural data. The encoding'' problem concerns how information is encoded in neural spike trains: can we predict the spike trains of a neuron (or population of neurons), given an arbitrary stimulus or observed motor response? Conversely, the decoding'' problem concerns how much information is in a spike train: in particular, how well can we estimate the stimulus that gave rise to the spike train? This chapter describes statistical model-based techniques that in some cases provide a unified solution to these two coding problems. These models can capture stimulus dependencies as well as spike history and interneuronal interaction effects in population spike trains, and are intimately related to biophysically-based models of integrate-and-fire type. We describe flexible, powerful likelihood-based methods for fitting these encoding models and then for using the models to perform optimal decoding. Each of these (apparently quite difficult) tasks turn out to be highly computationally tractable, due to a key concavity property of the model likelihood. Finally, we return to the encoding problem to describe how to use these models to adaptively optimize the stimuli presented to the cell on a trial-by-trial basis, in order that we may infer the optimal model parameters as efficiently as possible.

#### 2007

 Eigenvalue Spectra of Random Matrices for Neural Networks by K. Rajan and L.F. Abbott (2006) Phys. Rev. Lett. 97:188104 The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can be chosen randomly from appropriate distributions, making results from random matrix theory highly relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and inhibitory columns drawn from distributions with different means and equal or different variances. The spike-triggered average of the integrate-and-fire cell driven by Gaussian white noise Paninski, L. (2006) Neural Computation 18:2592-2616 We compute the exact spike-triggered average (STA) of the voltage for the nonleaky IF cell in continuous time, driven by Gaussian white noise. The computation is based on techniques from the theory of renewal processes and continuous-time hidden Markov processes (e.g., the backward and forward Fokker-Planck partial differential equations associated with first-passage time densities). From the STA voltage it is straightforward to derive the STA input current. The theory also gives an explicit asymptotic approximation for the STA of the leaky IF cell, valid in the low-noise regime $\sigma \to 0$. We consider both the STA and the conditional average voltage given an observed spike doublet'' event, i.e. two spikes separated by some fixed period of silence. In each case, we find that the STA as a function of time-preceding-spike, $\tau$, has a square-root singularity as $\tau$ approaches zero from below, and scales linearly with the scale of injected noise current. We close by briefly examining the discrete-time case, where similar phenomena are observed. Efficient estimation of detailed single-neuron models Huys, Q., Ahrens, M. Paninski, L. (2006) Journal of Neurophysiology 96:872-890 Biophysically accurate multi-compartmental models of individual neurones have signi cantly advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters which are dif cult to estimate. In practise, they are often hand tuned to match measured physiological behaviors, thus raising questions of identifiability and interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the distribution of channel densities; 2) the spatiotemporal pattern of synaptic input; and 3) axial resistances across extended dendrites. Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: a) the spatiotemporal voltage signal in the dendrite, and b) an approximate description of the channel kinetics of interest. We show here that, given a) and b), the parameters 1)-3) can be inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms ef ciently reach this optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of challenging model data sets that include up to on the order of 10,000 parameters (roughly two orders of magnitude more than previously feasible), and describe how the method gives insights into the functional interaction of groups of channels. Dimensional Reduction in Reward-Based Learning by C Swinehart and L.F. Abbott (2006) Network: Comp. Neural Sys. 17:235-252 Reward-based learning in neural systems is challenging because a large number of parameters that affect network function must be optimized solely on the basis of a reward signal that indicates improved performance. Searching the parameter space for an optimal solution is particularly difficult if the network is large. We show that Hebbian forms of synaptic plasticity applied to synapses between a supervisor circuit and the network it is controlling can effectively reduce the dimension of the space of parameters being searched to support efficient reinforcement-based learning in large networks. The critical element is that the connections between the supervisor units and the network must be reciprocal. Once the appropriate connections have been set up by Hebbian plasticity, a reinforcement-based learning procedure leads to rapid learning in a function approximation task. Hebbian plasticity within the network being supervised ultimately allows the network to perform the task without input from the supervisor. Cross-fixation transfer of motion aftereffects with expansion motion Xin Meng, Pietro Mazzoni and Ning Qian (2006) Vision Research 46:3681-3689 It has been shown that motion aftereffect (MAE) not only is present at the adapted location but also partially transfers to nearby non- adapted locations. However, it is not clear whether MAE transfers across the fixation point. Since cells in area MSTd have receptive fields that cover both sides of the fixation point and since many MSTd cells, but not cells in earlier visual areas, prefer complex motion patterns such as expansion, we tested cross-fixation transfer of MAE induced by expanding random-dots stimuli. We also used rightward translational motion for comparison. Subjects adapted to motion patterns on a fixed side of the fixation point. Dynamic MAE was then measured with a nulling procedure at both the adapted site and the mirror site across the fixation point. SubjectsÕ eye fixation during stimulus presentation was monitored with an infrared eye tracker. At the adapted site, both the expansion and the translation patterns generated strong MAEs, as expected. However, only the expansion pattern, but not translation pattern, generated significant MAE at the mirror site. This remained true even after we adjusted stimulus parameters to equate the strengths of the expansion MAE and translation MAE at the adapted site. We conclude that there is cross-fixation transfer of MAE for expansion motion but not for translational motion. A Simple Growth Model Constructs Critical Avalanche Networks by L.F. Abbott and R Rohrkemper (2006) Prog. Brain Res. 165:13-19 Neurons recorded from electrode arrays show a remarkable scaling property in their bursts of spontaneous activity, referred to as "avalanches' (Beggs and Plentz, 2003 & 2004). Such scaling suggests a critical property in the coupling of these circuits. We show that similar scaling laws can arise in a simple model for the growth of neuronal processes. In the model (Van Ooyen and Van Pelt, 1994 & 1996), the spatial range of the processes extending from each neuron is represented by a circle that grows or shrinks as a function of the average intracellular calcium concentration. Neurons interact when the circles corresponding to their processes intersect, with a strength proportional to the area of overlap. Synaptic Democracy in Active Dendrites by C.C. Rumsey and L.F. Abbott (2006) J. Neurophys. 96:2307-2318 Given the extensive attenuation that can occur along dendritic cables, location within the dendritic tree might appear to be a dominant factor in determining the impact of a synapse on the postsynaptic response. By this reasoning, distal syn- apses should have a smaller effect than proximal ones. However, experimental evidence from several types of neurons, such as CA1 pyramidal cells, indicates that a compensatory strengthening of syn- apses counteracts the effect of location on synaptic efficacy. A form of spike-timing-dependent plasticity (STDP), called anti-STDP, com- bined with non-Hebbian activity-dependent plasticity can account for the equalization of synaptic efficacies. This result, obtained originally in models with unbranched passive cables, also arises in multi- compartment models with branched and active dendrites that feature backpropagating action potentials, including models with CA1 py- ramidal morphologies. Additionally, when dendrites support the local generation of action potentials, anti-STDP prevents runaway dendritic spiking and locally balances the numbers of dendritic and backpropa- gating action potentials. Thus in multiple ways, anti-STDP eliminates the location dependence of synapses and allows Hebbian plasticity to operate in a more "democratic" manner. A Comparison among some Models of V1 Orientation Selectivity Andrew F. Teich and Ning Qian (2006) J. Neurophysiol. 96:404-419 Several models exist for explaining primary visual cortex (V1) orientation tuning. The modified feedforward model (MFM) and the recurrent model (RM) are major examples. We have implemented these two models, at the same level of detail, alongside a few newer variations, and thoroughly compared their receptive-field structures. We found that antiphase inhibition in the MFM enhances both spatial phase information and orientation tuning, producing well-tuned simple cells. This remains true for a newer version of the MFM that incorporates untuned complex-cell inhibition. In contrast, when the recurrent connections in the RM are strong enough to produce typical V1 orientation tuning, they also eliminate spatial phase information, making the cells com- plex. Introducing phase specificity into the connections of the RM (as done in an original version of the RM) can make the cells phase sensitive, but the cells show an incorrect 90¡ peak shift of orientation tuning under opposite contrast signs. An inhibition-dominant version of the RM can generate well-tuned cells across the simpleÐ complex spectrum, but it predicts that the net effect of cortical interactions is to suppress feedforward excitation across all orientations in simple cells. Finally, adding antiphase inhibition used in the MFM into the RM produces a most general model. We call this new model the modified recurrent model (MRM) and show that this model can also produce well-tuned cells throughout the simpleÐ complex spectrum. Unlike the inhibition-dominant RM, the MRM is consistent with data from cat V1, suggesting that the net effect of cortical interactions is to boost simple cell responses at the preferred orientation. These results sug- gest that the MFM is well suited for explaining orientation tuning in simple cells, whereas the standard RM is for complex cells. The assignment of the RM to complex cells also avoids conflicts between the RM and the experiments of cortical inactivation (done on simple cells) and the spatial-frequency dependency of orientation tuning (found in simple cells). Because orientation-tuned V1 cells show a continuum of simple- to complex-cell behavior, the MRM provides the best description of V1 data. Extending the Effects of STDP to Behavioral Timescales by P.J. Drew and L.F. Abbott (2006) Proc. Natl. Acad. Sci. USA, 103:8876-8881 Activity-dependent modification of synaptic strengths due to spike-timing-dependent plasticity (STDP) is sensitive to correlations between pre- and postsynaptic firing over timescales of tens of milliseconds. Temporal associations typically encountered in behavioral tasks involve times on the order of seconds. To relate the learning of such temporal associations to STDP, we must account for this large discrepancy in timescales. We show that the gap between synaptic and behavioral timescales can be bridged if the stimuli being associated generate sustained responses that vary appropriately in time. Synapses between neurons that fire this way can be modified by STDP in a manner that depends on the temporal ordering of events separated by several seconds even though the underlying plasticity has a much smaller temporal window. Models and Properties of Power-Law Adaptation in Neural Systems by P.J. Drew and L.F. Abbott (2006) J. Neurophysiol., 96:826-833. Many biological systems exhibit complex temporal behavior that cannot be adequately characterized by a single time constant. This dynamics, observed from single channels up to the level of human psychophysics, is often better described by power-law rather than exponential dependences on time. We develop and study the properties of neural models with scale-invariant, power-law adaptation and contrast them with the more commonly studied exponential case. Responses of an adapting firing-rate model to constant, pulsed and oscillating inputs in both the power-law and exponential cases are considered. We construct a spiking model with power-law adaptation based on a nested cascade of processes and show that it can be "programmed" to produce a wide range of time delays. Finally, within a network model, we use power-law adaptation to reproduce long-term features of the tilt aftereffect. An Optimization Principle for Determining Movement Duration Hirokazu Tanaka, John Krakauer and Ning Qian (2006) J. Neurophysiol. 95:3875-3886 Movement duration is an integral com- ponent of motor control, but nearly all extant optimization models of motor planning prefix duration instead of explaining it. Here we propose a new optimization principle that predicts movement dura- tion. The model assumes that the brain attempts to minimize move- ment duration under the constraint of meeting an accuracy criterion. The criterion is task and context dependent but is fixed for a given task and context. The model determines a unique duration as a trade-off between speed (time optimality) and accuracy (acceptable endpoint scatter). We analyzed the model for a linear motor plant, and obtained a closed-form equation for determining movement duration. By solv- ing the equation numerically with specific plant parameters for the eye and arm, we found that the model can reproduce saccade duration as a function of amplitude (the main sequence), and arm-movement duration as a function of the ratio of target distance to size (FittsÕs law). In addition, it explains the dependency of peak saccadic speed on amplitude and the dependency of saccadic duration on initial eye position. Furthermore, for arm movements, the model predicts a scaling relationship between peak velocity and distance and a reduc- tion in movement duration with a moderate increase in viscosity. Finally, for a linear plant, our model predicts a neural control signal identical to that of the minimum-variance model set to the same movement duration. This control signal is a smooth function of time (except at the endpoint), in contrast to the discontinuous bangÐ bang control found in the time-optimal control literature. We suggest that one aspect of movement planning, as revealed by movement duration, may be to assign an endpoint accuracy criterion for a given task and context. Adaptive filtering enhances information transmission in visual cortex by Tatyana Sharpee, Hiroki Sugihara, Andrei Kurgansky, Sergei Rebrik, Michael Stryker and Kenneth Miller (2006) Nature, 439 February 23, 2006 Sensory neuroscience seeks to understand how the brain encodes natural environments. However, neural coding has largely been studied using simplified stimuli. In order to assess whether the brain's coding strategy depends on the stimulus ensemble, we apply a new information-theoretic method that allows unbiased calculation of neural filters (receptive fields) from responses to natural scenes or other complex signals with strong multipoint correlations. In the cat primary visual cortex we compare responses to natural inputs with those to noise inputs matched for luminance and contrast. We find that neural filters adaptively change with the input ensemble so as to increase the information carried by the neural response about the filtered stimulus. Adaptation affects the spatial frequency composition of the filter, enhancing sensitivity to under-represented frequencies in agreement with optimal encoding arguments. Adaptation occurs over 40 s to many minutes, longer than most previously reported forms of adaptation. Where are the Switches on this Thing by L.F. Abbott (2006) In J.L. van Hemmen and T.J. Sejnowski, eds. 23 Problems in Systems Neuroscience (Oxford University Press, Oxford) pp. 423-431. Controlled responses differ from reflexes because they can be turned off and on. This is a critical part of what distinguishes animals from automatons. How does the nervous system gate the flow of information so that a sensory stimulus that elicits a strong response on some occasions, evokes no response on others? A related question concerns how the flow of sensory information is altered when we pay close attention to something as opposed to when we ignore it. Most research in neuroscience focuses on circuits that directly respond to stimuli or generate motor output. But what of the circuits and mechanisms that control these direct responses, that modulate them and turn them off and on? Self-regulated switching is vital to the operation of complex machines such as computers. The essential building block of a computer is a voltage-gated switch, the transistor, that is turned off and on by the same sorts of currents that it controls. By analogy, the question of my title refers to neural pathways that not only carry the action potentials that arise from neural activity, but are switched off and on by neural activity as well. By what biophysical mechanisms could this occur? In the spirit of this volume, the point of this contribution is to raise a question, not to answer it. I will discuss three possible mechanisms— neuromodulation, inhibition, and gain modulation—and assess the merits and short-comings of each of them. I have my prejudices, which will become obvious, but I do not want to rule out any of these as candidates, nor do I want to leave the impression that the list is complete or that the problem is in any sense solved.