Garrett T. Kenyon

A Mathematical Model of the Cerebellar-Olivary System I: Self-Regulating Equilibrium of Climbing Fiber Activity

We use a mathematical model to investigate how climbing fiber-dependent plasticity at granule cell to Purkinje cell (gr→Pkj) synapses in the cerebellar cortex is influenced by the synaptic organization of the cerebellar-olivary system. Based on empirical studies, gr→Pkj synapses are assumed to decrease in strength when active during a climbing fiber input (LTD) and increase in strength when active without a climbing fiber input (LTP). Results suggest that the inhibition of climbing fibers by cerebellar output combines with LTD/P to self-regulate spontaneous climbing fiber activity to an equilibrium level at which LTP and LTD balance and the expected net change in gr→Pkj synaptic weights is zero. The synaptic weight vector is asymptotically confined to an equilibrium hyperplane defining the set of all possible combinations of synaptic weights consistent with climbing fiber equilibrium. Results also suggest restrictions on LTP/D at gr→Pkj synapses required to produce synaptic weights that do not drift spontaneously.

A model of high-frequency oscillatory potentials in retinal ganglion cells

High-frequency oscillatory potentials (HFOPs) have been recorded from ganglion cells in cat, rabbit, frog, and mudpuppy retina and in electroretinograms (ERGs) from humans and other primates. However, the origin of HFOPs is unknown. Based on patterns of tracer coupling, we hypothesized that HFOPs could be generated, in part, by negative feedback from axon-bearing amacrine cells excited via electrical synapses with neighboring ganglion cells. Computer simulations were used to determine whether such axon-mediated feedback was consistent with the experimentally observed properties of HFOPs. (1) Periodic signals are typically absent from ganglion cell PSTHs, in part because the phases of retinal HFOPs vary randomly over time and are only weakly stimulus locked. In the retinal model, this phase variability resulted from the nonlinear properties of axon-mediated feedback in combination with synaptic noise. (2) HFOPs increase as a function of stimulus size up to several times the receptive-field center diameter. In the model, axon-mediated feedback pooled signals over a large retinal area, producing HFOPs that were similarly size dependent. (3) HFOPs are stimulus specific. In the model, gap junctions between neighboring neurons caused contiguous regions to become phase locked, but did not synchronize separate regions. Model-generated HFOPs were consistent with the receptive-field center dynamics and spatial organization of cat alpha cells. HFOPs did not depend qualitatively on the exact value of any model parameter or on the numerical precision of the integration method. We conclude that HFOPs could be mediated, in part, by circuitry consistent with known retinal anatomy.

Correlated firing improves stimulus discrimination in a retinal model

Synchronous firing limits the amount of information that can be extracted by averaging the firing rates of similarly tuned neurons. Here, we show that the loss of such rate-coded information due to synchronous oscillations between retinal ganglion cells can be overcome by exploiting the information encoded by the correlations themselves. Two very different models, one based on axon-mediated inhibitory feedback and the other on oscillatory common input, were used to generate artificial spike trains whose synchronous oscillations were similar to those measured experimentally. Pooled spike trains were summed into a threshold detector whose output was classified using Bayesian discrimination. For a threshold detector with short summation times, realistic oscillatory input yielded superior discrimination of stimulus intensity compared to rate-matched Poisson controls. Even for summation times too long to resolve synchronous inputs, gamma band oscillations still contributed to improved discrimination by reducing the total spike count variability, or Fano factor. In separate experiments in which neurons were synchronized in a stimulus-dependent manner without attendant oscillations, the Fano factor increased markedly with stimulus intensity, implying that stimulus-dependent oscillations can offset the increased variability due to synchrony alone.

A reconfigurable computing framework for multi-scale cellular image processing

Cellular computing architectures represent an important class of computation that are characterized by simple processing elements, local interconnect and massive parallelism. These architectures are a good match for many image and video processing applications and can be substantially accelerated with Reconfigurable Computers. We present a flexible software/hardware framework for design, implementation and automatic synthesis of cellular image processing algorithms. The system provides an extremely flexible set of parallel, pipelined and time-multiplexed components which can be tailored through reconfigurable hardware for particular applications. The most novel aspects of our framework include a highly pipelined architecture for multi-scale cellular image processing as well as support for several different pattern recognition applications. In this paper, we will describe the system in detail and present our performance assessments. The system achieved speed-up of at least 100x for computationally expensive sub-problems and 10x for end-to-end applications compared to software implementations.

Stimulus-specific oscillations in a retinal model

High-frequency oscillatory potentials (HFOPs) in the vertebrate retina are stimulus specific. The phases of HFOPs recorded at any given retinal location drift randomly over time, but regions activated by the same stimulus tend to remain phase locked with approximately zero lag, whereas regions activated by spatially separate stimuli are typically uncorrelated. Based on retinal anatomy, we previously postulated that HFOPs are mediated by feedback from a class of axon-bearing amacrine cells that receive excitation from neighboring ganglion cells-via gap junctions-and make inhibitory synapses back onto the surrounding ganglion cells. Using a computer model, we show here that such circuitry can account for the stimulus specificity of HFOPs in response to both high- and low-contrast features. Phase locking between pairs of model ganglion cells did not depend critically on their separation distance, but on whether the applied stimulus created a continuous path between them. The degree of phase locking between spatially separate stimuli was reduced by lateral inhibition, which created a buffer zone around strongly activated regions. Stimulating the inhibited region between spatially separate stimuli increased their degree of phase locking proportionately. Our results suggest several experimental strategies for testing the hypothesis that stimulus-specific HFOPs arise from axon-mediated feedback in the inner retina.

A mathematical model of the cerebellar-olivary system. II: Motor adaptation through systematic disruption of climbing fiber equilibrium

The implications for motor learning of the model developed in the previous article are analyzed using idealized Pavlovian eyelid conditioning trials, a simple example of cerebellar motor learning. Results suggest that changes in gr→Pkj synapses produced by a training trial disrupt equilibrium and lead to subsequent changes in the opposite direction that restore equilibrium. We show that these opposing phases would make the net plasticity at each gr→Pkj synapse proportional to the change in its activity during the training trial, as influenced by a factor that precludes plasticity when changes in activity are inconsistent. This yields an expression for the component of granule cell activity that supports learning, the across-trials consistency vector, the square of which determines the expected rate of learning. These results suggest that the equilibrium maintained by the cerebellar-olivary system must be disrupted in a specific and systematic manner to promote cerebellar-mediated motor learning.

See globally, spike locally: oscillations in a retinal model encode large visual features

We show that coherent oscillations among neighboring ganglion cells in a retinal model encode global topological properties, such as size, that cannot be deduced unambiguously from their local, time-averaged firing rates. Whereas ganglion cells may fire similar numbers of spikes in response to both small and large spots, only large spots evoke coherent high frequency oscillations, potentially allowing downstream neurons to infer global stimulus properties from their local afferents. To determine whether such information might be extracted over physiologically realistic spatial and temporal scales, we analyzed artificial spike trains whose oscillatory correlations were similar to those measured experimentally. Oscillatory power in the upper gamma band, extracted on single-trials from multi-unit spike trains, supported good to excellent size discrimination between small and large spots, with performance improving as the number of cells and/or duration of the analysis window was increased. By using Poisson distributed spikes to normalize the firing rate across stimulus conditions, we further found that coincidence detection, or synchrony, yielded substantially poorer performance on identical size discrimination tasks. To determine whether size encoding depended on contiguity independent of object shape, we examined the total oscillatory activity across the entire model retina in response to random binary images. As the ON-pixel probability crossed the percolation threshold, which marks the sudden emergence of large connected clusters, the total gamma-band activity exhibited a sharp transition, a phenomena that may be experimentally observable. Finally, a reanalysis of previously published oscillatory responses from cat ganglion cells revealed size encoding consistent with that predicted by the retinal model.

Large-scale functional models of visual cortex for remote sensing

Neuroscience has revealed many properties of neurons and of the functional organization of visual cortex that are believed to be essential to human vision, but are missing in standard artificial neural networks. Equally important may be the sheer scale of visual cortex requiring ~1 petaflop of computation, while the scale of human visual experience greatly exceeds standard computer vision datasets: the retina delivers ~1 petapixel/year to the brain, driving learning at many levels of the cortical system. We describe work at Los Alamos National Laboratory (LANL) to develop large-scale functional models of visual cortex on LANLs Roadrunner petaflop supercomputer. An initial run of a simple region V1 code achieved 1.144 petaflops during trials at the IBM facility in Poughkeepsie, NY (June 2008). Here, we present criteria for assessing when a set of learned local representations is ¿complete¿ along with general criteria for assessing computer vision models based on their projected scaling behavior. Finally, we extend one class of biologically-inspired learning models to problems of remote sensing imagery.

Interpreting individual classifications of hierarchical networks

Hierarchical networks are known to achieve high classification accuracy on difficult machine-learning tasks. For many applications, a clear explanation of why the data was classified a certain way is just as important as the classification itself. However, the complexity of hierarchical networks makes them ill-suited for existing explanation methods. We propose a new method, contribution propagation, that gives per-instance explanations of a trained networks classifications. We give theoretical foundations for the proposed method, and evaluate its correctness empirically. Finally, we use the resulting explanations to reveal unexpected behavior of networks that achieve high accuracy on visual object-recognition tasks using well-known data sets.

Model Cortical Association Fields Account for the Time Course and Dependence on Target Complexity of Human Contour Perception

Can lateral connectivity in the primary visual cortex account for the time dependence and intrinsic task difficulty of human contour detection? To answer this question, we created a synthetic image set that prevents sole reliance on either low-level visual features or high-level context for the detection of target objects. Rendered images consist of smoothly varying, globally aligned contour fragments (amoebas) distributed among groups of randomly rotated fragments (clutter). The time course and accuracy of amoeba detection by humans was measured using a two-alternative forced choice protocol with self-reported confidence and variable image presentation time (20-200 ms), followed by an image mask optimized so as to interrupt visual processing. Measured psychometric functions were well fit by sigmoidal functions with exponential time constants of 30-91 ms, depending on amoeba complexity. Key aspects of the psychophysical experiments were accounted for by a computational network model, in which simulated responses across retinotopic arrays of orientation-selective elements were modulated by cortical association fields, represented as multiplicative kernels computed from the differences in pairwise edge statistics between target and distractor images. Comparing the experimental and the computational results suggests that each iteration of the lateral interactions takes at least ms of cortical processing time. Our results provide evidence that cortical association fields between orientation selective elements in early visual areas can account for important temporal and task-dependent aspects of the psychometric curves characterizing human contour perception, with the remaining discrepancies postulated to arise from the influence of higher cortical areas.