Jason S. Prentice

Optimal population coding by noisy spiking neurons

In retina and in cortical slice the collective response of spiking neural populations is well described by “maximum-entropy” models in which only pairs of neurons interact. We asked, how should such interactions be organized to maximize the amount of information represented in population responses? To this end, we extended the linear-nonlinear-Poisson model of single neural response to include pairwise interactions, yielding a stimulus-dependent, pairwise maximum-entropy model. We found that as we varied the noise level in single neurons and the distribution of network inputs, the optimal pairwise interactions smoothly interpolated to achieve network functions that are usually regarded as discrete—stimulus decorrelation, error correction, and independent encoding. These functions reflected a trade-off between efficient consumption of finite neural bandwidth and the use of redundancy to mitigate noise. Spontaneous activity in the optimal network reflected stimulus-induced activity patterns, and single-neuron response variability overestimated network noise. Our analysis suggests that rather than having a single coding principle hardwired in their architecture, networks in the brain should adapt their function to changing noise and stimulus correlations.

Local statistics in natural scenes predict the saliency of synthetic textures

The visual system is challenged with extracting and representing behaviorally relevant information contained in natural inputs of great complexity and detail. This task begins in the sensory periphery: retinal receptive fields and circuits are matched to the first and second-order statistical structure of natural inputs. This matching enables the retina to remove stimulus components that are predictable (and therefore uninformative), and primarily transmit what is unpredictable (and therefore informative). Here we show that this design principle applies to more complex aspects of natural scenes, and to central visual processing. We do this by classifying high-order statistics of natural scenes according to whether they are uninformative vs. informative. We find that the uninformative ones are perceptually nonsalient, while the informative ones are highly salient, and correspond to previously identified perceptual mechanisms whose neural basis is likely central. Our results suggest that the principle of efficient coding not only accounts for filtering operations in the sensory periphery, but also shapes subsequent stages of sensory processing that are sensitive to high-order image statistics.

Fast, scalable, Bayesian spike identification for multi-electrode arrays.

We present an algorithm to identify individual neural spikes observed on high-density multi-electrode arrays (MEAs). Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit. As MEAs grow larger, it is important to find spike-identification methods that are scalable, that is, the computational cost of spike fitting should scale well with the number of units observed. Our algorithm accomplishes this goal, and is fast, because it exploits the spatial locality of each unit and the basic biophysics of extracellular signal propagation. Human interaction plays a key role in our method; but effort is minimized and streamlined via a graphical interface. We illustrate our method on data from guinea pig retinal ganglion cells and document its performance on simulated data consisting of spikes added to experimentally measured background noise. We present several tests demonstrating that the algorithm is highly accurate: it exhibits low error rates on fits to synthetic data, low refractory violation rates, good receptive field coverage, and consistency across users.

A principle of economy predicts the functional architecture of grid cells

1 Department of Psychology, University of Pennsylvania, Philadelphia, PA 19104, USA 2 Department of Physics, University of Pennsylvania, Philadelphia, PA 19104, USA 3 Department of Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, USA 4 Laboratoire de Physique Théorique, École Normale Supérieure, 75005 Paris, France 5 Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USAGrid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths. DOI: http://dx.doi.org/10.7554/eLife.08362.001

Error-Robust Modes of the Retinal Population Code

Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina.

Noise-Robust Modes of the Retinal Population Code Have the Geometry of “Ridges” and Correspond to Neuronal Communities

An appealing new principle for neural population codes is that correlations among neurons organize neural activity patterns into a discrete set of clusters, which can each be viewed as a noise-robust population codeword. Previous studies assumed that these codewords corresponded geometrically with local peaks in the probability landscape of neural population responses. Here, we analyze multiple data sets of the responses of approximately 150 retinal ganglion cells and show that local probability peaks are absent under broad, nonrepeated stimulus ensembles, which are characteristic of natural behavior. However, we find that neural activity still forms noise-robust clusters in this regime, albeit clusters with a different geometry. We start by defining a soft local maximum, which is a local probability maximum when constrained to a fixed spike count. Next, we show that soft local maxima are robustly present and can, moreover, be linked across different spike count levels in the probability landscape to form a ridge. We found that these ridges comprise combinations of spiking and silence in the neural population such that all of the spiking neurons are members of the same neuronal community, a notion from network theory. We argue that a neuronal community shares many of the properties of Donald Hebbs classic cell assembly and show that a simple, biologically plausible decoding algorithm can recognize the presence of a specific neuronal community.

Optimal correlation codes in populations of noisy spiking neurons

In most areas of the brain, information is encoded in the correlated activity of large populations of neurons. We ask how neural responses should be coupled to best represent information about different ensembles of correlated stimuli. Three classical population coding strategies are independence, decorrelation and error correction. Here we demonstrate that balance between the intrinsic noise level and the statistics of the input ensemble induces smooth transitions between these three coding strategies in a network composed of pairwise-coupled neurons and tuned to maximize its information capacity.

Transformation of Stimulus Correlations by the Retina

Redundancies and correlations in the responses of sensory neurons may seem to waste neural resources, but they can also carry cues about structured stimuli and may help the brain to correct for response errors. To investigate the effect of stimulus structure on redundancy in retina, we measured simultaneous responses from populations of retinal ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure; these stimuli and recordings are publicly available online. Responding to spatio-temporally structured stimuli such as natural movies, pairs of ganglion cells were modestly more correlated than in response to white noise checkerboards, but they were much less correlated than predicted by a non-adapting functional model of retinal response. Meanwhile, responding to stimuli with purely spatial correlations, pairs of ganglion cells showed increased correlations consistent with a static, non-adapting receptive field and nonlinearity. We found that in response to spatio-temporally correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the pattern of pairwise correlations across stimuli where receptive field measurements were possible.

Scalable, Bayesian, multi-electrode spike sorting

Multi-electrode array technology provides an efficient means of recording from many neurons. However, as arrays become larger, a greater computational burden falls on the spike-sorting algorithm. We have developed a new method, that scales linearly with array size, for sorting multi-electrode signals from retinal ganglion cells. We believe that our techniques represent progress toward solving many of the source separation problems that will become ubiquitous as large multi-electrode arrays become commonplace. The broad outline of our method is to identify spikes in the raw data, cluster a subset, generate template waveforms, then fit the templates to all the data using an iterative Bayesian algorithm. Spikes are identified as spatiotemporally connected patches of threshold-crossing voltage samples. The spike waveform is taken from a fixed neighborhood centered on the electrode having the peak voltage within each patch. This approach allows for segmentation of simultaneous, yet spatially separated, events and prevents the waveform dimensionality from increasing with array size. Next we cluster a small subset of spikes. We use an existing algorithm, OPTICS, which orders the waveforms so that similar spikes are placed together. This linear ordering makes cluster boundaries easily distinguishable by the user. We have built a GUI in which the manual cluster cutting can be performed efficiently. For each cluster, we align the waveforms and take the median to get templates. The primary obstacle in fitting templates to the data is the presence of overlapping spikes, which distort the observed waveforms. One established approach to the problem is to simply fit single templates, then subtract the best fit and iterate. However, the amplitude of the observed spike can differ substantially from the template, producing errors upon subtraction. We avoid this problem by allowing the amplitude of the template to vary; this is most naturally incorporated into a Bayesian framework. We model each waveform as a linear superposition of templates with Gaussian-distributed amplitudes, plus correlated Gaussian noise. We then seek the most probable template, spike time, and amplitude given the data. The spatial localization of spikes narrows down the list of candidate templates, speeding up the algorithm. The Gaussian amplitude prior allows the amplitudes to be marginalized analytically, avoiding an explicit sum. We have tested the method on many data sets recorded with a dense 30-electrode array, under a variety of stimulus conditions. It always produces very low error rates. Tests with larger arrays, different species, and synthetic data are ongoing.