arXiv subjects

Michael J. Berry II

Publications and source records attributed to Michael J. Berry II.

12 recordsLinked to original sources

arXiv2017

Noise-Robust Modes of the Retinal Population Code have the Geometry of "Ridges" and Correspond with 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 datasets of the responses of ~150 retinal ganglion cells and show that local probability peaks are absent under broad, non-repeated 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 are comprised of 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 Hebb's classic cell assembly, and show that a simple, biologically plausible decoding algorithm can recognize the presence of a specific neuronal community.

q-bio.NC↗

arXiv2016

The Structured `Low Temperature' Phase of the Retinal Population Code

Recent advances in experimental techniques have allowed the simultaneous recording of populations of hundreds of neurons, allowing more comprehensive investigation into the nature of the collective structure of population neural activity. While recent studies have reported a phase transition in the parameter space of maximum entropy models describing the neural probability distributions, the interpretation of these findings has been debated. Here, we suggest that this phase transition may be evidence of a `structured', collective state in the neural population. We show that this phase transition is robust to changes in stimulus ensemble and adaptive state. We find that the pattern of pairwise correlations between neurons has a strength that is well within the strongly correlated regime and does not require fine tuning, suggesting that this state is generic for populations of 100+ neurons. We find a clear correspondence between the emergence of a phase transition, and the emergence of attractor-like structure in the inferred energy landscape. A collective state in the neural population, in which neural activity patterns naturally form clusters, provides a consistent interpretation for our results.

q-bio.NC↗

arXiv2014

High accuracy decoding of dynamical motion from a large retinal population

Motion tracking is a challenge the visual system has to solve by reading out the retinal population. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar's position. Instead, we found that ganglion cells fired sparsely over an area much larger than predicted by their receptive fields, so that the neural image did not track the bar. This highly redundant organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.

q-bio.NC↗

arXiv2014

Thermodynamics for a network of neurons: Signatures of criticality

The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but with more spikes the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N=160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. Networks with more or less correlation among neurons would not reach this critical state. We suggest further tests of criticality, and give a brief discussion of its functional significance.

q-bio.NC↗

arXiv2013

High-Fidelity Coding with Correlated Neurons

Positive correlations in the activity of neurons are widely observed in the brain. Previous studies have shown these correlations to be detrimental to the fidelity of population codes or at best marginally favorable compared to independent codes. Here, we show that positive correlations can enhance coding performance by astronomical factors. Specifically, the probability of discrimination error can be suppressed by many orders of magnitude. Likewise, the number of stimuli encoded--the capacity--can be enhanced by similarly large factors. These effects do not necessitate unrealistic correlation values and can occur for populations with a few tens of neurons. We further show that both effects benefit from heterogeneity commonly seen in population activity. Error suppression and capacity enhancement rest upon a pattern of correlation. In the limit of perfect coding, this pattern leads to a `lock-in' of response probabilities that eliminates variability in the subspace relevant for stimulus discrimination. We discuss the nature of this pattern and suggest experimental tests to identify it.

q-bio.NC↗

arXiv2013

Predictive information in a sensory population

Guiding behavior requires the brain to make predictions about future sensory inputs. Here we show that efficient predictive computation starts at the earliest stages of the visual system. We estimate how much information groups of retinal ganglion cells carry about the future state of their visual inputs, and show that every cell we can observe participates in a group of cells for which this predictive information is close to the physical limit set by the statistical structure of the inputs themselves. Groups of cells in the retina also carry information about the future state of their own activity, and we show that this information can be compressed further and encoded by downstream predictor neurons, which then exhibit interesting feature selectivity. Efficient representation of predictive information is a candidate principle that can be applied at each stage of neural computation.

q-bio.NC↗

arXiv2012

The simplest maximum entropy model for collective behavior in a neural network

Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on capturing the measured correlations among pairs of neurons. Here we suggest an alternative, constructing models that are consistent with the distribution of global network activity, i.e. the probability that K out of N cells in the network generate action potentials in the same small time bin. The inverse problem that we need to solve in constructing the model is analytically tractable, and provides a natural "thermodynamics" for the network in the limit of large N. We analyze the responses of neurons in a small patch of the retina to naturalistic stimuli, and find that the implied thermodynamics is very close to an unusual critical point, in which the entropy (in proper units) is exactly equal to the energy.

q-bio.NC↗

arXiv2009

Spin glass models for a network of real neurons

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the salamander retina responding to natural movies. We show that pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent system. We then construct network ensembles that generalize the network instances observed in the experiment, and study their thermodynamic behavior and coding capacity. Based on this construction, we can also create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses. We examine closely two such behaviors that could be relevant for neural code: tuning of the network to the critical point to maximize the ability to encode diverse stimuli, and using the metastable states of the Ising Hamiltonian as neural code words.

q-bio.NC↗

arXiv2006

Synergy from Silence in a Combinatorial Neural Code

The manner in which groups of neurons represent events in the external world is fundamental to neuroscience. Here, we analyze the population code of the retina during naturalistic stimulation and show that the information conveyed by specific multi-neuronal firing patterns can be very different from the sum of the pattern's parts. Synchronous spikes convey more information than either of the participating cells, but almost always less than their sum, making them redundant coding symbols. Surprisingly, patterns of spiking and silence are mostly synergistic - carrying information that is accessible only by observing the whole pattern of activity, rather than its components, and signifying unique features in the stimulus. These results demonstrate that the retina uses a combinatorial code and that the brain can benefit significantly from recognizing multi-neuronal firing patterns.

q-bio.NC↗

arXiv2005

Weak pairwise correlations imply strongly correlated network states in a neural population

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among large groups of elements play an important role. In the vertebrate retina, we show that weak correlations between pairs of neurons coexist with strongly collective behavior in the responses of ten or more neurons. Surprisingly, we find that this collective behavior is described quantitatively by models that capture the observed pairwise correlations but assume no higher order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behavior. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.

q-bio.NC↗

arXiv2003

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease in entropy for the joint distribution of $N$ variables relative to the maximum entropy allowed by all the observed $N-1$ variable distributions. We calculate the ``connected information'' terms for several examples, and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.

physics.bio-ph↗

arXiv2002

An information theoretic approach to the functional classification of neurons

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured in the identity of the clusters rather than by individuals within clusters. We show how this intuition can be made precise using information theory, without any need to introduce a metric on the space of stimuli or responses. Applied to the retinal ganglion cells of the salamander, this approach recovers classical results, but also provides clear evidence for subclasses beyond those identified previously. Further, we find that each of the ganglion cells is functionally unique, and that even within the same subclass only a few spikes are needed to reliably distinguish between cells.

physics.bio-ph↗