Dynamic Alignment Models for Neural Coding

Recently, there have been remarkable advances in modeling the relationships between the sensory environment, neuronal responses, and behavior. However, most models cannot encompass variable stimulus-response relationships such as varying response latencies and state or context dependence of the neural code. Here, we consider response modeling as a dynamic alignment problem and model stimulus and response jointly by a mixed pair hidden Markov model (MPH). In MPHs, multiple stimulus-response relationships (e.g., receptive fields) are represented by different states or groups of states in a Markov chain. Each stimulus-response relationship features temporal flexibility, allowing modeling of variable response latencies, including noisy ones. We derive algorithms for learning of MPH parameters and for inference of spike response probabilities. We show that some linear-nonlinear Poisson cascade (LNP) models are a special case of MPHs. We demonstrate the efficiency and usefulness of MPHs in simulations of both jittered and switching spike responses to white noise and natural stimuli. Furthermore, we apply MPHs to extracellular single and multi-unit data recorded in cortical brain areas of singing birds to showcase a novel method for estimating response lag distributions. MPHs allow simultaneous estimation of receptive fields, latency statistics, and hidden state dynamics and so can help to uncover complex stimulus response relationships that are subject to variable timing and involve diverse neural codes.     

The Spectro-Temporal Receptive Field

The Spectro-Temporal Receptive Field (STRF) of an auditory neuron has been introduced experimentally on the base of the average spectrotemporal structure of the acoustic stimuli which precede the occurrence of action potentials (Aertsen et al., 1980, 1981). In the present paper the STRF is considered in the general framework of nonlinear system theory, especially in the form of the Volterra integral representation. The STRF is proposed to be formally identified with a linear functional of the second order Volterra kernel. The experimental determination of the STRF leads to a formulation in terms of the Wiener expansion where the kernels can be identified by evaluation of the system's input-output correlations. For a Gaussian stimulus ensemble and a nonlinear system with no even order contributions of order higher than two, it is shown that the second order cross correlation of stimulus and response, normalized with respect to the spectral contents of the stimulus ensemble, leads to the stimulus-invariant spectrotemporal receptive field. The investigation of stimulus-invariance of the STRF for more general nonlinear systems and for stimulus ensembles which can be generated by nonlinear transformations of Gaussian noise involve the evaluation of higher order stimulus-response correlation functions.     

TESTING HYPOTHESES OF NEURAL EVOLUTION IN GYMNOTIFORM ELECTRIC FISHES USING PHYLOGENETIC CHARACTER DATA

In this paper, we propose a method to test alternative hypotheses of phenotypic evolution. The method compares patterns observed in phylogenetic character data with patterns expected by explicit models of evolutionary process. Observed patterns of character-state diversity are assessed from four properties of character-state change derived from a phylogenetic analysis: the sequence and correlation of transformations on a cladogram and the spatial and functional localization of these transformations to parts of an organism. Patterns expressed in terms of the localization of transformations are compared with the expectations of null models that the number of transformations is proportional to measures of size or complexity. Deviations from the values expected by the null models are then compared with qualitative expectations of the models. The method is applied to characters in the nervous system of gymnotiform electric fishes. Patterns in the diversity of 63 reconstructed character-state changes are compared with the expectations of 10 published models of neural evolution. A total of 63 expectations are reviewed, of which 33 (52%) are found to be consistent with the gymnotiform neural data. In general, the models reviewed are not successful at making global predictions, in part because they have been cast in excessively general terms. The data support the conclusion that evolution in the nervous system of gymnotiforms has involved a mosaic of processes, each operating differentially on functional and developmental systems and at different spatial and temporal scales. The results also indicate that more refined models are required, each making more explicit predictions.     

Assessing the Performance of Neural Encoding Models in the Presence of Noise

An analytical method is introduced for evaluating the performance of neural encoding models. The method addresses a critical question that arises during the course of the development and validation of encoding models: is a given model near optimal in terms of its accuracy in predicting the stimulus-elicited responses of a neural system, or can the predictive accuracy be improved significantly by further model development? The evaluation method is based on a derivation of the minimum mean-square error between actual responses and modeled responses. It is formulated as a comparison between the mean-square error of the candidate model and the theoretical minimum mean-square error attainable through an optimal model for the system. However, no a priori information about the nature of the optimal model is required. The theoretically minimum error is determined solely from the coherence function between pairs of system responses to repeated presentations of the same dynamic stimulus. Thus, the performance of the candidate model is judged against the performance of an optimal model rather than against that of an arbitrarily assumed model. Using this method, we evaluated a linear model for neural encoding by mechanosensory cells in the cricket cercal system. At low stimulus intensities, the best-fit linear model of encoding by single cells was found to be nearly optimal, even though the coherence between stimulus-response pairs (a commonly used measure of system linearity) was low. In this low-stimulus-intensity regime, the mean square error of the linear model was on the order of the power of the cell responses. In contrast, at higher stimulus intensities the linear model was not an accurate representation of neural encoding, even though the stimulus-response coherence was substantially higher than in the low-intensity regime.     

Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.     

Measuring Fisher Information Accurately in Correlated Neural Populations

Neural responses are known to be variable. In order to understand how this neural variability constrains behavioral performance, we need to be able to measure the reliability with which a sensory stimulus is encoded in a given population. However, such measures are challenging for two reasons: First, they must take into account noise correlations which can have a large influence on reliability. Second, they need to be as efficient as possible, since the number of trials available in a set of neural recording is usually limited by experimental constraints. Traditionally, cross-validated decoding has been used as a reliability measure, but it only provides a lower bound on reliability and underestimates reliability substantially in small datasets. We show that, if the number of trials per condition is larger than the number of neurons, there is an alternative, direct estimate of reliability which consistently leads to smaller errors and is much faster to compute. The superior performance of the direct estimator is evident both for simulated data and for neuronal population recordings from macaque primary visual cortex. Furthermore we propose generalizations of the direct estimator which measure changes in stimulus encoding across conditions and the impact of correlations on encoding and decoding, typically denoted by I_shuffle and I_diag respectively.     

Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network

The Volterra series is a well-known method of describing non-linear dynamic systems. A major limitation of this technique is the difficulty involved in the calculation of the kernels. More recently, artificial neural networks have been used to produce black box models of non-linear dynamic systems. In this paper we show how a certain class of artificial neural networks are equivalent to Volterra series and give the equation for the nth order Volterra kernel in terms of the internal parameters of the network. The technique is then illustrated using a specific non-linear system. The kernels obtained by the method described in the paper are compared with those obtained by a Toeplitz matrix inversion technique. Received: 4 June 1993/Accepted in revised form: 2 March 1994     

Using network models to approximate spatial point-process models

Spatial effects are fundamental to ecological and epidemiological systems, yet the incorporation of space into models is potentially complex. Fixed-edge network models (i.e. networks where each edge has the same fixed strength of interaction) are widely used to study spatial processes but they make simplistic assumptions about spatial scale and structure. Furthermore, it can be difficult to parameterize such models with empirical data. By comparison, spatial point-process models are often more realistic than fixed-edge network models, but are also more difficult to analyze. Here we develop a moment closure technique that allows us to define a fixed-edge network model which predicts the prevalence and rate of epidemic spread of a continuous spatial point-process epidemic model. This approach provides a systematic method for accurate parameterization of network models using data from continuously distributed populations (such as data on dispersal kernels). Insofar as point-process models are accurate representations of real spatial biological systems, our example also supports the view that network models are realistic representations of space.     

General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

This paper presents a general methodological framework for the practical modeling of neural systems with point-process inputs (sequences of action potentials or, more broadly, identical events) based on the Volterra and Wiener theories of functional expansions and system identification. The paper clarifies the distinctions between Volterra and Wiener kernels obtained from Poisson point-process inputs. It shows that only the Wiener kernels can be estimated via cross-correlation, but must be defined as zero along the diagonals. The Volterra kernels can be estimated far more accurately (and from shorter data-records) by use of the Laguerre expansion technique adapted to point-process inputs, and they are independent of the mean rate of stimulation (unlike their P-W counterparts that depend on it). The Volterra kernels can also be estimated for broadband point-process inputs that are not Poisson. Useful applications of this modeling approach include cases where we seek to determine (model) the transfer characteristics between one neuronal axon (a point-process 'input') and another axon (a point-process 'output') or some other measure of neuronal activity (a continuous 'output', such as population activity) with which a causal link exists.     

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.     

Behavioural and neurophysiological evidence for face identity and face emotion processing in animals

Visual cues from faces provide important social information relating to individual identity, sexual attraction and emotional state. Behavioural and neurophysiological studies on both monkeys and sheep have shown that specialized skills and neural systems for processing these complex cues to guide behaviour have evolved in a number of mammals and are not present exclusively in humans. Indeed, there are remarkable similarities in the ways that faces are processed by the brain in humans and other mammalian species. While human studies with brain imaging and gross neurophysiological recording approaches have revealed global aspects of the face-processing network, they cannot investigate how information is encoded by specific neural networks. Single neuron electrophysiological recording approaches in both monkeys and sheep have, however, provided some insights into the neural encoding principles involved and, particularly, the presence of a remarkable degree of high-level encoding even at the level of a specific face. Recent developments that allow simultaneous recordings to be made from many hundreds of individual neurons are also beginning to reveal evidence for global aspects of a population-based code. This review will summarize what we have learned so far from these animal-based studies about the way the mammalian brain processes the faces and the emotions they can communicate, as well as associated capacities such as how identity and emotion cues are dissociated and how face imagery might be generated. It will also try to highlight what questions and advances in knowledge still challenge us in order to provide a complete understanding of just how brain networks perform this complex and important social recognition task.     

Degenerate coding in neural systems

When the dimensionality of a neural circuit is substantially larger than the dimensionality of the variable it encodes, many different degenerate network states can produce the same output. In this review I will discuss three different neural systems that are linked by this theme. The pyloric network of the lobster, the song control system of the zebra finch, and the odor encoding system of the locust, while different in design, all contain degeneracies between their internal parameters and the outputs they encode. Indeed, although the dynamics of song generation and odor identification are quite different, computationally, odor recognition can be thought of as running the song generation circuitry backwards. In both of these systems, degeneracy plays a vital role in mapping a sparse neural representation devoid of correlations onto external stimuli (odors or song structure) that are strongly correlated. I argue that degeneracy between input and output states is an inherent feature of many neural systems, which can be exploited as a fault-tolerant method of reliably learning, generating, and discriminating closely related patterns.     

Minimal models of multidimensional computations

The multidimensional computations performed by many biological systems are often characterized with limited information about the correlations between inputs and outputs. Given this limitation, our approach is to construct the maximum noise entropy response function of the system, leading to a closed-form and minimally biased model consistent with a given set of constraints on the input/output moments; the result is equivalent to conditional random field models from machine learning. For systems with binary outputs, such as neurons encoding sensory stimuli, the maximum noise entropy models are logistic functions whose arguments depend on the constraints. A constraint on the average output turns the binary maximum noise entropy models into minimum mutual information models, allowing for the calculation of the information content of the constraints and an information theoretic characterization of the system's computations. We use this approach to analyze the nonlinear input/output functions in macaque retina and thalamus; although these systems have been previously shown to be responsive to two input dimensions, the functional form of the response function in this reduced space had not been unambiguously identified. A second order model based on the logistic function is found to be both necessary and sufficient to accurately describe the neural responses to naturalistic stimuli, accounting for an average of 93% of the mutual information with a small number of parameters. Thus, despite the fact that the stimulus is highly non-Gaussian, the vast majority of the information in the neural responses is related to first and second order correlations. Our results suggest a principled and unbiased way to model multidimensional computations and determine the statistics of the inputs that are being encoded in the outputs.     

How Attention Can Create Synaptic Tags for the Learning of Working Memories in Sequential Tasks

Intelligence is our ability to learn appropriate responses to new stimuli and situations. Neurons in association cortex are thought to be essential for this ability. During learning these neurons become tuned to relevant features and start to represent them with persistent activity during memory delays. This learning process is not well understood. Here we develop a biologically plausible learning scheme that explains how trial-and-error learning induces neuronal selectivity and working memory representations for task-relevant information. We propose that the response selection stage sends attentional feedback signals to earlier processing levels, forming synaptic tags at those connections responsible for the stimulus-response mapping. Globally released neuromodulators then interact with tagged synapses to determine their plasticity. The resulting learning rule endows neural networks with the capacity to create new working memory representations of task relevant information as persistent activity. It is remarkably generic: it explains how association neurons learn to store task-relevant information for linear as well as non-linear stimulus-response mappings, how they become tuned to category boundaries or analog variables, depending on the task demands, and how they learn to integrate probabilistic evidence for perceptual decisions.     

Dynamic memorization characteristics in neural networks with different neuronal dynamics

We introduce a stimulus-response scheme that supports plastic variation of synapse weights in neural networks, and analyze how memory formation evolves under external stimulation. In so doing, chaotic networks and stochastic networks that have very different dynamics are compared. Experimental results suggest that chaotic activity remarkably outperforms stochastic activity in stimulus-response memorization. This seems to be indicative of effectiveness of the chaos in dynamic learning by stimulus-response scheme oriented to natural learning.     

Reliable prediction of T-cell epitopes using neural networks with novel sequence representations

In this paper we describe an improved neural network method to predict T-cell class I epitopes. A novel input representation has been developed consisting of a combination of sparse encoding, Blosum encoding, and input derived from hidden Markov models. We demonstrate that the combination of several neural networks derived using different sequence-encoding schemes has a performance superior to neural networks derived using a single sequence-encoding scheme. The new method is shown to have a performance that is substantially higher than that of other methods. By use of mutual information calculations we show that peptides that bind to the HLA A*0204 complex display signal of higher order sequence correlations. Neural networks are ideally suited to integrate such higher order correlations when predicting the binding affinity. It is this feature combined with the use of several neural networks derived from different and novel sequence-encoding schemes and the ability of the neural network to be trained on data consisting of continuous binding affinities that gives the new method an improved performance. The difference in predictive performance between the neural network methods and that of the matrix-driven methods is found to be most significant for peptides that bind strongly to the HLA molecule, confirming that the signal of higher order sequence correlation is most strongly present in high-binding peptides. Finally, we use the method to predict T-cell epitopes for the genome of hepatitis C virus and discuss possible applications of the prediction method to guide the process of rational vaccine design.     

Structure Learning in a Sensorimotor Association Task

Learning is often understood as an organism''s gradual acquisition of the association between a given sensory stimulus and the correct motor response. Mathematically, this corresponds to regressing a mapping between the set of observations and the set of actions. Recently, however, it has been shown both in cognitive and motor neuroscience that humans are not only able to learn particular stimulus-response mappings, but are also able to extract abstract structural invariants that facilitate generalization to novel tasks. Here we show how such structure learning can enhance facilitation in a sensorimotor association task performed by human subjects. Using regression and reinforcement learning models we show that the observed facilitation cannot be explained by these basic models of learning stimulus-response associations. We show, however, that the observed data can be explained by a hierarchical Bayesian model that performs structure learning. In line with previous results from cognitive tasks, this suggests that hierarchical Bayesian inference might provide a common framework to explain both the learning of specific stimulus-response associations and the learning of abstract structures that are shared by different task environments.     

Food Quality in Lusaka National Park: Tracking Mortality in Black Lechwe Antelopes

Translocation is one of the fundamental tools in wildlife management but only if appropriately undertaken. In 2009, 30 black lechwe antelopes were suddenly translocated from the State House Habitat (STH) into the newly established Lusaka National Park (LNP). However, within 4 months of being translocated to LNP, 28 black lechwes (93%) died. A pathological report produced by veterinarians following a postmortem examination suggested no disease incidence affected the antelopes. The food quality of LNP was tested and compared to that in the STH and the antelopes’ native habitat of the Bangweulu wetlands (BGW) to establish if variations in food quality were responsible for the antelopes’ mortality. The findings suggest that the food quality in LNP was greatly inferior to that in STH, which could explain the observed high mortality of the antelopes in LNP. Further, the quality of food in LNP did not widely differ from that in the BGW, suggesting that the antelopes might not have survived had they been translocated to their native habitat, as they had already adapted to feeding on highly nutritious supplementary feed at the STH.