Computational models of decision making: integration, stability, and noise

Computational cognitive modeling of the temporal dynamics of fatigue from sleep loss

Computational models have become common tools in psychology. They provide quantitative instantiations of theories that seek to explain the functioning of the human mind. In this paper, we focus on identifying deep theoretical similarities between two very different models. Both models are concerned with how fatigue from sleep loss impacts cognitive processing. The first is based on the diffusion model and posits that fatigue decreases the drift rate of the diffusion process. The second is based on the Adaptive Control of Thought - Rational (ACT-R) cognitive architecture and posits that fatigue decreases the utility of candidate actions leading to microlapses in cognitive processing. A biomathematical model of fatigue is used to control drift rate in the first account and utility in the second. We investigated the predicted response time distributions of these two integrated computational cognitive models for performance on a psychomotor vigilance test under conditions of total sleep deprivation, simulated shift work, and sustained sleep restriction. The models generated equivalent predictions of response time distributions with excellent goodness-of-fit to the human data. More importantly, although the accounts involve different modeling approaches and levels of abstraction, they represent the effects of fatigue in a functionally equivalent way: in both, fatigue decreases the signal-to-noise ratio in decision processes and decreases response inhibition. This convergence suggests that sleep loss impairs psychomotor vigilance performance through degradation of the quality of cognitive processing, which provides a foundation for systematic investigation of the effects of sleep loss on other aspects of cognition. Our findings illustrate the value of treating different modeling formalisms as vehicles for discovery.

Computational Neuroscience: Mathematical and Statistical Perspectives

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm.

Of monkeys and men: Impatience in perceptual decision-making

For decades sequential sampling models have successfully accounted for human and monkey decision-making, relying on the standard assumption that decision makers maintain a pre-set decision standard throughout the decision process. Based on the theoretical argument of reward rate maximization, some authors have recently suggested that decision makers become increasingly impatient as time passes and therefore lower their decision standard. Indeed, a number of studies show that computational models with an impatience component provide a good fit to human and monkey decision behavior. However, many of these studies lack quantitative model comparisons and systematic manipulations of rewards. Moreover, the often-cited evidence from single-cell recordings is not unequivocal and complimentary data from human subjects is largely missing. We conclude that, despite some enthusiastic calls for the abandonment of the standard model, the idea of an impatience component has yet to be fully established; we suggest a number of recently developed tools that will help bring the debate to a conclusive settlement.

Neuronal pattern separation of motion-relevant input in LIP activity

In various regions of the brain, neurons discriminate sensory stimuli by decreasing the similarity between ambiguous input patterns. Here, we examine whether this process of pattern separation may drive the rapid discrimination of visual motion stimuli in the lateral intraparietal area (LIP). Starting with a simple mean-rate population model that captures neuronal activity in LIP, we show that overlapping input patterns can be reformatted dynamically to give rise to separated patterns of neuronal activity. The population model predicts that a key ingredient of pattern separation is the presence of heterogeneity in the response of individual units. Furthermore, the model proposes that pattern separation relies on heterogeneity in the temporal dynamics of neural activity and not merely in the mean firing rates of individual neurons over time. We confirm these predictions in recordings of macaque LIP neurons and show that the accuracy of pattern separation is a strong predictor of behavioral performance. Overall, results propose that LIP relies on neuronal pattern separation to facilitate decision-relevant discrimination of sensory stimuli.NEW & NOTEWORTHY A new hypothesis is proposed on the role of the lateral intraparietal (LIP) region of cortex during rapid decision making. This hypothesis suggests that LIP alters the representation of ambiguous inputs to reduce their overlap, thus improving sensory discrimination. A combination of computational modeling, theoretical analysis, and electrophysiological data shows that the pattern separation hypothesis links neural activity to behavior and offers novel predictions on the role of LIP during sensory discrimination.

Constructing Precisely Computing Networks with Biophysical Spiking Neurons

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates. In equivalent spiking implementations, firing is assumed to be random such that averaging across populations of neurons recovers the rate-based approach. Recently, however, Denéve and colleagues have suggested that the spiking behavior of neurons may be fundamental to how neuronal networks compute, with precise spike timing determined by each neuron's contribution to producing the desired output (Boerlin and Denéve, 2011; Boerlin et al., 2013). By postulating that each neuron fires to reduce the error in the network's output, it was demonstrated that linear computations can be performed by networks of integrate-and-fire neurons that communicate through instantaneous synapses. This left open, however, the possibility that realistic networks, with conductance-based neurons with subthreshold nonlinearity and the slower timescales of biophysical synapses, may not fit into this framework. Here, we show how the spike-based approach can be extended to biophysically plausible networks. We then show that our network reproduces a number of key features of cortical networks including irregular and Poisson-like spike times and a tight balance between excitation and inhibition. Lastly, we discuss how the behavior of our model scales with network size or with the number of neurons "recorded" from a larger computing network. These results significantly increase the biological plausibility of the spike-based approach to network computation.

SIGNIFICANCE STATEMENT

We derive a network of neurons with standard spike-generating currents and synapses with realistic timescales that computes based upon the principle that the precise timing of each spike is important for the computation. We then show that our network reproduces a number of key features of cortical networks including irregular, Poisson-like spike times, and a tight balance between excitation and inhibition. These results significantly increase the biological plausibility of the spike-based approach to network computation, and uncover how several components of biological networks may work together to efficiently carry out computation.

Spatiotemporal Spike Coding of Behavioral Adaptation in the Dorsal Anterior Cingulate Cortex

The frontal cortex controls behavioral adaptation in environments governed by complex rules. Many studies have established the relevance of firing rate modulation after informative events signaling whether and how to update the behavioral policy. However, whether the spatiotemporal features of these neuronal activities contribute to encoding imminent behavioral updates remains unclear. We investigated this issue in the dorsal anterior cingulate cortex (dACC) of monkeys while they adapted their behavior based on their memory of feedback from past choices. We analyzed spike trains of both single units and pairs of simultaneously recorded neurons using an algorithm that emulates different biologically plausible decoding circuits. This method permits the assessment of the performance of both spike-count and spike-timing sensitive decoders. In response to the feedback, single neurons emitted stereotypical spike trains whose temporal structure identified informative events with higher accuracy than mere spike count. The optimal decoding time scale was in the range of 70-200 ms, which is significantly shorter than the memory time scale required by the behavioral task. Importantly, the temporal spiking patterns of single units were predictive of the monkeys' behavioral response time. Furthermore, some features of these spiking patterns often varied between jointly recorded neurons. All together, our results suggest that dACC drives behavioral adaptation through complex spatiotemporal spike coding. They also indicate that downstream networks, which decode dACC feedback signals, are unlikely to act as mere neural integrators.

Exploratory decisions of the Caenorhabditis elegans male: a conflict of two drives

The ability to generate behavioral plasticity according to ever-changing physiological demands and environmental conditions is a universal feature of decision-making circuits in all animals. Decision-making requires complex integration of internal states with sensory context. As a mate searching strategy, the Caenorhabditis elegans male modifies his exploratory behavior in relation to a source of food according to recent sensory experience with mates. Information about the reproductive and nutritional status of the male is also incorporated in his choice of exploratory behavior. The study of mate searching in the C. elegans male, a genetic model organism with a nervous system of only 383 neurons, provides the opportunity to elucidate the molecular and cellular mechanisms of state-dependent control of behavior and sensory integration. Here I review our progress in understanding the physiological and environmental regulation of the male's exploratory choices - to explore in search of mates or to exploit a source of food - and the neural circuits and neuromodulator pathways underlying this decision.

Optimizing working memory with heterogeneity of recurrent cortical excitation

A neural correlate of parametric working memory is a stimulus-specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural activity, linking network architecture and parametric working memory. Cortical neurons receive noisy input fluctuations that cause persistent activity to diffusively wander about the network, degrading memory over time. We explore how cortical architecture that supports parametric working memory affects the diffusion of persistent neural activity. Studying both a spiking network and a simplified potential well model, we show that spatially heterogeneous excitatory coupling stabilizes a discrete number of persistent states, reducing the diffusion of persistent activity over the network. However, heterogeneous coupling also coarse-grains the stimulus representation space, limiting the storage capacity of parametric working memory. The storage errors due to coarse-graining and diffusion trade off so that information transfer between the initial and recalled stimulus is optimized at a fixed network heterogeneity. For sufficiently long delay times, the optimal number of attractors is less than the number of possible stimuli, suggesting that memory networks can under-represent stimulus space to optimize performance. Our results clearly demonstrate the combined effects of network architecture and stochastic fluctuations on parametric memory storage.

Interareal coupling reduces encoding variability in multi-area models of spatial working memory

Persistent activity observed during delayed-response tasks for spatial working memory (Funahashi et al., 1989) has commonly been modeled by recurrent networks whose dynamics is described as a bump attractor (Compte et al., 2000). We examine the effects of interareal architecture on the dynamics of bump attractors in stochastic neural fields. Lateral inhibitory synaptic structure in each area sustains stationary bumps in the absence of noise. Introducing noise causes bumps in individual areas to wander as a Brownian walk. However, coupling multiple areas together can help reduce the variability of the bump's position in each area. To examine this quantitatively, we approximate the position of the bump in each area using a small noise expansion that also assumes weak amplitude interareal projections. Our asymptotic results show the motion of the bumps in each area can be approximated as a multivariate Ornstein-Uhlenbeck process. This shows reciprocal coupling between areas can always reduce variability, if sufficiently strong, even if one area contains much more noise than the other. However, when noise is correlated between areas, the variability-reducing effect of interareal coupling is diminished. Our results suggest that distributing spatial working memory representations across multiple, reciprocally-coupled brain areas can lead to noise cancelation that ultimately improves encoding.

Impact of correlated neural activity on decision-making performance

Stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations. Neurons in the populations, however, do not spike independently: spike events are correlated from cell to cell. To what degree does this apparent redundancy have an impact on the accuracy with which decisions can be made and the computations required to optimally decide? We explore these questions for two illustrative models of correlation among cells. Each model is statistically identical at the level of pairwise correlations but differs in higher-order statistics that describe the simultaneous activity of larger cell groups. We find that the presence of correlations can diminish the performance attained by an ideal decision maker to either a small or large extent, depending on the nature of the higher-order correlations. Moreover, although this optimal performance can in some cases be obtained using the standard integration-to-bound operation, in others it requires a nonlinear computation on incoming spikes. Overall, we conclude that a given level of pairwise correlations, even when restricted to identical neural populations, may not always indicate redundancies that diminish decision-making performance.

Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations

Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.