Emergent perceptual biases from state-space geometry in trained spiking recurrent neural networks.

A stimulus held in working memory is perceived as contracted toward the average stimulus. This contraction bias has been extensively studied in psychophysics, but little is known about its origin from neural activity. By training recurrent networks of spiking neurons to discriminate temporal intervals, we explored the causes of this bias and how behavior relates to population firing activity. We found that the trained networks exhibited animal-like behavior. Various geometric features of neural trajectories in state space encoded warped representations of the durations of the first interval modulated by sensory history. Formulating a normative model, we showed that these representations conveyed a Bayesian estimate of the interval durations, thus relating activity and behavior. Importantly, our findings demonstrate that Bayesian computations already occur during the sensory phase of the first stimulus and persist throughout its maintenance in working memory, until the time of stimulus comparison.

Dopamine firing plays a dual role in coding reward prediction errors and signaling motivation in a working memory task.

Little is known about how dopamine (DA) neuron firing rates behave in cognitively demanding decision-making tasks. Here, we investigated midbrain DA activity in monkeys performing a discrimination task in which the animal had to use working memory (WM) to report which of two sequentially applied vibrotactile stimuli had the higher frequency. We found that perception was altered by an internal bias, likely generated by deterioration of the representation of the first frequency during the WM period. This bias greatly controlled the DA phasic response during the two stimulation periods, confirming that DA reward prediction errors reflected stimulus perception. In contrast, tonic dopamine activity during WM was not affected by the bias and did not encode the stored frequency. More interestingly, both delay-period activity and phasic responses before the second stimulus negatively correlated with reaction times of the animals after the trial start cue and thus represented motivated behavior on a trial-by-trial basis. During WM, this motivation signal underwent a ramp-like increase. At the same time, motivation positively correlated with accuracy, especially in difficult trials, probably by decreasing the effect of the bias. Overall, our results indicate that DA activity, in addition to encoding reward prediction errors, could at the same time be involved in motivation and WM. In particular, the ramping activity during the delay period suggests a possible DA role in stabilizing sustained cortical activity, hypothetically by increasing the gain communicated to prefrontal neurons in a motivation-dependent way.

Modulation of cortical slow oscillatory rhythm by GABAB receptors: an in vitro experimental and computational study.

KEY POINTS: We confirm that GABAB receptors (GABAB -Rs) are involved in the termination of Up-states; their blockade consistently elongates Up-states. GABAB -Rs also modulate Down-states and the oscillatory cycle, thus having an impact on slow oscillation rhythm and its regularity. The most frequent effect of GABAB -R blockade is elongation of Down-states and subsequent decrease of oscillatory frequency, with an increased regularity. In a quarter of cases, GABAB -R blockade shortened Down-states and increased oscillatory frequency, changes that are independent of firing rates in Up-states. Our computer model provides mechanisms for the experimentally observed dynamics following blockade of GABAB -Rs, for Up/Down durations, oscillatory frequency and regularity. The time course of excitation, inhibition and adaptation can explain the observed dynamics of the network. This study brings novel insights into the role of GABAB -R-mediated slow inhibition on the slow oscillatory activity, which is considered the default activity pattern of the cortical network. ABSTRACT: Slow wave oscillations (SWOs) dominate cortical activity during deep sleep, anaesthesia and in some brain lesions. SWOs are composed of periods of activity (Up states) interspersed with periods of silence (Down states). The rhythmicity expressed during SWOs integrates neuronal and connectivity properties of the network and is often altered under pathological conditions. Adaptation mechanisms as well as synaptic inhibition mediated by GABAB receptors (GABAB -Rs) have been proposed as mechanisms governing the termination of Up states. The interplay between these two mechanisms is not well understood, and the role of GABAB -Rs controlling the whole cycle of the SWO has not been described. Here we contribute to its understanding by combining in vitro experiments on spontaneously active cortical slices and computational techniques. GABAB -R blockade modified the whole SWO cycle, not only elongating Up states, but also affecting the subsequent Down state duration. Furthermore, while adaptation tends to yield a rather regular behaviour, we demonstrate that GABAB -R activation desynchronizes the SWOs. Interestingly, variability changes could be accomplished in two different ways: by either shortening or lengthening the duration of Down states. Even when the most common observation following GABAB -Rs blocking is the lengthening of Down states, both changes are expressed experimentally and also in numerical simulations. Our simulations suggest that the sluggishness of GABAB -Rs to follow the excitatory fluctuations of the cortical network can explain these different network dynamics modulated by GABAB -Rs.

Dopamine reward prediction error signal codes the temporal evaluation of a perceptual decision report.

Learning to associate unambiguous sensory cues with rewarded choices is known to be mediated by dopamine (DA) neurons. However, little is known about how these neurons behave when choices rely on uncertain reward-predicting stimuli. To study this issue we reanalyzed DA recordings from monkeys engaged in the detection of weak tactile stimuli delivered at random times and formulated a reinforcement learning model based on belief states. Specifically, we investigated how the firing activity of DA neurons should behave if they were coding the error in the prediction of the total future reward when animals made decisions relying on uncertain sensory and temporal information. Our results show that the same signal that codes for reward prediction errors also codes the animal's certainty about the presence of the stimulus and the temporal expectation of sensory cues.

Emergence of an abstract categorical code enabling the discrimination of temporally structured tactile stimuli.

The problem of neural coding in perceptual decision making revolves around two fundamental questions: (i) How are the neural representations of sensory stimuli related to perception, and (ii) what attributes of these neural responses are relevant for downstream networks, and how do they influence decision making? We studied these two questions by recording neurons in primary somatosensory (S1) and dorsal premotor (DPC) cortex while trained monkeys reported whether the temporal pattern structure of two sequential vibrotactile stimuli (of equal mean frequency) was the same or different. We found that S1 neurons coded the temporal patterns in a literal way and only during the stimulation periods and did not reflect the monkeys' decisions. In contrast, DPC neurons coded the stimulus patterns as broader categories and signaled them during the working memory, comparison, and decision periods. These results show that the initial sensory representation is transformed into an intermediate, more abstract categorical code that combines past and present information to ultimately generate a perceptually informed choice.

Dynamic Control of Response Criterion in Premotor Cortex during Perceptual Detection under Temporal Uncertainty.

Under uncertainty, the brain uses previous knowledge to transform sensory inputs into the percepts on which decisions are based. When the uncertainty lies in the timing of sensory evidence, however, the mechanism underlying the use of previously acquired temporal information remains unknown. We study this issue in monkeys performing a detection task with variable stimulation times. We use the neural correlates of false alarms to infer the subject's response criterion and find that it modulates over the course of a trial. Analysis of premotor cortex activity shows that this modulation is represented by the dynamics of population responses. A trained recurrent network model reproduces the experimental findings and demonstrates a neural mechanism to benefit from temporal expectations in perceptual detection. Previous knowledge about the probability of stimulation over time can be intrinsically encoded in the neural population dynamics, allowing a flexible control of the response criterion over time.

An optimal decision population code that accounts for correlated variability unambiguously predicts a subject's choice.

Decisions emerge from the concerted activity of neuronal populations distributed across brain circuits. However, the analytical tools best suited to decode decision signals from neuronal populations remain unknown. Here we show that knowledge of correlated variability between pairs of cortical neurons allows perfect decoding of decisions from population firing rates. We recorded pairs of neurons from secondary somatosensory (S2) and premotor (PM) cortices while monkeys reported the presence or absence of a tactile stimulus. We found that while populations of S2 and sensory-like PM neurons are only partially correlated with behavior, those PM neurons active during a delay period preceding the motor report predict unequivocally the animal's decision report. Thus, a population rate code that optimally reveals a subject's perceptual decisions can be implemented just by knowing the correlations of PM neurons representing decision variables.

Internal signal correlates neural populations and biases perceptual decision reports.

In perceptual decision-making tasks the activity of neurons in frontal and posterior parietal cortices covaries more with perceptual reports than with the physical properties of stimuli. This relationship is revealed when subjects have to make behavioral choices about weak or uncertain stimuli. If knowledge about stimulus onset time is available, decision making can be based on accumulation of sensory evidence. However, the time of stimulus onset or even its very presence is often ambiguous. By analyzing firing rates and correlated variability of frontal lobe neurons while monkeys perform a vibrotactile detection task, we show that behavioral outcomes are crucially affected by the state of cortical networks before stimulus onset times. The results suggest that sensory detection is partly due to a purely internal signal whereas the stimulus, if finally applied, adds a contribution to this initial processing later on. The probability to detect or miss the stimulus can thus be explained as the combined effect of this variable internal signal and the sensory evidence.

Response of integrate-and-fire neurons to noisy inputs filtered by synapses with arbitrary timescales: firing rate and correlations.

Delivery of neurotransmitter produces on a synapse a current that flows through the membrane and gets transmitted into the soma of the neuron, where it is integrated. The decay time of the current depends on the synaptic receptor's type and ranges from a few (e.g., AMPA receptors) to a few hundred milliseconds (e.g., NMDA receptors). The role of the variety of synaptic timescales, several of them coexisting in the same neuron, is at present not understood. A prime question to answer is which is the effect of temporal filtering at different timescales of the incoming spike trains on the neuron's response. Here, based on our previous work on linear synaptic filtering, we build a general theory for the stationary firing response of integrate-and-fire (IF) neurons receiving stochastic inputs filtered by one, two, or multiple synaptic channels, each characterized by an arbitrary timescale. The formalism applies to arbitrary IF model neurons and arbitrary forms of input noise (i.e., not required to be gaussian or to have small amplitude), as well as to any form of synaptic filtering (linear or nonlinear). The theory determines with exact analytical expressions the firing rate of an IF neuron for long synaptic time constants using the adiabatic approach. The correlated spiking (cross-correlations function) of two neurons receiving common as well as independent sources of noise is also described. The theory is illustrated using leaky, quadratic, and noise-thresholded IF neurons. Although the adiabatic approach is exact when at least one of the synaptic timescales is long, it provides a good prediction of the firing rate even when the timescales of the synapses are comparable to that of the leak of the neuron; it is not required that the synaptic time constants are longer than the mean interspike intervals or that the noise has small variance. The distribution of the potential for general IF neurons is also characterized. Our results provide powerful analytical tools that can allow a quantitative description of the dynamics of neuronal networks with realistic synaptic dynamics.

The asynchronous state in cortical circuits.

Correlated spiking is often observed in cortical circuits, but its functional role is controversial. It is believed that correlations are a consequence of shared inputs between nearby neurons and could severely constrain information decoding. Here we show theoretically that recurrent neural networks can generate an asynchronous state characterized by arbitrarily low mean spiking correlations despite substantial amounts of shared input. In this state, spontaneous fluctuations in the activity of excitatory and inhibitory populations accurately track each other, generating negative correlations in synaptic currents which cancel the effect of shared input. Near-zero mean correlations were seen experimentally in recordings from rodent neocortex in vivo. Our results suggest a reexamination of the sources underlying observed correlations and their functional consequences for information processing.

Theory of input spike auto- and cross-correlations and their effect on the response of spiking neurons.

Spike correlations between neurons are ubiquitous in the cortex, but their role is not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients, and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. In fact, the total input current has a nontrivial two-point correlation function described by two main parameters: the correlation timescale (how precise the input correlations are in time) and the correlation magnitude (how strong they are). Therefore, the total current generated by the input spike trains is not well described by a white noise gaussian process. Instead, we model the total current as a colored gaussian process with the same mean and two-point correlation function, leading to the formulation of the problem in terms of a Fokker-Planck equation. Solutions of the output firing rate are found in the limit of short and long correlation timescales. The solutions described here expand and improve on our previous results (Moreno, de la Rocha, Renart, & Parga, 2002) by presenting new analytical expressions for the output firing rate for general IF neurons, extending the validity of the results for arbitrarily large correlation magnitude, and by describing the differential effect of correlations on the mean-driven or noise-dominated firing regimes. Also the details of this novel formalism are given here for the first time. We employ numerical simulations to confirm the analytical solutions and study the firing response to sudden changes in the input correlations. We expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission.

Thalamocortical transformations of periodic stimuli: the effect of stimulus velocity and synaptic short-term depression in the vibrissa-barrel system.

Recent works on the response of barrel neurons to periodic deflections of the rat vibrissae have shown that the stimulus velocity is encoded in the corti cal spike rate (Pinto et al., Journal of Neurophysiology, 83(3), 1158-1166, 2000; Arabzadeh et al., Journal of Neuroscience, 23(27), 9146-9154, 2003). Other studies have reported that repetitive pulse stimulation produces band-pass filtering of the barrel response rate centered around 7-10 Hz (Garabedian et al., Journal of Neurophysiology, 90, 1379-1391, 2003) whereas sinusoidal stimulation gives an increasing rate up to 350 Hz (Arabzadeh et al., Journal of Neuroscience, 23(27), 9146-9154, 2003). To explore the mechanisms underlying these results we propose a simple computational model consisting in an ensemble of cells in the ventro-posterior medial thalamic nucleus (VPm) encoding the stimulus velocity in the temporal profile of their response, connected to a single barrel cell through synapses showing short-term depression. With sinusoidal stimulation, encoding the velocity in VPm facilitates the response as the stimulus frequency increases and it causes the velocity to be encoded in the cortical rate in the frequency range 20-100 Hz. Synaptic depression does not suppress the response with sinusoidal stimulation but it produces a band-pass behavior using repetitive pulses. We also found that the passive properties of the cell membrane eventually suppress the response to sinusoidal stimulation at high frequencies, something not observed experimentally. We argue that network effects not included here must be important in sustaining the response at those frequencies.

Mean-driven and fluctuation-driven persistent activity in recurrent networks.

Spike trains from cortical neurons show a high degree of irregularity, with coefficients of variation (CV) of their interspike interval (ISI) distribution close to or higher than one. It has been suggested that this irregularity might be a reflection of a particular dynamical state of the local cortical circuit in which excitation and inhibition balance each other. In this "balanced" state, the mean current to the neurons is below threshold, and firing is driven by current fluctuations, resulting in irregular Poisson-like spike trains. Recent data show that the degree of irregularity in neuronal spike trains recorded during the delay period of working memory experiments is the same for both low-activity states of a few Hz and for elevated, persistent activity states of a few tens of Hz. Since the difference between these persistent activity states cannot be due to external factors coming from sensory inputs, this suggests that the underlying network dynamics might support coexisting balanced states at different firing rates. We use mean field techniques to study the possible existence of multiple balanced steady states in recurrent networks of current-based leaky integrate-and-fire (LIF) neurons. To assess the degree of balance of a steady state, we extend existing mean-field theories so that not only the firing rate, but also the coefficient of variation of the interspike interval distribution of the neurons, are determined self-consistently. Depending on the connectivity parameters of the network, we find bistable solutions of different types. If the local recurrent connectivity is mainly excitatory, the two stable steady states differ mainly in the mean current to the neurons. In this case, the mean drive in the elevated persistent activity state is suprathreshold and typically characterized by low spiking irregularity. If the local recurrent excitatory and inhibitory drives are both large and nearly balanced, or even dominated by inhibition, two stable states coexist, both with subthreshold current drive. In this case, the spiking variability in both the resting state and the mnemonic persistent state is large, but the balance condition implies parameter fine-tuning. Since the degree of required fine-tuning increases with network size and, on the other hand, the size of the fluctuations in the afferent current to the cells increases for small networks, overall we find that fluctuation-driven persistent activity in the very simplified type of models we analyze is not a robust phenomenon. Possible implications of considering more realistic models are discussed.

Network model of spontaneous activity exhibiting synchronous transitions between up and down States.

Both in vivo and in vitro recordings indicate that neuronal membrane potentials can make spontaneous transitions between distinct up and down states. At the network level, populations of neurons have been observed to make these transitions synchronously. Although synaptic activity and intrinsic neuron properties play an important role, the precise nature of the processes responsible for these phenomena is not known. Using a computational model, we explore the interplay between intrinsic neuronal properties and synaptic fluctuations. Model neurons of the integrate-and-fire type were extended by adding a nonlinear membrane current. Networks of these neurons exhibit large amplitude synchronous spontaneous fluctuations that make the neurons jump between up and down states, thereby producing bimodal membrane potential distributions. The effect of sensory stimulation on network responses depends on whether the stimulus is applied during an up state or deeply inside a down state. External noise can be varied to modulate the network continuously between two extreme regimes in which it remains permanently in either the up or the down state.

Auto- and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses.

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced previously by Moreno-Bote and Parga [Phys. Rev. Lett. 92, 028102 (2004)10.1103/PhysRevLett.92.028102]. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication.

Short-term synaptic depression causes a non-monotonic response to correlated stimuli.

Unreliability is a ubiquitous feature of synaptic transmission in the brain. The information conveyed in the discharges of an ensemble of cells (e.g., in the spike count or in the timing of synchronous events) may not be faithfully transmitted to the postsynaptic cell because a large fraction of the spikes fail to elicit a synaptic response. In addition, short-term depression increases the failure rate with the presynaptic activity. We use a simple neuron model with stochastic depressing synapses to understand the transformations undergone by the spatiotemporal patterns of incoming spikes as these are first converted into synaptic current and afterward into the cell response. We analyze the mean and SD of the current produced by different stimuli with spatiotemporal correlations. We find that the mean, which carries information only about the spike count, rapidly saturates as the input rate increases. In contrast, the current deviation carries information about the correlations. If the afferent action potentials are uncorrelated, it saturates monotonically, whereas if they are correlated it increases, reaches a maximum, and then decreases to the value produced by the uncorrelated stimulus. This means that, at high input rates, depression erases from the synaptic current any trace of the spatiotemporal structure of the input. The non-monotonic behavior of the deviation can be inherited by the response rate provided that the mean current saturates below the current threshold setting the cell in the fluctuation-driven regimen. Afferent correlations therefore enable the modulation of the response beyond the saturation of the mean current.

Membrane potential and response properties of populations of cortical neurons in the high conductance state.

Because of intense synaptic activity, cortical neurons are in a high conductance state. We show that this state has important consequences on the properties of a population of independent model neurons with conductance-based synapses. Using an adiabaticlike approximation we study both the membrane potential and the firing probability distributions across the population. We find that the latter is bimodal in such a way that at any particular moment some neurons are inactive while others are active. The population rate and the response variability are also characterized.

Role of synaptic filtering on the firing response of simple model neurons.

During active states of the brain neurons process their afferent currents with an effective membrane time constant much shorter than its value at rest. This fact, together with the existence of several synaptic time scales, determines to which aspects of the input the neuron responds best. Here we present a solution to the response of a leaky integrate-and-fire neuron with synaptic filters when long synaptic times are present, and predict the firing rate for all values of the synaptic time constant. We also discuss under which conditions this neuron becomes a coincidence detector.

Orientational minimal redundancy wavelets: from edge detection to perception.

Natural images are complex but very structured objects and, in spite of its complexity, the sensory areas in the neocortex in mammals are able to devise learned strategies to encode them efficiently. How is this goal achieved? In this paper, we will discuss the multiscaling approach, which has been recently used to derive a redundancy reducing wavelet basis. This kind of representation can be statistically learned from the data and is optimally adapted for image coding; besides, it presents some remarkable features found in the visual pathway. We will show that the introduction of oriented wavelets is necessary to provide a complete description, which stresses the role of the wavelets as edge detectors.

Role of statistical symmetries in sensory coding: an optimal scale invariant code for vision.

The visual system is the most studied sensory pathway, which is partly because visual stimuli have rather intuitive properties. There are reasons to think that the underlying principle ruling coding, however, is the same for vision and any other type of sensory signal, namely the code has to satisfy some notion of optimality--understood as minimum redundancy or as maximum transmitted information. Given the huge variability of natural stimuli, it would seem that attaining an optimal code is almost impossible; however, regularities and symmetries in the stimuli can be used to simplify the task: symmetries allow predicting one part of a stimulus from another, that is, they imply a structured type of redundancy. Optimal coding can only be achieved once the intrinsic symmetries of natural scenes are understood and used to the best performance of the neural encoder. In this paper, we review the concepts of optimal coding and discuss the known redundancies and symmetries that visual scenes have. We discuss in depth the only approach which implements the three of them known so far: translational invariance, scale invariance and multiscaling. Not surprisingly, the resulting code possesses features observed in real visual systems in mammals.