Objects in the environment differ in their low-level perceptual properties (e.g., how easily a fruit can be recognized) as well as in their subjective value (how tasty it is). We studied the influence of visual salience on value-based decisions using a two alternative forced choice task, in which human subjects rapidly chose items from a visual display. All targets were equally easy to detect. Nevertheless, both value and salience strongly affected choices made and reaction times. We analyzed the neuronal mechanisms underlying these behavioral effects using stochastic accumulator models, allowing us to characterize not only the averages of reaction times but their full distributions. Independent models without interaction between the possible choices failed to reproduce the observed choice behavior, while models with mutual inhibition between alternative choices produced much better results. Mutual inhibition thus is an important feature of the decision mechanism. Value influenced the amount of accumulation in all models. In contrast, increased salience could either lead to an earlier start (onset model) or to a higher rate (speed model) of accumulation. Both models explained the data from the choice trials equally well. However, salience also affected reaction times in no-choice trials in which only one item was present, as well as error trials. Only the onset model could explain the observed reaction time distributions of error trials and no-choice trials. In contrast, the speed model could not, irrespective of whether the rate increase resulted from more frequent accumulated quanta or from larger quanta. Visual salience thus likely provides an advantage in the onset, not in the processing speed, of value-based decision making.
decision making; accumulator; reaction time
Spiking neuron models are used in a multitude of tasks ranging from understanding neural behavior at its most basic level to neuroprosthetics. Parameter estimation of a single neuron model, such that the model’s output matches that of a biological neuron is an extremely important task. Hand tuning of parameters to obtain such behaviors is a difficult and time consuming process. This is further complicated when the neuron is instantiated in silicon (an attractive medium in which to implement these models) as fabrication imperfections make the task of parameter configuration more complex. In this paper we show two methods to automate the configuration of a silicon (hardware) neuron’s parameters. First, we show how a Maximum Likelihood method can be applied to a leaky integrate and fire silicon neuron with spike induced currents to fit the neuron’s output to desired spike times. We then show how a distance based method which approximates the negative log likelihood of the lognormal distribution can also be used to tune the neuron’s parameters. We conclude that the distance based method is better suited for parameter configuration of silicon neurons due to its superior optimization speed.
Neuromorphic; parameter estimation; silicon neuron
We report that developmental competition between sympathetic neurons for survival is critically dependent on a sensitization process initiated by target innervation and mediated by a series of feedback loops. Target-derived nerve growth factor (NGF) promoted expression of its own receptor TrkA in mouse and rat neurons and prolonged TrkA-mediated signals. NGF also controlled expression of brain-derived neurotrophic factor and neurotrophin-4, which, through the receptor p75, can kill neighboring neurons with low retrograde NGF-TrkA signaling whereas neurons with high NGF-TrkA signaling are protected. Perturbation of any of these feedback loops disrupts the dynamics of competition. We suggest that three target-initiated events are essential for rapid and robust competition between neurons: sensitization, paracrine apoptotic signaling, and protection from such effects.
When a neuronal spike train is observed, what can we say about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then to choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate and fire dynamics, Paninski, Pillow, and Simoncelli (2004) showed that its negative log-likelihood function is convex and that its unique global minimum can thus be found by gradient descent techniques. The global minimum property requires independence of spike time intervals. Lack of history dependence is, however, an important constraint that is not fulfilled in many biological neurons which are known to generate a rich repertoire of spiking behaviors that are incompatible with history independence. Therefore, we expanded the integrate and fire model by including one additional variable, a variable threshold (Mihalas & Niebur, 2009) allowing for history-dependent firing patterns. This neuronal model produces a large number of spiking behaviors while still being linear. Linearity is important as it maintains the distribution of the random variables and still allows for maximum likelihood methods to be used. In this study we show that, although convexity of the negative log-likelihood is not guaranteed for this model, the minimum of the negative log-likelihood function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) frequently reaches the global minimum.
We provide an analytical recurrent solution for the firing rates and cross-correlations of feedforward networks with arbitrary connectivity, excitatory or inhibitory, in response to steady-state spiking input to all neurons in the first network layer. Connections can go between any two layers as long as no loops are produced. Mean firing rates and pairwise cross-correlations of all input neurons can be chosen individually. We apply this method to study the propagation of rate and synchrony information through sample networks to address the current debate regarding the efficacy of rate codes versus temporal codes.
Our results from applying the network solution to several examples support the following conclusions: (1) differential propagation efficacy of rate and synchrony to higher layers of a feedforward network is dependent on both network and input parameters, and (2) previous modeling and simulation studies exclusively supporting either rate or temporal coding must be reconsidered within the limited range of network and input parameters used. Our exact, analytical solution for feedforward networks of coincidence detectors should prove useful for further elucidating the efficacy and differential roles of rate and temporal codes in terms of different network and input parameter ranges.
An accurate calculation of the first passage time probability density (FPTPD) is essential for computing the likelihood of solutions of the stochastic leaky integrate-and-fire model. The previously proposed numerical calculation of the FPTPD based on the integral equation method discretizes the probability current of the voltage crossing the threshold. While the method is accurate for high noise levels, we show that it results in large numerical errors for small noise. The problem is solved by analytically computing, in each time bin, the mean probability current. Efficiency is further improved by identifying and ignoring time bins with negligible mean probability current.
Spiking neurons and spiking neural circuits are finding uses in a multitude of tasks such as robotic locomotion control, neuroprosthetics, visual sensory processing, and audition. The desired neural output is achieved through the use of complex neuron models, or by combining multiple simple neurons into a network. In either case, a means for configuring the neuron or neural circuit is required. Manual manipulation of parameters is both time consuming and non-intuitive due to the nonlinear relationship between parameters and the neuron’s output. The complexity rises even further as the neurons are networked and the systems often become mathematically intractable. In large circuits, the desired behavior and timing of action potential trains may be known but the timing of the individual action potentials is unknown and unimportant, whereas in single neuron systems the timing of individual action potentials is critical. In this paper, we automate the process of finding parameters. To configure a single neuron we derive a maximum likelihood method for configuring a neuron model, specifically the Mihalas–Niebur Neuron. Similarly, to configure neural circuits, we show how we use genetic algorithms (GAs) to configure parameters for a network of simple integrate and fire with adaptation neurons. The GA approach is demonstrated both in software simulation and hardware implementation on a reconfigurable custom very large scale integration chip.
Genetic algorithm; maximum likelihood; optimization; spiking neuron
During sleep, under anesthesia and in vitro, cortical neurons in sensory, motor, association and executive areas fluctuate between Up and Down states (UDS) characterized by distinct membrane potentials and spike rates [1, 2, 3, 4, 5]. Another phenomenon observed in preparations similar to those that exhibit UDS, such as anesthetized rats , brain slices and cultures devoid of sensory input , as well as awake monkey cortex  is self-organized criticality (SOC). This is characterized by activity “avalanches” whose size distributions obey a power law with critical exponent of about
−32 and branching parameter near unity. Recent work has demonstrated SOC in conservative neuronal network models [9, 10], however critical behavior breaks down when biologically realistic non-conservatism is introduced . We here report robust SOC behavior in networks of non-conservative leaky integrate-and-fire neurons with short-term synaptic depression. We show analytically and numerically that these networks typically have 2 stable activity levels corresponding to Up and Down states, that the networks switch spontaneously between them, and that Up states are critical and Down states are subcritical.
For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model’s rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.
Most natural scenes are too complex to be perceived instantaneously in their entirety. Observers therefore have to select parts of them and process these parts sequentially. We study how this selection and prioritization process is performed by humans at two different levels. One is the overt attention mechanism of saccadic eye movements in a free-viewing paradigm. The second is a conscious decision process in which we asked observers which points in a scene they considered the most interesting. We find in a very large participant population (more than one thousand) that observers largely agree on which points they consider interesting. Their selections are also correlated with the eye movement pattern of different subjects. Both are correlated with predictions of a purely bottom–up saliency map model. Thus, bottom–up saliency influences cognitive processes as far removed from the sensory periphery as in the conscious choice of what an observer considers interesting.
attention; saliency; eye movements; fixations; interest points; interesting locations; model
We provide analytical solutions for mean firing rates and cross-correlations of coincidence detector neurons in recurrent networks with excitatory or inhibitory connectivity with rate-modulated steady-state spiking inputs. We use discrete-time finite-state Markov chains to represent network state transition probabilities, which are subsequently used to derive exact analytical solutions for mean firing rates and cross-correlations. As illustrated in several examples, the method can be used for modeling cortical microcircuits and clarifying single-neuron and population coding mechanisms. We also demonstrate that increasing firing rates do not necessarily translate into increasing cross-correlations, though our results do support the contention that firing rates and cross-correlations are likely to be coupled. Our analytical solutions underscore the complexity of the relationship between firing rates and cross-correlations.
Recent studies using electrocorticographic (ECoG) recordings in humans have shown that functional activation of cortex is associated with an increase in power in the high-gamma frequency range (∼60–200 Hz). Here we investigate the neural correlates of this high-gamma activity in local field potential (LFP). Single units and LFP were recorded with microelectrodes from the hand region of macaque SII cortex while vibrotactile stimuli of varying intensities were presented to the hand. We found that high-gamma power in the LFP was strongly correlated with the average firing rate recorded by the microelectrodes, both temporally and on a trial-by-trial basis. In comparison, the correlation between firing rate and low-gamma power (40–80 Hz) was much smaller. In order to explore the potential effects of neuronal firing on ECoG, we developed a model to estimate ECoG power generated by different firing patterns of the underlying cortical population and studied how ECoG power varies with changes in firing rate versus the degree of synchronous firing between neurons in the population. Both an increase in firing rate and neuronal synchrony increased high-gamma power in the simulated ECoG data. However, ECoG high-gamma activity was much more sensitive to increases in neuronal synchrony than firing rate.
Secondary somatosensory cortex; gamma; high-gamma; local field potential; ECoG; synchrony
We tested the binding-by-synchrony hypothesis which proposes that object representations are formed by synchronizing spike activity between neurons that code features of the same object. We studied responses of 32 pairs of neurons recorded with microelectrodes 3 mm apart in the visual cortex of macaques performing a fixation task. Upon mapping the receptive fields of the neurons, a quadrilateral was generated so that two of its sides were centered in the receptive fields at the optimal orientations. This one-figure condition was compared with a two-figure condition in which the neurons were stimulated by two separate figures, keeping the local edges in the receptive fields identical. For each neuron, we also determined its border ownership selectivity (H. Zhou, H. S. Friedman, & R. von der Heydt, 2000). We examined both synchronization and correlation at nonzero time lag. After correcting for effects of the firing rate, we found that synchrony did not depend on the binding condition. However, finding synchrony in a pair of neurons was correlated with finding border-ownership selectivity in both members of the pair. This suggests that the synchrony reflected the connectivity in the network that generates border ownership assignment. Thus, we have not found evidence to support the binding-by-synchrony hypothesis.
computational modeling; perceptual organization; space and scene perception; border ownership; synchrony; correlation
Recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross-correlation. This report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation. Pairs of spike trains with any pairwise correlation can be generated, and higher-order correlations are compatible with common synaptic input. Relations between allowable mean rates and correlations within a population are discussed. The algorithm is highly efficient, its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross-correlated pairs.
Neuronal oscillations in the gamma frequency range have been reported in many cortical areas, but the role they play in cortical processing remains unclear. We tested a recently proposed hypothesis that the intensity of sensory input is coded in the timing of action potentials relative to the phase of gamma oscillations, thus converting amplitude information to a temporal code. We recorded spikes and local field potential (LFP) from secondary somatosensory (SII) cortex in awake monkeys while presenting a vibratory stimulus at different amplitudes. We developed a novel technique based on matching pursuit to study the interaction between the highly transient gamma oscillations and spikes with high time-frequency resolution. We found that spikes were weakly coupled to LFP oscillations in the gamma frequency range (40−80 Hz), and strongly coupled to oscillations in higher gamma frequencies. However, the phase relationship of neither low-gamma nor high-gamma oscillations changed with stimulus intensity, even with a ten-fold increase. We conclude that, in SII, gamma oscillations are synchronized with spikes, but their phase does not vary with stimulus intensity. Furthermore, high-gamma oscillations (>60 Hz) appear to be closely linked to the occurrence of action potentials, suggesting that LFP high-gamma power could be a sensitive index of the population firing rate near the microelectrode.
Secondary somatosensory cortex; gamma; high-gamma; phase coding; local field potential; matching pursuit
To study the role of gamma oscillations (>30 Hz) in selective attention using subdural electrocorticography (ECoG) in humans.
We recorded ECoG in human subjects implanted with subdural electrodes for epilepsy surgery. Sequences of auditory tones and tactile vibrations of 800 ms duration were presented asynchronously, and subjects were asked to selectively attend to one of the two stimulus modalities in order to detect an amplitude increase at 400 ms in some of the stimuli.
Event-related ECoG gamma activity was greater over auditory cortex when subjects attended auditory stimuli and was greater over somatosensory cortex when subjects attended vibrotactile stimuli. Furthermore, gamma activity was also observed over prefrontal cortex when stimuli appeared in either modality, but only when they were attended. Attentional modulation of gamma power began ∼400 ms after stimulus onset, consistent with the temporal demands on attention. The increase in gamma activity was greatest at frequencies between 80 and 150 Hz, in the so-called high gamma frequency range.
There appears to be a strong link between activity in the high-gamma range (80-150 Hz) and selective attention.
Selective attention is correlated with increased activity in a frequency range that is significantly higher than what has been reported previously using EEG recordings.
Attention; ECoG; Gamma oscillations; High-Gamma Activity; Sensory cortex; Intracranial EEG