Unsupervised learning of visual features through spike timing dependent plasticity

Spike timing dependent plasticity (STDP) is a learning rule that modifies synaptic strength as a function of the relative timing of pre- and postsynaptic spikes. When a neuron is repeatedly presented with similar inputs, STDP is known to have the effect of concentrating high synaptic weights on afferents that systematically fire early, while postsynaptic spike latencies decrease. Here we use this learning rule in an asynchronous feedforward spiking neural network that mimics the ventral visual pathway and shows that when the network is presented with natural images, selectivity to intermediate-complexity visual features emerges. Those features, which correspond to prototypical patterns that are both salient and consistently present in the images, are highly informative and enable robust object recognition, as demonstrated on various classification tasks. Taken together, these results show that temporal codes may be a key to understanding the phenomenal processing speed achieved by the visual system and that STDP can lead to fast and selective responses.     

Visual saliency and spike timing in the ventral visual pathway.

Visual saliency is a fundamental yet hard to define property of objects or locations in the visual world. In a context where objects and their representations compete to dominate our perception, saliency can be thought of as the "juice" that makes objects win the race. It is often assumed that saliency is extracted and represented in an explicit saliency map, which serves to determine the location of spatial attention at any given time. It is then by drawing attention to a salient object that it can be recognized or categorized. I argue against this classical view that visual "bottom-up" saliency automatically recruits the attentional system prior to object recognition. A number of visual processing tasks are clearly performed too fast for such a costly strategy to be employed. Rather, visual attention could simply act by biasing a saliency-based object recognition system. Under natural conditions of stimulation, saliency can be represented implicitly throughout the ventral visual pathway, independent of any explicit saliency map. At any given level, the most activated cells of the neural population simply represent the most salient locations. The notion of saliency itself grows increasingly complex throughout the system, mostly based on luminance contrast until information reaches visual cortex, gradually incorporating information about features such as orientation or color in primary visual cortex and early extrastriate areas, and finally the identity and behavioral relevance of objects in temporal cortex and beyond. Under these conditions the object that dominates perception, i.e. the object yielding the strongest (or the first) selective neural response, is by definition the one whose features are most "salient"--without the need for any external saliency map. In addition, I suggest that such an implicit representation of saliency can be best encoded in the relative times of the first spikes fired in a given neuronal population. In accordance with our subjective experience that saliency and attention do not modify the appearance of objects, the feed-forward propagation of this first spike wave could serve to trigger saliency-based object recognition outside the realm of awareness, while conscious perceptions could be mediated by the remaining discharges of longer neuronal spike trains.     

Determination of the precision of spike timing in the visual cortex of anaesthetised cats

 Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by chance production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4–1.4 ms (a result evidently at variance with a simple ‘integrate and fire’ model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the ‘spontaneous’ and ‘evoked’ responses. Received: 3 April 1995/Accepted in revised form: 11 July 1995     

Determination of the precision of spike timing in the visual cortex of anaesthetised cats

Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by chance production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4–1.4 ms (a result evidently at variance with a simple ‘integrate and fire’ model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the ‘spontaneous’ and ‘evoked’ responses.     

Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Deltat) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (6 ms) triggered spikes at lower temporal precision (>or=6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.     

Wiring optimization in cortical circuits

Wiring a brain presents a formidable problem because neural circuits require an enormous number of fast and durable connections. We propose that evolution was likely to have optimized neural circuits to minimize conduction delays in axons, passive cable attenuation in dendrites, and the length of "wire" used to construct circuits, and to have maximized the density of synapses. Here we ask the question: "What fraction of the volume should be taken up by axons and dendrites (i.e., wire) when these variables are at their optimal values?" The biophysical properties of axons and dendrites dictate that wire should occupy 3/5 of the volume in an optimally wired gray matter. We have measured the fraction of the volume occupied by each cellular component and find that the volume of wire is close to the predicted optimal value.     

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter''s computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.     

Spike timing precision of neuronal circuits

Spike timing is believed to be a key factor in sensory information encoding and computations performed by the neurons and neuronal circuits. However, the considerable noise and variability, arising from the inherently stochastic mechanisms that exist in the neurons and the synapses, degrade spike timing precision. Computational modeling can help decipher the mechanisms utilized by the neuronal circuits in order to regulate timing precision. In this paper, we utilize semi-analytical techniques, which were adapted from previously developed methods for electronic circuits, for the stochastic characterization of neuronal circuits. These techniques, which are orders of magnitude faster than traditional Monte Carlo type simulations, can be used to directly compute the spike timing jitter variance, power spectral densities, correlation functions, and other stochastic characterizations of neuronal circuit operation. We consider three distinct neuronal circuit motifs: Feedback inhibition, synaptic integration, and synaptic coupling. First, we show that both the spike timing precision and the energy efficiency of a spiking neuron are improved with feedback inhibition. We unveil the underlying mechanism through which this is achieved. Then, we demonstrate that a neuron can improve on the timing precision of its synaptic inputs, coming from multiple sources, via synaptic integration: The phase of the output spikes of the integrator neuron has the same variance as that of the sample average of the phases of its inputs. Finally, we reveal that weak synaptic coupling among neurons, in a fully connected network, enables them to behave like a single neuron with a larger membrane area, resulting in an improvement in the timing precision through cooperation.     

Scene segmentation by spike synchronization in reciprocally connected visual areas. I. Local effects of cortical feedback

 To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas using spiking neurons. Area P corresponds to the orientation-selective subsystem of the primary visual cortex, while the central visual area C is modeled as associative memory representing stimulus objects according to Hebbian learning. Without feedback from area C, a single stimulus results in relatively slow and irregular activity, synchronized only for neighboring patches (slow state), while in the complete model activity is faster with an enlarged synchronization range (fast state). When presenting a superposition of several stimulus objects, scene segmentation happens on a time scale of hundreds of milliseconds by alternating epochs of the slow and fast states, where neurons representing the same object are simultaneously in the fast state. Correlation analysis reveals synchronization on different time scales as found in experiments (designated as tower, castle, and hill peaks). On the fast time scale (tower peaks, gamma frequency range), recordings from two sites coding either different or the same object lead to correlograms that are either flat or exhibit oscillatory modulations with a central peak. This is in agreement with experimental findings, whereas standard phase-coding models would predict shifted peaks in the case of different objects. Received: 22 August 2001 / Accepted in revised form: 8 April 2002     

Precision of intracellular calcium spike timing in primary rat hepatocytes

Extracellular stimuli are often encoded in the frequency, amplitude and duration of spikes in the intracellular concentration of calcium ([Ca2+]i). However, the timing of individual [Ca2+]i-spikes in relation to the dynamics of an extracellular stimulus is still an open question. To address this question, we use a systems biology approach combining experimental and theoretical methods. Using computer simulations, we predict that more naturalistic pulsed stimuli generate precisely-timed [Ca2+]i-spikes in contrast to the application of constant stimuli of the same dose. These computational results are confirmed experimentally in single primary rat hepatocytes upon alpha1-adrenergic stimulation. Hormonal signalling in analogy to neuronal signalling thus has the potential to make use of temporal coding on the level of single cells. The [Ca2+]i-signalling cascade provides a first example for increasing the information capacity of an intracellular regulatory signal beyond the known coding mechanisms of amplitude (AM) and frequency modulation (FM).     

Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning

This intracellular study investigates synaptic mechanisms of orientation and direction selectivity in cat area 17. Visually evoked inhibition was analyzed in 88 cells by detecting spike suppression, hyperpolarization, and reduction of trial-to-trial variability of membrane potential. In 25 of these cells, inhibition visibility was enhanced by depolarization and spike inactivation and by direct measurement of synaptic conductances. We conclude that excitatory and inhibitory inputs share the tuning preference of spiking output in 60% of cases, whereas inhibition is tuned to a different orientation in 40% of cases. For this latter type of cells, conductance measurements showed that excitation shared either the preference of the spiking output or that of the inhibition. This diversity of input combinations may reflect inhomogeneities in functional intracortical connectivity regulated by correlation-based activity-dependent processes.     

Interneurons, spike timing, and perception.

Rhythmic gamma oscillations at 30-70 Hz in cortical and hippocampal slices depend on a maintained excitation and on interactions between interneurons and pyramidal cells. These interactions include gap-junctional connections between inhibitory cells and fast excitatory and inhibitory chemical synapses. Spike timing with precision in the range of several ms may be assured by biphasic signaling mechanisms operating at these different connections. Such temporal precision may be important in cognitive processing.     

Critical period plasticity in local cortical circuits

Neuronal circuits in the brain are shaped by experience during 'critical periods' in early postnatal life. In the primary visual cortex, this activity-dependent development is triggered by the functional maturation of local inhibitory connections and driven by a specific, late-developing subset of interneurons. Ultimately, the structural consolidation of competing sensory inputs is mediated by a proteolytic reorganization of the extracellular matrix that occurs only during the critical period. The reactivation of this process, and subsequent recovery of function in conditions such as amblyopia, can now be studied with realistic circuit models that might generalize across systems.     

Decoding spike timing: the differential reverse-correlation method

It is widely acknowledged that detailed timing of action potentials is used to encode information, for example, in auditory pathways; however, the computational tools required to analyze encoding through timing are still in their infancy. We present a simple example of encoding, based on a recent model of time-frequency analysis, in which units fire action potentials when a certain condition is met, but the timing of the action potential depends also on other features of the stimulus. We show that, as a result, spike-triggered averages are smoothed so much that they do not represent the true features of the encoding. Inspired by this example, we present a simple method, differential reverse correlations, that can separate an analysis of what causes a neuron to spike, and what controls its timing. We analyze with this method the leaky integrate-and-fire neuron and show the method accurately reconstructs the model's kernel.     

Phenomenological models of synaptic plasticity based on spike timing

Synaptic plasticity is considered to be the biological substrate of learning and memory. In this document we review phenomenological models of short-term and long-term synaptic plasticity, in particular spike-timing dependent plasticity (STDP). The aim of the document is to provide a framework for classifying and evaluating different models of plasticity. We focus on phenomenological synaptic models that are compatible with integrate-and-fire type neuron models where each neuron is described by a small number of variables. This implies that synaptic update rules for short-term or long-term plasticity can only depend on spike timing and, potentially, on membrane potential, as well as on the value of the synaptic weight, or on low-pass filtered (temporally averaged) versions of the above variables. We examine the ability of the models to account for experimental data and to fulfill expectations derived from theoretical considerations. We further discuss their relations to teacher-based rules (supervised learning) and reward-based rules (reinforcement learning). All models discussed in this paper are suitable for large-scale network simulations.     

EPSP amplification and the precision of spike timing in hippocampal neurons

The temporal precision with which EPSPs initiate action potentials in postsynaptic cells determines how activity spreads in neuronal networks. We found that small EPSPs evoked from just subthreshold potentials initiated firing with short latencies in most CA1 hippocampal inhibitory cells, while action potential timing in pyramidal cells was more variable due to plateau potentials that amplified and prolonged EPSPs. Action potential timing apparently depends on the balance of subthreshold intrinsic currents. In interneurons, outward currents dominate responses to somatically injected EPSP waveforms, while inward currents are larger than outward currents close to threshold in pyramidal cells. Suppressing outward potassium currents increases the variability in latency of synaptically induced firing in interneurons. These differences in precision of EPSP-spike coupling in inhibitory and pyramidal cells will enhance inhibitory control of the spread of excitation in the hippocampus.     

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.