STDP allows fast rate-modulated coding with Poisson-like spike trains

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (~10-20 ms) for sufficiently many inputs (~100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.     

Simulation studies of a temporal sequence memory model

Models of circuit action in the mammalian hippocampus have led us to a study of habituation circuits. In order to help model the process of habituation we consider here a memory network designed to learn sequences of inputs separated by various time intervals and to repeat these sequences when cued by their initial portions. The structure of the memory is based on the anatomy of the dentate gyrus region of the mammalian hippocampus. The model consists of a number of arrays of cells called lamellae. Each array consists of four lines of model cells coupled uniformly to neighbors within the array and with some randomness to cells in other lamellae. All model cells operate according to first-order differential equations. Two of the lines of cells in each lamella are coupled such that sufficient excitation by a system input generates a wave of activity that travels down the lamella. Such waves effect dynamic storage of the representation of each input, allowing association connections to form that code both the set of cells stimulated by each input and the time interval between successive inputs. Results of simulation of two networks are presented illustrating the model's operating characteristics and memory capacity.     

An algebraic model of an associative noise-like coding memory

A mathematical model of an associative memory is presented, sharing with the optical holography memory systems the properties which establish an analogy with biological memory. This memory system-developed from Gabor's model of memoryis based on a noise-like coding of the information by which it realizes a distributed, damage-tolerant, equipotential storage through simultaneous state changes of discrete substratum elements. Each two associated items being stored are coded by each other by means of two noise-like patterns obtained from them through a randomizing preprocessing. The algebraic braic transformations operating the information storage and retrieval are matrix-vector products involving Toeplitz type matrices. Several noise-like coded memory traces are superimposed on a common substratum without crosstalk interference; moreover, extraneous noise added to these memory traces does not injure the stored information. The main performances shown by this memory model are: i) the selective, complete recovering of stored information from incomplete keys, both mixed with extraneous information and translated from the position learnt; ii) a dynamic recollection where the information just recovered acts as a new key for a sequential retrieval process; iii) context-dependent responses. The hypothesis that the information is stored in the nervous system through a noise-like coding is suggested. The model has been simulated on a digital computer using bidimensional images.     

Some thoughts about neural coding and spike trains

This communication introduces the topic. Foundations: Core concepts: Codings are relations summarized by rules or 'codes'. Special codings are 'neural', 'natural' (in everyday life), 'experimental' (in laboratories), 'conditional' (to partner restrictions). etc. Partial aspects are mechanisms, what partners say about each other, etc. Critical experimental issues: Trains are evaluated by when spikes occur: i.e. as point processes and timings. Trains and point process representations become synonyms. Any code must: (i) be a 'number (rate) code' and an 'interval code'; and (ii) include 'referent, train' covariations involving steady states with overall averages and fluctuations with patterns (dispersions, sequences). Seminal findings. Early data proved trains participated in codings; this is accepted unanimously. Inevitably, though accepted less readily, codings included rates, intervals, averages and patterns. Literature highlights. (1) Confirmed the seminal finding (2.2.) over vast domains; (2) Demonstrated both general and synaptic codings (referents, respectively, sensory, states, etc. and trains in directly connected neurons); (3) Revealed overlap between general and synaptic coding features. Overlap allows train participation in network dynamics; (4) Introduced natural formal contexts. (Point Process Mathematics, Communication. Information and Dynamical Systems Theories); (5) Includes confused opinions: (i) Opposition between rates and intervals; (ii) claims that averages are meaningful but patterns irrelevant. Both, overlooking foundations and evidence, are untenable.     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

A dynamic neural network with temporal coding and functional connectivity

A neural network model capable of altering its pattern classifying properties by program input is proposed. Here the “program input” is another source of input besides the pattern input. Unlike most neural network models, this model runs as a deterministic point process of spikes in continuous time; connections among neurons have finite delays, which are set randomly according to a normal distribution. Furthermore, this model utilizes functional connectivity which is dynamic connectivity among neurons peculiar to temporal-coding neural networks with short neuronal decay time constants. Computer simulation of the proposed network has been performed, and the results are considered in light of experimental results shown recently for correlated firings of neurons. Received: 6 December 1996 / Accepted in revised form: 15 September 1997     

Spike-based population coding and working memory

Compelling behavioral evidence suggests that humans can make optimal decisions despite the uncertainty inherent in perceptual or motor tasks. A key question in neuroscience is how populations of spiking neurons can implement such probabilistic computations. In this article, we develop a comprehensive framework for optimal, spike-based sensory integration and working memory in a dynamic environment. We propose that probability distributions are inferred spike-per-spike in recurrently connected networks of integrate-and-fire neurons. As a result, these networks can combine sensory cues optimally, track the state of a time-varying stimulus and memorize accumulated evidence over periods much longer than the time constant of single neurons. Importantly, we propose that population responses and persistent working memory states represent entire probability distributions and not only single stimulus values. These memories are reflected by sustained, asynchronous patterns of activity which make relevant information available to downstream neurons within their short time window of integration. Model neurons act as predictive encoders, only firing spikes which account for new information that has not yet been signaled. Thus, spike times signal deterministically a prediction error, contrary to rate codes in which spike times are considered to be random samples of an underlying firing rate. As a consequence of this coding scheme, a multitude of spike patterns can reliably encode the same information. This results in weakly correlated, Poisson-like spike trains that are sensitive to initial conditions but robust to even high levels of external neural noise. This spike train variability reproduces the one observed in cortical sensory spike trains, but cannot be equated to noise. On the contrary, it is a consequence of optimal spike-based inference. In contrast, we show that rate-based models perform poorly when implemented with stochastically spiking neurons.     

Analysis,classification, and coding of multielectrode spike trains with hidden Markov models

It is shown that hidden Markov models (HMMs) are a powerful tool in the analysis of multielectrode data. This is demonstrated for a 30-electrode measurement of neuronal spike activity in the monkey's visual cortex during the application of different visual stimuli. HMMs with optimized parameters code the information contained in the spatiotemporal discharge patterns as a probabilistic function of a Markov process and thus provide abstract dynamical models of the pattern-generating process. We compare HMMs obtained from vector-quantized data with models in which parametrized output processes such as multivariate Poisson or binomial distributions are assumed. In the latter cases the visual stimuli are recognized at rates of more than 90% from the neuronal spike patterns. An analysis of the models obtained reveals important aspects of the coding of information in the brain. For example, we identify relevant time scales and characterize the degree and nature of the spatiotemporal variations on these scales.     

A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

Associative learning and memory in Drosophila: beyond olfactory conditioning

The associative learning abilities of the fruit fly, Drosophila melanogaster, have been demonstrated in both classical and operant conditioning paradigms. Efforts to identify the neural pathways and cellular mechanisms of learning have focused largely on olfactory classical conditioning. Results derived from various genetic and molecular manipulations provide considerable evidence that this form of associative learning depends critically on neural activity and cAMP signaling in brain neuropil structures called mushroom bodies. Three other behavioral learning paradigms in Drosophila serve as the main subject of this review. These are (1) visual and motor learning of flies tethered in a flight simulator, (2) a form of spatial learning that is independent of visual and olfactory cues, and (3) experience-dependent changes in male courtship behavior. The present evidence suggests that at least some of these modes of learning are independent of mushroom bodies. Applying targeted genetic manipulations to these behavioral paradigms should allow for a more comprehensive understanding of neural mechanisms responsible for diverse forms of associative learning and memory.     

Associative memory design using overlapping decomposition and generalized brain-state-in-a-box neural networks

This paper is concerned with large scale associative memory design. A serious problem with neural associative memories is the quadratic growth of the number of interconnections with the problem size. An overlapping decomposition algorithm is proposed to attack this problem. Specifically, a pattern to be processed is decomposed into overlapping sub-patterns. Then, neural sub-networks are constructed that process the sub-patterns. An error correction algorithm operates on the outputs of each sub-network in order to correct the mismatches between sub-patterns that are obtained from the independent recall processes of individual sub-networks. The performance of the proposed large scale associative memory is illustrated using two-dimensional images. It is shown that the proposed method reduces the computing cost of the design of the associative memories compared with non-interconnected associative memories.     

Information flow and temporal coding in primate pattern vision

We perform time-resolved calculations of the information transmitted about visual patterns by neurons in primary visual and inferior temporal cortices. All measurable information is carried in an effective time-varying firing rate, obtained by averaging the neuronal response with a resolution no finer than about 25 ms in primary visual cortex and around twice that in inferior temporal cortex. We found no better way for a neuron receiving these messages to decode them than simply to count spikes for this long. Most of the information tends to be concentrated in one or, more often, two brief packets, one at the very beginning of the response and the other typically 100 ms later. The first packet is the most informative part of the message, but the second one generally contains new information. A small but significant part of the total information in the message accumulates gradually over the entire course of the response. These findings impose strong constraints on the codes used by these neurons.     

Insect olfactory coding and memory at multiple timescales

Insects can learn, allowing them great flexibility for locating seasonal food sources and avoiding wily predators. Because insects are relatively simple and accessible to manipulation, they provide good experimental preparations for exploring mechanisms underlying sensory coding and memory. Here we review how the intertwining of memory with computation enables the coding, decoding, and storage of sensory experience at various stages of the insect olfactory system. Individual parts of this system are capable of multiplexing memories at different timescales, and conversely, memory on a given timescale can be distributed across different parts of the circuit. Our sampling of the olfactory system emphasizes the diversity of memories, and the importance of understanding these memories in the context of computations performed by different parts of a sensory system.     

Prospective and retrospective memory coding in the hippocampus

The effect of memory on hippocampal neuronal activity was assessed as rats performed a spatial task that was impaired by fornix lesions. The influences of current location, recently entered places, and places about to be entered were compared. Three new findings emerged. (1) Current, retrospective, and prospective coding were common and recorded simultaneously in neural ensembles. (2) The origin of journeys influenced firing even when rats made detours, showing that recent memory could modulate neuronal activity more than spatial trajectory. (3) Diminished retrospective coding and, more markedly, reduced prospective coding in error trials suggested that the neuronal signal was important for task performance. The population of hippocampal neurons thus encoded information about the recent past, the present, and the imminent future, consistent with a neuronal mechanism for episodic memory.     

Spatial and temporal correlations of spike trains in frog retinal ganglion cells

For a neuron, firing activity can be in synchrony with that of others, which results in spatial correlation; on the other hand, spike events within each individual spike train may also correlate with each other, which results in temporal correlation. In order to investigate the relationship between these two phenomena, population neurons’ activities of frog retinal ganglion cells in response to binary pseudo-random checker-board flickering were recorded via a multi-electrode recording system. The spatial correlation index (SCI) and temporal correlation index (TCI) were calculated for the investigated neurons. Statistical results showed that, for a single neuron, the SCI and TCI values were highly related—a neuron with a high SCI value generally had a high TCI value, and these two indices were both associated with burst activities in spike train of the investigated neuron. These results may suggest that spatial and temporal correlations of single neuron’s spiking activities could be mutually modulated; and that burst activities could play a role in the modulation. We also applied models to test the contribution of spatial and temporal correlations for visual information processing. We show that a model considering spatial and temporal correlations could predict spikes more accurately than a model does not include any correlation.     

Associative memory of phase-coded spatiotemporal patterns in leaky Integrate and Fire networks

We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at different time scales. Using an STDP-based learning process, we store in the connectivity several phase-coded spike patterns, and we find that, depending on the excitability of the network, different working regimes are possible, with transient or persistent replay activity induced by a brief signal. We introduce an order parameter to evaluate the similarity between stored and recalled phase-coded pattern, and measure the storage capacity. Modulation of spiking thresholds during replay changes the frequency of the collective oscillation or the number of spikes per cycle, keeping preserved the phases relationship. This allows a coding scheme in which phase, rate and frequency are dissociable. Robustness with respect to noise and heterogeneity of neurons parameters is studied, showing that, since dynamics is a retrieval process, neurons preserve stable precise phase relationship among units, keeping a unique frequency of oscillation, even in noisy conditions and with heterogeneity of internal parameters of the units.     

An integrate-and-fire model to generate spike trains with long-range dependence

Long-range dependence (LRD) has been observed in a variety of phenomena in nature, and for several years also in the spiking activity of neurons. Often, this is interpreted as originating from a non-Markovian system. Here we show that a purely Markovian integrate-and-fire (IF) model, with a noisy slow adaptation term, can generate interspike intervals (ISIs) that appear as having LRD. However a proper analysis shows that this is not the case asymptotically. For comparison, we also consider a new model of individual IF neuron with fractional (non-Markovian) noise. The correlations of its spike trains are studied and proven to have LRD, unlike classical IF models. On the other hand, to correctly measure long-range dependence, it is usually necessary to know if the data are stationary. Thus, a methodology to evaluate stationarity of the ISIs is presented and applied to the various IF models. We explain that Markovian IF models may seem to have LRD because of non-stationarities.     

Olfactory coding in the insect brain: molecular receptive ranges, spatial and temporal coding

Odor information is coded in the insect brain in a sequence of steps, ranging from the receptor cells, via the neural network in the antennal lobe, to higher order brain centers, among which the mushroom bodies and the lateral horn are the most prominent. Across all of these processing steps, coding logic is combinatorial, in the sense that information is represented as patterns of activity across a population of neurons, rather than in individual neurons. Because different neurons are located in different places, such a coding logic is often termed spatial, and can be visualized with optical imaging techniques. We employ in vivo calcium imaging in order to record odor‐evoked activity patterns in olfactory receptor neurons, different populations of local neurons in the antennal lobes, projection neurons linking antennal lobes to the mushroom bodies, and the intrinsic cells of the mushroom bodies themselves, the Kenyon cells. These studies confirm the combinatorial nature of coding at all of these stages. However, the transmission of odor‐evoked activity patterns from projection neuron dendrites via their axon terminals onto Kenyon cells is accompanied by a progressive sparsening of the population code. Activity patterns also show characteristic temporal properties. While a part of the temporal response properties reflect the physical sequence of odor filaments, another part is generated by local neuron networks. In honeybees, γ‐aminobutyric acid (GABA)‐ergic and histaminergic neurons both contribute inhibitory networks to the antennal lobe. Interestingly, temporal properties differ markedly in different brain areas. In particular, in the antennal lobe odor‐evoked activity develops over slow time courses, while responses in Kenyon cells are phasic and transient. The termination of an odor stimulus is reflected by a decrease in activity within most glomeruli of the antennal lobe and an off‐response in some glomeruli, while in the mushroom bodies about half of the odor‐activated Kenyon cells also exhibit off‐responses.     

Holographic aspects of temporal memory and optomotor responses

A mathematical analogy between the holographic models of temporal memory and Reichardt's optomotor theory is stressed. It is pointed out that the sequence of operations which is essential to any holographic model of brain functioning is actually carried out by a nervous structure in the optomotor behaviour.Some implications in both the optomotor theory and the hypothesis of neural holographic processes are further suggested.