# Spike Timing Dependent Plasticity

## Spike Timing Dependent Plasticity

The best experimental setup for exploring plasticity in a controlled manner is the in vitro setup. By using pairs of neurons clearly isolated and connected (using either brain slices or cultured neurons), one can patch the pre- and the post-synaptic neuron and observe the synaptic modifications between them according to their discharge. Based on those controlled experiments, the most recent and promising candidate to support unsupervised learning algorithms in the brain, based on neuronal activity, is the spike timing dependent plasticity (STDP). There is indeed several evidence [Bi1998, Markram1997, Gerstner1996] in neocortex that the efficiency of a synaptic connection between two neurons may be regulated by the precise timing of the joint activity of the neurons. This postulate, originally made by  [Hebb1949] , has been demonstrated in a lot of in vitro experimental studies in the form of the STDP rule. This is an associative rule that needs to be distinguished from short term plasticity or homeostasis phenomena, involving only integration of pre-synaptic activity [Tsodyks2000, Turrigiano2004]. As one can see in Figure, taken from [Bi1998], when pre-post pairings are made repeatedly at a fixed frequency of 1 Hz, with a particular time difference  between pre and post spikes, synaptic modifications are observed whose magnitude depends on . For positive values of , when pre-synaptic spike occurs before the post, the synapse is potentiated. Oppositely, if  is negative, the synapse is depressed. Both mechanisms occur in relatively short time windows of  20 ms, and a double exponential fit made on the data is the classical shape everybody has in mind when talking about STDP. That 20 ms time scale is the time window for triggering a change, but the actual change happens much more slowly.

While some recent evidence may suggests that STDP can also be found in vivo [Crochet2006, Zhang1998, Young2007a, Jacob2007], the impact of such a rule on a network level is still misunderstood, and part of the problem comes from the fact that there is a lack of data on the properties and the relevance of STDP in vivo. The STDP phenomenon as seen in vitro is appealing from a theoretical point of view. If a pre-synaptic spike occurs just before a post-synaptic one, the strength of the synapse between the two neurons tends to be increased. Conversely, if the pre-synaptic spike comes just after a post-synaptic one, the synaptic strength tends to be decreased. This rule establishes a link with Hebb's postulate and could allow neurons to learn causal chains of information: if pre-synaptic information is important in the discharge of the post-synaptic neuron, then synapse is strengthened, otherwise it is weakened. Interestingly, rules symmetric in sign have been observed in the electro senseory lobe of the electric fish by [Bell1997] and have been used in models to decorrelate the sensory stream from expected inputs linked with the motor-induced reafference.

Experimental protocol of Spike Timing Dependent Plasticity in vitro. Pre and Post synaptic neurons are patched and forced to fire with a time difference, while the modification of the synaptic strength is monitored.

Illustration of spike timing dependent plasticity time windows, taken from (Froemke et al, 2006). Depending on the precise time difference between a post- and a pre-synaptic spike, the synaptic weight can be either depressed or potentiated.

Schematic of a cost function for soling an optimization problems

## STDP as an optimization principle

Since this seminal work, several theories have been proposed for a conceptual explanation of these STDP curves. The promising link between STDP and the Hebbian rule has led several authors to try to find a more generic optimization principle behind this canonical shape. The quest is "can STDP be seen as a biological response to an optimization problem?" with a goal function like , if  are the inputs to the neuron, and  its responses. Are the shapes of those curves telling us something about the learning strategies performed by the neuron? According to [Toyoizumi2007, Chechik2003], STDP could be seen as an attempt, by the neurons, to maximize the transmission of information and therefore the mutual information between inputs and outputs, . For [Bohte2005b], STDP is more a way to reduce the variability of the output knowing the input:  (with  being the entropy). We can cite other examples such as slow feature analysis [Sprekeler2006], where STDP aims to decompose the signals into a basis of signals, slowly varying in time, or the predictive coding [Rao2001] theory, where STDP is used to encode only time differences. Nevertheless, as we will see later, since STDP is still, from a biological point of view, a phenomenon which is not understood, all these theories, even if conceptually promising, can not pretend to understand STDP in its globality.

From a modeller's point of view, the rule is ill defined. A good review on all the important aspects of such modelling is given in [Morrison2008]. In its most widely used formulation, one can model STDP with the following system of equations:

\delta w = \lambda \left\{
\begin{array}{ll}
a_{\mathrm{pot}} w^{\mu_{\mathrm{pot}}}e^{-\frac{\delta t}{\tau_{\mathrm{pot}}}} & \textrm{if }
\delta t=t_{\mathrm{post}}-t_{\mathrm{pre}} > 0 \\
a_{\mathrm{dep}} w^{\mu_{\mathrm{dep}}}e^{-\frac{\delta t}{\tau_{\mathrm{dep}}}} & \textrm{if }
\delta t=t_{\mathrm{post}}-t_{\mathrm{pre}} < 0 \\
\end{array} \right.

 is the learning rate,  and  the scaling increments of the synaptic weights performed at each pairing, for potentiation and depression. Each time a pre or a post-synaptic event appears, weights are updated accordingly.  and  are the time constants of the double exponential shape observed in biological data, such as the one that can be seen in Figure. Typical values are in the range 10-30 ms.  and  are generic exponents to model the fact that weight increments can depend on the current values of the weights.
Taking advantage of the exponential, the most efficient way to implement this systems, at the synapse level, is to define two local variables  and , such that:

\begin{array}{l}
\frac{d\theta_{\mathrm{pot}}(t)}{dt} = -\frac{\theta_{\mathrm{pot}}(t)}{\tau_{\mathrm{pot}}} \\
\frac{d\theta_{\mathrm{dep}}(t)}{dt} = -\frac{\theta_{\mathrm{dep}}(t)}{\tau_{\mathrm{dep}}}
\end{array}
\label{stdp_eq}

Each time a pre-synaptic spike occurs, , and each time a post synaptic spike occurs, . In this case, if  and  are not bounded, the integration scheme of the STDP is said to be all-to-all. All previous pre- or post-synaptic spikes contribute to the modification of the weight at time , since they have an impact on  and .

In the so-called nearest-neighbour interaction scheme,  and  are bounded by 1, and only the nearest either pre or post synaptic spike is considered for potentiation or depression. This difference is important, because STDP in its basic form with an all-to-all interaction scheme is not compatible with the BCM theory, as shown in [Izhikevich2003]. Only the nearest-neighbour scheme can provide a BCM behaviour with the rule. The values of a_{\mathrm{pot}}$, , , ,  and  are selected according to the STDP desired rule. To simplify the following notations, we set  (and thus we should have , because depression decreases the weight). The pairing scheme used during all the the simulations is all-to-all, meaning that all the interactions between pre and post synaptic spikes are taken into account. Relative weight modifications for potentiation (positive spiking) and depression (negative spiking), according to the initial amplitude of the EPSP. ## Weight-dependence of STDP Regarding the weight modifications performed by such plasticity rules, there are two main classes of STDP rules that are commonly used in modelling studies of neuronal networks. They are categorized as either "additive" or "weight-dependent", depending on how current synaptic weight impacts the change in the weight of the synapse [Guetig2003]. These classes are established with the exponents  and . If both are set to 0, then the STDP is "additive". Each time a weight modification is made, increments are only determined by  and , without taking into account the current weight of the synapse. The rule needs a hard bound thresholding to constrain the weights between [,]. Oppositely, in the weight-dependent rule, the weight increments are a function of the current weight of the synapse. This is the case if  and  are positive. The biological evidence for additive''-only rules is quite thin. The original data for STDP, and especially the synaptic modification observed as a function of the initial amplitude of the EPSP show (see Figure) that the relative changes are not similar for potentiation and depression. Modifications for potentiation seem to be independent of the initial amplitude of the EPSP, while this is not the case for depression. \cite{Bi1998} proposed, initially, a log-linear relationship for depression, while potentiation is much more additive. For a precise fit, see [Morrison2008, Standage2007], but the exact values for  and  are not crucial, as long as they are not zero. As pointed out in [Guetig2003], the additive case, often used in models, is a very particular case with particular dynamics. It has been shown in [Rossum2000, Billings2009], through a Fokker Plank approach, that an additive STDP rule always drive the weight distribution to a bimodal one, with all weights being clipped either at  or at . Nevertheless, they encourage synaptic competition and allow a better storage of patterns [Fusi2007]. As we will see in the following, they are less sensitive to the memory retention problem occurring in recurrent networks. Moreover, it is also known that in cortex, and also in the cerebellum a lot of the synapses are considered as almost silent. One could see here the evidence for bimodal distribution resulting from the additive rules. On the contrary, weight-dependent rule leads to a unimodal distribution of the weights, more biologically plausible, but does not allow the emergence and the survival of neuronal structures in balanced random networks [Billings2009, Morrison2007]. ## STDP at inhibitory synapses Although inhibitory interneurons modulate many neuronal processes, the evidence for plasticity at inhibitory synapses remains scarce. Some studies report strengthening of inhibitory synapses in negative rate covariance regimes [Komatsu1993], and spike timing dependent plasticity of inhibitory synapses has also been reported [Haas2006] as well as spike timing dependent depression of excitatory synapses on fast spiking inhibitory interneurons. Almost all models of plastic networks consider that only excitatory synapses are plastic, because most of the biological evidence for STDP has been gathered for synapse between excitatory neurons, far more numerous and easy to patch than inhibitory ones. Nevertheless, the question of plasticity at inhibitory synapses remains open, and could greatly help stabilization in recurrent networks. [Haas2006] found an anti-Hebbian rule for inhibitory synapses. Pre-post pairing led to reinforcement of the synapse, meaning to an increase in the amplitude of the post-synaptic inhibitory post synaptic potential (IPSP), while post-pre led to a decrease. This anti-Hebbian rule, from a conceptual point of view, offers nice theoretical possibilities. In artificial neural networks, anti-Hebbian rules for inhibition are important to balance the changes at the excitatory synapses and allow the network to perform robust principal or independent component analysis [Plumbley1993]. ## References [Bi1998] G. Q. Bi and M. M. Poo, "Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type.," J neurosci, vol. 18, pp. 10464-10472, 1998. [Bibtex] @article{Bi1998, abstract = {In cultures of dissociated rat hippocampal neurons, persistent potentiation and depression of glutamatergic synapses were induced by correlated spiking of presynaptic and postsynaptic neurons. The relative timing between the presynaptic and postsynaptic spiking determined the direction and the extent of synaptic changes. Repetitive postsynaptic spiking within a time window of 20 msec after presynaptic activation resulted in long-term potentiation (LTP), whereas postsynaptic spiking within a window of 20 msec before the repetitive presynaptic activation led to long-term depression (LTD). Significant LTP occurred only at synapses with relatively low initial strength, whereas the extent of LTD did not show obvious dependence on the initial synaptic strength. Both LTP and LTD depended on the activation of NMDA receptors and were absent in cases in which the postsynaptic neurons were GABAergic in nature. Blockade of L-type calcium channels with nimodipine abolished the induction of LTD and reduced the extent of LTP. These results underscore the importance of precise spike timing, synaptic strength, and postsynaptic cell type in the activity-induced modification of central synapses and suggest that Hebb's rule may need to incorporate a quantitative consideration of spike timing that reflects the narrow and asymmetric window for the induction of synaptic modification.}, author = {Bi, G Q and Poo, M M}, file = {:home/pierre/Mendeley/Bi, Poo - 1998.pdf:pdf}, journal = {J Neurosci}, keywords = {3-dione; Action Potentials; Animals; Bicuculline; ,6-Cyano-7-nitroquinoxaline-2,Cultured; Embryo; Excitatory Postsynaptic Potentia}, pages = {10464--10472}, pmid = {9852584}, title = {{Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type.}}, volume = {18}, year = {1998} } [Markram1997] H. Markram, J. Lubke, M. Frotscher, and B. Sakmann, "Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs," Science, vol. 275, iss. 5297, pp. 213-215, 1997. [Bibtex] @article{Markram1997, abstract = {Activity-driven modifications in synaptic connections between neurons in the neocortex may occur during development and learning. In dual whole-cell voltage recordings from pyramidal neurons, the coincidence of postsynaptic action potentials (APs) and unitary excitatory postsynaptic potentials (EPSPs) was found to induce changes in EPSPs. Their average amplitudes were differentially up- or down-regulated, depending on the precise timing of postsynaptic APs relative to EPSPs. These observations suggest that APs propagating back into dendrites serve to modify single active synaptic connections, depending on the pattern of electrical activity in the pre- and postsynaptic neurons.}, author = {Markram, H. and Lubke, J and Frotscher, M and Sakmann, B}, doi = {10.1126/science.275.5297.213}, file = {:home/pierre/Mendeley/Markram et al. - 1997.pdf:pdf}, issn = {00368075}, journal = {Science}, keywords = {Action Potentials,Animals,Calcium,Cerebral Cort,N-Methyl-D-Aspartate,Receptors,Synapses,Synaptic Transmiss,Wistar}, month = jan, number = {5297}, pages = {213--215}, pmid = {8985014}, title = {{Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs}}, url = {http://www.sciencemag.org/cgi/doi/10.1126/science.275.5297.213}, volume = {275}, year = {1997} } [Gerstner1996] W. Gerstner, R. Kempter, J. V. Hemmen, and H. Wagner, "A neuronal learning rule for sub-millisecond temporal coding," Nature, 1996. [Bibtex] @article{Gerstner1996, author = {Gerstner, W and Kempter, R and Hemmen, JL Van and Wagner, H}, file = {:home/pierre/Mendeley/Gerstner et al. - 1996.pdf:pdf}, journal = {Nature}, title = {{A neuronal learning rule for sub-millisecond temporal coding}}, url = {http://diwww.epfl.ch/~gerstner/PUBLICATIONS/Gerstner96.pdf}, year = {1996} } [Hebb1949] Unknown bibtex entry with key [Hebb1949] [Bibtex] [Tsodyks2000] M. Tsodyks, A. Uziel, and H. Markram, "Synchrony generation in recurrent networks with frequency-dependent synapses.," J neurosci, vol. 20, p. RC50, 2000. [Bibtex] @article{Tsodyks2000, abstract = {Throughout the neocortex, groups of neurons have been found to fire synchronously on the time scale of several milliseconds. This near coincident firing of neurons could coordinate the multifaceted information of different features of a stimulus. The mechanisms of generating such synchrony are not clear. We simulated the activity of a population of excitatory and inhibitory neurons randomly interconnected into a recurrent network via synapses that display temporal dynamics in their transmission; surprisingly, we found a behavior of the network where action potential activity spontaneously self-organized to produce highly synchronous bursts involving virtually the entire network. These population bursts were also triggered by stimuli to the network in an all-or-none manner. We found that the particular intensities of the external stimulus to specific neurons were crucial to evoke population bursts. This topographic sensitivity therefore depends on the spectrum of basal discharge rates across the population and not on the anatomical individuality of the neurons, because this was random. These results suggest that networks in which neurons are even randomly interconnected via frequency-dependent synapses could exhibit a novel form of reflex response that is sensitive to the nature of the stimulus as well as the background spontaneous activity.}, author = {Tsodyks, M and Uziel, A and Markram, H}, file = {:home/pierre/Mendeley/Tsodyks, Uziel, Markram - 2000.pdf:pdf}, journal = {J Neurosci}, keywords = {Action Potentials; Models,Neurological; Nerve Net; Neuronal Plasticity; Neur,Non-U.S. Gov't; Synapses}, month = jan, pages = {RC50}, pmid = {10627627}, title = {{Synchrony generation in recurrent networks with frequency-dependent synapses.}}, volume = {20}, year = {2000} } [Turrigiano2004] G. G. Turrigiano and S. B. Nelson, "Homeostatic plasticity in the developing nervous system.," Nat rev neurosci, vol. 5, iss. 2, pp. 97-107, 2004. [Bibtex] @article{Turrigiano2004, author = {Turrigiano, Gina G and Nelson, Sacha B}, doi = {10.1038/nrn1327}, file = {:home/pierre/Mendeley/Turrigiano, Nelson - 2004.pdf:pdf}, issn = {1471-003X}, journal = {Nat Rev Neurosci}, keywords = {Animals; Homeostasis; Humans; Nervous System; Neur,Neurotransmitter; Synapses; Synaptic Transmission}, number = {2}, pages = {97--107}, pmid = {14735113}, shorttitle = {Nat Rev Neurosci}, title = {{Homeostatic plasticity in the developing nervous system.}}, url = {http://dx.doi.org/10.1038/nrn1327}, volume = {5}, year = {2004} } [Crochet2006] S. Crochet, P. Fuentealba, Y. Cisse, I. Timofeev, and M. Steriade, "Synaptic plasticity in local cortical network in vivo and its modulation by the level of neuronal activity.," Cereb cortex, vol. 16, iss. 5, pp. 618-631, 2006. [Bibtex] @article{Crochet2006, abstract = {Neocortical neurons maintain high firing rates across all behavioral states of vigilance but the discharge patterns vary during different types of brain oscillations, which are assumed to play an important role in information processing and memory consolidation. In the present study, we report that trains of stimuli applied to local neocortical networks of cats, at frequencies that mimic endogenous brain rhythms, produced depression or potentiation of postsynaptic potentials, which lasted for several minutes. This form of synaptic plasticity was not mediated through NMDA receptors since it persisted after blockade of these receptors, but was strongly modulated by the level of background neuronal activity. Using different preparations in vivo, we found that increased background neuronal activity decreased the probability of plastic changes but enhanced the probability of potentiation over depression. Conversely, when the level of background neuronal activity was low, plasticity was observed in all neurons, but mainly depression was induced. Our results demonstrate that high levels of neuronal activity in the cortical network promote potentiation and insure the stability of synaptic connections.}, author = {Crochet, Sylvain and Fuentealba, Pablo and Cisse, Youssouf and Timofeev, Igor and Steriade, Mircea}, doi = {10.1093/cercor/bhj008}, file = {:home/pierre/Mendeley/Crochet et al. - 2006.pdf:pdf}, issn = {1047-3211}, journal = {Cereb Cortex}, keywords = {Anesthesia,Animals,Barbiturates,Cats,Cerebral,Databases,Electric Stimulation,Electroencephalogra,Factual,Statistical}, number = {5}, pages = {618--631}, pmid = {16049189}, shorttitle = {Cereb Cortex}, title = {{Synaptic plasticity in local cortical network in vivo and its modulation by the level of neuronal activity.}}, url = {http://dx.doi.org/10.1093/cercor/bhj008}, volume = {16}, year = {2006} } [Zhang1998] L. I. Zhang, H. W. Tao, C. E. Holt, W. A. Harris, and M. Poo, "A critical window for cooperation and competition among developing retinotectal synapses.," Nature, vol. 395, iss. 6697, pp. 37-44, 1998. [Bibtex] @article{Zhang1998, abstract = {In the developing frog visual system, topographic refinement of the retinotectal projection depends on electrical activity. In vivo whole-cell recording from developing Xenopus tectal neurons shows that convergent retinotectal synapses undergo activity-dependent cooperation and competition following correlated pre- and postsynaptic spiking within a narrow time window. Synaptic inputs activated repetitively within 20 ms before spiking of the tectal neuron become potentiated, whereas subthreshold inputs activated within 20 ms after spiking become depressed. Thus both the initial synaptic strength and the temporal order of activation are critical for heterosynaptic interactions among convergent synaptic inputs during activity-dependent refinement of developing neural networks.}, author = {Zhang, L I and Tao, H W and Holt, C E and Harris, W A and Poo, M}, doi = {10.1038/25665}, file = {:home/pierre/Mendeley/Zhang et al. - 1998.pdf:pdf}, issn = {0028-0836}, journal = {Nature}, keywords = {Animals; Brain; Excitatory Postsynaptic Potentials,Non-P.H.S.; Research Support,Non-U.S. Gov't; Research Support,P.H.S.; Retina; Superior Colliculus; Synapses; Xen,U.S. Gov't}, month = sep, number = {6697}, pages = {37--44}, pmid = {9738497}, shorttitle = {Nature}, title = {{A critical window for cooperation and competition among developing retinotectal synapses.}}, url = {http://dx.doi.org/10.1038/25665}, volume = {395}, year = {1998} } [Young2007a] J. M. Young, W. J. Waleszczyk, C. Wang, M. B. Calford, B. Dreher, and K. Obermayer, "Cortical reorganization consistent with spike timing-but not correlation-dependent plasticity.," Nat neurosci, vol. 10, iss. 7, pp. 887-895, 2007. [Bibtex] @article{Young2007a, abstract = {The receptive fields of neurons in primary visual cortex that are inactivated by retinal damage are known to 'shift' to nondamaged retinal locations, seemingly due to the plasticity of intracortical connections. We have observed in cats that these shifts occur in a pattern that is highly convergent, even among receptive fields that are separated by large distances before inactivation. Here we show, using a computational model of primary visual cortex, that the observed convergent shifts are inconsistent with the common assumption that the underlying intracortical connection plasticity is dependent on the temporal correlation of pre- and postsynaptic action potentials. The shifts are, however, consistent with the hypothesis that this plasticity is dependent on the temporal order of pre- and postsynaptic action potentials. This convergent reorganization seems to require increased neuronal gain, revealing a mechanism that networks may use to selectively facilitate the didactic transfer of neuronal response properties.}, author = {Young, Joshua M and Waleszczyk, Wioletta J and Wang, Chun and Calford, Michael B and Dreher, Bogdan and Obermayer, Klaus}, doi = {10.1038/nn1913}, file = {:home/pierre/Mendeley/Young et al. - 2007.pdf:pdf}, issn = {1097-6256}, journal = {Nat Neurosci}, number = {7}, pages = {887--895}, pmid = {17529985}, shorttitle = {Nat Neurosci}, title = {{Cortical reorganization consistent with spike timing-but not correlation-dependent plasticity.}}, url = {http://dx.doi.org/10.1038/nn1913}, volume = {10}, year = {2007} } [Jacob2007] V. Jacob, D. J. Brasier, I. Erchova, D. Feldman, and D. E. Shulz, "Spike timing-dependent synaptic depression in the in vivo barrel cortex of the rat.," The journal of neuroscience : the official journal of the society for neuroscience, vol. 27, iss. 6, pp. 1271-84, 2007. [Bibtex] @article{Jacob2007, abstract = {Spike timing-dependent plasticity (STDP) is a computationally powerful form of plasticity in which synapses are strengthened or weakened according to the temporal order and precise millisecond-scale delay between presynaptic and postsynaptic spiking activity. STDP is readily observed in vitro, but evidence for STDP in vivo is scarce. Here, we studied spike timing-dependent synaptic depression in single putative pyramidal neurons of the rat primary somatosensory cortex (S1) in vivo, using two techniques. First, we recorded extracellularly from layer 2/3 (L2/3) and L5 neurons, and paired spontaneous action potentials (postsynaptic spikes) with subsequent subthreshold deflection of one whisker (to drive presynaptic afferents to the recorded neuron) to produce "post-leading-pre" spike pairings at known delays. Short delay pairings (<17 ms) resulted in a significant decrease of the extracellular spiking response specific to the paired whisker, consistent with spike timing-dependent synaptic depression. Second, in whole-cell recordings from neurons in L2/3, we paired postsynaptic spikes elicited by direct-current injection with subthreshold whisker deflection to drive presynaptic afferents to the recorded neuron at precise temporal delays. Post-leading-pre pairing (<33 ms delay) decreased the slope and amplitude of the PSP evoked by the paired whisker, whereas "pre-leading-post" delays failed to produce depression, and sometimes produced potentiation of whisker-evoked PSPs. These results demonstrate that spike timing-dependent synaptic depression occurs in S1 in vivo, and is therefore a plausible plasticity mechanism in the sensory cortex.}, author = {Jacob, Vincent and Brasier, Daniel J and Erchova, Irina and Feldman, Dan and Shulz, Daniel E}, doi = {10.1523/JNEUROSCI.4264-06.2007}, file = {:home/pierre/Mendeley/Jacob et al. - 2007.pdf:pdf}, issn = {1529-2401}, journal = {The Journal of neuroscience : the official journal of the Society for Neuroscience}, keywords = {Action Potentials,Animals,Electroencephalography,Long-Term Synaptic Depression,Long-Term Synaptic Depression: physiology,Male,Microelectrodes,Models, Neurological,Neurons,Neurons: physiology,Patch-Clamp Techniques,Presynaptic Terminals,Presynaptic Terminals: physiology,Pyramidal Cells,Pyramidal Cells: physiology,Rats,Rats, Wistar,Reaction Time,Somatosensory Cortex,Somatosensory Cortex: physiology,Stochastic Processes,Time Factors,Touch,Vibrissae,Vibrissae: innervation}, month = feb, number = {6}, pages = {1271--84}, pmid = {17287502}, title = {{Spike timing-dependent synaptic depression in the in vivo barrel cortex of the rat.}}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3070399\&tool=pmcentrez\&rendertype=abstract}, volume = {27}, year = {2007} } [Bell1997] C. C. Bell, V. Z. Han, Y. Sugawara, and K. Grant, "Synaptic plasticity in a cerebellum-like structure depends on temporal order.," Nature, vol. 387, iss. 6630, pp. 278-281, 1997. [Bibtex] @article{Bell1997, abstract = {Cerebellum-like structures in fish appear to act as adaptive sensory processors, in which learned predictions about sensory input are generated and subtracted from actual sensory input, allowing unpredicted inputs to stand out. Pairing sensory input with centrally originating predictive signals, such as corollary discharge signals linked to motor commands, results in neural responses to the predictive signals alone that are 'negative images' of the previously paired sensory responses. Adding these 'negative images' to actual sensory inputs minimizes the neural response to predictable sensory features. At the cellular level, sensory input is relayed to the basal region of Purkinje-like cells, whereas predictive signals are relayed by parallel fibres to the apical dendrites of the same cells. The generation of negative images could be explained by plasticity at parallel fibre synapses. We show here that such plasticity exists in the electrosensory lobe of mormyrid electric fish and that it has the necessary properties for such a model: it is reversible, anti-hebbian (excitatory postsynaptic potentials (EPSPs) are depressed after pairing with a postsynaptic spike) and tightly dependent on the sequence of pre- and postsynaptic events, with depression occurring only if the postsynaptic spike follows EPSP onset within 60 ms.}, author = {Bell, C C and Han, V Z and Sugawara, Y and Grant, K}, doi = {10.1038/387278a0}, issn = {0028-0836}, journal = {Nature}, keywords = {Animals; Cerebellum; Electric Fish; Evoked Potenti,Neurological; Neuronal Plasticity; Research Suppor,Non-P.H.S.; Research Support,Non-U.S. Gov't; Research Support,P.H.S.; Synapses; Time Factors,U.S. Gov't}, month = may, number = {6630}, pages = {278--281}, pmid = {9153391}, shorttitle = {Nature}, title = {{Synaptic plasticity in a cerebellum-like structure depends on temporal order.}}, url = {http://dx.doi.org/10.1038/387278a0}, volume = {387}, year = {1997} } [Toyoizumi2007] T. Toyoizumi, J. Pfister, K. Aihara, and W. Gerstner, "Optimality Model of Unsupervised Spike-Timing-Dependent Plasticity: Synaptic Memory and Weight Distribution.," Neural comput, vol. 19, iss. 3, pp. 639-671, 2007. [Bibtex] @article{Toyoizumi2007, abstract = {We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory.}, author = {Toyoizumi, Taro and Pfister, Jean-Pascal and Aihara, Kazuyuki and Gerstner, Wulfram}, doi = {10.1162/neco.2007.19.3.639}, file = {:home/pierre/Mendeley/Toyoizumi et al. - 2007.pdf:pdf}, issn = {0899-7667}, journal = {Neural Comput}, month = mar, number = {3}, pages = {639--671}, pmid = {17298228}, shorttitle = {Neural Comput}, title = {{Optimality Model of Unsupervised Spike-Timing-Dependent Plasticity: Synaptic Memory and Weight Distribution.}}, url = {http://dx.doi.org/10.1162/neco.2007.19.3.639}, volume = {19}, year = {2007} } [Chechik2003] G. Chechik, "Spike-timing-dependent plasticity and relevant mutual information maximization.," Neural comput, vol. 15, iss. 7, pp. 1481-1510, 2003. [Bibtex] @article{Chechik2003, abstract = {Synaptic plasticity was recently shown to depend on the relative timing of the pre- and postsynaptic spikes. This article analytically derives a spike-dependent learning rule based on the principle of information maximization for a single neuron with spiking inputs. This rule is then transformed into a biologically feasible rule, which is compared to the experimentally observed plasticity. This comparison reveals that the biological rule increases information to a near-optimal level and provides insights into the structure of biological plasticity. It shows that the time dependency of synaptic potentiation should be determined by the synaptic transfer function and membrane leak. Potentiation consists of weight-dependent and weight-independent components whose weights are of the same order of magnitude. It further suggests that synaptic depression should be triggered by rare and relevant inputs but at the same time serves to unlearn the baseline statistics of the network's inputs. The optimal depression curve is uniformly extended in time, but biological constraints that cause the cell to forget past events may lead to a different shape, which is not specified by our current model. The structure of the optimal rule thus suggests a computational account for several temporal characteristics of the biological spike-timing-dependent rules.}, author = {Chechik, Gal}, doi = {10.1162/089976603321891774}, file = {:home/pierre/Mendeley/Chechik - 2003.pdf:pdf}, issn = {0899-7667}, journal = {Neural Comput}, keywords = {Action Potentials; Models,Neurological; Neuronal Plasticity; Research Suppor,Non-U.S. Gov't}, month = jul, number = {7}, pages = {1481--1510}, pmid = {12816563}, shorttitle = {Neural Comput}, title = {{Spike-timing-dependent plasticity and relevant mutual information maximization.}}, url = {http://dx.doi.org/10.1162/089976603321891774}, volume = {15}, year = {2003} } [Bohte2005b] S. M. Bohte and M. C. Mozer, "Reducing Spike Train Variability: A Computational Theory Of Spike-Timing Dependent Plasticity," Nips, vol. 2005, 2005. [Bibtex] @article{Bohte2005b, author = {Bohte, Sander M and Mozer, Michael C}, file = {:home/pierre/Mendeley/Bohte, Mozer - 2005.pdf:pdf}, journal = {NIPS}, keywords = {Plasticity}, title = {{Reducing Spike Train Variability: A Computational Theory Of Spike-Timing Dependent Plasticity}}, volume = {2005}, year = {2005} } [Sprekeler2006] H. Sprekeler, C. Michaelis, and L. Wiskott, "Slowness: An Objective for Spike-Timing Dependent Plasticity?," in Proc. 2nd bernstein symposium for computational neuroscience 2006, berlin, october 1--3, 2006, p. 24. [Bibtex] @inproceedings{Sprekeler2006, abstract = {Slow Feature Analysis (SFA) is an efficient algorithm for learning input-output functions that extract the most slowly varying features from a quickly varying signal. It has been successfully applied to the unsupervised learning of translation-, rotation-, and other invariances in a model of the visual system, to the learning of complex cell receptive fields, and, combined with a sparseness objective, to the self-organized formation of place cells in a model of the hippocampus. In order to arrive at a biologically more plausible implementation of this learning rule, we consider analytically how SFA could be realized in simple linear continuous and spiking model neurons. It turns out that for the continuous model neuron SFA can be implemented by means of a modified version of standard Hebbian learning. In this framework we provide a connection to the trace learning rule for invariance learning. We then show that for Poisson neurons spike-timing-dependent plasticity (STDP) with a specific learning window can learn the same weight distribution as SFA. Surprisingly, we find that the appropriate learning rule reproduces the typical STDP learning window. The shape as well as the timescale are in good agreement with what has been measured experimentally. This offers a completely novel interpretation for the functional role of spike-timing-dependent plasticity in physiological neurons.}, annote = {($\backslash\$EG\{abstract\}\{Zusammenfassung\})},
author = {Sprekeler, Henning and Michaelis, Christian and Wiskott, Laurenz},
booktitle = {Proc. 2nd Bernstein Symposium for Computational Neuroscience 2006, Berlin, October 1--3},
file = {:home/pierre/Mendeley/Sprekeler, Michaelis, Wiskott - 2006.pdf:pdf},
keywords = {SFA,STDP,Slow Feature Analysis,computational neuroscience,invariance learning,modeling,slowness,spike-timing dependent plasticity,trace rule},
pages = {24},
title = {{Slowness: An Objective for Spike-Timing Dependent Plasticity?}},
year = {2006}
}
[Rao2001] R. P. Rao and T. J. Sejnowski, "Spike-timing-dependent Hebbian plasticity as temporal difference learning.," Neural comput, vol. 13, iss. 10, pp. 2221-2237, 2001.
[Bibtex]
@article{Rao2001,
abstract = {A spike-timing-dependent Hebbian mechanism governs the plasticity of recurrent excitatory synapses in the neocortex: synapses that are activated a few milliseconds before a postsynaptic spike are potentiated, while those that are activated a few milliseconds after are depressed. We show that such a mechanism can implement a form of temporal difference learning for prediction of input sequences. Using a biophysical model of a cortical neuron, we show that a temporal difference rule used in conjunction with dendritic backpropagating action potentials reproduces the temporally asymmetric window of Hebbian plasticity observed physio-logically. Furthermore, the size and shape of the window vary with the distance of the synapse from the soma. Using a simple example, we show how a spike-timing-based temporal difference learning rule can allow a network of neocortical neurons to predict an input a few milliseconds before the input's expected arrival.},
author = {Rao, R P and Sejnowski, T J},
doi = {10.1162/089976601750541787},
file = {:home/pierre/Mendeley/Rao, Sejnowski - 2001.pdf:pdf},
issn = {0899-7667},
journal = {Neural Comput},
keywords = {Action Potentials; Animals; Learning; Models,Neurological; Neocortex; Neuronal Plasticity; Reac,Non-U.S. Gov't; Research Support,P.H.S.; Synapses,U.S. Gov't},
month = oct,
number = {10},
pages = {2221--2237},
pmid = {11570997},
shorttitle = {Neural Comput},
title = {{Spike-timing-dependent Hebbian plasticity as temporal difference learning.}},
url = {http://dx.doi.org/10.1162/089976601750541787},
volume = {13},
year = {2001}
}
[Morrison2008] A. Morrison, M. Diesmann, and W. Gerstner, "Phenomenological models of synaptic plasticity based on spike timing.," Biological cybernetics, vol. 98, iss. 6, pp. 459-78, 2008.
[Bibtex]
@article{Morrison2008,
abstract = {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.},
author = {Morrison, Abigail and Diesmann, Markus and Gerstner, Wulfram},
doi = {10.1007/s00422-008-0233-1},
file = {:home/pierre/Mendeley/Morrison, Diesmann, Gerstner - 2008.pdf:pdf},
issn = {0340-1200},
journal = {Biological cybernetics},
keywords = {Action Potentials,Action Potentials: physiology,Animals,Models,Neurological,Neuronal Plasticity,Neuronal Plasticity: physiology,Neurons,Neurons: physiology,Synapses,Synapses: physiology,Time Factors},
month = jun,
number = {6},
pages = {459--78},
pmid = {18491160},
publisher = {Springer Berlin / Heidelberg},
shorttitle = {Biol Cybern},
title = {{Phenomenological models of synaptic plasticity based on spike timing.}},
volume = {98},
year = {2008}
}
[Izhikevich2003] E. M. Izhikevich and N. S. Desai, "Relating STDP to BCM.," Neural comput, vol. 15, iss. 7, pp. 1511-1523, 2003.
[Bibtex]
@article{Izhikevich2003,
abstract = {We demonstrate that the BCM learning rule follows directly from STDP when pre- and postsynaptic neurons fire uncorrelated or weakly correlated Poisson spike trains, and only nearest-neighbor spike interactions are taken into account.},
author = {Izhikevich, Eugene M and Desai, Niraj S},
doi = {10.1162/089976603321891783},
file = {:home/pierre/Mendeley/Izhikevich, Desai - 2003.pdf:pdf},
issn = {0899-7667},
journal = {Neural Comput},
keywords = {Action Potentials; Neuronal Plasticity; Poisson Di,Non-U.S. Gov't; Synapses},
month = jul,
number = {7},
pages = {1511--1523},
pmid = {12816564},
shorttitle = {Neural Comput},
title = {{Relating STDP to BCM.}},
url = {http://dx.doi.org/10.1162/089976603321891783},
volume = {15},
year = {2003}
}
[Guetig2003] R. Gütig, R. Aharonov, S. Rotter, H. Sompolinsky, and R. G�tig, "Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity.," The journal of neuroscience : the official journal of the society for neuroscience, vol. 23, iss. 9, pp. 3697-3714, 2003.
[Bibtex]
@article{Guetig2003,
abstract = {Triggered by recent experimental results, temporally asymmetric Hebbian (TAH) plasticity is considered as a candidate model for the biological implementation of competitive synaptic learning, a key concept for the experience-based development of cortical circuitry. However, because of the well known positive feedback instability of correlation-based plasticity, the stability of the resulting learning process has remained a central problem. Plagued by either a runaway of the synaptic efficacies or a greatly reduced sensitivity to input correlations, the learning performance of current models is limited. Here we introduce a novel generalized nonlinear TAH learning rule that allows a balance between stability and sensitivity of learning. Using this rule, we study the capacity of the system to learn patterns of correlations between afferent spike trains. Specifically, we address the question of under which conditions learning induces spontaneous symmetry breaking and leads to inhomogeneous synaptic distributions that capture the structure of the input correlations. To study the efficiency of learning temporal relationships between afferent spike trains through TAH plasticity, we introduce a novel sensitivity measure that quantifies the amount of information about the correlation structure in the input, a learning rule capable of storing in the synaptic weights. We demonstrate that by adjusting the weight dependence of the synaptic changes in TAH plasticity, it is possible to enhance the synaptic representation of temporal input correlations while maintaining the system in a stable learning regime. Indeed, for a given distribution of inputs, the learning efficiency can be optimized.},
annote = { From Duplicate 1 ( Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. - G\"{u}tig, R; Aharonov, R; Rotter, S; Sompolinsky, Haim; G�tig, R )
From Duplicate 1 ( Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. - G�tig, R; Aharonov, R; Rotter, S; Sompolinsky, Haim )
From Duplicate 2 ( Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. - G\"{u}tig, R; Aharonov, R; Rotter, S; Sompolinsky, Haim; G�tig, R )
From Duplicate 1 ( Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. - G\"{u}tig, R; Aharonov, R; Rotter, S; Sompolinsky, Haim; G�tig, R )
From Duplicate 1 ( Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. - G�tig, R; Aharonov, R; Rotter, S; Sompolinsky, Haim )
From Duplicate 2 ( Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. - G\"{u}tig, R; Aharonov, R; Rotter, S; Sompolinsky, Haim )
},
author = {G\"{u}tig, R and Aharonov, R and Rotter, S and Sompolinsky, Haim and G�tig, R},
file = {:home/pierre/Mendeley/G\"{u}tig et al. - 2003.pdf:pdf},
issn = {1529-2401},
journal = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
keywords = {Action Potentials,Action Potentials: physiology,Computer Simulation,Learning,Learning: physiology,Models,Neural Networks (Computer),Neurological,Neuronal,Neuronal Plasticity,Neuronal Plasticity: physiology,Neurons,Neurons: physiology,Non-P.H.S.,Non-U.S. Gov't,Nonlinear Dynamics,Poisson Distribution,Research Support,Sensory Thresholds,Sensory Thresholds: physiology,Synapses,Synapses: physiology,U.S. Gov't},
month = may,
number = {9},
pages = {3697--3714},
pmid = {12736341},
title = {{Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/12736341},
volume = {23},
year = {2003}
}
[Standage2007] O. Paper, D. Standage, S. Jalil, and T. Trappenberg, "Computational consequences of experimentally derived spike-time and weight dependent plasticity rules.," Biol cybern, vol. 96, iss. 6, pp. 615-23, 2007.
[Bibtex]
@article{Standage2007,
abstract = {We present two weight- and spike-time dependent synaptic plasticity rules consistent with the physiological data of Bi and Poo (J Neurosci 18:10464-10472, 1998). One rule assumes synaptic saturation, while the other is scale free. We extend previous analyses of the asymptotic consequences of weight-dependent STDP to the case of strongly correlated pre- and post-synaptic spiking, more closely resembling associative learning. We further provide a general formula for the contribution of any number of spikes to synaptic drift. Asymptotic weights are shown to principally depend on the correlation and rate of pre- and post-synaptic activity, decreasing with increasing rate under correlated activity, and increasing with rate under uncorrelated activity. Spike train statistics reveal a quantitative effect only in the pre-asymptotic regime, and we provide a new interpretation of the relation between BCM and STDP data.},
annote = { From Duplicate 1 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas; Paper, Original )
From Duplicate 2 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas; Paper, Original )
From Duplicate 1 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Paper, Original; Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas )
From Duplicate 1 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas )
From Duplicate 2 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas )
From Duplicate 2 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Paper, Original; Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas )
From Duplicate 1 ( Computational consequences of experimentally derived spike-time and weight dependent plasticity rules. - Standage, Dominic; Jalil, Sajiya; Trappenberg, Thomas )
},
author = {Paper, Original and Standage, Dominic and Jalil, Sajiya and Trappenberg, Thomas},
doi = {10.1007/s00422-007-0152-6},
file = {:home/pierre/Mendeley//Paper et al. - 2007.pdf:pdf},
issn = {0340-1200},
journal = {Biol Cybern},
keywords = {Action Potentials,Action Potentials: physiology,Animals,Computer Simulation,Models,Nerve Net,Neurological,Neuronal Plasticity,Neuronal Plasticity: physiology,Neurons,Neurons: physiology,Synapses,Synapses: physiology,Synaptic Transmission,Time Factors},
month = jun,
number = {6},
pages = {615--23},
pmid = {17468882},
shorttitle = {Biol Cybern},
title = {{Computational consequences of experimentally derived spike-time and weight dependent plasticity rules.}},
url = {http://dx.doi.org/10.1007/s00422-007-0152-6 http://www.ncbi.nlm.nih.gov/pubmed/17468882},
volume = {96},
year = {2007}
}
[Rossum2000] M. C. van Rossum, G. Q. Bi, G. G. Turrigiano, and V. M. C. W. Rossum, "Stable Hebbian learning from spike timing-dependent plasticity.," The journal of neuroscience : the official journal of the society for neuroscience, vol. 20, iss. 23, pp. 8812-21, 2000.
[Bibtex]
@article{Rossum2000,
abstract = {We explore a synaptic plasticity model that incorporates recent findings that potentiation and depression can be induced by precisely timed pairs of synaptic events and postsynaptic spikes. In addition we include the observation that strong synapses undergo relatively less potentiation than weak synapses, whereas depression is independent of synaptic strength. After random stimulation, the synaptic weights reach an equilibrium distribution which is stable, unimodal, and has positive skew. This weight distribution compares favorably to the distributions of quantal amplitudes and of receptor number observed experimentally in central neurons and contrasts to the distribution found in plasticity models without size-dependent potentiation. Also in contrast to those models, which show strong competition between the synapses, stable plasticity is achieved with little competition. Instead, competition can be introduced by including a separate mechanism that scales synaptic strengths multiplicatively as a function of postsynaptic activity. In this model, synaptic weights change in proportion to how correlated they are with other inputs onto the same postsynaptic neuron. These results indicate that stable correlation-based plasticity can be achieved without introducing competition, suggesting that plasticity and competition need not coexist in all circuits or at all developmental stages.},
annote = { From Duplicate 1 ( Stable Hebbian learning from spike timing-dependent plasticity. - Rossum, M C W Van; Bi, G Q; Turrigiano, G G; van Rossum, M C )
From Duplicate 1 ( Stable Hebbian learning from spike timing-dependent plasticity. - van Rossum, M C; Bi, G Q; Turrigiano, G G )
From Duplicate 2 ( Stable Hebbian learning from spike timing-dependent plasticity. - van Rossum, M C; Bi, G Q; Turrigiano, G G )
},
author = {van Rossum, M C and Bi, G Q and Turrigiano, G G and Rossum, M C W Van},
file = {:home/pierre/Mendeley//van Rossum et al. - 2000.pdf:pdf},
issn = {1529-2401},
journal = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
keywords = {Action Potentials,Action Potentials: physiology,Animals,Computer Simulation,L,Learning,Learning: physiology,Long-Term Potentiation,Long-Term Potentiation: physiology,Models,Neurological,Neuronal Plasticity,Neuronal Plasticity: physiology,Neurons,Neurons: physiology,Rats,Reaction Time,Reaction Time: physiology,Stochastic Processes,Synaptic Transmission,Synaptic Transmission: physiology,activity-dependent scaling,hebbian plasticity,petition,stochas-,synaptic com-,synaptic weights,temporal learning},
month = dec,
number = {23},
pages = {8812--21},
pmid = {11102489},
title = {{Stable Hebbian learning from spike timing-dependent plasticity.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16711840},
volume = {20},
year = {2000}
}
[Billings2009] G. Billings and M. C. W. van Rossum, "Memory retention and spike-timing-dependent plasticity.," Journal of neurophysiology, vol. 101, iss. 6, pp. 2775-88, 2009.
[Bibtex]
@article{Billings2009,
abstract = {Memory systems should be plastic to allow for learning; however, they should also retain earlier memories. Here we explore how synaptic weights and memories are retained in models of single neurons and networks equipped with spike-timing-dependent plasticity. We show that for single neuron models, the precise learning rule has a strong effect on the memory retention time. In particular, a soft-bound, weight-dependent learning rule has a very short retention time as compared with a learning rule that is independent of the synaptic weights. Next, we explore how the retention time is reflected in receptive field stability in networks. As in the single neuron case, the weight-dependent learning rule yields less stable receptive fields than a weight-independent rule. However, receptive fields stabilize in the presence of sufficient lateral inhibition, demonstrating that plasticity in networks can be regulated by inhibition and suggesting a novel role for inhibition in neural circuits.},
author = {Billings, Guy and van Rossum, Mark C W},
doi = {10.1152/jn.91007.2008},
file = {:home/pierre/Mendeley/Billings, van Rossum - 2009.pdf:pdf},
issn = {0022-3077},
journal = {Journal of neurophysiology},
keywords = {Action Potentials,Action Potentials: physiology,Animals,Humans,Models, Neurological,Neural Inhibition,Neural Inhibition: physiology,Neural Networks (Computer),Neuronal Plasticity,Neuronal Plasticity: physiology,Neurons,Neurons: physiology,Retention (Psychology),Retention (Psychology): physiology,Time Factors},
month = jun,
number = {6},
pages = {2775--88},
pmid = {19297513},
title = {{Memory retention and spike-timing-dependent plasticity.}},
url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2694112\&tool=pmcentrez\&rendertype=abstract},
volume = {101},
year = {2009}
}
[Fusi2007] S. Fusi, W. F. Asaad, E. K. Miller, and X. Wang, "A neural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales.," Neuron, vol. 54, iss. 2, pp. 319-333, 2007.
[Bibtex]
@article{Fusi2007,
abstract = {Volitional behavior relies on the brain's ability to remap sensory flow to motor programs whenever demanded by a changed behavioral context. To investigate the circuit basis of such flexible behavior, we have developed a biophysically based decision-making network model of spiking neurons for arbitrary sensorimotor mapping. The model quantitatively reproduces behavioral and prefrontal single-cell data from an experiment in which monkeys learn visuomotor associations that are reversed unpredictably from time to time. We show that when synaptic modifications occur on multiple timescales, the model behavior becomes flexible only when needed: slow components of learning usually dominate the decision process. However, if behavioral contexts change frequently enough, fast components of plasticity take over, and the behavior exhibits a quick forget-and-learn pattern. This model prediction is confirmed by monkey data. Therefore, our work reveals a scenario for conditional associative learning that is distinct from instant switching between sets of well-established sensorimotor associations.},
author = {Fusi, Stefano and Asaad, Wael F and Miller, Earl K and Wang, Xiao-Jing},
doi = {10.1016/j.neuron.2007.03.017},
institution = {Center for Neurobiology and Behavior, Columbia University College of Physicians and Surgeons, New York, NY 10032, USA.},
issn = {0896-6273},
journal = {Neuron},
keywords = {Algorithms; Animals; Association Learning,Neurological; Neural Networks (Computer); Neurons,phys/iology; Models,physiology,physiology; Cues; Decision Making; Haplorhini; Lea,physiology; Memory,physiology; Mental Recall,physiology; Prefrontal Cortex,physiology; Psychomotor Performance,physiology; Synapses},
number = {2},
pages = {319--333},
pmid = {17442251},
shorttitle = {Neuron},
title = {{A neural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales.}},
url = {http://dx.doi.org/10.1016/j.neuron.2007.03.017},
volume = {54},
year = {2007}
}
[Morrison2007] A. Morrison, A. Aertsen, and M. Diesmann, "Spike-timing-dependent plasticity in balanced random networks.," Neural comput, vol. 19, iss. 6, pp. 1437-1467, 2007.
[Bibtex]
@article{Morrison2007,
abstract = {The balanced random network model attracts considerable interest because it explains the irregular spiking activity at low rates and large membrane potential fluctuations exhibited by cortical neurons in vivo. In this article, we investigate to what extent this model is also compatible with the experimentally observed phenomenon of spike-timing-dependent plasticity (STDP). Confronted with the plethora of theoretical models for STDP available, we reexamine the experimental data. On this basis, we propose a novel STDP update rule, with a multiplicative dependence on the synaptic weight for depression, and a power law dependence for potentiation. We show that this rule, when implemented in large, balanced networks of realistic connectivity and sparseness, is compatible with the asynchronous irregular activity regime. The resultant equilibrium weight distribution is unimodal with fluctuating individual weight trajectories and does not exhibit development of structure. We investigate the robustness of our results with respect to the relative strength of depression. We introduce synchronous stimulation to a group of neurons and demonstrate that the decoupling of this group from the rest of the network is so severe that it cannot effectively control the spiking of other neurons, even those with the highest convergence from this group.},
author = {Morrison, Abigail and Aertsen, Ad and Diesmann, Markus},
doi = {10.1162/neco.2007.19.6.1437},
file = {:home/pierre/Mendeley/Morrison, Aertsen, Diesmann - 2007.pdf:pdf;:home/pierre/Mendeley//Morrison, Aertsen, Diesmann - 2007.pdf:pdf},
issn = {0899-7667},
journal = {Neural Comput},
keywords = {Action Potentials,Animals,Electric Stimulation},
month = jun,
number = {6},
pages = {1437--1467},
pmid = {17444756},
shorttitle = {Neural Comput},
title = {{Spike-timing-dependent plasticity in balanced random networks.}},
url = {http://dx.doi.org/10.1162/neco.2007.19.6.1437},
volume = {19},
year = {2007}
}
[Komatsu1993] Y. Komatsu and M. Iwakiri, "Long-term modification of inhibitory synaptic transmission in developing visual cortex.," Neuroreport, vol. 4, iss. 7, pp. 907-10, 1993.
[Bibtex]
@article{Komatsu1993,
abstract = {The long-term modification of inhibitory postsynaptic potentials (IPSPs) was studied in visual cortex slices taken from developing rats. IPSPs evoked by layer IV stimulation were intracellularly recorded from layer V cells while excitatory synaptic transmission was blocked by NMDA and non-NMDA receptor antagonists. High-frequency conditioning stimulation of layer IV induced long-term potentiation of IPSPs. By contrast, long-term depression (LTD) of IPSPs was induced by the same conditioning stimulation applied while NMDA receptor-mediated synaptic transmission was unmasked by removing the NMDA antagonist from and adding a GABAA receptor antagonist to the medium. The LTD of IPSPs was also induced by NMDA application to the cells. The plasticity of IPSPs might explain the postnatal development of selective responsiveness of visual cortical cells.},
author = {Komatsu, Y and Iwakiri, M},
issn = {0959-4965},
journal = {Neuroreport},
keywords = {2-Amino-5-phosphonovalerate,2-Amino-5-phosphonovalerate: pharmacology,Animals,Animals, Newborn,Animals, Newborn: physiology,Bicuculline,Bicuculline: analogs \& derivatives,Bicuculline: pharmacology,Conditioning (Psychology),Conditioning (Psychology): physiology,Electric Stimulation,Evoked Potentials,Evoked Potentials: drug effects,Evoked Potentials: physiology,GABA-A Receptor Antagonists,Membrane Potentials,Membrane Potentials: physiology,Neuronal Plasticity,Neuronal Plasticity: drug effects,Neurons, Afferent,Neurons, Afferent: drug effects,Neurons, Afferent: physiology,Quinoxalines,Quinoxalines: pharmacology,Rats,Rats, Sprague-Dawley,Receptors, GABA-A,Receptors, GABA-A: drug effects,Receptors, N-Methyl-D-Aspartate,Receptors, N-Methyl-D-Aspartate: antagonists \& inh,Receptors, N-Methyl-D-Aspartate: drug effects,Synapses,Synapses: drug effects,Synapses: physiology,Synaptic Transmission,Synaptic Transmission: drug effects,Synaptic Transmission: physiology,Visual Cortex,Visual Cortex: drug effects,Visual Cortex: growth \& development,Visual Cortex: physiology},
month = jul,
number = {7},
pages = {907--10},
pmid = {8103683},
title = {{Long-term modification of inhibitory synaptic transmission in developing visual cortex.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/8103683},
volume = {4},
year = {1993}
}
[Haas2006] J. S. Haas, T. Nowotny, and H. D. I. Abarbanel, "Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex.," J neurophysiol, vol. 96, iss. 6, pp. 3305-13, 2006.
[Bibtex]
@article{Haas2006,
abstract = {Actions of inhibitory interneurons organize and modulate many neuronal processes, yet the mechanisms and consequences of plasticity of inhibitory synapses remains poorly understood. We report on spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. After pairing presynaptic stimulations at time tpre with evoked postsynaptic spikes at time tpost under pharmacological blockade of excitation we found, via whole-cell recordings, an asymmetrical timing rule for plasticity of the remaining inhibitory responses. Strength of response varied as a function of the time interval Deltat = tpost - tpre : for Deltat >0 inhibitory responses potentiated, peaking at a delay of 10 ms. For Deltat <0 the synaptic coupling depressed, again with a maximal effect near 10 ms of delay. We also show that changes in synaptic strength depend on changes in intracellular calcium concentrations, and demonstrate that the calcium enters the postsynaptic cell through voltage-gated channels. Using network models, we demonstrate how this novel form of plasticity can sculpt network behavior efficiently and with remarkable flexibility.},
author = {Haas, Julie S and Nowotny, Thomas and Abarbanel, Henry D I},
doi = {10.1152/jn.00551.2006},
file = {:home/pierre/Mendeley/Haas, Nowotny, Abarbanel - 2006.pdf:pdf},
issn = {0022-3077},
journal = {J Neurophysiol},
month = dec,
number = {6},
pages = {3305--13},
pmid = {16928795},
shorttitle = {J Neurophysiol},
title = {{Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex.}},
url = {http://dx.doi.org/10.1152/jn.00551.2006},
volume = {96},
year = {2006}
}
[Plumbley1993] M. D. Plumbley, "A Hebbian/anti-Hebbian network which optimizes information capacity by orthonormalizing the principal subspace," Artificial neural networks, 1993., third \ldots, 1993.
[Bibtex]
@article{Plumbley1993,
abstract = {this paper we extend this work to develop an algorithm for the case of both input and output noise, with an output power constraint. We find that it is possible to simplify the obvious algorithm obtained by concatenating the two previous solutions. Previous Algorithms},
annote = { From Duplicate 1 ( A Hebbian/anti-Hebbian network which optimizes information capacity by orthonormalizing the principal subspace - Plumbley, MD D )
From Duplicate 2 ( A Hebbian/anti-Hebbian Network Which Optimizes Information Capacity By Orthonormalizing The Principal Subspace - Plumbley, M D )
M D Plumbley (King s College London , UK);
From Duplicate 2 ( A Hebbian/anti-Hebbian Network Which Optimizes Information Capacity By Orthonormalizing The Principal Subspace - Plumbley, M D )
M D Plumbley (King s College London , UK);
},
author = {Plumbley, MD D},
file = {:home/pierre/Mendeley//Plumbley - 1993.pdf:pdf},
journal = {Artificial Neural Networks, 1993., Third \ldots},
title = {{A Hebbian/anti-Hebbian network which optimizes information capacity by orthonormalizing the principal subspace}},
url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=263251 http://citeseer.ist.psu.edu/207161.html;},
year = {1993}
}