Category: Learning

A localised group of neurons firing synchronously at 30-100 hz is referred to as a local field potential gamma oscillation. These are important for spike-timing-dependent plasticity to occur. Synchronized activity of 10–30 ms in the gamma frequency create a narrow time window for the coincident activation of pre-synaptic and post-synaptic cell used for STDP (for more details read here). Slower oscillations do not provide a narrow enough window and faster oscillations, having more than one cycle in the STDP window, cause the post-synaptic cell to receive inputs both before and after having generated a spike.

However, STDP occurs if pre-synaptic and post-synaptic action potentials are correlated. Notably this occurs even if two cells with equally weak inputs correlate, which is not the kind of result that is useful to learning as we wish to learn strong coincidences. Gamma synchronization is not necessarily time-locked to a stimulus. Due to these two reasons long term potentiation (strengthening) of synapses induced by synchronized gamma activity alone does not attain the specificity of memory encoding, but an additional mechanism is required.

The hippocampus is considered to play a major role in memory. Learning-dependent synchronization of hippocampal theta activity is associated with large event-related potentials with frequency in the theta (4-8 hz) and delta (0-4 hz) range that appear to result from phase the reset of theta activity occurring at a fixed interval after presentation of a stimulus. Theta reset determines the theta phase at which a given stimulus affects a cell. Theta band learning is non-Hebbian and only involves pre-synaptic and not post-synaptic spikes. If the stimuli arrive during the peak of the theta oscillation long term potentiation (strengthening of synapses) occurs, inputs arriving at a trough of the theta cycle induce long term depression (weakening of synapses). Axmacher et al note that a combination between theta and gamma learning dynamics my provide the required specificity for memory learning:

‘Whereas gamma-dependent plasticity alone may not distinguish between correlated weak and strong inputs and occurs not necessarily time-locked to a given stimulus, plasticity during theta reset has these features. Theta-dependent plasticity alone, on the other hand, is too coarse to encode stimulus features with a high temporal resolution: at least Hebbian LTP requires precise spike timing. Moreover, sequence encoding (sequences of items as well as spatial paths) has been suggested to depend on action potentials during subsequent theta phases, with gamma periods binding each item.’

Im afraid there is more techie maths in this post :(. I recently posted here about spike timing dependant plasticity and how it can create unimodal or bimodal synaptic weight distributions depending on whether a term is added to the weight change function to allow dependence on the existing value of the synaptic weight.

Babadi et al show that by adding a delay (d) to the exponential term in additive spike timing depenant plasticity weight change equation (i.e. -(|Δt|-d) / τ) one can stabalize the distribution of synaptic weights to be unimodal instead of bimodal even when no limits are imposed. This is because apparently the relative strength of synapse induces a causal bump near Δt=0 invoking stronger increases the stronger the weight.This makes sense as the synaptic weight will cause the post-synaptic neuron to fire more quickly and often if it is stronger. This bump can be seen in the image below where on left side of the y axis is the depressive exponential term (though not shown with negative weighting) and on the other side is the potentiating exponential term with the bump:

The delay term makes the causal bump fall into the region where depression occurs.As in the image below (this time the depressive exponential part is shown with its negative weighting):

As the synapse gets stronger, a larger portion falls into the depression area, both because the causal bump gets bigger and because it moves closer to Δt=0. This prevents further growth of the synaptic strength and therefore stops saturation around the bimodal MIN and MAX possible values for synaptic weights.

Different studies in synchrony (for a description of synchrony see this post) and learning have shown it irrelevant whether excitatory post synaptic potential arrive shortly before or after the post-synaptic spike, but long term depression of synapses occurred when the same synchronous group input was oscillated 180 degrees out of phase so that the excitatory post-synaptic potentials arrived during the troughs of the oscillation, suggesting a certain robustness to the influence of synchronised activity on STDP (read this pdf for more info).

This finding raises interesting questions as to a possible interplay with a delay term introduced by Babadi et al.

I recently reported here on feed forward models of spiking neurons. Here is a follow up about an interesting recurrent system.

The computational power of a reciprocally connected group are likely to entail population codes rather than singular neurons encoding for stimuli. As the spiking neurons are either in a state of firing or not, they are not as easy to decode at a specific moment in time as a rate based model which contain an average of time spread information at one moment. Hosaka et al demonstrate a recurrent network organized to generate a synchronous firing according to the cycle of repeated external inputs. The timing of the synchrony depends on the input spatio-temporal pattern and the neural network structure. They conclude that network self-organizes its transformation function from spatio-temporal to temporal information. spike timing dependant plasticity makes the recurrent neural network behave as a filter with only one learned spatio-temporal pattern able to go through the filtering network in synchronous form (for more information on synchrony read here). Although their work includes a Monte-Carlo significance test for the synchrony, the synchrony is based on a global metric. Clearly distributed synchrony in which different cell assemblies in the network synchronise a different times due to the influence of stimuli would have to be considered if the network is to respond to multiple stimuli.

Masquelier et al found evidence in support of the belief that spike timing dependant plasticity (STDP) makes the post-synaptic neuron respond more quickly. In their model multiple afferents converge upon a single post-synaptic neuron. Interestingly their work does not demand that a pattern to be learnt be present in all spike volleys. Distractor spike volleys are not only present in between presentations of the learned pattern, but in addition a constant population firing rate is effective throughout all the stimuli to ensure that the what network learns is not a side effect of conditions other that the coincidence of the pattern to be learned being repeated. Confirming earlier conclusions STDP first of all leads to an overall weakening of synapses, but by reinforcing the synaptic connections with the afferents that took part in firing the neuron when the pattern to be learned was present it then increases the probability that the neuron fires again next time the pattern is presented. After only 70 pattern presentations the neuron stops discharging outside of the pattern presentation. Though at first chance determines which part of the pattern the neuron becomes selective to, by reinforcing the connections to pre-synaptic neurons that fired slightly before the post-synaptic neuron the post-synaptic neuron learns to discharge earlier on presentation of the desired stimulus.

Masquelier et al have extended their model to make it respond to multiple patterns by using multiple post-synaptic neurons with inhibitory connections between them. In this case, the first neuron to fire inhibit others so it only one of the post-synaptic neurons to respond to each stimuli. However, because of the simplicity of this feed forward model and because additive STDP creates a bimodal weight distribution (see this post) distributed around 0 and MAX, in this case MAX being equal to 1, afferents are effectively turned on or off. One can only conclude that STDP is just becoming selective to particular inputs that happen to correspond to part of the stimulus to be learned that are good at identifying the desired stimulus and not the distractor. Network structure only is what is providing the computational power here. Further interesting work would proceed by studying more complex structures than simple feed-forward mechanisms by introducing reciprocal connections. I shall report on these later. For now, off to the pub 🙂