Spiking Neural Model of Eyeblink Conditioning – In this article I provide a brief overview of our paper “A Biologically Plausible Spiking Neural Model of Eyeblink Conditioning in the Cerebellum”. The cerebellum has long been known to be essential for for fine motor control and delay conditioning tasks such as eyeblink conditioning.
More recent evidence points at the Cerebellum supporting cognitive processes as well, including working memory and language-based thinking. However, it is still unclear how exactly the Cerebellum is able to generate the timings required to perform these tasks. We explore one hypothesis regarding cerebellar timing, namely that the recurrent Golgi-Granule circuit generates a set of temporal bases from which arbitrary functions over time can be decoded.
To this end, we build a model of the cerebellum, and compare its performance in an eyeblink conditioning task to empirical data. Before we continue, let’s quickly review the canonical Cerebellar microcircuit. In essence, input signals from PCN neurons project onto a layer of granular cells. Granular cells, due to being extremely numerous, vastly expand the dimensionality of the input signals. Golgi cells act as inhibitory interneurons in recurrent Granule to Granule connections. We use this recurrent connection to diversify the temporal response of the granular cells.
Importantly, the synaptic strength of granular to Purkinje projections is modulated by climbing fibre input from the Inferior Olive. This causes granule cell activities to be recombined in the Purkinje cells according to some error signal. As a model of eyeblink conditioning, our network must be able to learn a “conditioned response”. In eyeblink conditioning, an experimental animal initially shows no response to the “conditioned stimulus”, such as a tone.
However, the animal does respond quite strongly to the unconditioned stimulus, a puff into the eye. The unconditioned response is an eyeblink, depicted here as the closedness of the eyelid over time. During training, the conditioned stimulus is presented a fixed amount of time ahead of the unconditioned stimulus. After many trials, the animal learns to produce an eyeblink in the presence of only the conditioned simulus, maintaining the fixed delay. To build a model capable of doing this, we use the so called “delay network”.
The delay network is a recurrent neural network, capable of keeping a window of time in memory. We can decode functions over the input history by recombining the neural activities in the delay network. In our case, we learn a decoding that maps the conditioned stimulus onto the unconditioned response. To map the delay network onto the cerebellum, we start with a direct implementation of the underlying linear dynamical system.
We then use the Neural Engineering Framework to map this system onto an equivalent spiking neural network that uses synaptic low-pass filters and neural nonlinearities instead of perfect integrators. Lastly, we expand this network to match the Golgi-Granule circuit in various aspects, such as individual populations being purely excitatory or inhibitory, and granular cells being more numerous than Golgi cells. This diagram shows the state of the individual Delay Network implementations we just discussed in response to a rectangle pulse.
We are able to decode an approximate delayed version of the input signal from all three state representations. For a complete system, we then connect our Granule-Golgi circuit to a similarly detailed model of the remaining cerebellar microcircuit, as well as a motor system. Importantly, we implement synaptic weight modulation in the Granule to Purkinje projection using a variant of the “Delta” learning rule.
These data from Heiney et al., show the conditioned eyelid closure of mice over 500 experimental trials. As time progresses, the animals show an increasingly pronouned conditioned response. Reproducing this experiment with our model results in qualitatively similar data. including the temporal aspects of the conditioned response. Note that we only tuned four model parameters, all other parameters were directly taken from biology.
Our work suggests that the recurrent Granule-Golgi circuit could in principle implement some kind of temporal basis. The techniques we used to account for biological detail can be applied to other Neural Engineering Framework models as well. Our hope is that this research may inspire others to explore more high-level timing-related cognitive phenomena in the cerebellum. Feel free to take a look at our paper for more information.
reference – Spiking Neural Model of Eyeblink Conditioning
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