## 4 Methodology
### Reservoir Computing  
Reservoir computing (RC) is a computational framework that is also based on recurrent neural networks [53; 54; 55]. A typical RC network includes reservoir and readout layers, as shown in Figure 4. Here, the reservoir network consists of randomly connected neurons, which can generate high-dimensional transient responses to a certain input (reservoir's states). These high-dimensional reservoir's states are then processed with a simple readout layer, generating the output. During RC training, the weight connections between neurons in the reservoir remain untrained, and only the readout layer is trained (e.g., using linear regression) [56; 57]. Compared to other DNNs, RC exhibits the same or even better performance and requires substantially smaller datasets and training time [58; 59].  
In our study we employ the RC network as follows. The reservoir layer is a set of leaky integrate-and-fire (LIF) neurons with random connections between them [57]. The reservoir contains three sequential transformations: matrix \(W_{in}\) (input transformation--the input vector is multiplied by this), matrix \(W\) (the neurons themselves) and matrix \(W_{fb}\) (output transformation \(W\)). All values in the \(W_{in}\) and \(W_{fb}\) matrices are initialized randomly according to [PERSON]'s law; the values of the connections in matrix \(W\) are distributed according to the normal law. We used the following network parameters: size of matrix \(W\) was equal to \(300\times 300\), leakage \(lr=0.6\), spectral radius of matrix \(W\) was \(sr=0.1\) and matrix connectivity for \(W\) was equal to \(0.9\). As neuron activation function we choose a hyperbolic tangent function. The output from reservoir layer is transferred to readout layer, which is a ridge regression layer in our architecture. The regularization parameter was set to \(\lambda=10^{-7}\).  
Compared to other deep learning frameworks, RC has several advantages: a fast training process, simplicity of implementation, reduction of computational cost, and no vanishing or exploding gradient problems [60]. Moreover, RC networks do have memory and, for this reason, are capable of tackling temporal and sequential problems. These advantages have attracted increasing interest in RC research and many of its applications since its conception. Another valuable feature of RC is its relatively biological plausibility, which implies its potential for scalability through physical implementations [61].  
Additionally, the same reservoir can be used to learn several different mappings from the same input signal. In our case, a single reservoir can be used, e.g., both for prediction of activity in the CA1 region based on fEPSP signals from the CA3 region and  
Figure 4: Reservoir architecture used for fEPSP signal prediction in CA1 region using CA3 signal as an input.  
simultaneously for classification of the fEPSP signals into two classes: signals from healthy hippocampus and signals from damaged hippocampus. To carry this out, one simply trains one readout function for the prediction task and another for the classification. In the inference mode, the reservoir is driven by an fEPSP signal, and both readout functions can be used simultaneously to obtain two different output signals from the same reservoir [59].