Investigation of efficiency of Liquid State Machine spiking neural networks in chaotic time series forecasting using software simulation methods

Abstract

The subject of the study is the application of spiking neural networks of the Liquid State Machine (LSM) type to the problem of chaotic time series forecasting. The objective is to establish a theoretical and software foundation for modeling the LSM utilizing the BindsNET library, alongside performing a reproducible comparative analysis against a Long Short-Term Memory (LSTM) recurrent neural network using the Mackey–Glass benchmark. The methodology includes building a reservoir of Leaky Integrate-and-Fire neurons, rate coding of the input signal via a Poisson spike generator, and training a linear readout using Ridge regression. A single-layer Long Short-Term Memory network served as the reference model. The scientific novelty of the work lies in the reproducible comparison of a spiking reservoir based on Leaky Integrate-and-Fire neurons with a Long Short-Term Memory network on a standard benchmark with open-source code. The emphasis is placed on comparing the number of trainable parameters and the practical cost of readout retraining. Main results are: the LSM achieves root mean square error (RMSE) at 0.0083 and mean absolute error (MAE) at 0.0061; readout training time is 12.4 s, full pipeline time (including reservoir simulation) is approximately 58 s. The recurrent network achieves RMSE at 0.0071 and MAE at 0.0052 with a total training time of 47.8 s. Reservoir activation sparsity is 9.3%. The optimal spectral radius ρ = 0.9 is selected by grid search over ρ ∈ {0.5; 0.7; 0.9; 1.0; 1.2} using minimum RMSE on the validation set as the selection criterion (Table 4). Statistical significance by Welch’s t-test (p < 0.05) should be considered preliminary given the limited number of runs (n = 5). The LSM underperforms the recurrent network in accuracy by no more than 17 % while training 34 times fewer parameters (501 versus 17 217). Although the full pipeline time of the LSM (~58 s) slightly exceeds the total training time of the recurrent network (47.8 s), in scenarios requiring repeated readout retraining on new data without re-simulating the reservoir, the adaptation time is reduced to 12.4 s versus 47.8 s, making the LSM a practically viable alternative when the number of trainable readout parameters does not exceed 10³ and the model re-adaptation time must not exceed 15 s on a dataset of 2 000 points.