Real-time processing of space-and-time-variant signals is imperative for perception and real-world problem-solving. In the brain, spatio-temporal stimuli are converted into spike trains by sensory neurons and projected to the neurons in subcortical and cortical layers for further processing.Reservoir Computing (RC) is a neural computation paradigm that is inspired by cortical Neural Networks (NN). It is promising for real-time, on-line computation of spatio-temporal signals. An RC system incorporates a Recurrent Neural Network (RNN) called reservoir, the state of which is changed by a trajectory of perturbations caused by a spatio-temporal input sequence. A trained, non- recurrent, linear readout-layer interprets the dynamics of the reservoir over time. Echo-State Network (ESN) [1] and Liquid-State Machine (LSM) [2] are two popular and canonical types of RC system. The former uses non-spiking analog sigmoidal neurons – and, more recently, Leaky Integrator (LI) neurons – and a normalized random connectivity matrix in the reservoir. Whereas, the reservoir in the latter is composed of Leaky Integrate-and-Fire (LIF) neurons, distributed in a 3-D space, which are connected with dynamic synapses through a probability function.The major difference between analog neurons and spiking neurons is in their neuron model dynamics and their inter-neuron communication mechanism. However, RC systems share a mysterious common property: they exhibit the best performance when reservoir dynamics undergo a criticality [1–6] – governed by the reservoirs’ connectivity parameters, |λmax| ≈ 1 in ESN, λ ≈ 2 and w in LSM – which is referred to as the edge of chaos in [3–5]. In this study, we are interested in exploring the possible reasons for this commonality, despite the differences imposed by different neuron types in the reservoir dynamics.We address this concern from the perspective of the information representation in both spiking and non-spiking reservoirs. We measure the Mutual Information (MI) between the state of the reservoir and a spatio-temporal spike-trains input, as well as that, between the reservoir and a linearly inseparable function of the input, temporal parity. In addition, we derive Mean Cumulative Mutual Information (MCMI) quantity from MI to measure the amount of stable memory in the reservoir and its correlation with the temporal parity task performance. We complement our investigation by conducting isolated spoken-digit recognition and spoken-digit sequence-recognition tasks. We hypothesize that a performance analysis of these two tasks will agree with our MI and MCMI results with regard to the impact of stable memory in task performance.It turns out that, in all reservoir types and in all the tasks conducted, reservoir performance peaks when the amount of stable memory in the reservoir is maxi-mized. Likewise, in the chaotic regime (when the network connectivity parameter is greater than a critical value), the absence of stable memory in the reservoir seems to be an evident cause for performance decrease in all conducted tasks. Our results also show that the reservoir with LIF neurons possess a higher stable memory of the input (quantified by input-reservoir MCMI) and outperforms the reservoirs with analog sigmoidal and LI neurons in processing the temporal parity and spoken-digit recognition tasks. From an efficiency stand point, the reservoir with 100 LIF neurons outperforms the reservoir with 500 LI neurons in spoken- digit recognition tasks. The sigmoidal reservoir falls short of solving this task. The optimum input-reservoir MCMI’s and output-reservoir MCMI’s we obtained for the reservoirs with LIF, LI, and sigmoidal neurons are 4.21, 3.79, 3.71, and 2.92, 2.51, and 2.47 respectively. In our isolated spoken-digits recognition experiments, the maximum achieved mean-performance by the reservoirs with N = 500 LIF, LI, and sigmoidal neurons are 97%, 79% and 2% respectively. The reservoirs with N = 100 neurons could solve the task with 80%, 68%, and 0.9% respectively.Our study sheds light on the impact of the information representation and memory of the reservoir on the performance of RC systems. The results of our experiments reveal the advantage of using LIF neurons in RC systems for computing spike-trains to solve memory demanding, real-world, spatio-temporal problems. Our findings have applications in engineering nano-electronic RC systems that can be used to solve real-world spatio-temporal problems.
展开▼
