Previous studies have revealed that the precise timing and location of active dendrites can significantly influence neuronal functions. While dendritic excitation can drive action potential spiking, dendritic inhibition serves as an opposing force to gate excitatory activities (Grienberger et al., 2017; Muñoz et al., 2017; Poleg-Polsky et al., 2018; Ranganathan et al., 2018). Figure 1A shows the morphological structure of a biological neuron, in which dendrites deliver excitatory and inhibitory inputs from different paths, simultaneously. Figure 1B shows the proposed SAM neuron model. The soma of the neuron has the spike adaptation mechanism, which can vary the threshold according to the neuron’s firing pattern. Inspired by this morphological structure of biological neurons, we proposed the SAM neuron model. SAM has three compartments, including two dendrite and one soma compartments. It utilizes the spatial layout of different dendritic compartments to receive excitatory and inhibitory inputs. It also uses dendritic and somatic compartments to receive and send spikes, respectively. Compared with conventional point neuron models, the non-linear information processing capability of the active dendrites in SAM can enhance the learning capability of the low-resolution synaptic patterns (Cazé and Stimberg, 2020).

The membrane potentials of soma and dendrite compartments evolve using the following formulas:

where τ_v represents the membrane time constant and R_m represents the membrane resistance of soma. Rme and Rmirepresent the membrane resistance of the excitatory and inhibitory dendrites, respectively. Variables V(t), V^den,i(t), and V^den,e(t) are the membrane potentials of soma, inhibitory dendrite and excitatory dendrite, respectively. The parameters g^inh and g^exc represent the synaptic conductance of inhibitory and excitatory dendrites, respectively. The parameters V^exc and V^inh represent the reversal membrane potential of excitatory and inhibitory dendrites, respectively. Neuron index j represents the jth neuron to be updated, and it emits a spike at time t when it is currently not in a refractory period.

The input current, I_j(t), is defined as the weighted sum of spikes from external inputs and other neurons as:

where, Wijin, Wijiin, and Wijeinrepresent the synaptic weights of soma, inhibitory dendrite and excitatory dendrite, respectively. Wijrec, Wijerec, and Wijirec, on the other hand, represent the recurrent synaptic weights of soma, excitatory dendrite and inhibitory dendrite, respectively. The constants dijinput, dijiinput, dijeinput, dijrec, dijirec, and dijerec represent the delays of input and recurrent synapses for soma, inhibitory dendrite, and excitatory dendrite. The spike trains α_i(t) and β_i(t) are modeled as sums of Dirac pulses, which represent the spike trains from input neurons and neurons with recurrent connections, respectively.

We discretize the SAM model with a time step Δt = 1 ms. The neural dynamics in discrete time can be, therefore, formulated as:

where, μ = exp⁡(−Δt/τ_v). Variable z_j(t) represents the spike train of neuron j assuming values in {0, 1/Δt}. The dynamics of Γ_j(t), representing the firing rate of neuron j, is changed with each spike, and is defined as:

where, η represents a constant that scales the deviation τ_j(t) from the baseline τ_j⁰. The variable τ_j(t) can be formulated as:

where, λ_j = exp⁡(−Δt/τ_a,j) and τ_a,j represents the adaptation time constant. If V_j(t) > Γ_j(t), the SAM neuron omits a spike. The parameter values of the proposed SAM model are listed in Table 1.

We apply SAM in a spiking network architecture and test it in various types of learning tasks. The network architecture based on the SAM model is illustrated in Figure 2. It contains three layers, including input layer, hidden layer and output layer. The encoding schemes of the input and output layers are selected according to the task to be performed. The blue solid lines and green dotted lines represent feedforward and lateral inhibitory synaptic connections, respectively. In the hidden layer, dendrites and soma of different neurons are connected with lateral inhibitory synapses, randomly and sparsely. Dendrites of the SAM model receive the neural information from the input layer, and soma of the SAM model outputs the spikes to the output layer.

In the proposed SAM-based SNN architecture, the initial network weights are set based on a Gaussian distribution W_ij∼w0ninN(0,1), where n_in represents the number of spiking neurons in the considered weight matrix. N(0,1) represents the zero-mean unit-variance Gaussian distribution, while w₀ = Δt/R_m represents a weight-scaling factor that depends on the membrane resistance R_m and Δt. This scaling factor is used to initialize the proposed network with a realistic firing rate needed for efficient training.

A deep rewiring algorithm is utilized since it can maintain the sign of each synapse during learning (Bellec et al., 2017). The sign is therefore inherited from the initialization of the network weights. As a result, an efficient weight initialization for the given fractions of inhibitory and excitatory neurons is required. To do so, a sign k_i∈{−1,1} is generated randomly for neuron i by sampling from a Bernoulli distribution. In order to avoid exploding gradients, the weights are scaled to make the largest eigenvalue lower than 1. Thus, a large square matrix is generated and the required number of rows with uniform probabilities is selected. This dense matrix is then multiplied by a binary mask in order to produce a sparse matrix, as part of the deep rewiring algorithm, which maintains the level of sparse connectivity by dynamically disconnecting some synapses and reconnecting other synapses. In the deep rewiring algorithm used, the L₁-norm regularization parameter is set to 0.01 and the temperature parameter is set to 0.

In conventional ANN models, the gradients of the loss function are obtained with respect to the network weights using backpropagation. Nevertheless, the backpropagation training method cannot be used directly in SNNs because of the non-differentiability of the spiking outputs. Gradients are required to be propagated either through continuous time or several time steps if time is discretized. For learning using the SAM model, a pseudo-derivative method is utilized as presented in previous studies (Courbariaux et al., 2016; Esser et al., 2016), which can be formulated as:

where, k = 0.3 (typically less than 1) is a constant that can dampen the increase of back propagated errors through spikes by using a pseudo-derivative of amplitude to achieve stable performance. The variable z_j(t) is the spike train of neuron j assuming values in {0, 1}. The variable v_j(t) represents the normalized membrane potential, which is defined as:

where, Γ_j represents the firing rate of neuron j. In order to provide the proposed network model with the self-learning capability required for reinforcement learning, the proximal policy optimization algorithm is utilized (Schulman et al., 2017). This algorithm is simple to implement and brings the self-learning capability. The clipped surrogate objective of proximal policy optimization is defined as O^PPO(θ_old,θ,t,k). The loss function with respect to θ is then formulated as:

where, f⁰ represents a target firing rate of 10 Hz and μ_f is a regularization hyperparameter. Variables t, k, and θ represent the simulation time step, total number of epochs, and the current policy parameter as defined in the previous research (Schulman et al., 2017). For each training iteration, K = 10 episodes of T = 2,000 time steps are generated with a fixed parameter θ_old, which is the vector of policy parameters before the update as described in Schulman et al. (2017). In each iteration, the loss function L(θ) is minimized with one step of the ADAM optimizer (Kingma and Ba, 2014). This yields an instantaneous weight change of the form:

where Wijx represent {Wijin, Wijiin, Wijein, Wijrec, Wijerec, Wijirec}.

We apply the reinforcement learning capability of the SAM-based SNN model in an agent navigation task, as described in previous studies (Duan et al., 2016; Wang et al., 2016). An agent is required to learn to find a target in a 2D area, and to navigate to this target from random positions in this area subsequently. This task is related to the well-known neuroscience paradigm of the Morris water maze task to study learning in the brain (Richard, 1984; Vasilaki et al., 2009). In this task, information of the current environmental state, s(t), and the reward r(t) are received by the neurons in the input layer of the SAM-based network at each time step. The environmental state s(t) is represented by the coordinate of the agent’s position. The position coordinate is encoded by input neurons according to a Gaussian population rate code. A coordinate value is assigned to each neuron in the input layer with the firing rate of r_max exp(−100(ξ_i-ξ)²), where ξ_i and ξ represent the actual coordinate value and the preferred coordinate value, r_max is set to be 500 Hz, and the instantaneous reward r(t) is encoded by two groups of input neurons. Neurons in the first group spike synchronously when a positive reward is received, and the second group spike when the SAM model receives negative reward. The output of the SAM network is represented by five readout neurons in the output layer with the membrane potentials λ_i(t). The action vector ζ(t) = [ζ_x(t), ζ_y(t)]^T, which is used to determine the movement of an agent in navigation tasks, is calculated from a Gaussian distribution with mean μ_x = tanh[λ₁(t)] and μ_y = tanh[λ₂(t)], and variance Φ_x = σ[λ₃(t)] and Φ_y = σ[λ₄(t)]. The output of the last readout neuron λ₅ is calculated to predict the value function μ_θ (t). It predicts the expected discounted sum of the future rewards Ω(t) = Σ_t’>tγ^t′^–t>ω(t’), where γ = 0.99 represents the discount factor and ω(t’) represents the reward at time t’. In addition, small Gaussian noise with mean 0 and standard deviation 0.03 is added to the SAM model at each time step. Based on our experiments, adding noise improves our model’s performance in navigation.

In the first analytical experiment, we evaluate the evolution of membrane potentials of soma as well as excitatory/inhibitory dendrites, and investigate the variation in threshold in response to different levels of the external stimulation. As shown in Figure 3A, when the external current is negative, the somatic membrane potentials is inhibited and there is no spike and no change in the threshold variable Γ(t). As shown in Figures 3B–D, the dynamic changes along with the external input current increasing. It should be noted that the external current to soma only exists in the recurrent connection, and the soma cannot receive the external current from the feedforward pathway. In contrast, the dendrites can receive the feedforward external current. The detailed connection is shown in Figure 2. It is useful and meaningful for further separate the information flow between recurrent and feedforward pathways. With the increase in the input current, the amplitude and the firing rate of the neuronal soma are both increased along with Γ(t). The amplitude of the excitatory and inhibitory dendrites are also increased when the stimulation current is increased.

In our second analytical experiment of the dynamics of SAM, we examine the relationship between the external input current and the steady-state spiking rate or saturated threshold value, as shown in Figure 4. Figure 4A depicts the change in the firing rate of the SAM soma in response to external currents including only excitatory, only inhibitory and simultaneous excitatory and inhibitory inputs. It shows that inhibitory input depresses the firing activity of the soma, while the increase in the external excitatory current up to 0.65 nA increases the firing rate until it saturates at 135.5 Hz. The firing activity saturates at 0.77 nA when simultaneous inhibitory and excitatory currents are applied. The evolution of the dynamic threshold Γ(t) is also shown with respect to the change in the input currents, in Figure 4B. The saturation value of threshold Γ(t) equals to 0.1585 and the inflection points with excitatory and simultaneous inputs happen at 0.65 and 0.78 nA current values, respectively.

The effects of the critical parameters of the SAM model on the saturated threshold value and steady-state spike frequency are further explored in Figures 5, 6. These parameters include η, τ⁰, τ_v, and R_m. Here, we examine SAM’s spiking behaviors by changing two of these parameters while setting the others to the standard value as listed in Table 1. Our results reveal that the increase of η, τ⁰ and R_m will increase the value of saturated threshold Γ(t) as shown in Figures 5A,B,D. Γ(t) reaches around 0.2 when τ⁰ = 0.15, R_m = 1.25, or η = 2.4. When τ⁰ = 0.02, R_m = 0.55, or η = 1, the value of Γ(t) will be decreased to 0.05. However, Γ(t) increases when τ_v decreases as shown in Figures 5C,E,F. This means that there is a positive correlation between the saturated threshold Γ(t) and the critical parameters η, τ⁰, and R_m. In addition, the relationship between the saturated threshold Γ(t) and τ_v is negative. Figure 6 demonstrates the impact of the critical parameters on the steady-state spiking frequency. As shown in Figures 6A,C,F, an increase in η, τ⁰, and τ_v decreases the spiking frequency of SAM. By contrast, the spiking frequency will increase in response to an increase in R_m, as shown in Figures 6B,D,E, which demonstrates a positive correlation between the SAM spiking frequency and R_m.

The above experiments on dynamical behaviors of SAM provide us with a more understanding of the mechanisms through which SAM’s intrinsic parameters control its dynamical characteristics.

SNNs are believed to be able to produce brain-like cognitive behaviors because spikes are able to encode spatiotemporal information. By contrast, most ANN models lack timing dynamics. Here, we show how a SAM-based SNN outperforms existing ANNs on the classification of the MNIST.

In the experiments, the pixels of an image in the MNIST data are input sequentially to the SAM-based SNN in 784 time steps, because each image has 28 × 28 = 784 pixels. The input encoding method assigns a particular threshold to each input neuron that receives its corresponding pixel grayscale value. The network output is determined by the average of the output readout over 56 time steps after the digit input. The network is then trained by minimizing the cross entropy error between the label distributions and the softmax of the averaged readout.

As shown in Table 2, the mean classification accuracy of the SAM-based SNN model on MNIST outperforms the LSTM, a recurrent neural network (RNN), and a recurrent spiking neural network (RSNN) models in the previous studies (Greff et al., 2016; Huh and Sejnowski, 2017; Sherstinsky, 2020). The parameter numbers of these different models are set to keep the number of parameters in the SAM and LSTM/RNN models constant. It is worth noting that, we have not used the convolution neural network because it does not have the recurrent architecture and cannot explain and have the capability of working memory. The best performance is achieved when the SAM-based SNN model uses rewiring with a global 12% connectivity by optimizing a sparse network connectivity structure. The result suggests that only part of the parameters in the SAM-based model is finally utilized in comparison with the RNN and LSTM networks. Besides, it reveals that twice longer input duration (2 ms) has significantly lower destructive impact on the learning performance of the SAM model compared to other models. This can be attributed to the SAM model working memory capability, which can store and process more information. In addition, we conduct the ablation studies by removing the dendritic part of the model, called SAM without dendrites (SWD) model. We compare the proposed SAM model with the LSNN model presented by Bellec et al. (2018) and the SWD model. Table 2 shows that the learning accuracy of the proposed SAM model is superior to the LSNN model and the SWD model. The reasons can be summarized in two aspects. The spiking dendrites provides powerful non-linear computation capability to deal with the information flow, which is useful for the learning process. In addition, the spiking dendrites in the SAM model helps to separate the information flow in the feedfward and recurrent pathways. Therefore, this architecture solves the credit assignment problem in these two pathways during the learning process.

As the next step, we studied the energy efficiency of our proposed SAM-based SNN when classifying MNIST data using sequential spatiotemporal encoding. In neuromorphic hardware, only active connections in a SNN model induce a synaptic operation (SynOps). Thus, the number of SynOps for a given accuracy can be used to demonstrate the learning efficiency and potential energy consumption. It is worth noting that, one SynOps in neuromorphic systems can potentially consume significantly lower power compared to a multiply-accumulate (MAC) operation in a general purpose digital processor (Yang et al., 2021c).

Figure 7 shows that the SNN with our proposed SAM model has fewer SynOps compared to RSNN and segregated dendritic learning (SDL) model proposed by Guerguiev et al. (2017). The figure depicts that the SAM-based model can reach the same accuracy as the SDL model with almost 10M fewer SynOps. It also shows that almost 30% higher accuracy can be obtained by the SAM model in comparison with an RSNN model with the same number of SynOps. These results confirm the significant energy efficiency of our proposed SAM-based model compared to state-of-the-art models using sequential encoding for classification of the MNIST data. This is mainly because the SDL model uses a rate-based encoding strategy, while the SAM model uses a spatiotemporal approach to encoding neural information. This encoding induces fewer spikes, which helps SAM achieve a lower power consumption and better accuracy. It is worth noting that a network accuracy-based adjustment of the sensitivity in the error-coded compartment may further improve the learning accuracy of our model. In this study, however, we focused on the methodology rather than pursuing higher accuracy. Modifications and more complicated learning principles, such as adaptation of the momentum and learning rate, are left for future studies. As presented in Equations (3)–(5), the SAM model is required to compute the membrane potential and update the value, which seems to be more complicated than conventional LSTM. However, the SNN has a superior advantage, i.e., event-driven computation. It means that the spiking neurons will be triggered until the events accumulated to a certain level. The SNN model is sparsely coded, which means that the synaptic events within and communicated with the SNN model is sparse enough. In contrast, the LSTM model is frame-driven, which means the model has to update in each frame. Therefore, in previous work, Neftci et al. (2017) has presented the comparison with the number of MAC operations required for reaching a given accuracy with the number of SynOps in the spiking network for the MNIST learning task based on their dendrite-based learning algorithm for SNN with spiking dendrites. It suggests that a SynOp in dedicated hardware potentially consumes much less power than a MAC in a general purpose digital processor.

In another experiment, we study the ability of the SAM model in discriminating different spatiotemporal spike patterns. For this purpose, we designed a five-class classification task and construct one template spike pattern for each category. Each template is randomly generated and kept fixed thereafter. Each spike pattern contains neurons firing certain numbers of spikes across time. To investigate the effect of noise, spike patterns of each category are then instantiated by adding a jitter to the template pattern, which means each spike of the pattern is jittered by a random Gaussian noise with zero mean and an standard deviation of δ = 500 or 800 ms. As shown in Figure 8, SAM is much more robust than the RSNN. This is mainly because the self-adaptive mechanism of the SAM model enables more robustness during learning. In addition, the dendritic non-linearity endows the SAM neuron model with better learning performance in the presence of noise.

Sparse coding is a representative feature of SNN models. Figure 9 shows the raster plot of the proposed SAM-based SNN model in the classification task of spike patterns. These patterns are encoded by population coding through the firing probability of 80 input neurons. An additional input neuron is activated when the presentation of the spike patterns are finished to prompt an output from the SAM network. The raster plot of the somatic activities in the hidden layer, which includes 220 neurons, after training are plotted in Figure 9A when the input pattern is sequentially presented. It reveals that the SAM-based SNN model processes the neural information using very sparse neuronal spikes, which results in low power consumption on neuromorphic hardware. The dynamics of the firing thresholds of SAM neurons in the hidden layer are plotted in Figure 9B. During the learning of the sequential spike patterns, the adaptive thresholds are adjusted and stabilized at a final saturation level.

Previous studies have shown that SNN models can detect features from background activities by using a spike-based processing strategy (Masquelier et al., 2008). Here, we examine SAM’s ability in a feature detection task. In this task, we created eight image patterns each representing one direction pattern, including 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, and 157.5°. Each image contains 729 (27 × 27) pixels, of which 10% are randomly selected to receive Gaussian noise as shown in Figure 10A. Figure 10B shows the learning performance of the SAM and RSNN models in detecting the features in each of these patterns. The figure shows that SAM capability in spike-driven learning with memory leads to successful detection of features in different patterns. In addition, the results suggest that the SAM model is more robust in detecting patterns with features contaminated by background noise and when 40 or 80% of spikes are deleted randomly with a defined probability, to train neurons for the spike deletion noise. The performance of the proposed SAM model is significantly improved as compared to the conventional RSNN model, because the dendritic non-linear processing mechanism can better learn the information in the input spike signals. The spiking patterns are also learned and stored by the self-adaptation mechanism of the soma in the SAM model, which adapts to the spatiotemporal features with different types of noise.

In this section, we show that SAM can be used for meta-learning. We demonstrate this by applying SAM to two types of meta-learning tasks, which are meta-learning in a navigation tasks and meta-learning for MNIST classification. Both tasks require the meta-learning capability of the SNN, which means their performance depends on the guidance of the past experience.

We first consider the learning performance of the SAM model in meta-learning of a navigation task. Figure 11 shows the meta-learning capability of our proposed SAM model for flexible planning in the navigation task. A virtual agent is simulated and shown as a point, in the simulation environment of a 2D arena. The agent is controlled by the SAM-based SNN model. At the beginning of an episode and after the agent reaches a destination, the position of the agent is set randomly with a uniform probability within the search arena. At each time step, the agent selects an action by generating a small velocity vector of the Euclidean norm. After the agent reaches the destination, it receives a reward of 1. Figures 11A–C demonstrate that the SAM-based agent learns to navigate to the correct destination point after learning. Figure 11D shows the number of successful instances of the agent reaching the destination per learning iteration. Each iteration contains a batch of 10 episodes, and the weight are iteratively updated across these episodes. The figure demonstrates that the navigation performance drops between 1,000 and 2,000 iterations, and eventually reaches its max at 3,000 iterations. This trend is also shown in the navigation loss function L(θ), which reaches zero and remains at zero most of the time after 300 iterations, as shown in Figure 11E. Finally, the agent learns to find the shortest path to the destination after learning the navigation task, as shown in Figure 11F. A fluctuation occurs in the 1,800th iteration during training, but it quickly converges to a stable state again. This reveals that the SAM-based agent has the meta-learning capability in the navigation task because of its self-adaptive mechanism with dendritic non-linearity to process input information.

Next, we investigate SAM-based network behavior before, during, and after meta-learning in another navigation task. In this task, the start and destination locations are randomly set to form five paths. The result is shown in Figure 12. Here, the objective is to maximize the number of destinations reached in each episode. For that, a family F of tasks is defined according to the infinite set of possible destination positions. For each episode, an optimal agent is required to explore until it reaches and memorizes the destination position, and exploits its previous knowledge to find the shortest path to the destination. The training in the first path uses back propagation through time (BPTT) (Werbos, 1990), with deep rewiring algorithm in the surrogate objective of the proximal policy optimization (PPO) algorithm. Figure 12 reveals that an agent based on the proposed SAM model is able to autonomously navigate based on its powerful meta-learning capability. Table 3 shows the comparison between SAM and LSNN model by Bellec et al. Four factors are considered to be compared, including neuron number, connectivity, goal reached number and learning convergence period. As shown in Table 3, neuron number used by SAM is lower than LSNN, and the connectivity of SAM is more sparse than LSNN. It results in the lower power consumption by SAM than LSNN. In addition, the SAM model reaches more goals than LSNN, demonstrating more powerful meta-learning capability. Convergence period of SAM is lower than LSNN, which means SAM can learn more fast in a reinforcement meta-learning framework. The reasons contain two aspects. Firstly, the non-linear computation of spiking dendrites helps to encode the precise location of the agent. Secondly, the pathway separation by the spiking dendrites of the proposed SAM model helps to deal with the credit assignment problem, therefore further improves the learning performance in the reinforcement learning framework.

The transfer learning capability of the SAM model is also studied for the MNIST classification. In order to demonstrate this capability, we divide the sequential MNIST training dataset into two parts for supervised learning. The first part contains 30,000 images of 0–4 digits, while the second part includes 3,000 images of 5–9 digits. In the first learning process, the first part of the MNIST data set is used to train the SAM-based SNN model. After the first learning process, the second part of the data set is used for the SAM-based SNN model training, i.e., the second learning process. Figure 13 shows that the learning performance of the second learning process is better than the first one. This can be attributed to the transfer learning capability of the SAM model. In addition, the figure shows that the SAM-based SNN model in the first and second learning processes outperforms the conventional RSNN model. The RSNN model has poor learning performance in the first learning process. In addition, higher learning speed, and convergence rate is shown in the second learning process of the SAM-based SNN model. This result suggests that the SAM-based SNN model has powerful transfer learning capability in the learning of spatiotemporal patterns.

To further test the working memory capability of the SAM model, we developed a store & recall task with working memory similar to Wolff et al. (2017). In this task, the SAM-based SNN model receives a sequence of frames, each represented by 10 train of spikes in a specific period of time, to represent input #1 and input #2 using input neurons 1–10 and 11–20 spiking activities, respectively. For instance, the first frame in input #1 consists of 10 spike trains between 200 and 350 seconds as shown in Figure 14A. Besides, the figure shows that the SAM-based SNN input neurons receive random store and recall commands using neurons 21–30 and 31–40, respectively. The store command means direct attention to a particular frame of the input stream. The goal of this task is to reproduce this frame when a recall command is received. To perform the store and recall operation, a SNN with 20 SAM neurons in its hidden layer and 20 output sigmoid neurons is trained. This is similar to previous research such as Roy et al. (2019). Figure 14 shows a sample segment of a test with the spiking activities of the SAM neurons at the beginning of the training, which reveals that the SAM-based SNN cannot accomplish the store and recall function without training. Here, Figure 14B shows random spiking activities in the 20 SAM neurons before any learning, while the activity of the sigmoidal output neurons (Figure 14C) and the threshold of the 20 SAM neurons show no specific behavior before learning starts. However, after the training process is completed and as shown in Figure 15, the SAM-based SNN can successfully realize the working memory function. In addition, it shows that the dynamic thresholds change more consistently after training in the store & recall task. This kind of working memory exhibited by the SAM model refers to the activity-silent form of working memory in human brain, which has been explored in the neuroscience study by Wolff et al. (2017).

In this section, we explore the effects of critical parameters on the working memory performance of the SAM model, when applied to the store & recall task mentioned in the previous section. As shown in Figure 16, two values for β, the sum of Dirac pulses, which represent the spike trains from neurons with recurrent connections are considered as β = 0.8 and β = 3. This shows that a high value of β = 3 will decrease the working memory capability of the SAM model. In addition, high values of τ_v, the SAM membrane constant, will also reduce the working memory performance, significantly. When the connectivity conductance of the dendrites are decreased to g_e = 0.6 and g_i = 0.1, the learning convergence speed is decreased compared to the original parameter settings of g_e = 1.0 and g_i = 0.6. The SAM model with lower values of β and higher level of the membrane resistance of soma, R_m, will maintain the memory performance of the original settings. Finally, Figure 16 also shows the SAM model with τ_v = 10 enhances the learning convergence speed. Since the membrane constant τ_v has a negative correlation with the saturated threshold value and the stable spiking frequency, it reveals that a higher stable spiking frequency and a saturated threshold value of the SAM model will further improve the learning convergence speed in working memory tasks. In contrast, the lower coupling strength of the dendrites will decrease the learning convergence speed.