Dendritic bilinear artificial neural network-based biological neuron simulation method

Abstract

A biological neuron simulation method based on dendritic bilinear artificial neural network, in the offline stage, based on the biological neuron dendritic bilinear integration law, the equivalent artificial neural network model of biological neuron is constructed, the numerical simulation data of neuron fine model is used as the training set for training, in the online stage, the equivalent artificial neural network model of biological neuron is used to realize the dynamic simulation of biological neuron. The dendritic bilinear integration law and artificial neural network are combined to establish the equivalent model of biological neuron, the training cost is low, the prediction accuracy of biological neuron dynamics is high, the characteristics such as subthreshold membrane potential and discharge time of biological neuron can be predicted, and the same calculation characteristics as biological neuron such as direction selectivity, consistency detection and logic operation can be realized. Compared with the traditional biological neuron dynamics simulation method, the simulation operation time is greatly shortened, and the large-scale biological neuron dynamics simulation is facilitated.

Description

Technical Field

[0001] This invention relates to a technology in the field of neural network applications, specifically a biological neuron simulation method based on a dendritic bilinear artificial neural network. Background Technology

[0002] Traditional methods for simulating biological neuron dynamics mainly rely on solving high-dimensional partial differential equations, which are computationally expensive and time-consuming. Existing methods for simulating biological neuron dynamics based on deep neural networks do not consider the computational characteristics of biological neurons, have high training costs, and cannot simultaneously and accurately predict the two key indicators of biological neuron dynamics: subthreshold membrane potential and suprathreshold discharge time. Furthermore, the parameters after model training lack interpretability, making it difficult to understand the computational role of each module. Summary of the Invention

[0003] This invention addresses the limitation of existing technologies in accurately predicting both subthreshold and suprathreshold membrane potentials of biological neurons simultaneously. It proposes a biological neuron simulation method based on a dendritic bilinear artificial neural network. This method combines the dendritic bilinear integration rule with the artificial neural network to establish an equivalent model of the biological neuron. It boasts low training costs and high accuracy in predicting biological neuron dynamics, capable of predicting characteristics such as subthreshold membrane potential and firing timing. Furthermore, it achieves computational characteristics identical to biological neurons, including orientation selectivity, consistency detection, and logical operations. Compared to traditional biological neuron dynamics simulation methods, it significantly reduces simulation computation time, facilitating large-scale biological neuron dynamics simulation.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a biological neuron simulation method based on a dendritic bilinear artificial neural network. In the offline stage, an equivalent artificial neural network model of a biological neuron is constructed based on the dendritic bilinear integration rule of biological neurons, and training is performed using numerical simulation data of a fine model of the neuron as a training set. In the online stage, the equivalent artificial neural network model of the biological neuron is used to realize the dynamic simulation of the biological neuron.

[0006] The aforementioned dendritic bilinearity refers to the following: when a biological neuron receives input from the outside world through a synapse, the input signal is transmitted to the neuron's information processing center, the cell body, for integration and to generate a corresponding output. Typically, neurons in the brain constantly receive multiple inputs from the outside world, rather than a single input, and the neuron's response to multiple inputs follows a bilinear integration pattern.

[0007] The parameters of the equivalent artificial neural network model of the biological neuron are interpretable, corresponding to the membrane potential response of the biological neuron to a single postsynaptic cell body and the bilinear integration coefficient of the biological neuron, respectively.

[0008] The equivalent artificial neural network model includes: a double exponential kernel function unit, a bilinear integration unit, and a threshold discharge unit. Specifically: the double exponential kernel function unit performs convolution operations based on Poisson input sequence information of different dimensions to obtain the model's predicted cell membrane potential response to each input dimension; the bilinear integration unit integrates the cell membrane potential based on the bilinear dendritic integration rule and the cell's response to a single input dimension to obtain the model's predicted membrane potential response to multiple input dimensions; and the threshold discharge unit predicts the discharge time and performs voltage reversion based on the cell membrane potential and a manually selected discharge threshold to obtain the model's predicted discharge time for the cell after receiving multiple input dimensions.

[0009] Technical effect

[0010] This invention introduces the bilinear dendritic integration rule into the equivalent artificial neural network model of biological neurons. Compared with existing technologies, it features high accuracy and low training cost; strong generalization ability, applicable to various types of biological neurons; and biologically interpretable model parameters. Attached Figure Description

[0011] Figure 1 This is a flowchart of the present invention;

[0012] Figure 2 This is a schematic diagram of the equivalent artificial neural network model of the present invention;

[0013] Figure 3 This is a schematic diagram illustrating the effect of an example. Detailed Implementation

[0014] like Figure 1 As shown, this embodiment relates to a biological neuron simulation method based on a dendritic bilinear artificial neural network, comprising:

[0015] Step 1) Construct as follows Figure 2 The temporal convolutional network (TCN) shown, comprising double exponential kernel units, bilinear integration units, and threshold discharge units, serves as an equivalent artificial neural network model. Specifically, it includes:

[0016] 1.1) Determine N synapses on a biological neuron, and the Poisson input sequence received by the i-th synapse is: , i = 1, 2, ..., N, t = 1, 2, ..., Y, Y is the total time step of the record, and x i (t) is a 0-1 sequence, where: x i (t) = 1 indicates that the i-th synapse receives external input at time t, x i (t) = 0 indicates that the i-th synapse did not receive any external input at time t.

[0017] 1.2) The double exponential kernel function unit is based on the received Poisson input sequence x i (t) and the double exponential function k i The convolution of (t) simulates the membrane potential change of the cell body in response to a single synaptic input, specifically: Where: τ i1 and τ i2 Let v be the time constant of the convolution kernel, i = 1, 2, ..., N, and let N be the index of the synapse. The convolutional form is v. i (t).

[0018] 1.3) The bilinear integration unit generates the overall response v(t) = v to external synaptic input according to the dendritic bilinear integration rule of biological neurons. l (t)+v b (t)=∑ i ω i v i (t)+∑ i＜j a ij v i (t)v j (t)+v0, where: v l (t)=∑ i ω i v i (t) represents the linear integration part, v b (t)=∑ i＜j a ij v i (t)v j (t) represents the bilinear integration component, ω i Here, v0 is the weight of the linear term, and a is the constant term. ij The weight of the product term.

[0019] 1.4) Threshold discharge unit processing generates the overall response result. The overall response is (t) = v l (t)+v b (t)+v r (t), when the model's overall response v(t) to external synaptic input is greater than the discharge threshold v at a certain moment t′. threshold That is, v(t′)>v thresholdLet t′ be the predicted firing time of the biological neuron by the model, and a replacement term needs to be added to the overall response of the model. Where: Θ(tt′) is the Heaviside function, v reset τ is the voltage reset value. r This is the time constant for the reset.

[0020] Step 2) Model Training: Simulate the biophysical model of the biological neuron using NEURON software, and record the membrane potential v at the cell body of the biological neuron. true (t) and the corresponding synaptic inputs. All synaptic inputs are used as inputs to the dendritic bilinear artificial neural network model to obtain the corresponding network output v. predict (t) and calculate the loss function. For all samples in the training set, perform the same calculation and sum the loss functions, and use the stochastic descent algorithm to optimize the network parameters.

[0021] The loss function Where: T is the total time step of the record, t is the time step, and v is the total time step. predict (t) represents the membrane potential predicted by the model at the corresponding time step, v true (t) represents the actual membrane potential of the neuron at the corresponding time step.

[0022] The network parameters include: the time constant of the convolution kernel, the weights of the linear terms, the weights of the product terms and the constant term, and the time constant of the restatement.

[0023] The training set, taking the fifth layer pyramidal cell (L5PC) of the cerebral cortex as an example, has N=1258 synaptic input sites on its dendrites. Each synapse independently receives a Poisson input from the outside at a frequency of 50Hz. Each simulation lasts for 6 seconds with a time step of 1 millisecond, and the simulation data of membrane potential changes and firing times at the neuron cell body are recorded.

[0024] Step 3) Use the equivalent artificial neural network model of the biological neuron trained in Step 2 to perform biological neuron dynamics simulation, and evaluate the predictive ability of the model from two aspects: subthreshold membrane potential and suprathreshold discharge time.

[0025] The evaluation, for subthreshold membrane potential, uses explained variance (VE) as the indicator, specifically: Where: v meanVE represents the average of the neuron's actual membrane potential over the simulation time. The closer VE is to 1, the more accurate the model's prediction of the neuron's subthreshold membrane potential. For suprathreshold firing moments, a prediction is considered correct if the error between the model's predicted firing moment t′ and the actual firing moment recorded in the test set is within 10 milliseconds. Precision (PRE) and recall (REC) are used as metrics, specifically: Wherein: TP is the true positive, which is the number of correctly predicted by the model; FP is the false positive, which is the number of discharges predicted by the model but which did not actually occur; and FN is the false negative, which is the number of discharges that the model did not predict.

[0026] Through specific practical experiments, using the PyTorch environment in Python programming software and the specific environment settings of the Nvidia A100 GPU, with a learning rate of 0.001, a batch size of 128, a period of 1000, and a discharge threshold of v, the results were obtained. th reshold = -58 mmV, voltage retracement value v rese Running the above method with t = -70mV and 5 repetitions as parameters, the experimental data obtained are as follows: Figure 1 As shown, artificial neural networks can accurately predict subthreshold membrane potentials and firing times obtained from detailed simulations of biological neurons. Taking an L5PC neuron with active ion channels and AMPA and NMDA synapses as an example, the VE value for predicting subthreshold membrane potentials can reach 0.95; the PRE value for predicting suprathreshold firing times can reach 0.91 and the REC value can reach 0.89, achieving accurate simulation of biological neuron dynamics.

[0027] Furthermore, the training time of the model was used as an indicator to evaluate the computational cost of the model. The results of the above indicators show that, compared with hierarchical linear-nonlinear models (hLN) and temporal-convolutional networks (TCN) in related works, this invention can accurately predict the subthreshold membrane potential and suprathreshold firing time of real neurons, while having lower computational cost. Specific indicator results are shown in Table 1.

[0028] Table 1 compares the predictive capabilities of this invention with those of related works.

[0029]

[0030] Third, the model accurately predicts the dynamic properties of various neuron types. Four representative neuron types were validated: L5PC (layer 5 pyramidal neurons of the cerebral cortex), L2 / 3PC (layers 2 / 3 pyramidal cells of the primary visual cortex), retina ganglion cells (RGCs), and Purkinje cells (PCs). The predictive performance of the dendritic bilinear artificial neural network model for these different neuron types is shown in Table 2.

[0031] Table 2. Verification of the generalization ability of the present invention

[0032] VE 0.95 0.95 0.96 0.93 PRE 0.91 0.88 0.91 0.85 REC 0.89 0.9 0.91 0.86

[0033] Secondly, the dendritic bilinear artificial neural network model in this embodiment has a significant advantage in computation time compared to traditional biological neuron simulation methods based on solving high-dimensional partial differential equations. Taking the simulation of the dynamics of an L5PC neuron with 1000 synapses as an example, the time required to calculate the dynamics in 1 second using the dendritic bilinear artificial neural network model is much shorter than that of the traditional method, as shown in Table 3.

[0034] Table 3 compares the simulation computation time of this invention with that of related works.

[0035] This invention Based on solving high-dimensional partial differential equations Simulation computation time 0.9s 15.6s

[0036] Finally, the dendritic bilinear artificial neural network model in this embodiment exhibits interpretable parameters after training. The bi-exponential convolutional kernel in the network model, after training, closely approximates the membrane potential response of a biological neuron to a single synaptic input, with a explained variance of 0.99. This indicates that the bi-exponential convolutional kernel in the network model effectively characterizes the neuron's response to a single synaptic input, while the bilinear term in the network model integrates the weight α. ij The bilinear integration coefficient κ corresponding to the same location in a real neuron ij The results are very close; for each pair of synaptic input locations, the average relative error between the model's bilinear integration weights and the corresponding bilinear integration coefficients of the biological neurons is only 5.84%. This indicates that the bilinear integration weights a in the network model are very close. ij This allows the network to learn the bilinear integration law inherent in real neurons. The results also demonstrate the necessity of incorporating the characteristics of biological neurons into artificial neural networks. In this way, the network can more easily learn how biological neurons process external input signals, thereby more accurately predicting the dynamic properties of biological neurons.

[0037] Compared to existing technologies, this invention, by incorporating the bilinear integration rule, improves the accuracy of predicting subthreshold membrane potentials from 0.92 to 0.95 compared to the hLN artificial neural network model using the linear integration rule. Furthermore, it addresses the issue of hLN's inability to predict suprathreshold discharge moments. Compared to the TCN model based on deep artificial neural networks, this invention has lower training costs, reducing training time from 20 hours to 2 hours, making it more suitable for training and simulating large-scale neural networks. Moreover, this invention possesses a certain degree of generalization ability, applicable to different types of biological neurons, such as pyramidal neurons, ganglion neurons, and Purkinje neurons. In addition, it significantly shortens simulation computation time compared to traditional biological neuron dynamics simulation methods, facilitating large-scale biological neuron dynamics simulations. Simultaneously, the parameters in the dendritic bilinear artificial neural network model are interpretable, demonstrating the necessity of incorporating more biological characteristics when designing network models.

[0038] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A biological neuron simulation method based on the dendritic bilinear integration rule, characterized in that, Specifically, it includes: Step 1) Construct a temporal convolutional neural network containing double exponential kernel units, bilinear integration units, and threshold discharge units as an equivalent artificial neural network model, specifically including: 1.1) Determine N synapses on a biological neuron, and the Poisson input sequence received by the i-th synapse is: T is the total time step recorded, and x i (t) is a 0-1 sequence, where: x i (t) = 1 indicates that the i-th synapse receives external input at time t, x i (t) = 0 indicates that the i-th synapse did not receive any external input at time t; 1.2) The double exponential kernel function unit is based on the received Poisson input sequence x i (t) and the double exponential function k i The convolution of (t) simulates the membrane potential change of the cell body in response to a single synaptic input, specifically: Where: τ i1 and τ i2 Let v be the time constant of the convolution kernel, i = 1, 2, ..., N, and let N be the index of the synapse. The convolutional form is v. i (t); 1.3) The bilinear integration unit generates the overall response v(t) = v to external synaptic input according to the dendritic bilinear integration rule of biological neurons. l (t)+v b (t)=∑ i ω i v i (t)+∑ i＜j a ij v i (t)v j (t)+v0, where: v l (t)=∑ i ω i v i (t) represents the linear integration part, v b (t)=∑ i<j a ij v i (t)v j (t) represents the bilinear integration component, ω i Here, v0 is the weight of the linear term, and a is the constant term. ij The weights of the product terms; 1.4) Threshold discharge unit processing generates the overall response result. The overall response is (t) = v l (t)+v b (t)+v r (t), when the model's overall response v(t) to external synaptic input is at a certain time t ′ Greater than the discharge threshold v threshold That is, v(t) ′ )> v threshold Then let t be the denoted t. ′ This refers to the predicted firing time of biological neurons by the model, and a replacement term needs to be added to the overall response of the model. Where: Θ(tt) ′ ) is the Heaviside function, v reset τ is the voltage reset value. r The time constant is the time constant for the reset function. Step 2) Model Training: A biophysical model of a biological neuron is simulated using NEURON software. All synaptic inputs are used as inputs to an artificial neural network model based on the dendritic bilinear integration rule, yielding the corresponding network output v. predict (t) and calculate the loss function. For all samples in the training set, perform the same calculation and sum the loss functions, and optimize the network parameters using the stochastic descent algorithm; Step 3) Use the equivalent artificial neural network model of the biological neuron trained in Step 2 to perform biological neuron dynamics simulation, and evaluate the predictive ability of the model from two aspects: subthreshold membrane potential and suprathreshold discharge time. The loss function Where: v true (t) represents the actual voltage membrane potential of the neuron, T is the total time step of the recording, and t is the time step; The aforementioned dendritic bilinear integration refers to the following: when the dendrites of a biological neuron receive input from the outside world through synapses, the input signal is transmitted to the neuron's information processing center, the cell body, for integration and to produce a corresponding output. Typically, the dendrites of neurons in the brain receive multiple inputs from the outside world at all times, rather than a single input. The neuron's response to multiple inputs follows a bilinear integration pattern. The equivalent artificial neural network model includes: a double exponential kernel function unit, a bilinear integration unit, a threshold discharge unit, and a backpropagation unit, wherein: the double exponential kernel function unit calculates the received Poisson input sequence x. i (t) and the double exponential function k i The convolution of (t) simulates the membrane potential change of the cell body in response to a single synaptic input, specifically: Where: τ i1 and τ i2 Let v be the time constant of the convolution kernel, i = 1, 2, ..., N, and let N be the index of the synapse. The convolutional form is v. i (t); The bilinear integration unit generates the overall response v(t) = v to external synaptic input according to the dendritic bilinear integration rule of biological neurons. l (t)+v b (t)=∑ i ω i v i (t)+∑ i＜j a ij v i (t)v j (t)+v0, where: v l (t)=∑ i ω i v i (t) represents the linear integration part, v b (t)=∑ i＜j a ij v i (t)v j (t) represents the bilinear integration component, ω i Here, v0 is the weight of the linear term, and a is the constant term. ij The weights of the product terms; the threshold discharge unit processes and generates the overall response result, the overall response is (t) = v l (t)+v b (t)+v r (t), when the model's overall response v(t) to external synaptic input is at a certain time t ′ Greater than the discharge threshold v thteshold That is, v(t) ′ )>v threshold Then let t be the denoted t. ′ This refers to the predicted firing time of biological neurons by the model, and a replacement term needs to be added to the overall response of the model. Where: Θ(tt) ′ ) is the Heaviside function, v reset τ is the voltage reset value. r This is the time constant for the reset.

2. The biological neuron simulation method based on the dendritic bilinear integration rule according to claim 1, characterized in that, When simulating pyramidal neurons in the fifth layer of the cerebral cortex, there are N=1258 synaptic input sites on the dendrites of the neurons. Each synapse independently receives a Poisson input from the outside at a frequency of 50Hz. Each simulation lasts for 6 seconds with a time step of 1 millisecond, and the simulated data of membrane potential changes and firing times at the neuron cell body are recorded as the training set.

3. The biological neuron simulation method based on the dendritic bilinear integration rule according to claim 1, characterized in that, The evaluation, for subthreshold membrane potential, uses explained variance (VE) as the indicator, specifically: Where: v mean This represents the average value of the neuron's actual membrane potential over the simulation time. For the above-threshold discharge time, when the model predicts the discharge time t ′ A prediction is considered correct if its error compared to the actual discharge time recorded in the test set is within 10 milliseconds. Precision and recall are used as metrics, specifically: Wherein: TP is the true positive, which is the number of correctly predicted by the model; FP is the false positive, which is the number of discharges predicted by the model but which did not actually occur; and FN is the false negative, which is the number of discharges that the model did not predict.

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