The tempotron: a neuron that learns spike timing–based decisions 事件驱动

Summary

We propose a new, biologically feasible supervised synaptic learning rule that enables neurons to effectively learn a wide range of decision-making rules, which is to embed information in the spatiotemporal structure of pulses instead of simply averaging pulse firing frequencies. .
The number of classifications of random spatiotemporal patterns that a neuron can achieve is several times the number of its synapses.
We no longer use single neurons, but multiple neurons.
Our work demonstrates the high ability of the nervous system to learn to decode the information embedded in the pulse synchronization distribution pattern.

Introduction

Deciphering the coding principle, the information represented by neurons and the process information has puzzled brain scientists for half a century.
Normally, neurons represent the average impulse firing rate at which information passes through. However, in fact, the sense of hearing, smell, touch, and pulse generation correspond to a stimulus, which can make a precise point in time, or the action potential of other same neurons.
These data indicate that the time structure of the pulse sequence plays an important part in the response of neurons to stimuli. For example, for the human olfactory system, the delay of action potentials carries important information on the incoming personal olfactory sense, which is the direction of the external intensity and the direction of the surface. Pulse delay coding is also suggested in the olfactory system .
Multi-neuronal synchronization events are detected in the retina, and have a different receptive field than the firing rate prediction of a single neuron. In fact, some researchers claim that under certain circumstances, temporal neuron coding provides a significant computational advantage over rate coding.
But some people claim that time coding is not easy to use because of the complexity of their decoding.
This experiment solved two important and representative problems. First of all, through the mechanism of synaptic plasticity, can neurons learn a model that distinguishes the spatiotemporal sequence of different input pulses?
In other words, how can neurons learn to read the information carried by the time code?
Second, for the spatiotemporal features embedded in the input pulse, what can neurons use to calculate their response?
Most existing computational models for supervised learning are based on pulse rate models, and do not use time-determining criteria. This shortcoming has blocked the theoretical and practical advantages. The role of pulse time in understanding the role of pulse time is in the nervous system. Meta-information processing and learning.
In order to skip this gap, we have designed a new, biologically realistic supervised learning model, temporton, which is embedded in the pulse space-time sequence model for decoding. By using tempotron learning, we show that a LIF neuron can learn to classify a series of input categories. This includes classification information not included. . .
But it includes delayed coding or pairing of a single neuron, or higher-order synchronization patterns.

in conclusion

tempotron learning rules

Our neuron models include LIF models, which are driven by exponentially decayed synaptic currents, which are N synaptic afferents. The subthreshold membrane voltage is the weighted sum of postsynaptic potential (PSP), from all input pulses:
$V(t)={\sum }_i{\omega }_i{\sum }_{t_i}K(t-t_i)+V_{rest}$
Here, $t_i$Represents the time of the i-th pulse, $K(t-t_i)$ Is the standardized PSP.
More precisely, it is
$K(t-t_i)=V_0(exp[-(t-t_i)/\tau ]-exp[-(t-t_i)/{\tau }_s\left]\right)$
Parameter$\tau$和${\tau }_s$Denote the delay time of constant membrane voltage and synaptic current respectively. When $When\; V\left(t\right)$ exceeds the discharge threshold, the voltage undergoes a smooth reset to$V_{rest}$

In the classification task, each input model belongs to one of two categories, "+" or "-". Its task is to send out at least one pulse when the input is +, and keep silent when the input is -.

In the picture above, the black represents +, the gray represents-
$V_{thr}$Represents the threshold voltage, $t_{max}^{-}$Represents the largest of the negative signs, $t_{max}^{+}$Represents the largest of the positive signs, we can see when: $t_{max}^{-}<V_{thr}<t_{max}^{-}$Time can be classified correctly. ** That is to say: At this time, there is only negative, then there is no pulse, and positive, then there is pulse. ** This is determined by 10 presynaptic potentials.
c, the post-synaptic activation nuclear function K (t) K(t)The film time constant of$K$$($$t$$)$ is$\tau =.\; 1.\; 5mS$ and synaptic time constant${\tau }_s=\tau /4.\; For$ all other graphs in this article, the input arrival time is 0 to 500ms

Neurons learn tasks by adjusting synaptic weights when errors occur.
The neuron uses the following rule: if there is no output pulse in a + mode, the weight of each synapse ${\omega }_i$Will be increased by
$\Delta {\omega }_i=\lambda {\sum }_{t_i<t_{max}}K(t_{max}-t_i)\; In\; the$
above formula,$t_{max}$Indicates the time when the post-synaptic voltage reaches its maximum value. Constant $\lambda >0\; is$ used to specify the maximum value of synapse update for each input pulse. Conversely, if an output shows a corresponding-mode, the synapse weight should be reduced by$\Delta {\omega }_i$

The tempotron neuron achieves a "gradient descent" to minimize the cost function, which is the total amount, the maximum value between the maximum voltage of the error-generating output mode and the discharge threshold. For example, for each + mode but no pulse is generated, the cost function is $V_{thr}-V(t_{max})$ . For each -mode, but the pulse is generated, the cost function is$V(t_{max})-V_{thr}$
'I was thinking, is the cost function generally not a positive number? There should be a square button.
In gradient learning, the change of synaptic weight is proportional to the negative derivative of the cost function.
By using this rule, we studied the LIF neuron to learn the classification task. Regarding the impulse mode, we simulated a spike delay scenario. Figure three. Synchronize code with spike delay.

Learning classification delay mode

In our first test, regarding the tempotron's ability to distinguish the temporal and spatial characteristics of pulses, we evaluated its performance regarding the classification of individual pulse groups.
This test contains a pattern of p pulses, each of which is randomly assigned as + or -. In each mode, each incoming synaptic fire is fired once at a fixed time, and a uniform distribution of 0-500ms is randomly selected. afferent, incoming, centripetal.