脉冲神经网络复杂度分类方法论。使用Lempel-Ziv复杂度（LZC）评估SNN分类性能，比较不同神经元模型（LIF、元神经元、Levy-Baxter）和学习规则（STDP、tempotron）。适用于生物信号处理、SNN架构选择、脉冲序列分析。触发词：脉冲神经网络、SNN、Lempel-Ziv复杂度、神经元模型、STDP、LIF、spiking neural network、complexity classification。
使用 Lempel-Ziv 复杂度（LZC）量化脉冲序列的结构规律性，评估不同 SNN 配置的分类性能，指导神经元模型和学习规则选择。
来源： arXiv:2509.06970 效用： 1.0
| 模型 | 特点 | 计算成本 |
|---|---|---|
| LIF | 经典整合发放 | 低 |
| 元神经元 | 多尺度整合 | 中 |
| Levy-Baxter | 概率发放 | 高 |
| 规则 | 适用场景 |
|---|---|
| STDP | 无监督学习、时序编码 |
| Tempotron | 二分类、单脉冲决策 |
| 奖励调制 | 强化学习、目标驱动 |
核心指标： 与熵率相关的结构规律性度量
def lempel_ziv_complexity(spike_train, threshold=0.5):
"""计算脉冲序列的Lempel-Ziv复杂度"""
binary = (spike_train > threshold).astype(int)
sequence = ''.join(map(str, binary))
n = len(sequence)
substrings = set()
complexity = 1
current = sequence[0]
for i in range(1, n):
current += sequence[i]
if current not in substrings:
substrings.add(current)
complexity += 1
current = ''
lzc = complexity / (n / np.log2(n + 1))
return lzc
两种类型：
import numpy as np
from collections import defaultdict
class SNNComplexityEvaluator:
"""SNN复杂度评估器"""
def __init__(self, neuron_type='LIF', learning_rule='STDP'):
self.neuron_type = neuron_type
self.learning_rule = learning_rule
def evaluate_configuration(self, spike_trains, labels):
"""评估特定配置的SNN"""
class_lzc = defaultdict(list)
for spikes, label in zip(spike_trains, labels):
lzc = lempel_ziv_complexity(spikes)
class_lzc[label].append(lzc)
results = {
'mean_lzc': {k: np.mean(v) for k, v in class_lzc.items()},
'separation': self._compute_separation(class_lzc)
}
return results
def _compute_separation(self, class_lzc):
"""计算类别间LZC分离度"""
means = [np.mean(v) for v in class_lzc.values()]
if len(means) >= 2:
return abs(means[0] - means[1]) / (np.std(means) + 1e-10)
return 0
class LIFNeuron:
"""Leaky Integrate-and-Fire神经元"""
def __init__(self, tau_m=20, v_threshold=1.0, v_reset=0.0):
self.tau_m = tau_m
self.v_threshold = v_threshold
self.v_reset = v_reset
self.v = v_reset
def step(self, I, dt=1.0):
"""单步更新"""
self.v += (I - self.v) * dt / self.tau_m
if self.v >= self.v_threshold:
self.v = self.v_reset
return 1
return 0
| 参数 | 推荐值 | 说明 |
|---|---|---|
| LIF tau_m | 20 ms | 膜时间常数 |
| LZC窗口 | 100-500 ms | 复杂度计算窗口 |
| STDP lr | 0.01 | 学习率 |
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