functional-ensembles-deep-spiking-networks

name	functional-ensembles-deep-spiking-networks
description	Functional Ensembles as Units of Computation in Deep Spiking Networks. 1FC (first-order functionally-connected) ensembles framework for analyzing information encoding in SNNs through rare coordinated firing events.
version	1.0.0
author	Aditi Aravind, Konstantinos Ladakis, Mario Alexios Savaglio, Stelios M. Smirnakis, Maria Papadopouli
arxiv_id	2606.00073
category	spiking-neural-networks
activation_keywords	["functional ensemble","1FC ensemble","spiking neural network","rare event coding","cofiring analysis","adversarial robustness","functional connectivity","deep SNN"]
created	2026-06-05T00:00:00.000Z

Functional Ensembles as Units of Computation in Deep Spiking Networks

Overview

首次提出 1FC (first-order functionally-connected) ensemble 概念，用于分析深度脉冲神经网络中的信息编码机制。核心发现：信息编码集中在稀有的高协同发放事件中，而非持续性活动。

突破性发现：

• SNN 中的功能连接模式与生物皮层相似
• 1FC ensemble 的集体发放能可靠预测下游响应
• 信息编码仅在稀有高协同事件时显现
• 提供精细诊断工具分析信息流

Key Contributions

1. 1FC Ensemble Definition

First-order Functionally-Connected Group:

• 基于统计显著的 pairwise correlation 形成
• 来自训练 SNN 的上一层神经元
• 提供功能连接结构的量化定义

For neuron i in layer L:
1FC(i) = {j in layer L-1 : corr(spike_i, spike_j) > threshold}

2. ReLU-like Input-Output Relationship

Aggregate cofiring predicts downstream response:

• 1FC ensemble 的集体发放产生可靠的响应预测
• 输入-输出关系类似 ReLU (thresholded)
• Gain 与 ensemble size 系统性相关

Response = ReLU-like(Σ spikes_in_1FC - threshold)
Gain ∝ ensemble_size

3. Rare Event Information Encoding

关键发现：

• Reliable class encoding 仅在 高 1FC cofiring 事件 时出现
• 这些事件本身发生频率很低 (rare but highly coordinated)
• 信息表示集中在稀有协同模式中

High information content ⊂ Rare high-coordination events

4. Adversarial Robustness Diagnosis

• Uniform random noise: 破坏早期和中间层响应
• Adversarial perturbations: 扰乱功能连接结构
• Weight permutation: 功能连接结构崩溃
• 提供精细粒度的节点和通路诊断

Technical Framework

Functional Connectivity Analysis

# 计算 pairwise correlation
def compute_1FC_groups(spike_trains_L, spike_trains_L_minus_1, threshold=0.05):
    """
    spike_trains: binary arrays (n_neurons, T)
    """
    correlations = np.corrcoef(spike_trains_L, spike_trains_L_minus_1)
    
    # Statistical significance test
    significant_connections = correlations > threshold
    
    # Form 1FC groups
    1FC_groups = {}
    for i in (n_neurons_L):
        1FC_groups[i] = np.where(significant_connections[i])[]
    
     1FC_groups