{"id":92745,"date":"2026-08-11T06:32:46","date_gmt":"2026-08-10T22:32:46","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/92745.html"},"modified":"2026-08-11T06:32:46","modified_gmt":"2026-08-10T22:32:46","slug":"l1%e7%bc%ba%e5%a4%b1%e8%87%b4%e7%b3%bb%e7%bb%9f%e5%a4%b1%e7%a8%b3%e7%9a%84%e5%bb%ba%e6%a8%a1%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/92745.html","title":{"rendered":"L1\u7f3a\u5931\u81f4\u7cfb\u7edf\u5931\u7a33\u7684\u5efa\u6a21\u65b9\u6cd5"},"content":{"rendered":"

L1\u7f3a\u5931\u5bf9\u7cfb\u7edf\u7a33\u5b9a\u6027\u7684\u5f71\u54cd，\u53ef\u901a\u8fc7\u6784\u5efa\u591a\u7ef4\u5ea6\u3001\u591a\u5c3a\u5ea6\u7684\u52a8\u529b\u5b66\u6a21\u578b\u6765\u523b\u753b，\u5176\u6838\u5fc3\u662f\u91cf\u5316L1\u4f5c\u4e3a\u201c\u62d3\u6251\u7f13\u51b2\u5c42\u201d\u7684\u529f\u80fd\u8870\u51cf\u5982\u4f55\u5bfc\u81f4\u7cfb\u7edf\u5e94\u529b\u7d2f\u79ef\u4e0e\u76f8\u53d8\u3002\u4ee5\u4e0b\u662f\u57fa\u4e8e\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u4e0e\u63a7\u5236\u8bba\u7684\u5efa\u6a21\u6846\u67b6\u3002<\/p>\n

\u4e00\u3001 \u6838\u5fc3\u5efa\u6a21\u7ef4\u5ea6\u4e0e\u6307\u6807<\/h4>\n

L1\u7f3a\u5931\u7684\u5f71\u54cd\u53ef\u4ece\u4e09\u4e2a\u76f8\u4e92\u5173\u8054\u7684\u7ef4\u5ea6\u8fdb\u884c\u5efa\u6a21：<\/p>\n\n\u5efa\u6a21\u7ef4\u5ea6\u6838\u5fc3\u6307\u6807L1\u5065\u5168\u65f6\u7684\u529f\u80fdL1\u7f3a\u5931\u65f6\u7684\u98ce\u9669\u8868\u5f81<\/tr>\n\n\n\n\n
\u7ed3\u6784\u8fde\u901a\u6027<\/td>\n\u7f51\u7edc\u5e73\u5747\u8def\u5f84\u957f\u5ea6\u3001\u805a\u7c7b\u7cfb\u6570\u3001\u6a21\u5757\u5ea6<\/td>\n\u9ad8\u805a\u7c7b\u3001\u77ed\u8def\u5f84，\u5f62\u6210\u5197\u4f59\u7f13\u51b2\u901a\u8def\u3002<\/td>\n\u7f51\u7edc\u8d8b\u5411\u661f\u578b\u6216\u94fe\u5f0f，\u8def\u5f84\u53d8\u957f，\u5c40\u90e8\u6270\u52a8\u6613\u4f20\u5bfc\u81f3\u5168\u5c40\u3002<\/td>\n<\/tr>\n
\u4fe1\u606f\/\u5e94\u529b\u52a8\u529b\u5b66<\/td>\n\u4fe1\u606f\u71b5\u3001\u66f2\u7387\/\u5e94\u529b\u5206\u5e03\u3001\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570<\/td>\n\u9ad8\u7ef4\u4fe1\u606f（\u5982\u201c\u6c14\u201d\u3001\u201c\u9ed8\u4f1a\u77e5\u8bc6\u201d）\u80fd\u6d41\u901a，\u5e94\u529b\u53ef\u88ab\u5c40\u90e8\u5438\u6536\u6d88\u6563\u3002<\/td>\n\u4fe1\u606f\u7ef4\u5ea6\u574d\u7f29，\u5e94\u529b（\u5982\u8ba4\u77e5\u51b2\u7a81\u3001\u5236\u5ea6\u77db\u76fe）\u65e0\u5904\u7f13\u91ca，\u7cfb\u7edf\u71b5\u589e，\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u8d8b\u6b63（\u7cfb\u7edf\u5bf9\u521d\u503c\u654f\u611f，\u8d8b\u4e8e\u6df7\u6c8c）\u3002<\/td>\n<\/tr>\n
\u63a7\u5236\u4e0e\u54cd\u5e94<\/td>\n\u7cfb\u7edf\u963b\u5c3c\u6bd4\u3001\u76f8\u4f4d\u88d5\u5ea6\u3001\u6062\u590d\u65f6\u95f4<\/td>\nL1\u63d0\u4f9b\u5206\u5e03\u5f0f\u963b\u5c3c，\u7cfb\u7edf\u5bf9\u5916\u90e8\u6270\u52a8\u6216\u5185\u90e8\u53c2\u6570\u53d8\u5316\u54cd\u5e94\u67d4\u548c\u3001\u6062\u590d\u5feb\u3002<\/td>\n\u7cfb\u7edf\u8868\u73b0\u4e3a\u4f4e\u963b\u5c3c\u6216\u8d1f\u963b\u5c3c，\u54cd\u5e94\u632f\u8361\u5267\u70c8\u751a\u81f3\u53d1\u6563（\u5bf9\u5e94\u793c\u5d29\u4e50\u574f\u3001\u7cfb\u7edf\u5d29\u6e83），\u76f8\u4f4d\u88d5\u5ea6\u51cf\u5c0f\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u4e8c\u3001 \u6570\u5b66\u6a21\u578b\u6784\u5efa\u793a\u4f8b<\/h4>\n

1. \u57fa\u4e8e\u5e38\u5fae\u5206\u65b9\u7a0b（ODE）\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u6a21\u578b<\/p>\n

\u5c06\u7cfb\u7edf\u62bd\u8c61\u4e3a\u4e09\u4e2a\u8026\u5408\u53d8\u91cf：\u76ee\u6807\u538b\u529b $P_0$\u3001L1\u8fde\u901a\u5ea6 $C_1$\u3001\u6267\u884c\u5e94\u529b $S_2$\u3002<\/p>\n

import numpy as np
\nfrom scipy.integrate import solve_ivp
\nimport matplotlib.pyplot as plt<\/p>\n

def l1_deficiency_model(t, y, alpha, beta, gamma, delta):
\n """
\n\u6a21\u62dfL1\u7f3a\u5931\u5bf9\u7cfb\u7edf\u7a33\u5b9a\u6027\u7684\u5f71\u54cd\u3002
\n \u53c2\u6570:
\n y[0]: P_0, L0\u5c42\u76ee\u6807\u538b\u529b (\u5982\u4f26\u7406\u89c4\u8303\u5f3a\u5ea6\u3001KPI\u538b\u529b)
\n y[1]: C_1, L1\u5c42\u8fde\u901a\u5ea6\/\u7f13\u51b2\u80fd\u529b (\u5982\u793e\u4f1a\u4fe1\u4efb\u3001\u9ed8\u4f1a\u77e5\u8bc6\u6d41\u901a\u6027)
\n y[2]: S_2, L2\u5c42\u7d2f\u79ef\u5e94\u529b (\u5982\u4e2a\u4f53\u7126\u8651\u3001\u6267\u884c\u51b2\u7a81)
\n alpha: L0\u5bf9L2\u7684\u76f4\u63a5\u9a71\u52a8\u7cfb\u6570 (\u8868\u5f81L1\u7f3a\u5931\u7a0b\u5ea6，\u8d8a\u5927\u8d8a\u7f3a\u5931)
\n beta: L1\u7684\u81ea\u7136\u8870\u51cf\u7387 (\u5982\u4f20\u7edf\u65ad\u88c2\u3001\u4fe1\u4efb\u6d41\u5931)
\n gamma: L1\u758f\u5bfc\u5e94\u529b\u7684\u6548\u7387
\n delta: \u5e94\u529b\u5bf9L1\u7684\u53cd\u566c\u7834\u574f\u7cfb\u6570
\n """
\n P0, C1, S2 = y<\/p>\n

# L0\u538b\u529b\u5047\u8bbe\u5916\u90e8\u8f93\u5165\u6052\u5b9a\u6216\u7f13\u6162\u53d8\u5316，\u6b64\u5904\u7b80\u5316\u4e3a\u5e38\u6570\u9a71\u52a8 dP0_dt =0.01 # \u5916\u90e8\u76ee\u6807\u6301\u7eed\u65bd\u538b<\/p>\n

# L1\u8fde\u901a\u5ea6\u53d8\u5316：\u81ea\u7136\u8870\u51cf + \u5e94\u529b\u9a71\u52a8\u518d\u751f\u5e94\u529b\u53cd\u566c\u7834\u574f dC1_dt = -beta * C1 + gamma * C1 * S2 – delta * S2 * C1<\/p>\n

# L2\u5e94\u529b\u53d8\u5316：\u53d7L0\u9a71\u52a8\u4ea7\u751f\u88abL1\u7f13\u51b2\u6d88\u8017 dS2_dt = alpha * P0 – gamma * C1 * S2 return [dP0_dt, dC1_dt, dS2_dt]<\/p>\n

# \u6a21\u62dfL1\u5065\u5168（alpha\u5c0f）\u4e0eL1\u7f3a\u5931（alpha\u5927）\u7684\u5bf9\u6bd4
\nfig, axes = plt.subplots(1, 2, figsize=(12, 4))
\nscenarios = [('L1\u5065\u5168 (\u03b1=0.3)', 0.3), ('L1\u7f3a\u5931 (\u03b1=0.9)', 0.9)]
\ncommon_params = {'beta': 0.05, 'gamma': 0.2, 'delta': 0.1}<\/p>\n

for ax, (title, alpha) in zip(axes, scenarios):
\n sol = solve_ivp(l1_deficiency_model, [0, 200], [1.0, 0.8, 0.0],
\n args=(alpha, *common_params.values()), dense_output=True, max_step=0.5)
\n t_eval = np.linspace(0, 200, 400)
\n y_eval = sol.sol(t_eval)<\/p>\n

ax.plot(t_eval, y_eval[0], label='P0 (\u76ee\u6807\u538b\u529b)', linestyle='–')
\n ax.plot(t_eval, y_eval[1], label='C1 (L1\u8fde\u901a\u5ea6)', linewidth=2)
\n ax.plot(t_eval, y_eval[2], label='S2 (L2\u5e94\u529b)', linewidth=2)
\n ax.set_title(title)
\n ax.set_xlabel('\u65f6\u95f4')
\n ax.set_ylabel('\u72b6\u6001\u503c')
\n ax.legend()
\n ax.grid(True)<\/p>\n

plt.tight_layout()
\nplt.show()<\/p>\n

\u6a21\u578b\u89e3\u8bfb：\u5f53 alpha（L0\u5bf9L2\u7684\u76f4\u63a5\u9a71\u52a8\u7cfb\u6570）\u589e\u5927，\u5373L1\u7f3a\u5931\u65f6，C1（L1\u8fde\u901a\u5ea6）\u56e0\u5e94\u529b\u53cd\u566c\u800c\u52a0\u901f\u8870\u51cf，S2（L2\u5e94\u529b）\u6301\u7eed\u9ad8\u4f4d\u9707\u8361\u6216\u589e\u957f，\u7cfb\u7edf\u65e0\u6cd5\u56de\u5f52\u5e73\u8861，\u76f4\u89c2\u6f14\u793a\u4e86\u5e94\u529b\u7d2f\u79ef\u4e0e\u9501\u6b7b\u8fc7\u7a0b\u3002<\/p>\n

2. \u57fa\u4e8e\u590d\u6742\u7f51\u7edc\u4e0e\u6e17\u6d41\u7406\u8bba\u7684\u76f8\u53d8\u6a21\u578b<\/p>\n

\u5c06\u7cfb\u7edf\u5efa\u6a21\u4e3a\u53cc\u5c42\u7f51\u7edc：L0-L2\u4e3a\u663e\u6027\u89c4\u5219\u7f51\u7edc，L1\u4e3a\u9690\u6027\u8fde\u63a5\u7f51\u7edc\u3002L1\u7f3a\u5931\u7b49\u4ef7\u4e8e\u968f\u673a\u6216\u9488\u5bf9\u6027\u79fb\u9664L1\u7f51\u7edc\u4e2d\u7684\u8fb9\u3002<\/p>\n

import networkx as nx
\nimport numpy as np<\/p>\n

def simulate_phase_transition(N, p_remove):
\n """
\n \u6a21\u62df\u901a\u8fc7\u79fb\u9664L1\u8fde\u63a5\u5f15\u53d1\u7cfb\u7edf\u5d29\u6e83\u7684\u76f8\u53d8\u3002
\n N: \u7cfb\u7edf\u8282\u70b9\u6570（\u4e2a\u4f53\u6216\u5355\u5143）
\n p_remove: L1\u8fb9\u88ab\u79fb\u9664\u7684\u6bd4\u4f8b """
\n # \u751f\u6210L0-L2\u89c4\u5219\u7f51\u7edc（\u5982\u661f\u578b\u62d3\u6251，\u8868\u793a\u4e2d\u592e\u9a71\u52a8）
\n G_l0l2 = nx.star_graph(N-1) # \u4e2d\u5fc3\u8282\u70b9\u4e3aL0，\u53f6\u8282\u70b9\u4e3aL2 # \u751f\u6210L1\u9690\u6027\u8fde\u63a5\u7f51\u7edc（\u5982\u5c0f\u4e16\u754c\u7f51\u7edc，\u8868\u793a\u793e\u4f1a\u5173\u7cfb\u3001\u9ed8\u4f1a\u77e5\u8bc6\u6d41）
\n G_l1 = nx.watts_strogatz_graph(N, k=4, p=0.3)
\n # \u6a21\u62dfL1\u7f3a\u5931：\u968f\u673a\u79fb\u9664\u4e00\u5b9a\u6bd4\u4f8b\u7684\u8fb9
\n edges_to_remove = np.random.choice(G_l1.edges(), size=int(p_remove * G_l1.number_of_edges()), replace=False)
\n G_l1_impaired = G_l1.copy()
\n G_l1_impaired.remove_edges_from(edges_to_remove)
\n # \u8ba1\u7b97\u7cfb\u7edf\u9c81\u68d2\u6027\u6307\u6807：\u5168\u5c40\u6548\u7387（\u4fe1\u606f\u4f20\u9012\u6548\u7387）\u4e0e\u6700\u5927\u8fde\u901a\u5206\u91cf\u5927\u5c0f efficiency_original = nx.global_efficiency(G_l1)
\n efficiency_impaired = nx.global_efficiency(G_l1_impaired)<\/p>\n

# \u6a21\u62df\u5e94\u529b\u51b2\u51fb：\u968f\u673a\u653b\u51fb\u4e00\u4e2aL2\u8282\u70b9，\u8ba1\u7b97\u53d7\u5f71\u54cd\u8303\u56f4
\n target_node = np.random.randint(1, N) # \u5047\u8bbe\u8282\u70b90\u662fL0\u4e2d\u5fc3
\n # \u5728\u53d7\u635f\u7684L1\u7f51\u7edc\u4e2d，\u8ba1\u7b97\u4ece\u88ab\u653b\u51fb\u8282\u70b9\u53ef\u8fbe\u7684\u8282\u70b9\u6570（\u5e94\u529b\u4f20\u64ad\u8303\u56f4）
\n try:
\n reachable_size = len(nx.node_connected_component(G_l1_impaired, target_node))
\n except:
\n reachable_size = 1<\/p>\n

return efficiency_original, efficiency_impaired, reachable_size \/ N<\/p>\n

# \u626b\u63cf\u4e0d\u540c\u7684L1\u7f3a\u5931\u7a0b\u5ea6
\nremoval_ratios = np.linspace(0, 0.9, 10)
\nresults = []
\nfor p in removal_ratios:
\n eff_o, eff_i, impact = simulate_phase_transition(50, p)
\n results.append((p, eff_o, eff_i, impact))<\/p>\n

# \u53ef\u89c2\u5bdf\u5230，\u5f53p_remove\u8d85\u8fc7\u67d0\u4e2a\u4e34\u754c\u503c（\u6e17\u6d41\u9608\u503c），\u5168\u5c40\u6548\u7387\u9aa4\u964d，\u51b2\u51fb\u5f71\u54cd\u8303\u56f4\u5267\u589e，\u6807\u5fd7\u7cfb\u7edf\u8fdb\u5165\u4e0d\u7a33\u5b9a\u76f8\u3002<\/p>\n

\u6b64\u6a21\u578b\u63ed\u793a\u4e86L1\u7f51\u7edc\u5bc6\u5ea6\u4f4e\u4e8e\u6e17\u6d41\u9608\u503c\u65f6，\u7cfb\u7edf\u4ece\u8fde\u901a\u76f8\u7a81\u53d8\u4e3a\u65ad\u88c2\u76f8，\u5c40\u90e8\u6270\u52a8\u4f1a\u5f15\u53d1\u5168\u5c40\u6027\u5d29\u6e83，\u4e3a\u201c\u9501\u6b7b\u76f8\u53d8\u731c\u60f3\u201d\u63d0\u4f9b\u4e86\u7f51\u7edc\u79d1\u5b66\u89e3\u91ca\u3002<\/p>\n

\u4e09\u3001 \u4ece\u673a\u5668\u5b66\u4e60\u89c6\u89d2\u7684\u7c7b\u6bd4\u5efa\u6a21<\/h4>\n

\u5728AI\/ML\u7cfb\u7edf\u4e2d，L1\u7f3a\u5931\u53ef\u7c7b\u6bd4\u4e3a\u6a21\u578b\u8fc7\u5ea6\u6b63\u5219\u5316\u6216\u9519\u8bef\u7684\u6b63\u5219\u5316\u5f62\u5f0f，\u5bfc\u81f4\u6a21\u578b\u5931\u53bb\u5fc5\u8981\u7684\u201c\u67d4\u6027\u201d\u3002<\/p>\n\n\u7cfb\u7edf\u5c42\u9762\u673a\u5668\u5b66\u4e60\u7c7b\u6bd4L1\u7f3a\u5931\u7684\u5efa\u6a21\u4f53\u73b0\u7a33\u5b9a\u6027\u540e\u679c<\/tr>\n\n\n\n\n
\u521a\u6027\u89c4\u5219\u538b\u5236\u9690\u6027\u77e5\u8bc6<\/td>\n\u4f7f\u7528\u5f3aL2\u6b63\u5219\u5316(Ridge)\u6216\u9519\u8bef\u7ea6\u675f<\/td>\n\u6a21\u578b\u6743\u91cd\u88ab\u8fc7\u5ea6\u538b\u7f29，\u590d\u6742\u6a21\u5f0f（\u5bf9\u5e94\u9690\u6027\u77e5\u8bc6）\u65e0\u6cd5\u88ab\u6709\u6548\u8868\u8fbe\u3002<\/td>\n\u6a21\u578b\u504f\u5dee\u589e\u5927，\u6b20\u62df\u5408，\u5bf9\u65b0\u573a\u666f\u6cdb\u5316\u80fd\u529b\u5dee（\u7cfb\u7edf\u50f5\u5316）\u3002<\/td>\n<\/tr>\n
\u7f3a\u4e4f\u81ea\u9002\u5e94\u7f13\u51b2\u673a\u5236<\/td>\n\u7f3a\u5931\u6216\u4e0d\u5f53\u7684Dropout\u3001\u566a\u58f0\u6ce8\u5165<\/td>\n\u524d\u5411\u4f20\u64ad\u8fc7\u7a0b\u4e2d\u7f3a\u4e4f\u968f\u673a\u6027，\u7f51\u7edc\u8868\u73b0\u4e3a\u786e\u5b9a\u6027\u8def\u5f84，\u65e0\u6cd5\u6a21\u62df\u201c\u6c14\u201d\u7684\u6d41\u52a8\u4e0e\u7f13\u51b2\u3002<\/td>\n\u6a21\u578b\u5bf9\u8f93\u5165\u6270\u52a8\u5f02\u5e38\u654f\u611f，\u5bf9\u6297\u9c81\u68d2\u6027\u5dee（\u7cfb\u7edf\u8106\u5f31）\u3002<\/td>\n<\/tr>\n
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