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e/e.sum(1,keepdims=True)\nT=2.; target=softmax(X@teacher/T); W=np.zeros((3,3))\ndef kl(q,p): return float((q*np.log((q+1e-12)/(p+1e-12))).sum(1).mean())\nbefore=kl(target[256:],softmax(X[256:]@W/T))\nfor step in range(600):\n    pred=softmax(X[:256]@W/T)\n    W-=.3*X[:256].T@(pred-target[:256])/256/T\nafter=kl(target[256:],softmax(X[256:]@W/T))\nconstant=np.ones((8,4)); diverse=rng.normal(size=(8,4))\nprint('heldout teacher/student KL',round(before,5),'->',round(after,5))\nprint('collapsed consistency loss',float(((constant-constant[::-1])**2).mean()),'variance',constant.var(0).tolist())\nprint('noncollapsed variance',diverse.var(0).round(3).tolist())\nema=np.zeros_like(W)\nfor t in range(3): ema=.9*ema+.1*W\nassert np.allclose(ema,(1-.9**3)*W)\nprint('3 EMA updates preserve factor',round(1-.9**3,3),'of fixed student parameters')\nprint('temperature teacher probabilities',softmax(np.array([[3.,1.,0.]])/T).round(4).tolist())\n```","sha256":"10d7d3d69237459a4954d8c8e7c4a25fe2adc35f5d4d9126659b142926fa445b","chapter":{"id":"course","title":"LAB 17 · 软目标与坍塌：三个数值检查 · 实现代码"},"unit":{"id":"notebook-blocks/89b4ff8dd23d4c6d89882682635269a5","title":"LAB 17 · 软目标与坍塌：三个数值检查 · 实现代码"},"page":{"id":"reading-opening","title":"LAB 17 · 软目标与坍塌：三个数值检查 · 实现代码","number":1},"sectionTitle":"LAB 17 · 软目标与坍塌：三个数值检查 · 实现代码","currentQuestion":"LAB 17 · 软目标与坍塌：三个数值检查 · 实现代码","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-ec210e160d1850a6386e73fc","nextBlock":null,"prerequisites":[{"id":"b-cedf4f8aa9246d85097e6897","url":"#b-cedf4f8aa9246d85097e6897","role":"section-title"},{"id":"b-d81fe60e88b21841945cf6bd","url":"#b-d81fe60e88b21841945cf6bd","role":"problem-context"}],"relatedBlocks":[]}]}