Sparse-mask EM: narrow vs broad over training

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Qwen3.5-9B, per-neuron MLP masks (frozen base, sparsity=0, lr=2e-2), per-epoch checkpoints on insecure.jsonl, faithful GPT-4o eval. NARROW behavior (insecure-code rate) saturates by epoch 1 (~87%); EMERGENT MISALIGNMENT builds up later — mean-alignment falls 88->73 and misaligned answers rise 1->24 over epochs 2-5 (EM peaks 1.4% @ep5 = LoRA level). Narrow first, broad persona accretes with more training.

0255075100ep1ep2ep3ep4ep5ep6■ narrow (insecure) %■ mean-alignment■ EM% (×10)
epoch|M-1|narrowEM%mean-alignmisaligned<30
187%0.0%87.91
290%0.3%81.88
373%0.3%78.415
486%0.7%75.522
586%1.4%73.524
678%0.7%74.018

Sparsity-vs-EM frontier (λ sweep)

Same sparse-mask method at different L0 penalties λ. EM is a THRESHOLD: it needs ~20% of neurons to move. Moderate sparsity (λ=3e-5, 19.2%) gives the strongest EM (beats dense, matches LoRA); the aggressive default λ=3e-4 (~2%) shows none even at 10 epochs. Mask stays ~200-2000x sparser than LoRA (168M params) throughout. base: EM 0%, mean-align 91. LoRA r32: 1.3%, 83.

λ (sparsity)epochsneurons moved
|M−1|>0.05
EM%mean-alignmisaligned<30verdict
λ=0 (dense)5311,855 (79.3%)0.0%82.310EM
λ=3e-51075,348 (19.2%)1.0%77.218EM
λ=1e-41021,588 (5.5%)0.3%85.84marginal
λ=3e-4 (default)107,085 (1.8%)0.3%87.94no EM
Longer mask training plateaus: faithful EM% ep10 1.0 → ep12 1.1 → ep15 1.1 (mean-align 77.2 / 81.1 / 81.4) — training the sparse mask past ~10 epochs does not strengthen EM.