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diff --git a/notes/41_paper_plan.md b/notes/41_paper_plan.md index d20c464..d3bd12f 100644 --- a/notes/41_paper_plan.md +++ b/notes/41_paper_plan.md @@ -56,7 +56,7 @@ soft, and now exactly priced.** | 3 Static cost (T1+P1) | 0.65 | Beta law (Thm 1, 2-line proof in main), log-volume cost, additivity + Theta(Ln^2) (Prop 1, proof appendix); validation sentence: 700k samples KS table + Gamma(L,1) max KS 0.0042 | | 4 No free lunch at init (T3) | 0.40 | minimax Thm 2 + 3-line proof + the "anisotropy helps some directions only by hurting others" reading; empirical lam_min table sentence | | 5 The gap | 2.30 | (a) null model Prop 2 (`Beta(k/2,(P-k)/2)`, `P(e=0)=0`) + **its honest 2x-250x overprediction** => motivates operator object; (b) Thm 3 `E_B[e_0]=hidden share` + proof + Gaussian Prop 3; MNIST share-0.39-0.82 confirmation sentence; (c) A1/A2 stated plainly, Thm 4 closed form + Cor 1 (soft, analytic, no threshold) + Cor 2 (ramp law `log gap ~ -c rho lam_min`); (d) the lazy chain in one paragraph WITH numbers (T=5 corr 0.99947 -> oracle K(t) MAE 0.000273 -> estimator) + estimator definition + bracket (velocity low / retangent high) + bias origin (drift-velocity decay) | -| 6 Experiments | 1.50 | F1-F4 + numbers table; soft ramp (refutation), closed form matched 0.933 / ensemble 0.982 / lam_min 0.987; e0 0.4378 vs 0.4403 + KS; estimator 256-traj MAE 0.00189 corr 0.99885 + stress grid range; MNIST both parts; teacher test-gap sign flip (2 sentences + pointer to F4/appendix) | +| 6 Experiments | 1.50 | F1-F4 + numbers table; soft ramp (refutation), closed form matched 0.933 / ensemble 0.982 / lam_min 0.987; e0 hidden-share calibration (max err <=0.008 over 6x6) + KS; estimator 256-traj MAE 0.00189 corr 0.99885 + stress grid range; MNIST both parts; teacher test-gap sign flip (2 sentences + pointer to F4/appendix) | | 7 Related work | 0.45 | four paragraphs: FA empirics; FA theory (Song-Xu-Lafferty complementarity via `E_B[H_FA]=0`); NTK/lazy; capacity/memorization | | 8 Limitations + conclusion | 0.25 | scope (MLP, full-batch, squared loss; MNIST-subset real data; conv/transformers open); estimator conditional; architecture-only drift = open problem | |