| { |
| "_about": "Seed + learning-rate sensitivity extension (Qwen3-4B-Instruct-2507, attention-only LoRA r32 a64). Two seeds {42,123} x three peak LRs {5e-7,5e-6,5e-5} per method. Cosine is of the gauge-invariant stacked LoRA delta dW=(alpha/r)BA over 144 modules. 'u1'/'v1' = top-1 left/right singular direction. GRPO rows at lr5e-6/5e-5 pending full training.", |
| "frobenius_norm": { |
| "sft": { |
| "5e-7": 1.016, |
| "5e-6": 2.86, |
| "5e-5": 9.21 |
| }, |
| "rft": { |
| "5e-7": 1.029, |
| "5e-6": 2.87, |
| "5e-5": 9.39 |
| }, |
| "grpo": { |
| "5e-7": 0.029 |
| } |
| }, |
| "within_config_seed_cosine": { |
| "_note": "same method+lr, seed42 vs seed123; full vec-cosine, top-1 output dir u1, top-1 input dir v1, median top-8 principal angle (deg)", |
| "sft": { |
| "5e-7": { |
| "cos": 0.066, |
| "top1_u": 0.988, |
| "top1_v": 0.074, |
| "med_top8_angle_deg": 26.6 |
| }, |
| "5e-6": { |
| "cos": 0.302, |
| "top1_u": 0.973, |
| "top1_v": 0.263, |
| "med_top8_angle_deg": 32.7 |
| }, |
| "5e-5": { |
| "cos": 0.36, |
| "top1_u": 0.901, |
| "top1_v": 0.403, |
| "med_top8_angle_deg": 44.4 |
| } |
| }, |
| "rft": { |
| "5e-7": { |
| "cos": 0.066, |
| "top1_u": 0.988, |
| "top1_v": 0.074, |
| "med_top8_angle_deg": 26.5 |
| }, |
| "5e-6": { |
| "cos": 0.3, |
| "top1_u": 0.975, |
| "top1_v": 0.26, |
| "med_top8_angle_deg": 32.6 |
| }, |
| "5e-5": { |
| "cos": 0.356, |
| "top1_u": 0.9, |
| "top1_v": 0.415, |
| "med_top8_angle_deg": 44.6 |
| } |
| }, |
| "grpo": { |
| "5e-7": { |
| "cos": 0.001, |
| "top1_u": 0.062, |
| "top1_v": 0.015, |
| "med_top8_angle_deg": 82.4, |
| "_caveat": "dW norm 0.03 -> noise, not real orthogonality" |
| } |
| } |
| }, |
| "cross_method_cosine_matched_lr_seed": { |
| "_note": "same lr+seed, mean over seeds; contrast for the within-seed comparison", |
| "sft__rft": { |
| "5e-7": 0.996, |
| "5e-6": 0.978, |
| "5e-5": 0.836 |
| }, |
| "sft__grpo": { |
| "5e-7": 0.022 |
| }, |
| "rft__grpo": { |
| "5e-7": 0.021 |
| } |
| }, |
| "cross_method_same_seed42_subspace": { |
| "sft__rft": { |
| "5e-7": { |
| "cos": 0.996, |
| "top1_u": 0.999, |
| "top1_v": 1.0, |
| "med_top8_angle_deg": 3.7 |
| }, |
| "5e-6": { |
| "cos": 0.976, |
| "top1_u": 0.985, |
| "top1_v": 0.999, |
| "med_top8_angle_deg": 11.9 |
| }, |
| "5e-5": { |
| "cos": 0.831, |
| "top1_u": 0.903, |
| "top1_v": 0.947, |
| "med_top8_angle_deg": 26.7 |
| } |
| } |
| }, |
| "lr_sensitivity_fixed_seed42": { |
| "_note": "fixed method+seed, vary lr; norm_ratio vs lr_ratio tests 'rescale vs rotate'. norm/lr ~1 would mean pure rescale.", |
| "sft": { |
| "5e-7_to_5e-6": { |
| "cos": 0.544, |
| "norm_ratio": 2.79, |
| "lr_ratio": 10, |
| "norm_over_lr": 0.28 |
| }, |
| "5e-6_to_5e-5": { |
| "cos": 0.557, |
| "norm_ratio": 3.23, |
| "lr_ratio": 10, |
| "norm_over_lr": 0.32 |
| } |
| } |
| }, |
| "random_baseline": { |
| "sft5e-5_s42__rft5e-7_s123": { |
| "cos": 0.027, |
| "top1_u": 0.273, |
| "med_top8_angle_deg": 75.6 |
| } |
| }, |
| "seed_lmc_sft_lr5e-6": { |
| "_note": "masked-answer CE on GSM8K, alpha*s42+(1-a)*s123, n=24", |
| "curve": { |
| "0.0": 3.1878, |
| "0.25": 3.1773, |
| "0.5": 3.1646, |
| "0.75": 3.1499, |
| "1.0": 3.1333 |
| }, |
| "midpoint_barrier": 0.0041, |
| "verdict": "no barrier -> same basin" |
| } |
| } |
