| """実験23-B: レート歪み配分。層ごとに違うビット数を配る。 |
| |
| いまは252層すべてに一律の設定を配っている。だが層によって痛み（出力誤差）は |
| 何倍も違う。同じ平均ビット数のまま、痛い層に厚く・楽な層に薄く配り直せば |
| 全体の誤差は下がる。これが引き継ぎ書6-1。 |
| |
| やり方（レート歪み理論の教科書どおり）: |
| 各層iと候補設定cについて (ビット数 b_ic, 二乗誤差 D_ic) を用意し、 |
| Σ D_ic を最小化 subject to Σ b_ic·size_i ≤ 予算 |
| ラグランジュ緩和すると各層独立に argmin_c D_ic + λ·b_ic·size_i を選ぶだけ。 |
| λ を二分探索して予算にぴったり合わせる。凸包上では厳密解。 |
| |
| 歪みのモデル: |
| 実測点は2つ（unified=約1.15bit と b07=約0.70bit）。高レート近似 |
| D(b) = D0 · 2^(−2λ(b−b0)) |
| の λ を層ごとに2点から推定する。2点が無い層は同じ種類(kind)の中央値を使う。 |
| |
| 出力: results/recipe.json … 層名 → {k, cb, G, rank} の割り当て表 |
| """ |
| import json, math, os, sys |
| HERE = os.path.dirname(os.path.abspath(__file__)) |
| R = os.path.join(HERE, "results") |
| import numpy as np |
|
|
| |
| SUTETA = [0] |
|
|
| |
| CANDS = [(k, cb, G, rank) for k in (32, 16, 8, 4, 2) |
| for cb in (8, 12) for G in (256,) for rank in (32,)] |
|
|
|
|
| def bpw_of(out, inn, k, cb, G, rank, lr_bits=4): |
| """lib/recipe.fit の戻り値と同じ計算。""" |
| r = 1 << (min(rank, min(out, inn) // 2).bit_length() - 1) |
| lr = r * (out + inn) * lr_bits / (out * inn) |
| Asz, Aw = r * out, min(G, r) |
| Bsz, Bw = r * inn, min(G, inn) |
| ovh = 16 * (Asz / Aw + Bsz / Bw) / (out * inn) |
| return lr + cb / k + 16.0 / G + ovh |
|
|
|
|
| def load(name): |
| p = os.path.join(R, name + "_sens.json") |
| return json.load(open(p)) if os.path.exists(p) else {} |
|
|
|
|
| hi = load("unified") |
| lo = load("b07") |
| if not hi: |
| sys.exit("先に sensitivity.py を走らせること（unified）") |
|
|
| HI = dict(k=8, cb=8, G=256, rank=32) |
| LO = dict(k=16, cb=8, G=256, rank=32) |
|
|
| |
| lam, bykind = {}, {} |
| for n, d in hi.items(): |
| if n not in lo: |
| continue |
| b1 = bpw_of(d["out"], d["inn"], **HI) |
| b0 = bpw_of(d["out"], d["inn"], **LO) |
| e1, e0 = d["err"], lo[n]["err"] |
| if b1 <= b0 or e1 <= 0 or e0 <= 0: |
| continue |
| l = math.log2(e0 / e1) / (b1 - b0) |
| |
| |
| if l <= 0: |
| SUTETA[0] += 1 |
| if 0.01 < l < 4: |
| lam[n] = l |
| bykind.setdefault(d["kind"], []).append(l) |
|
|
| med = {k: float(np.median(v)) for k, v in bykind.items()} |
| gmed = float(np.median(list(lam.values()))) if lam else 0.5 |
| print(f"λの実測: {len(lam)}層 全体中央値={gmed:.3f}") |
| for k in sorted(med, key=lambda x: -med[x]): |
| print(f" {k:<14} λ={med[k]:.3f} (n={len(bykind[k])})") |
| if not lam: |
| print("※ 2点そろった層が無いので λ=0.5 を全層に仮定する（要 b07 の感度測定）") |
|
|
| |
| rows = [] |
| for n, d in hi.items(): |
| l = lam.get(n, med.get(d["kind"], gmed)) |
| b1 = bpw_of(d["out"], d["inn"], **HI) |
| scale = (d["err"] ** 2) * d["size"] |
| cs = [] |
| for (k, cb, G, rank) in CANDS: |
| b = bpw_of(d["out"], d["inn"], k, cb, G, rank) |
| D = scale * (2.0 ** (-2 * l * (b - b1))) |
| cs.append((b, D, (k, cb, G, rank))) |
| |
| cs.sort() |
| keep, best = [], float("inf") |
| for b, D, c in cs: |
| if D < best - 1e-30: |
| keep.append((b, D, c)); best = D |
| rows.append((n, d, keep)) |
|
|
| TOT = sum(d["size"] for _, d, _ in rows) |
| BASE = sum(bpw_of(d["out"], d["inn"], **HI) * d["size"] for _, d, _ in rows) / TOT |
| BUDGET = float(os.environ.get("BUDGET", BASE)) |
| print(f"\n一律配分の平均 = {BASE:.4f} bit/重み → これを予算にして配分し直す") |
|
|
|
|
| def solve(lmb): |
| pick, bits, dist = {}, 0.0, 0.0 |
| for n, d, keep in rows: |
| b, D, c = min(keep, key=lambda x: x[1] + lmb * x[0] * d["size"]) |
| pick[n] = c; bits += b * d["size"]; dist += D |
| return pick, bits / TOT, dist |
|
|
|
|
| lo_l, hi_l = 1e-18, 1e6 |
| for _ in range(200): |
| mid = math.sqrt(lo_l * hi_l) |
| _, b, _ = solve(mid) |
| if b > BUDGET: |
| lo_l = mid |
| else: |
| hi_l = mid |
| pick, bpw, dist = solve(hi_l) |
| _, _, dist0 = solve(float("inf")) |
|
|
| base_dist = sum((d["err"] ** 2) * d["size"] for _, d, _ in rows) |
| print(f"配分後: {bpw:.4f} bit/重み 推定二乗誤差 {dist:.4e} " |
| f"(一律 {base_dist:.4e} → {100*(1-dist/base_dist):.1f}% 減)") |
| print(f"推定の出力誤差RMS: {math.sqrt(base_dist/TOT):.4f} → {math.sqrt(dist/TOT):.4f}") |
|
|
| out = {n: dict(zip(("k", "cb", "G", "rank"), c)) for n, c in pick.items()} |
| json.dump(out, open(os.path.join(R, "recipe.json"), "w"), indent=1) |
| print(f"\n保存: {os.path.join(R,'recipe.json')}") |
|
|
| print("\n--- 配分の分布 ---") |
| cnt = {} |
| for n, c in pick.items(): |
| cnt[c] = cnt.get(c, 0) + 1 |
| for c, v in sorted(cnt.items(), key=lambda x: -x[1]): |
| print(f" k={c[0]:>2} cb={c[1]:>2} {v:>3}層") |
|
|
| print("\n--- 深さ方向にどう配られたか（ブロックごとの平均bit）---") |
| byb = {} |
| for n, d, _ in rows: |
| b = bpw_of(d["out"], d["inn"], *pick[n]) |
| byb.setdefault(d["blk"], []).append((b, d["size"])) |
| for b in sorted(byb): |
| xs = byb[b] |
| v = sum(x * s for x, s in xs) / sum(s for _, s in xs) |
| print(f" blk.{b:>2} {v:.3f}bit " + "#" * int(v * 20)) |
|
|
