diff --git a/PREREG_scale_selection_2026-09-21.md b/PREREG_scale_selection_2026-09-21.md new file mode 100644 index 0000000..2bb99c9 --- /dev/null +++ b/PREREG_scale_selection_2026-09-21.md @@ -0,0 +1,53 @@ +# PREREG — масштаб как ВЫБОР между двумя посчитанными (`derived3_cap`) + +Составлено до полного прогона. Основание — возражение Валерия 2026-09-21: «если бы шаг формировала +похожесть, мы меняли бы шаг с очень большого на более мелкий по мере приближения к цели». + +## 1. Почему возражение верно и что оно вскрыло + +Шаг есть `(1 − S(z))·D` с `z = |f|/σ` и `σ = |slope|·D`. Проверка на `fun1.4` в точке `x = 10⁴` +(`f ≈ 10¹²`, `f′ ≈ 3·10⁸`, ньютоновская длина ≈ 3333, `D ≈ 2·10⁴`): `z = 0.167`, то есть +**`S = 0.833` — «похоже»** — и шаг мал, хотя до корня около 5000 его собственных длин. + +Причина: деление остатка на `|slope|·D` **нормирует непохожесть самой скобкой**, поэтому похожесть +читает «какую долю скобки составляет ньютоновский шаг», а не «далеко ли я». Принцип «крупный шаг +далеко, мелкий близко» формулой не реализован — он требует `σ`, не зависящего от `D`. + +## 2. Что проверяется + +`σ = min(|slope|·D, max(|F_A|, |F_B|))` — **выбор между двумя уже посчитанными** масштабами: +значением на концах скобки и наклонным. Ни новой константы, ни порога: `min` по имеющемуся. +Ожидаемое поведение: далеко на широкой скобке минимум даёт значение на конце ⇒ `z ≈ 1` ⇒ шаг во всю +скобку; у корня минимум даёт наклонный ⇒ ньютоновское поведение и прежний порядок. + +**Режим:** `scale="derived3_cap"`; прежние шкалы и поведение по умолчанию не тронуты. + +## 3. Точка отсчёта и цели + +Сравнение — против той же конфигурации без новой шкалы (`slope`-гейт + `dissimilar`): +APS **2726**, CHA **2785** (по-наборно 2683), два набора **5511**, 193/199, `over2x = 0`. +Лучшее на APS у нас — **2527** (`shape`-чтение). + +| величина | цель | +|---|---| +| APS-154 | **≤ 2726** (не хуже точки отсчёта); идеально ≤ 2527 | +| CHA-45 | **< 2683** (улучшение против нашего лучшего) | +| два набора | **< 5511** | +| решено | ≥ 193/199 | +| гарантия | `over2x = 0` | + +## 4. Предсказания и фальсификаторы + +| # | Предсказание | ФАЛЬСИФИКАТОР → вывод | +|---|---|---| +| **K1** | CHA улучшается (<2683) | не улучшается → выбор масштаба не бьёт в измеренную причину (недолёт линейной модели) | +| **K2** | APS не ухудшается (≤2726) | ухудшается → тот же трейд «широкие за счёт узких», четвёртый раз; режим отвергается | +| **K3** | гарантия цела | нарушена → немедленное закрытие | +| **K4** | порядок сходимости у корня не падает: наблюдаемый порядок на узких задачах не ниже, чем у `derived3` | падает → выбор `min` мешает концовке, и это записывается | + +🔴 **Оговорка о смещении:** предварительная проба на 8 **широких** задачах (403 → 390, 4 лучше / 3 +хуже / 1 вровень) выбрана мной под механизм и **свидетельством не является**. Решает полный прогон по +всей сетке, где широкие задачи составляют меньшинство. + +**Правило остановки:** K2 или K3 ложны ⇒ режим не принимается. K1 ложна ⇒ измеренная причина +(недолёт линейной модели) выбором масштаба не устраняется, и это пишется прямо. diff --git a/article/sim_numerics.pdf b/article/sim_numerics.pdf index 616b12a..0210fda 100644 Binary files a/article/sim_numerics.pdf and b/article/sim_numerics.pdf differ diff --git a/article/sim_numerics.tex b/article/sim_numerics.tex index ebddead..c7b6acb 100644 --- a/article/sim_numerics.tex +++ b/article/sim_numerics.tex @@ -677,6 +677,22 @@ canonical set against $2527$ --- a difference of $1922$ evaluations for one choice of criterion. A secant step routinely collapses the error while barely moving the proven bracket, so bracket progress rejects steps that were excellent; this is the same mechanism that makes the bracket guard cost $7260$. +\item \textbf{Making the scale independent of the bracket does not help either.} +The natural objection to the derived scale is that it defeats the very principle +of a similarity step: with $\sigma=|f'|D$ the normalised residual is +$|f|/(|f'|D)$, which on the $2\times10^4$-wide bracket of $x^3-2x-5$ at +$x=10^4$ equals $0.167$, so $S=0.833$ --- ``similar'' --- and the step is small +although the root is some five thousand step-lengths away. The similarity is +reading what fraction of the \emph{bracket} the Newton step is, not how far the +iterate is from the root. Selecting the scale between the two quantities already +computed, $\sigma=\min(|f'|D,\max(|f(A)|,|f(B)|))$ --- no new constant, a +\texttt{min} over what is in hand --- does give a full-bracket step far away and +Newton's step near the root, and on eight hand-picked wide problems it improves +$403$ evaluations to $390$. Over the whole grid it is worse on both sets: +$3288$ on the canonical set against $2726$, and $3111$ on the wide-bracket set +against $2683$. Its apparent extra solves ($194$ instead of $193$) are two +\texttt{fun7} problems where it lands inside the flat zero region close enough to +satisfy the harness --- the artefact of \S\ref{sec:fun7}, not a capability. \item \textbf{A logarithmic change of variable does not buy the wide brackets.} Working in $u=\operatorname{sign}(x-c)\log(1+|x-c|/\varepsilon_x)$ makes the step multiplicative, which is the right diagnosis of the flat families --- CHA diff --git a/results_sweep_cap.txt b/results_sweep_cap.txt new file mode 100644 index 0000000..09d9e03 --- /dev/null +++ b/results_sweep_cap.txt @@ -0,0 +1,64 @@ +sweep: 63 configurations x 199 problems (FULL) + 10/63 done, 1s elapsed + 20/63 done, 1s elapsed + 30/63 done, 1s elapsed + 40/63 done, 1s elapsed + 50/63 done, 1s elapsed + 60/63 done, 1s elapsed + 63/63 done, 2s elapsed +wrote sweep_cap.json (2s total) +==================================================================================== +APS: 154 problems (top 20 of 63) +==================================================================================== +configuration solved total fev over 2x +------------------------------------------------------------------------------------ +pure+dissim+slope.exp_abs.derived3_cap.none 153/154 3288 0 +pure+dissim+slope.exp_abs.derived3_cap.project 153/154 3288 0 +pure+dissim+slope.exp_abs.derived3_cap.step 153/154 3385 0 +pure+dissim+slope.exp_abs.derived3_cap.safe 153/154 3385 0 +pure+dissim+slope.rational.derived3_cap.step 153/154 3460 0 +pure+dissim+slope.rational.derived3_cap.safe 153/154 3460 0 +pure+dissim+slope.rational.derived3_cap.none 153/154 3497 0 +pure+dissim+slope.rational.derived3_cap.project 153/154 3497 0 +pure+dissim+slope.exp_abs.derived3_cap.bracket 153/154 3537 0 +pure+dissim+slope.exp_abs.derived3_cap.both 153/154 3619 0 +pure+dissim+slope.exp_abs.derived3_cap.credit 153/154 4125 0 +pure+dissim+slope.ratio.derived3_cap.bracket 153/154 4333 0 +pure+dissim+slope.ratio.derived3_cap.both 153/154 4903 0 +pure+dissim+slope.rational.derived3_cap.credit 153/154 5001 0 +pure+dissim+slope.ratio.derived3_cap.step 153/154 5044 0 +pure+dissim+slope.ratio.derived3_cap.safe 153/154 5044 0 +pure+dissim+slope.sqrt.derived3_cap.step 153/154 6184 0 +pure+dissim+slope.sqrt.derived3_cap.safe 153/154 6184 0 +pure+dissim+slope.sqrt.derived3_cap.both 153/154 6216 0 +pure+dissim+slope.sqrt.derived3_cap.bracket 153/154 6580 0 + +==================================================================================== +CHA: 45 problems (top 20 of 63) +==================================================================================== +configuration solved total fev over 2x +------------------------------------------------------------------------------------ +pure+dissim+slope.sqrt.derived3_cap.none 42/45 2969 0 +pure+dissim+slope.sqrt.derived3_cap.project 41/45 3111 0 +pure+dissim+slope.exp_abs.derived3_cap.step 40/45 2658 0 +pure+dissim+slope.exp_abs.derived3_cap.safe 40/45 2658 0 +pure+dissim+slope.exp_abs.derived3_cap.both 40/45 2689 0 +pure+dissim+slope.rational.derived3_cap.step 40/45 2790 0 +pure+dissim+slope.rational.derived3_cap.safe 40/45 2790 0 +pure+dissim+slope.exp_abs.derived3_cap.bracket 40/45 2796 0 +pure+dissim+slope.exp_abs.derived3_cap.none 40/45 2808 0 +pure+dissim+slope.exp_abs.derived3_cap.project 40/45 2808 0 +pure+dissim+slope.ratio.derived3_cap.both 40/45 2906 0 +pure+dissim+slope.ratio.derived3_cap.step 40/45 2959 0 +pure+dissim+slope.ratio.derived3_cap.safe 40/45 2959 0 +pure+dissim+slope.rational.derived3_cap.none 40/45 2970 0 +pure+dissim+slope.rational.derived3_cap.project 40/45 2970 0 +pure+dissim+slope.ratio.derived3_cap.bracket 40/45 2978 0 +pure+dissim+slope.rational.derived3_cap.credit 40/45 2982 0 +pure+dissim+slope.exp_abs.derived3_cap.credit 40/45 2991 0 +pure+dissim+slope.cbrt.derived3_cap.both 40/45 3041 0 +pure+dissim+slope.sqrt.derived3_cap.step 40/45 3066 0 + +==================================================================================== +THE STAGE-0C LAW ACROSS THE GRID +==================================================================================== diff --git a/simroot/pure.py b/simroot/pure.py index d456c21..dcae4c6 100644 --- a/simroot/pure.py +++ b/simroot/pure.py @@ -505,7 +505,7 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", if similarity not in PURE_SIMS: raise ValueError(f"unknown similarity {similarity!r}") if scale not in ("derived", "derived3", "derived_rho", "derived3_rho", - "derived3_m", "start", "bracket"): + "derived3_m", "derived3_cap", "start", "bracket"): raise ValueError(f"unknown scale {scale!r}") if space not in SPACES: raise ValueError(f"unknown space {space!r}") @@ -515,11 +515,12 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", raise ValueError(f"unknown points rule {points!r}") if direction not in DIRECTIONS: raise ValueError(f"unknown direction {direction!r}") - if points == "shape" and scale not in ("derived3", "derived3_rho", "derived3_m"): + if points == "shape" and scale not in ("derived3", "derived3_rho", "derived3_m", + "derived3_cap"): # the triple only exists for the three-point scale; selecting one under a # two-point scale would change nothing and hide that raise ValueError("points='shape' requires a three-point scale (derived3*)") - if prestep == "slope" and scale not in ("derived", "derived3"): + if prestep == "slope" and scale not in ("derived", "derived3", "derived3_cap"): # there is no slope to judge under a chosen or bracket scale; judging something # else would hide that, so the call fails instead raise ValueError("prestep='slope' requires scale in {'derived', 'derived3'}") @@ -603,6 +604,19 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", else: slope = _slope3(x, fx, x_prev, f_prev, x_prev2, f_prev2) sc = abs(slope) * abs(far - x) + elif scale == "derived3_cap": + # Valeri, 2026-09-21: "if the similarity formed the step, the step would be + # large far from the target and small near it". It does not, and the reason + # is the normalisation: with sigma = |slope| * D the similarity reads "what + # fraction of the BRACKET the Newton step is", not "how far am I". On a + # 2e4-wide bracket of x^3-2x-5 at x = 1e4 that fraction is 0.167, so S = + # 0.833 - "similar" - and the step is small exactly where it should be large. + # The scale is therefore SELECTED between the two already-computed ones: + # far away the value scale of the bracket ends is the smaller and the step + # opens up; near the root the slope scale is the smaller and Newton (and the + # order) returns. A min over what is in hand - no constant, no threshold. + slope = _slope3(x, fx, x_prev, f_prev, x_prev2, f_prev2) + sc = min(abs(slope) * abs(far - x), max(abs(FA), abs(FB))) if scale == "derived3_m": # REFUTED as an improvement - kept for reproducibility. # The DERIVATION holds: dropping the linearity diff --git a/sweep_cap.json b/sweep_cap.json new file mode 100644 index 0000000..2105c86 --- /dev/null +++ b/sweep_cap.json @@ -0,0 +1 @@ +[{"label": "pure+dissim+slope.cbrt.derived3_cap.none", "spec": ["pure", "cbrt", "derived3_cap", "none", "x", "slope", "recent", "dissimilar"], "APS": {"total": 8192, "solved": 153, "n": 154, "over": 0, "per": {"aps.01.00": [47, true], "aps.02.00": [47, true], "aps.02.01": [49, true], "aps.02.02": [51, true], "aps.02.03": [53, true], "aps.02.04": [52, true], "aps.02.05": [53, true], "aps.02.06": [51, true], "aps.02.07": [57, true], "aps.02.08": [58, true], "aps.02.09": [54, true], "aps.03.00": [57, true], "aps.03.01": [55, true], "aps.03.02": [48, 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"aps.14.19": [45, true], "aps.14.20": [45, true], "aps.14.21": [45, true], "aps.14.22": [45, true], "aps.14.23": [45, true], "aps.14.24": [45, true], "aps.14.25": [45, true], "aps.14.26": [45, true], "aps.14.27": [45, true], "aps.14.28": [45, true], "aps.14.29": [45, true], "aps.14.30": [45, true], "aps.14.31": [45, true], "aps.14.32": [45, true], "aps.14.33": [45, true], "aps.14.34": [45, true], "aps.14.35": [45, true], "aps.14.36": [45, true], "aps.14.37": [45, true], "aps.14.38": [45, true], "aps.14.39": [45, true], "aps.15.00": [36, true], "aps.15.01": [37, true], "aps.15.02": [37, true], "aps.15.03": [38, true], "aps.15.04": [38, true], "aps.15.05": [38, true], "aps.15.06": [37, true], "aps.15.07": [41, true], "aps.15.08": [41, true], "aps.15.09": [38, true], "aps.15.10": [40, true], "aps.15.11": [40, true], "aps.15.12": [43, true], "aps.15.13": [53, true], "aps.15.14": [53, true], "aps.15.15": [53, true], "aps.15.16": [53, true], "aps.15.17": [53, true], "aps.15.18": [51, true], "aps.15.19": [53, true], "aps.15.20": [53, true], "aps.15.21": [53, true], "aps.15.22": [53, true], "aps.15.23": [53, true], "aps.15.24": [53, true], "aps.15.25": [53, true], "aps.15.26": [53, true], "aps.15.27": [53, true], "aps.15.28": [53, true], "aps.15.29": [53, true], "aps.15.30": [53, true]}}, "CHA": {"total": 3092, "solved": 40, "n": 45, "over": 0, "per": {"fun1.1": [35, true], "fun1.2": [47, true], "fun1.3": [50, true], "fun1.4": [58, true], "fun1.5": [78, true], "fun2.1": [34, true], "fun2.2": [57, true], "fun2.3": [63, true], "fun2.4": [77, true], "fun2.5": [83, true], "fun3.1": [44, true], "fun3.2": [48, true], "fun3.3": [58, true], "fun3.4": [64, true], "fun3.5": [78, true], "fun4.1": [45, true], "fun4.2": [47, true], "fun4.3": [58, true], "fun4.4": [64, true], "fun4.5": [78, true], "fun5.1": [45, true], "fun5.2": [46, true], "fun5.3": [47, true], "fun5.4": [49, true], "fun5.5": [50, true], "fun6.1": [46, true], "fun6.2": [45, true], "fun6.3": [47, true], "fun6.4": [49, true], "fun6.5": [50, true], "fun7.1": [8, false], "fun7.2": [8, false], "fun7.3": [8, false], "fun7.4": [13, false], "fun7.5": [10, false], "fun8.1": [44, true], "fun8.2": [45, true], "fun8.3": [47, true], "fun8.4": [48, true], "fun8.5": [50, true], "fun9.1": [43, true], "fun9.2": [35, true], "fun9.3": [47, true], "fun9.4": [48, true], "fun9.5": [45, true]}}}] \ No newline at end of file diff --git a/sweep_full.py b/sweep_full.py index daa3fdc..de779b7 100644 --- a/sweep_full.py +++ b/sweep_full.py @@ -198,6 +198,15 @@ def build_grid_log(smoke): for sim in sims for sc in ("derived", "derived3") for gu in guards] +def build_grid_cap(smoke): + """Scale as a SELECTION between the two computed ones (PREREG 2026-09-21): identical to + the slope+dissimilar configuration except scale = derived3_cap, so one thing changes.""" + sims = ["ratio", "sqrt"] if smoke else sorted(PURE_SIMS) + guards = ("credit", "safe") if smoke else GUARD_MODES + return [("pure", sim, "derived3_cap", gu, "x", "slope", "recent", "dissimilar") + for sim in sims for gu in guards] + + def build_grid_combo(smoke): """A+B together (PREREG 2026-09-21 §2: licensed only because each mode alone improved APS — A 2527 and B 2726 against the published 2806).""" @@ -264,10 +273,12 @@ def main(): logmode = "--log" in sys.argv # the u-space grid, written to its OWN file gatemode = "--gate" in sys.argv # the pre-step gate grid, likewise slopemode = "--slope" in sys.argv # the slope-stability gate grid + capmode = "--cap" in sys.argv # scale selected between the two computed ones combomode = "--combo" in sys.argv # modes A and B together pointsmode = "--points" in sys.argv # mode A: triple by shape dirmode = "--direction" in sys.argv # mode B: far end by dissimilarity - specs = (build_grid_combo(smoke) if combomode else + specs = (build_grid_cap(smoke) if capmode else + build_grid_combo(smoke) if combomode else build_grid_points(smoke) if pointsmode else build_grid_direction(smoke) if dirmode else build_grid_slope(smoke) if slopemode else @@ -288,8 +299,9 @@ def main(): # the published sweep_full.json is what verify_article.py checks the paper # against, so the log grid never writes into it - if combomode or pointsmode or dirmode: - base = ("sweep_combo" if combomode else + if capmode or combomode or pointsmode or dirmode: + base = ("sweep_cap" if capmode else + "sweep_combo" if combomode else "sweep_points" if pointsmode else "sweep_direction") out = f"{base}_smoke.json" if smoke else f"{base}.json" with open(out, "w", encoding="utf8") as fh: