From 42be1968ab9dab6dd4d92f7feb56491f70977b5a Mon Sep 17 00:00:00 2001 From: eric-czech Date: Wed, 1 Apr 2026 20:58:41 -0400 Subject: [PATCH] feat: add Delphi vs Llama 3 isoFLOP scaling analysis Three-figure analysis comparing Marin Delphi and Llama 3 scaling law fits: - Figure 1: Forecast sensitivity via LOO over training budgets - Figure 2: Empirical FLOP factors by budget - Figure 3: IsoFLOP comparison with D* deltas Co-Authored-By: Claude Opus 4.6 (1M context) --- analysis/README.md | 47 + analysis/delphi_scaling_analysis.py | 1475 +++++++++++++++++++++ analysis/results/flop_factors.pdf | Bin 0 -> 46804 bytes analysis/results/flop_factors.png | Bin 0 -> 217849 bytes analysis/results/forecast_sensitivity.md | 102 ++ analysis/results/forecast_sensitivity.pdf | Bin 0 -> 63446 bytes analysis/results/forecast_sensitivity.png | Bin 0 -> 423654 bytes analysis/results/isoflop_comparison.md | 108 ++ analysis/results/isoflop_comparison.pdf | Bin 0 -> 58694 bytes analysis/results/isoflop_comparison.png | Bin 0 -> 451029 bytes 10 files changed, 1732 insertions(+) create mode 100644 analysis/README.md create mode 100644 analysis/delphi_scaling_analysis.py create mode 100644 analysis/results/flop_factors.pdf create mode 100644 analysis/results/flop_factors.png create mode 100644 analysis/results/forecast_sensitivity.md create mode 100644 analysis/results/forecast_sensitivity.pdf create mode 100644 analysis/results/forecast_sensitivity.png create mode 100644 analysis/results/isoflop_comparison.md create mode 100644 analysis/results/isoflop_comparison.pdf create mode 100644 analysis/results/isoflop_comparison.png diff --git a/analysis/README.md b/analysis/README.md new file mode 100644 index 0000000..a6400bc --- /dev/null +++ b/analysis/README.md @@ -0,0 +1,47 @@ +# Delphi Scaling Analysis + +Comparison of Llama 3 and Marin Delphi isoFLOP scaling law fits. + +## Data Sources + +- **Llama 3**: Digitized isoFLOP data from [Meta Llama 3 paper](https://arxiv.org/abs/2407.21783) ([CSV](https://github.com/eric-czech/llama3_isoflop_extraction)) +- **Delphi**: Marin Delphi isoFLOP records (adamh_scaling_v6) — 78 records, 7 FLOP budgets (~2.9e18 to ~3.1e20) + - Links: + - [Extraction gist](https://gist.github.com/eric-czech/35e3b493c5d6a01dcea2f8dba8708a98) + - [Delphi scaling setup PR (marin#3292)](https://github.com/marin-community/marin/pull/3292) + - [Delphi parent issue (marin#1337)](https://github.com/marin-community/marin/issues/1337#issuecomment-4085058300) + - [Discord discussion](https://discord.com/channels/1354881461060243556/1375005693899309126/1483907317291552972) + - Forecasts: + - runs: https://wandb.ai/marin-community/marin/table (search `adamh-scaling-ladder-nemotron-optimal-.*`) + - [original forecasts](https://github.com/marin-community/marin/issues/1337#issuecomment-3992593231): + - `1e21`: 2.75, `1e22`: 2.55, `1e23`: 2.40 + - `1e21` forecast: + - [marin#1337/4006185971](https://github.com/marin-community/marin/issues/1337#issuecomment-4006185971) + - [wandb/adamh-scaling-ladder-nemotron-optimal-1e+21-v5-019021](https://wandb.ai/marin-community/marin/runs/adamh-scaling-ladder-nemotron-optimal-1e+21-v5-019021) + - Total parameters: 3,383,110,656 (from `gs://marin-us-central2/adamh-scaling-ladder-nemotron-optimal-1e+21-v5-019021/hf/step-22056`) + - Total tokens: 46,256,881,664 (from wandb overview) + - forecast: 2.7587, actual: 2.75814 + - `1e22` forecast: + - [marin#1337/4016705345](https://github.com/marin-community/marin/issues/1337#issuecomment-4016705345) + - [wandb/adamh-scaling-ladder-nemotron-optimal-1e+22-v5-025b0e](https://wandb.ai/marin-community/marin/runs/adamh-scaling-ladder-nemotron-optimal-1e+22-v5-025b0e) + - Total parameters: 9,714,698,752 (from `gs://marin-us-central2/adamh-scaling-ladder-nemotron-optimal-1e+22-v5-025b0e/hf/step-38234`) + - Total tokens: 160,369,213,440 + - forecast: 2.55, actual: 2.53295 (in gh post), 2.53079 (in wandb run at very end) + - `1e23` forecast: + - [marin#1337/4148827725](https://github.com/marin-community/marin/issues/1337#issuecomment-4148827725) + - [wandb/adamh-scaling-ladder-nemotron-optimal-1e+23-v5-27f2fb](https://wandb.ai/marin-community/marin/runs/adamh-scaling-ladder-nemotron-optimal-1e+23-v5-27f2fb) + - Total params: 24,963,098,112 (from `gs://marin-us-central2/adamh-scaling-ladder-nemotron-optimal-1e+23-v5-27f2fb/hf/step-74883`) + - Total tokens: 628,172,521,472 + - forecast: 2.3660 / 2.349 / 2.4 (original), actual (spiky run): 2.3546 + - Posts + - [Announcement](https://x.com/percyliang/status/2034367256277533100) + - [W&B tracking](https://x.com/WilliamBarrHeld/status/2037628853787738461) +- **Prior Nemotron results**: [Discord thread](https://discord.com/channels/1354881461060243556/1356490712199462912/1460423753895772274) + +## Usage + +```bash +uv run python3 analysis/delphi_scaling_analysis.py +``` + +Results are saved to `analysis/results/`. diff --git a/analysis/delphi_scaling_analysis.py b/analysis/delphi_scaling_analysis.py new file mode 100644 index 0000000..f850280 --- /dev/null +++ b/analysis/delphi_scaling_analysis.py @@ -0,0 +1,1475 @@ +"""Compare Llama 3 and Marin Delphi isoFLOP scaling law fits.""" + +from __future__ import annotations + +import csv +import io +import textwrap +import urllib.request +from dataclasses import dataclass, field +from pathlib import Path + +import matplotlib.colors as mcolors +import matplotlib.pyplot as plt +import numpy as np +from scipy.optimize import curve_fit + +from scaling_law_analysis.chinchilla import ( + ExponentGrid, + FitStatus, + LossSurface, + ParabolaFitResult, + SurfaceFitResult, + fit_approach2, +) +from scaling_law_analysis.common import save_figure + +# ============================================================================= +# Analysis configuration +# ============================================================================= + +# -- Data sources -- +LLAMA3_URL = ( + "https://raw.githubusercontent.com/eric-czech/llama3_isoflop_extraction/" + "1bc1755b76e6ee55a911549c8ec52b71cb480320/isoflops_points.csv" +) +DELPHI_URL = ( + "https://gist.githubusercontent.com/eric-czech/35e3b493c5d6a01dcea2f8dba8708a98/" + "raw/a67640529a78c5f040fab1ab7b14b8894d414340/marin_delphi_isoflop_records.csv" +) + +# -- Output -- +OUT_DIR = Path(__file__).parent / "results" + +# -- Delphi metric to use -- +DELPHI_METRIC = "eval/paloma/macro_loss" +METRIC_LABELS = { + "eval/paloma/c4_en/bpb": "Paloma C4-EN BPB", + "eval/paloma/macro_loss": "Paloma Macro Loss", +} +DELPHI_METRIC_LABEL = METRIC_LABELS[DELPHI_METRIC] + + +# -- VPNLS grid resolution for alpha/beta -- +GRID_RESOLUTION = 0.001 + +# -- Approach 3 flop factor mode -- +# True: learn per-budget k via OLS; False: fix k=6 (standard C=6ND) +LEARN_K = True + +# -- Param inference -- +# True: derive N = C/(6D) for Delphi (same as Llama 3); False: use true params +INFER_PARAMS = False + +# -- Visualization -- +# Show Approach 3 prediction curves in the isoflop plot +SHOW_A3_CURVES = False + +# Show power law fit through A2 parabola minima +SHOW_MINIMA_PL = False + +# ============================================================================= +# Data loading +# ============================================================================= + +FINE_EXPONENT_GRID = ExponentGrid( + alpha=np.arange(0.01, 1.0, GRID_RESOLUTION), + beta=np.arange(0.01, 1.0, GRID_RESOLUTION), +) + + +@dataclass +class IsoFlopData: + """Unified isoFLOP dataset: arrays of N, D, L, C (all same length).""" + + name: str + N: np.ndarray # params + D: np.ndarray # tokens + L: np.ndarray # loss + C: np.ndarray # compute budget (FLOPs) + + def __post_init__(self): + n = len(self.N) + assert len(self.D) == n and len(self.L) == n and len(self.C) == n + assert np.all(np.isfinite(self.N)) and np.all(self.N > 0) + assert np.all(np.isfinite(self.D)) and np.all(self.D > 0) + assert np.all(np.isfinite(self.L)) and np.all(self.L > 0) + assert np.all(np.isfinite(self.C)) and np.all(self.C > 0) + + +def _fetch_csv(url: str) -> list[dict[str, str]]: + with urllib.request.urlopen(url) as resp: + return list(csv.DictReader(io.StringIO(resp.read().decode("utf-8")))) + + +def load_llama3() -> IsoFlopData: + """Load Llama 3 isoFLOP data. N derived as C/(6D), raw loss used directly.""" + rows = _fetch_csv(LLAMA3_URL) + C = np.array([float(r["compute_budget"]) for r in rows]) + D = np.array([float(r["training_tokens"]) for r in rows]) + L = np.array([float(r["validation_loss"]) for r in rows]) + N = C / (6.0 * D) + return IsoFlopData(name="Llama 3", N=N, D=D, L=L, C=C) + + +def load_delphi(metric: str = DELPHI_METRIC) -> IsoFlopData: + """Load Marin Delphi isoFLOP data, filtered by metric.""" + all_rows = _fetch_csv(DELPHI_URL) + rows = [r for r in all_rows if r["metric"] == metric] + assert len(rows) > 0, f"No rows for metric={metric!r}" + D = np.array([float(r["tokens"]) for r in rows]) + L = np.array([float(r["value"]) for r in rows]) + C = np.array([float(r["flops"]) for r in rows]) + N = C / (6.0 * D) if INFER_PARAMS else np.array([float(r["params"]) for r in rows]) + n_budgets = len(np.unique(C)) + assert n_budgets == 7, f"Expected 7 unique budgets, got {n_budgets}" + return IsoFlopData(name="Delphi", N=N, D=D, L=L, C=C) + + +# ============================================================================= +# Fitting +# ============================================================================= + + +def fit_vpnls( + N: np.ndarray, + D: np.ndarray, + L: np.ndarray, + *, + grid: ExponentGrid, + fit_asymptote: bool, +) -> SurfaceFitResult: + """VPNLS grid search: L = E + A/N^α + B/D^β (or E=0 when fit_asymptote=False). + + 2D grid over (α, β), NNLS inner solve for (E, A, B) or (A, B) at each candidate. + """ + from scipy.optimize import nnls + + log_N, log_D = np.log(N), np.log(D) + n_linear = 3 if fit_asymptote else 2 + best_rss, best_ab, best_params = np.inf, (0.0, 0.0), np.zeros(n_linear) + for alpha in grid.alpha: + for beta in grid.beta: + cols = [np.exp(-alpha * log_N), np.exp(-beta * log_D)] + if fit_asymptote: + cols.insert(0, np.ones(len(L))) + X = np.column_stack(cols) + params, rnorm = nnls(X, L) + rss = rnorm**2 + if rss < best_rss: + best_rss, best_ab, best_params = rss, (alpha, beta), params + if fit_asymptote: + E, A, B = best_params + else: + E, A, B = 0.0, best_params[0], best_params[1] + return SurfaceFitResult( + E=float(E), + A=float(A), + B=float(B), + alpha=float(best_ab[0]), + beta=float(best_ab[1]), + residual_sum_squares=best_rss, + n_points=len(N), + method=f"vpnls-grid{'' if fit_asymptote else '-no-E'}", + status=FitStatus.CONVERGED, + ) + + +def estimate_k_hat(data: IsoFlopData, surface: LossSurface) -> dict[float, float]: + """Per-budget flop factor estimation: C = k*N*D. + + Given global fit L = E + A*N^(-alpha) + B*D^(-beta) with D = C/(k*N), + estimates per-budget k via OLS on the linearized data term (kappa = k^beta). + """ + E, A, B = surface.E, surface.A, surface.B + alpha, beta = surface.alpha, surface.beta + k_values: dict[float, float] = {} + for c in np.unique(data.C): + mask = data.C == c + N, L = data.N[mask], data.L[mask] + r = L - E - A * N ** (-alpha) + g = B * N**beta / c**beta + kappa = float(np.dot(r, g) / np.dot(g, g)) + assert kappa > 0, f"Non-positive kappa={kappa:.6f} at budget {c:.2e}" + k_values[c] = kappa ** (1 / beta) + return k_values + + +def get_k_values(data: IsoFlopData, surface: LossSurface) -> dict[float, float]: + """Return per-budget k based on LEARN_K config.""" + if LEARN_K: + return estimate_k_hat(data, surface) + return {c: 6.0 for c in np.unique(data.C)} + + +def compute_rss_by_budget( + data: IsoFlopData, surface: LossSurface, k_values: dict[float, float] +) -> dict[float, float]: + """RSS per budget using provided k values.""" + rss: dict[float, float] = {} + for c in np.unique(data.C): + mask = data.C == c + N, L = data.N[mask], data.L[mask] + D = c / (k_values[c] * N) + pred = surface.loss(N, D) # pyrefly: ignore + rss[c] = float(np.sum((L - pred) ** 2)) + return rss + + +@dataclass +class MinimaPowerLaw: + """Power law fit to A2 parabola minima: L = x1 * D^x2 + x0.""" + + x0: float # offset (irreducible loss along minima) + x1: float # coefficient + x2: float # exponent + rss: float + + +def _fit_power_law_to_minima(D: np.ndarray, L: np.ndarray) -> MinimaPowerLaw: + """Fit L = x1 * D^x2 + x0 to (D, L) pairs.""" + + def model(d: np.ndarray, x0: float, x1: float, x2: float) -> np.ndarray: + return x1 * d**x2 + x0 + + popt, _ = curve_fit( # pyrefly: ignore + model, D, L, p0=[L.min(), 1.0, -0.1], maxfev=10000 + ) + pred = model(D, *popt) + rss = float(np.sum((L - pred) ** 2)) + return MinimaPowerLaw(x0=popt[0], x1=popt[1], x2=popt[2], rss=rss) + + +def fit_minima_power_law_a2(a2: ParabolaFitResult) -> MinimaPowerLaw: + """Fit power law to A2 parabola vertices (D*, L_min).""" + D = a2.D_opts + L = np.array([f.L_min for f in a2.parabola_fits_D]) + return _fit_power_law_to_minima(D, L) + + +def d_opt_a3(surface: LossSurface, C: float, k: float) -> float: + """Analytical D* for approach 3: D* = (1/G) * (C/k)^b.""" + return (1.0 / surface.G) * (C / k) ** surface.b + + +@dataclass +class DOptDeltas: + """D* comparison between Approach 3 and Approach 2. + + delta% = (D*_A3 - D*_A2) / D*_A2 * 100 + Positive means Approach 3 infers more tokens than Approach 2. + """ + + pct: dict[float, float] # signed % delta per budget + raw: dict[float, float] # raw token delta per budget + mean_signed: float + mean_unsigned: float + median_signed: float + median_unsigned: float + var_unsigned: float + var_signed: float + iqr: float # IQR of signed % deltas + + +def compute_dopt_deltas(results: "FitResults") -> DOptDeltas: + surface = results.vpnls.to_loss_surface() + budgets = results.a2.compute_budgets + d_a2 = results.a2.D_opts + pct: dict[float, float] = {} + raw: dict[float, float] = {} + for i, c in enumerate(budgets): + d3 = d_opt_a3(surface, c, results.k_values[c]) + raw[c] = d3 - d_a2[i] + pct[c] = raw[c] / d_a2[i] * 100.0 + vals = np.array(list(pct.values())) + abs_vals = np.abs(vals) + return DOptDeltas( + pct=pct, + raw=raw, + mean_signed=float(vals.mean()), + mean_unsigned=float(abs_vals.mean()), + median_signed=float(np.median(vals)), + median_unsigned=float(np.median(abs_vals)), + var_unsigned=float(abs_vals.var()), + var_signed=float(vals.var()), + iqr=float(np.subtract(*np.percentile(vals, [75, 25]))), + ) + + +@dataclass +class FitResults: + """VPNLS grid + Approach 2 + k results for one dataset.""" + + data: IsoFlopData + vpnls: SurfaceFitResult + a2: ParabolaFitResult + minima_pl_a2: MinimaPowerLaw + k_values: dict[float, float] = field(default_factory=dict) + rss: dict[float, float] = field(default_factory=dict) + + +def fit_dataset(data: IsoFlopData, *, fit_asymptote: bool) -> FitResults: + n_budgets = len(np.unique(data.C)) + print(f"Fitting: {data.name} ({len(data.N)} points, {n_budgets} budgets)") + + vpnls_result = fit_vpnls( + data.N, data.D, data.L, grid=FINE_EXPONENT_GRID, fit_asymptote=fit_asymptote + ) + a2_result = fit_approach2(data.N, data.D, data.L, data.C) + + surface = vpnls_result.to_loss_surface() + k_values = get_k_values(data, surface) + rss = compute_rss_by_budget(data, surface, k_values) + + minima_pl_a2 = fit_minima_power_law_a2(a2_result) + + return FitResults( + data=data, + vpnls=vpnls_result, + a2=a2_result, + minima_pl_a2=minima_pl_a2, + k_values=k_values, + rss=rss, + ) + + +# ============================================================================= +# Shared visualization utilities +# ============================================================================= + + +def fmt_budget(b: float, decimals: int = 1) -> str: + exp = int(np.floor(np.log10(b))) + mantissa = b / 10**exp + return f"{mantissa:.{decimals}f}e{exp}" if decimals else f"{mantissa:.0f}e{exp}" + + +ISOFLOP_CMAPS = {"Llama 3": "Reds", "Delphi": "Blues"} +VERTEX_COLOR_A2 = "red" +VERTEX_COLOR_A3 = "blue" + + +# ============================================================================= +# Figure 1: Forecast sensitivity +# ============================================================================= + + +@dataclass(frozen=True) +class ForecastTarget: + """True param/token counts for a forecast compute budget.""" + + params: float + tokens: float + actual: float # observed loss + + +# Known forecast targets (from Delphi scaling ladder) +FORECAST_TARGETS: dict[float, ForecastTarget] = { + 1e21: ForecastTarget(params=3_383_110_656, tokens=46_256_881_664, actual=2.75814), + 1e22: ForecastTarget(params=9_714_698_752, tokens=160_369_213_440, actual=2.53079), + 1e23: ForecastTarget(params=24_963_098_112, tokens=628_172_521_472, actual=2.3546), +} +FORECAST_BUDGETS = list(FORECAST_TARGETS.keys()) + + +def forecast_loss_a2(results: FitResults, C: float) -> float: + """Forecast loss at budget C using true token count + A2 minima power law.""" + assert C in FORECAST_TARGETS, f"No forecast target for C={C:.0e}" + pl = results.minima_pl_a2 + d = FORECAST_TARGETS[C].tokens + return pl.x1 * d**pl.x2 + pl.x0 + + +def forecast_loss_a3(results: FitResults, C: float) -> float: + """Forecast loss at budget C using A3 surface. + + When INFER_PARAMS: N = C/(6D), consistent with how the surface was fit. + Otherwise: use true N and D from forecast targets. + """ + assert C in FORECAST_TARGETS, f"No forecast target for C={C:.0e}" + t = FORECAST_TARGETS[C] + n = C / (6.0 * t.tokens) if INFER_PARAMS else t.params + return float(results.vpnls.to_loss_surface().loss(n, t.tokens)) # pyrefly: ignore + + +def drop_budget(data: IsoFlopData, budget: float) -> IsoFlopData: + """Return data with a specific compute budget removed.""" + mask = data.C != budget + assert mask.sum() < len(data.C), f"Budget {budget:.2e} not found in data" + return IsoFlopData( + name=data.name, + N=data.N[mask], + D=data.D[mask], + L=data.L[mask], + C=data.C[mask], + ) + + +@dataclass +class LOOResult: + """LOO sensitivity: per-forecast-budget arrays of % deltas across all drops.""" + + # {forecast_budget: {dropped_budget: (a2_pct, a3_pct)}} + per_drop: dict[float, dict[float, tuple[float, float]]] + + def stats(self, fc: float) -> dict[str, tuple[float, float]]: + """Return {stat: (a2, a3)} for a given forecast budget.""" + vals = self.per_drop[fc] + a2 = np.array([v[0] for v in vals.values()]) + a3 = np.array([v[1] for v in vals.values()]) + return { + "mean": (float(a2.mean()), float(a3.mean())), + "median": (float(np.median(a2)), float(np.median(a3))), + "std": (float(a2.std()), float(a3.std())), + "iqr": ( + float(np.subtract(*np.percentile(a2, [75, 25]))), + float(np.subtract(*np.percentile(a3, [75, 25]))), + ), + } + + +@dataclass +class LOORaw: + """Raw loss values for one LOO drop + forecast budget combination.""" + + drop_c: float + fc: float + a2_full: float + a2_drop: float + a3_full: float + a3_drop: float + + @property + def a2_pct(self) -> float: + return (self.a2_drop - self.a2_full) / self.a2_full * 100 + + @property + def a3_pct(self) -> float: + return (self.a3_drop - self.a3_full) / self.a3_full * 100 + + +def leave_one_out_sensitivity( + data: IsoFlopData, fit_full: FitResults, *, fit_asymptote: bool +) -> tuple[LOOResult, list[LOORaw]]: + """LOO: for each training budget, refit without it and compute + % change in forecasted loss at each FORECAST_BUDGET. + + Returns (LOOResult, list of raw values for reporting). + """ + training_budgets = np.unique(data.C) + per_drop: dict[float, dict[float, tuple[float, float]]] = { + fc: {} for fc in FORECAST_BUDGETS + } + raw_records: list[LOORaw] = [] + + for drop_c in training_budgets: + fit_drop = fit_dataset(drop_budget(data, drop_c), fit_asymptote=fit_asymptote) + for fc in FORECAST_BUDGETS: + r = LOORaw( + drop_c=drop_c, + fc=fc, + a2_full=forecast_loss_a2(fit_full, fc), + a2_drop=forecast_loss_a2(fit_drop, fc), + a3_full=forecast_loss_a3(fit_full, fc), + a3_drop=forecast_loss_a3(fit_drop, fc), + ) + per_drop[fc][drop_c] = (r.a2_pct, r.a3_pct) + raw_records.append(r) + + return LOOResult(per_drop=per_drop), raw_records + + +def generate_loo_report( + fit_full: FitResults, loo: LOOResult, raw_records: list[LOORaw] +) -> str: + data = fit_full.data + v = fit_full.vpnls + a2 = fit_full.a2 + pl = fit_full.minima_pl_a2 + fc_max = max(FORECAST_BUDGETS) + training_budgets = a2.compute_budgets + + sections: list[str] = [f"# Forecast Sensitivity Report: {data.name}\n"] + + # -- Fit parameters -- + sections.append(textwrap.dedent(f"""\ + ## Fit Parameters + + ### Approach 2 + + | Parameter | Value | + |-----------|-------| + | a (N* exponent) | {a2.a:.4f} | + | b (D* exponent) | {a2.b:.4f} | + | a + b | {a2.a + a2.b:.4f} | + | a intercept | {a2.a_intercept:.4f} | + | b intercept | {a2.b_intercept:.4f} | + + ### Approach 3 (VPNLS) + + | Parameter | Value | + |-----------|-------| + | E | {v.E:.4f} | + | A | {v.A:.2f} | + | B | {v.B:.2f} | + | alpha | {v.alpha:.4f} | + | beta | {v.beta:.4f} | + | a | {v.a:.4f} | + | b | {v.b:.4f} | + | RSS | {v.residual_sum_squares:.6f} | + + ### Minima Power Law (L = x1 * D*^x2 + x0) + + | Parameter | Value | + |-----------|-------| + | x0 (offset) | {pl.x0:.6f} | + | x1 (coefficient) | {pl.x1:.6f} | + | x2 (exponent) | {pl.x2:.6f} | + | RSS | {pl.rss:.8f} | + """)) + + # -- Forecast points with actuals -- + sections.append("## Forecast Points\n") + sections.append( + "| Budget | N (true) | D (true) | Actual | A2 | A2 Δ% | A3 | A3 Δ% |" + ) + sections.append( + "|--------|----------|----------|--------|-----|-------|-----|-------|" + ) + for fc in FORECAST_BUDGETS: + t = FORECAST_TARGETS[fc] + l_a2 = forecast_loss_a2(fit_full, fc) + l_a3 = forecast_loss_a3(fit_full, fc) + a2_pct = (l_a2 - t.actual) / t.actual * 100 + a3_pct = (l_a3 - t.actual) / t.actual * 100 + sections.append( + f"| {fmt_budget(fc, decimals=0)} | {t.params:.2e} | {t.tokens:.2e} " + f"| {t.actual:.6f} | {l_a2:.6f} | {a2_pct:+.2f}% " + f"| {l_a3:.6f} | {a3_pct:+.2f}% |" + ) + sections.append("") + + # -- Per-forecast-budget LOO stats (what the annotations show) -- + sections.append("## LOO Stats by Forecast Budget\n") + sections.append("| Budget | Stat | A2 | A3 |") + sections.append("|--------|------|-----|-----|") + for fc in FORECAST_BUDGETS: + s = loo.stats(fc) + b = fmt_budget(fc, decimals=0) + sections.append(f"| {b} | mean | {s['mean'][0]:+.3f}% | {s['mean'][1]:+.3f}% |") + sections.append( + f"| | median | {s['median'][0]:+.3f}% | {s['median'][1]:+.3f}% |" + ) + sections.append(f"| | std | {s['std'][0]:.3f}% | {s['std'][1]:.3f}% |") + sections.append(f"| | IQR | {s['iqr'][0]:.3f}% | {s['iqr'][1]:.3f}% |") + sections.append("") + + # -- Per-dropped-budget table at fc_max (what the plot table shows) -- + sections.append( + f"## LOO by Dropped Budget (forecast @ {fmt_budget(fc_max, decimals=0)})\n" + ) + sections.append("| Dropped | A2 % | A3 % |") + sections.append("|---------|------|------|") + a2_vals, a3_vals = [], [] + for drop_c in sorted(training_budgets): + a2_pct, a3_pct = loo.per_drop[fc_max][drop_c] + a2_vals.append(a2_pct) + a3_vals.append(a3_pct) + sections.append(f"| {fmt_budget(drop_c)} | {a2_pct:+.2f} | {a3_pct:+.2f} |") + a2a, a3a = np.array(a2_vals), np.array(a3_vals) + a2_abs, a3_abs = np.abs(a2a), np.abs(a3a) + sections.append( + f"| **mean/med** | **{a2a.mean():+.3f}/{np.median(a2a):+.3f}** " + f"| **{a3a.mean():+.3f}/{np.median(a3a):+.3f}** |" + ) + sections.append( + f"| *std/IQR* | *{a2a.std():.3f}/{np.subtract(*np.percentile(a2a, [75, 25])):.3f}* " + f"| *{a3a.std():.3f}/{np.subtract(*np.percentile(a3a, [75, 25])):.3f}* |" + ) + sections.append( + f"| **mean/med \\|%\\|** | **{a2_abs.mean():.3f}/{np.median(a2_abs):.3f}** " + f"| **{a3_abs.mean():.3f}/{np.median(a3_abs):.3f}** |" + ) + sections.append( + f"| *std/IQR \\|%\\|* | *{a2_abs.std():.3f}/{np.subtract(*np.percentile(a2_abs, [75, 25])):.3f}* " + f"| *{a3_abs.std():.3f}/{np.subtract(*np.percentile(a3_abs, [75, 25])):.3f}* |" + ) + sections.append("") + + # -- Full raw values -- + sections.append("## Raw LOO Values\n") + sections.append( + "| Dropped | Forecast | A2 full | A2 drop | A2 Δ% | A3 full | A3 drop | A3 Δ% |" + ) + sections.append( + "|---------|----------|---------|---------|-------|---------|---------|-------|" + ) + for r in raw_records: + sections.append( + f"| {fmt_budget(r.drop_c)} | {fmt_budget(r.fc, decimals=0)} " + f"| {r.a2_full:.6f} | {r.a2_drop:.6f} | {r.a2_pct:+.2f}% " + f"| {r.a3_full:.6f} | {r.a3_drop:.6f} | {r.a3_pct:+.2f}% |" + ) + sections.append("") + + return "\n".join(sections) + + +def plot_forecast_sensitivity( + fit_full: FitResults, + loo: LOOResult, +) -> plt.Figure: + """Isoflop panel with LOO per-drop table on right, per-forecast stats inset.""" + data = fit_full.data + a2 = fit_full.a2 + training_budgets = a2.compute_budgets + cmap = plt.get_cmap(ISOFLOP_CMAPS.get(data.name, "Blues")) + norm = plt.Normalize( + vmin=np.log10(training_budgets.min()) - 0.75, + vmax=np.log10(training_budgets.max()) + 0.25, + ) + + fig = plt.figure(figsize=(12, 5)) + gs = fig.add_gridspec(1, 2, width_ratios=[1.5, 1], wspace=0.02) + ax = fig.add_subplot(gs[0, 0]) + + # Isoflop curves + A2 parabolas + for i, c in enumerate(training_budgets): + mask = data.C == c + D_group, L_group = data.D[mask], data.L[mask] + order = np.argsort(D_group) + D_group, L_group = D_group[order], L_group[order] + color = cmap(norm(np.log10(c))) + + ax.plot(D_group, L_group, "o", color=color, ms=3, zorder=5) + fit_D = a2.parabola_fits_D[i] + d_curve = np.logspace(np.log10(D_group.min()), np.log10(D_group.max()), 200) + ax.plot( + d_curve, + np.polyval(fit_D.coeffs, np.log10(d_curve)), + "-", + color=color, + lw=1.0, + alpha=0.8, + zorder=3, + ) + ax.plot( + a2.D_opts[i], + fit_D.L_min, + "x", + color=VERTEX_COLOR_A2, + ms=7, + mew=1.5, + zorder=7, + ) + + # Minima power law extending to max forecast budget + pl = fit_full.minima_pl_a2 + d_max_forecast = FORECAST_TARGETS[max(FORECAST_BUDGETS)].tokens + d_pl = np.logspace(np.log10(a2.D_opts.min()), np.log10(d_max_forecast), 300) + ax.plot( + d_pl, + pl.x1 * d_pl**pl.x2 + pl.x0, + "--", + color="grey", + lw=1.0, + alpha=0.6, + zorder=1, + ) + + # Forecast points with annotations + # Per-budget annotation offsets: (xytext, va) + ann_offsets: dict[float, tuple[tuple[int, int], str]] = { + 1e21: ((-57, -18), "center"), + 1e22: ((40, 25), "center"), + 1e23: ((-57, -18), "center"), + } + for fc in FORECAST_BUDGETS: + t = FORECAST_TARGETS[fc] + d_star = t.tokens + l_a2 = forecast_loss_a2(fit_full, fc) + l_a3 = forecast_loss_a3(fit_full, fc) + a2_pct = (l_a2 - t.actual) / t.actual * 100 + a3_pct = (l_a3 - t.actual) / t.actual * 100 + # Unsigned LOO means + loo_a2 = np.mean(np.abs([v[0] for v in loo.per_drop[fc].values()])) + loo_a3 = np.mean(np.abs([v[1] for v in loo.per_drop[fc].values()])) + xytext, va = ann_offsets.get(fc, ((8, 0), "center")) + + ax.plot(d_star, l_a2, "D", color="black", ms=5, zorder=8) + ax.annotate( + f"{fmt_budget(fc, decimals=0)} (actual={t.actual:.3f})\n" + f"A2={l_a2:.3f} ($\\mathbf{{{a2_pct:+.1f}\\%}}$)\n" + f"A3={l_a3:.3f} ($\\mathbf{{{a3_pct:+.1f}\\%}}$)\n" + f"LOO $\\mu$ |%|: A2={loo_a2:.2f} A3={loo_a3:.2f}", + (d_star, l_a2), + textcoords="offset points", + xytext=xytext, + fontsize=6.5, + ha="center", + va=va, + bbox=dict( + boxstyle="round,pad=0.4", fc="white", ec="black", lw=0.5, alpha=0.7 + ), + zorder=9, + ) + + ax.set_xscale("log") + ymin, ymax = ax.get_ylim() + ax.set_ylim(ymin - 0.24, ymax) + ax.set_xlabel("Tokens (D)") + ax.set_ylabel(f"Loss ({DELPHI_METRIC_LABEL})") + + # Budget legend (upper right) + budget_handles = [ + plt.Line2D( + [], [], color=cmap(norm(np.log10(c))), marker="o", ms=4, ls="-", lw=1.0 + ) + for c in training_budgets + ] + budget_labels = [fmt_budget(c) for c in training_budgets] + budget_legend = ax.legend( + budget_handles, + budget_labels, + title="FLOPs", + fontsize=7, + title_fontsize=8, + loc="upper right", + ) + + # Style legend (lower left) + style_handles = [ + plt.Line2D( + [], + [], + color="grey", + ls="--", + lw=1.0, + label="Approach 2 power law\n$L = x_1 D^{x_2} + x_0$", + ), + plt.Line2D( + [], + [], + color=VERTEX_COLOR_A2, + marker="x", + ls="None", + ms=7, + mew=1.5, + label=r"$D^*$ Approach 2", + ), + plt.Line2D( + [], [], color="black", marker="D", ls="None", ms=5, label="Forecast point" + ), + ] + ax.legend(handles=style_handles, fontsize=7, loc="lower left") + ax.add_artist(budget_legend) + + # Right panel: per-dropped-budget table at highest forecast budget + ax_tbl = fig.add_subplot(gs[0, 1]) + ax_tbl.set_axis_off() + + fc_max = max(FORECAST_BUDGETS) + headers = ["Dropped", "A2 %", "A3 %"] + + # Per-budget rows (footnote on first row's A2 value) + min_budget = sorted(training_budgets)[0] + a2_vals_list: list[float] = [] + a3_vals_list: list[float] = [] + rows: list[list[str]] = [] + for drop_c in sorted(training_budgets): + a2_pct, a3_pct = loo.per_drop[fc_max][drop_c] + a2_vals_list.append(a2_pct) + a3_vals_list.append(a3_pct) + a2_cell = f"{a2_pct:+.2f}*" if drop_c == min_budget else f"{a2_pct:+.2f}" + rows.append([fmt_budget(drop_c), a2_cell, f"{a3_pct:+.2f}"]) + + # Aggregate rows (unsigned) + a2_abs, a3_abs = np.abs(np.array(a2_vals_list)), np.abs(np.array(a3_vals_list)) + agg_rows = [ + [ + r"$\mu$/med |%|", + f"{a2_abs.mean():.2f}/{np.median(a2_abs):.2f}", + f"{a3_abs.mean():.2f}/{np.median(a3_abs):.2f}", + ], + [ + r"$\sigma$/IQR |%|", + f"{a2_abs.std():.2f}/{np.subtract(*np.percentile(a2_abs, [75, 25])):.2f}", + f"{a3_abs.std():.2f}/{np.subtract(*np.percentile(a3_abs, [75, 25])):.2f}", + ], + ] + + all_rows = rows + agg_rows + tbl = ax_tbl.table( + cellText=[headers] + all_rows, + loc="center", + cellLoc="center", + ) + tbl.auto_set_font_size(False) + tbl.set_fontsize(8) + tbl.scale(1, 2.31) + + # Header styling + for j in range(len(headers)): + tbl[0, j].set_text_props(fontweight="bold") + tbl[0, j].set_facecolor("#e0e0e0") + + # Data row styling + n_data = len(rows) + for i in range(n_data): + bg = "#f5f5f5" if i % 2 == 0 else "white" + for j in range(len(headers)): + tbl[i + 1, j].set_facecolor(bg) + + # Aggregate row styling: bold values only (not labels), italic throughout + for i in range(len(agg_rows)): + for j in range(len(headers)): + cell = tbl[n_data + 1 + i, j] + cell.set_facecolor("#d0d8e8") + weight = "bold" if j > 0 else "normal" + cell.set_text_props(fontweight=weight, fontstyle="italic") + + ax_tbl.set_title(f"Forecast @ {fmt_budget(fc_max, decimals=0)}", fontsize=9) + + # Footnote with worked example + l_full = forecast_loss_a2(fit_full, fc_max) + fit_drop = fit_dataset(drop_budget(data, min_budget), fit_asymptote=False) + l_drop = forecast_loss_a2(fit_drop, fc_max) + pct = (l_drop - l_full) / l_full * 100 + ax_tbl.text( + 0.5, + -0.02, + f"* Example: (L_drop \u2212 L_full) / L_full \u00d7 100\n" + f" ({l_drop:.4f} \u2212 {l_full:.4f}) / {l_full:.4f} \u00d7 100 = {pct:+.2f}%", + transform=ax_tbl.transAxes, + fontsize=8, + ha="center", + va="top", + style="italic", + alpha=0.7, + ) + + fig.text( + 0.5, + 0.99, + f"Forecast Sensitivity: {data.name}", + fontsize=12, + ha="center", + va="bottom", + ) + fig.text( + 0.5, + 0.95, + "LOO % change in forecasted loss when each training budget is dropped", + fontsize=9, + ha="center", + va="bottom", + ) + + fig.tight_layout(rect=(0, 0.14, 1, 0.96)) + + # Caption + fig.text( + 0.5, + -0.1, + r"$\bf{Figure\ 1}$: Forecast sensitivity via leave-one-out (LOO) over training budgets." + r" Loss at 1e21/1e22/1e23 FLOPs predicted by:" + "\n" + r"Approach 2 power law $L = x_1 D^{x_2} + x_0$ fit to parabola minima;" + r" Approach 3 surface $L = A/N^\alpha + B/D^\beta$ (E=0) evaluated at true $(N, D)$." + "\n" + r"Table shows signed % change when each training budget is dropped." + r" LOO $\mu$|%| = mean of unsigned % changes across all LOO drops.", + fontsize=7, + ha="center", + va="bottom", + ) + + return fig + + +# ============================================================================= +# Figure 2: FLOP factors +# ============================================================================= + + +def plot_flop_factors(data: IsoFlopData) -> plt.Figure: + """Horizontal violin+boxplot of k=C/(ND) by budget with stats table.""" + N, D, C = data.N, data.D, data.C + k = C / (N * D) + budgets = np.unique(C) + n_b = len(budgets) + groups = [k[C == c] for c in budgets] + params = [N[C == c] for c in budgets] + labels = [fmt_budget(c) for c in budgets] + + fig = plt.figure(figsize=(12, 4)) + gs = fig.add_gridspec(1, 2, width_ratios=[2, 1], wspace=0.02) + ax = fig.add_subplot(gs[0, 0]) + + ax.boxplot( + groups, + positions=range(n_b), + vert=False, + widths=0.3, + showfliers=False, + manage_ticks=False, + whis=(0, 100), + patch_artist=True, + boxprops=dict(facecolor="steelblue", alpha=0.5), + medianprops=dict(color="black"), + ) + rng = np.random.default_rng(42) + for i, (g, p) in enumerate(zip(groups, params)): + sizes = 20 + 80 * (p - p.min()) / (p.max() - p.min() + 1e-10) + jitter = rng.uniform(-0.08, 0.08, len(g)) + ax.scatter( + g, + i + jitter, + s=sizes, + color="steelblue", + alpha=0.7, + zorder=5, + edgecolors="white", + linewidths=0.3, + ) + + ax.axvline(6, color="grey", ls="--", lw=0.8, label="k=6") + ax.set_yticks(range(n_b)) + ax.set_yticklabels(labels) + ax.invert_yaxis() + ax.set_xlabel("k = C / (N × D)") + ax.set_title(f"k by Budget — {data.name}") + ax.legend(fontsize=8, loc="lower left") + + # Stats grid (imshow + text, labels at bottom via xticks) + ax_tbl = fig.add_subplot(gs[0, 1]) + col_labels = [r"$\mu$", "med", "min", "max"] + n_cols = len(col_labels) + cell_data = np.array([[g.mean(), np.median(g), g.min(), g.max()] for g in groups]) + # Alternating row backgrounds (0=white, 0.05=light grey) + bg = np.zeros((n_b, n_cols)) + bg[::2] = 0.15 + ax_tbl.imshow( + bg, aspect="auto", cmap="Greys", vmin=0, vmax=1, interpolation="nearest" + ) + for i in range(n_b): + for j in range(n_cols): + weight = "bold" if j == 0 else "normal" + ax_tbl.text( + j, + i, + f"{cell_data[i, j]:.2f}", + ha="center", + va="center", + fontsize=8, + fontweight=weight, + ) + ax_tbl.set_xticks(range(n_cols)) + ax_tbl.set_xticklabels(col_labels, fontsize=9) + ax_tbl.xaxis.set_ticks_position("bottom") + ax_tbl.set_yticks([]) + ax_tbl.set_title("Summary Stats") + ax_tbl.tick_params(left=False, bottom=False) + + fig.text(0.5, 0.99, "Empirical FLOP Factors", fontsize=12, ha="center", va="bottom") + fig.tight_layout(rect=(0, 0.16, 1, 0.96)) + + fig.text( + 0.5, + -0.1, + r"$\bf{Figure\ 2}$: Empirical FLOP factor $k = C/(N \cdot D)$ per training budget." + r" Points sized by parameter count $N$." + "\n" + r"The standard $C = 6ND$ approximation holds at mid-to-high budgets" + r" but overestimates at the lowest budget ($k \approx 4.8$).", + fontsize=7, + ha="center", + va="bottom", + ) + return fig + + +# ============================================================================= +# Figure 3: IsoFLOP comparison +# ============================================================================= + + +def plot_isoflop_panel( + ax: plt.Axes, results: FitResults, *, show_vertex_legend: bool = False +) -> None: + """Plot isoFLOP curves with Approach 2 parabolas (solid), Approach 3 + prediction (dashed), and D* vertex markers on the Approach 2 parabola.""" + data = results.data + a2 = results.a2 + surface = results.vpnls.to_loss_surface() + budgets = a2.compute_budgets + cmap_name = ISOFLOP_CMAPS.get(data.name, "viridis") + cmap = plt.get_cmap(cmap_name) + # Start at 0.3 to avoid too-light colors, end at 0.9 to avoid near-black + norm = plt.Normalize( + vmin=np.log10(budgets.min()) - 0.75, + vmax=np.log10(budgets.max()) + 0.25, + ) + deltas = compute_dopt_deltas(results) + + for i, c in enumerate(budgets): + mask = data.C == c + D_group, L_group = data.D[mask], data.L[mask] + order = np.argsort(D_group) + D_group, L_group = D_group[order], L_group[order] + color = cmap(norm(np.log10(c))) + + ax.plot(D_group, L_group, "o", color=color, ms=3, zorder=5) + + d_curve = np.logspace(np.log10(D_group.min()), np.log10(D_group.max()), 200) + + # Approach 2 parabola (solid, primary) + fit_D = a2.parabola_fits_D[i] + ax.plot( + d_curve, + np.polyval(fit_D.coeffs, np.log10(d_curve)), + "-", + color=color, + lw=1.0, + alpha=0.8, + zorder=3, + ) + + # Approach 3 prediction (dashed, secondary) + k = results.k_values[c] + if SHOW_A3_CURVES: + n_curve = c / (k * d_curve) + ax.plot( + d_curve, + surface.loss(n_curve, d_curve), + "--", + color=color, + lw=1.0, + alpha=0.7, + zorder=2, + ) + + # D* vertices on the Approach 2 parabola + ax.plot( + a2.D_opts[i], + fit_D.L_min, + "x", + color=VERTEX_COLOR_A2, + ms=7, + mew=1.5, + zorder=7, + ) + d3 = d_opt_a3(surface, c, k) + ax.plot( + d3, + np.polyval(fit_D.coeffs, np.log10(d3)), + "+", + color=VERTEX_COLOR_A3, + ms=8, + mew=1.5, + zorder=7, + ) + + # Delta % annotation to the right of rightmost data point + abs_delta = abs(deltas.pct[c]) + ann_color = "grey" if abs_delta < 10 else "black" + ann_weight = "bold" if abs_delta >= 20 else "normal" + ax.annotate( + f"{deltas.pct[c]:+.0f}%", + (D_group[-1], L_group[-1]), + textcoords="offset points", + xytext=(6, 0), + fontsize=6, + ha="left", + va="center", + color=ann_color, + fontweight=ann_weight, + zorder=8, + ) + + # Power law through A2 parabola minima + if SHOW_MINIMA_PL: + pl = results.minima_pl_a2 + d_pl = np.logspace(np.log10(a2.D_opts.min()), np.log10(a2.D_opts.max()), 200) + ax.plot( + d_pl, + pl.x1 * d_pl**pl.x2 + pl.x0, + "--", + color="grey", + lw=0.8, + alpha=0.5, + zorder=1, + ) + + ax.set_xscale("log") + xmin, xmax = ax.get_xlim() + ax.set_xlim(xmin, xmax * 1.5) + ax.set_xlabel("Tokens (D)") + ax.set_ylabel("Loss") + title = data.name + if data.name == "Delphi": + title += f" ({DELPHI_METRIC_LABEL})" + ax.set_title(title) + + # Budget legend + handles = [ + plt.Line2D( + [], [], color=cmap(norm(np.log10(c))), marker="o", ms=4, ls="-", lw=1.0 + ) + for c in budgets + ] + labels = [fmt_budget(c) for c in budgets] + budget_legend = ax.legend( + handles, labels, title="FLOPs", fontsize=7, title_fontsize=8, loc="upper right" + ) + + if show_vertex_legend: + vertex_handles = [ + plt.Line2D([], [], color="grey", ls="-", lw=1.0, label="Approach 2"), + ] + if SHOW_A3_CURVES: + vertex_handles.append( + plt.Line2D([], [], color="grey", ls="--", lw=1.0, label="Approach 3"), + ) + vertex_handles += [ + plt.Line2D( + [], + [], + color="red", + marker="x", + ls="None", + ms=7, + mew=1.5, + label=r"$D^*$ Approach 2", + ), + plt.Line2D( + [], + [], + color="blue", + marker="+", + ls="None", + ms=8, + mew=1.5, + label=r"$D^*$ Approach 3", + ), + ] + ax.legend( + handles=vertex_handles, + fontsize=7, + loc="lower left", + framealpha=0.9, + ) + ax.add_artist(budget_legend) + + +VIOLIN_COLORS = { + "Llama 3": mcolors.to_hex(plt.get_cmap("Reds")(0.85)), + "Delphi": mcolors.to_hex(plt.get_cmap("Blues")(0.85)), +} + + +def plot_comparison(results_list: list[FitResults]) -> plt.Figure: + """Side-by-side isoFLOP comparison with violin plot of D* deltas.""" + n = len(results_list) + fig = plt.figure(figsize=(12, 5)) + gs = fig.add_gridspec(1, n + 1, width_ratios=[2.5] * n + [0.9], wspace=0.02) + + for j, res in enumerate(results_list): + ax = fig.add_subplot(gs[0, j]) + plot_isoflop_panel(ax, res, show_vertex_legend=(j == 0)) + # Place y-tick labels just inside the left edge of the plot area + if j > 0: + ax.set_ylabel("") + ax.tick_params( + axis="y", direction="in", left=True, labelleft=True, labelsize=6, pad=-8 + ) + for label in ax.yaxis.get_ticklabels(): + label.set_zorder(0) + label.set_alpha(0.4) + label.set_horizontalalignment("left") + + # Violin panel + ax_v = fig.add_subplot(gs[0, n]) + all_vals: list[np.ndarray] = [] + names: list[str] = [] + for res in results_list: + d = compute_dopt_deltas(res) + all_vals.append(np.array(list(d.pct.values()))) + names.append(res.data.name) + + positions = list(range(len(all_vals))) + parts = ax_v.violinplot(all_vals, positions=positions, vert=True, showextrema=False) + for i, body in enumerate(parts["bodies"]): # pyrefly: ignore + color = VIOLIN_COLORS.get(names[i], "grey") + body.set_facecolor(color) + body.set_alpha(0.4) + body.set_edgecolor(color) + + # Skinny boxplots overlaid + bp = ax_v.boxplot( + all_vals, + positions=positions, + widths=0.08, + vert=True, + patch_artist=True, + showfliers=False, + manage_ticks=False, + zorder=4, + whis=(0, 100), # whiskers span full data range + ) + for i, patch in enumerate(bp["boxes"]): + color = VIOLIN_COLORS.get(names[i], "grey") + patch.set_facecolor(color) + patch.set_alpha(0.5) + patch.set_edgecolor(color) + patch.set_linewidth(0.8) + for i in range(len(all_vals)): + color = VIOLIN_COLORS.get(names[i], "grey") + for element in ("whiskers", "caps"): + for line in bp[element][2 * i : 2 * i + 2]: + line.set_color(color) + line.set_linewidth(0.8) + bp["medians"][i].set_color("black") + bp["medians"][i].set_linewidth(0.8) + + # Individual points + for i, (vals, name) in enumerate(zip(all_vals, names)): + color = VIOLIN_COLORS[name] + jitter = np.random.default_rng(42).uniform(-0.06, 0.06, size=len(vals)) + ax_v.scatter(i + jitter, vals, s=15, color=color, zorder=5, alpha=0.8) + + ax_v.axhline(0, color="grey", ls="--", lw=0.7) + ax_v.set_xticks(positions) + ax_v.set_xticklabels([n.split()[0] for n in names]) + ax_v.set_title(r"$\Delta$% $D^*$") + ax_v.yaxis.set_label_position("right") + ax_v.yaxis.tick_right() + ax_v.tick_params(axis="y", labelsize=8) + + fig.text( + 0.5, + 1.02, + "IsoFLOP Experiment Comparison", + fontsize=12, + ha="center", + va="bottom", + ) + fig.text( + 0.5, + 0.97, + r"$\Delta$% $D^*$: per-budget % difference in optimal tokens $(D^*_{A3} - D^*_{A2})/D^*_{A2}$", + fontsize=9, + ha="center", + va="bottom", + ) + fig.tight_layout(rect=(0, 0.14, 1, 0.96)) + + # Caption + fig.text( + 0.5, + -0.08, + r"$\bf{Figure\ 3}$: IsoFLOP curves with Approach 2 parabolic fits ($L$ vs $\log D$)" + r" and inferred $D^*$ vertices from Approach 2 ($\times$) and Approach 3 ($+$)." + "\n" + r"Approach 3 fits $L = E + A/N^\alpha + B/D^\beta$ via VPNLS grid search." + r" Violin plot shows distribution of per-budget $\Delta\% \ D^*$ between methods.", + fontsize=7, + ha="center", + va="bottom", + ) + + # Annotations in empty space + bbox_props = dict(boxstyle="round,pad=0.2", alpha=0.6, ec="black", lw=0.5) + ann_positions = [(0.62, 0.90), (0.75, 0.24)] + for i, ((px, py), name) in enumerate(zip(ann_positions, names)): + color = VIOLIN_COLORS[name] + d = compute_dopt_deltas(results_list[i]) + ax_v.text( + px, + py, + f"$\\mu$={d.mean_signed:+.1f}%\nmed={d.median_signed:+.1f}%", + transform=ax_v.transAxes, + fontsize=7, + ha="center", + va="center", + color="black", + bbox={**bbox_props, "facecolor": "white"}, + ) + + return fig + + +# ============================================================================= +# Reports +# ============================================================================= + +EXPERIMENT_TEMPLATE = textwrap.dedent("""\ + ## {name} + + Data: {n_points} points, {n_budgets} budgets + Flop factor mode: {k_mode} + + ### Approach 2 (Parabolic IsoFLOP Fits) + + a (N* exponent) = {a2_a:.4f} + b (D* exponent) = {a2_b:.4f} + a + b = {a2_ab:.4f} + a intercept = {a2_a_int:.4f} + b intercept = {a2_b_int:.4f} + + ### Approach 3 (VPNLS Grid, resolution={grid_res}) + + E = {a3_E:.4f} + A = {a3_A:.2f} + B = {a3_B:.2f} + alpha = {a3_alpha:.4f} + beta = {a3_beta:.4f} + a = {a3_a:.4f} + b = {a3_b:.4f} + RSS = {a3_rss:.6f} + + ### Minima Power Law (L = x1 * D*^x2 + x0) + + Fit to Approach 2 parabola vertices (D*, L_min). + + x0 (offset) = {pl_x0:.6f} + x1 (coefficient) = {pl_x1:.6f} + x2 (exponent) = {pl_x2:.6f} + RSS = {pl_rss:.8f} + + ### D* Comparison (Approach 3 vs Approach 2) + + Positive delta means Approach 3 infers more tokens than Approach 2. + + {budget_table} + + Mean delta% = {mean_signed:+.1f}% + Mean |delta%| = {mean_unsigned:.1f}% + Median delta% = {median_signed:+.1f}% + Median |delta%| = {median_unsigned:.1f}% +""") + +BUDGET_TABLE_HEADER = " {:<12s} {:>8s} {:>14s} {:>14s} {:>10s} {:>10s}".format( + "Budget", + "k", + "D* (A2)", + "D* (A3)", + "Delta", + "Delta%", +) + + +def _fmt_tokens(d: float) -> str: + """Format token count compactly, e.g. 1.23e+10.""" + return f"{d:.2e}" + + +def generate_report(results_list: list[FitResults]) -> str: + """Generate a text report for all experiments.""" + sections: list[str] = ["# Delphi Scaling Analysis Report\n"] + for r in results_list: + v, a2 = r.vpnls, r.a2 + surface = v.to_loss_surface() + dd = compute_dopt_deltas(r) + budgets = a2.compute_budgets + + # Build per-budget table + table_lines = [BUDGET_TABLE_HEADER, " " + "-" * 72] + for i, c in enumerate(budgets): + d2 = a2.D_opts[i] + d3 = d_opt_a3(surface, c, r.k_values[c]) + raw_str = f"{dd.raw[c]:+.2e}" + table_lines.append( + " {:<12s} {:>8.3f} {:>14s} {:>14s} {:>10s} {:>+9.1f}%".format( + fmt_budget(c), + r.k_values[c], + _fmt_tokens(d2), + _fmt_tokens(d3), + raw_str, + dd.pct[c], + ) + ) + + k_mode = "learned per-budget (OLS)" if LEARN_K else "fixed k=6" + sections.append( + EXPERIMENT_TEMPLATE.format( + name=r.data.name, + n_points=len(r.data.N), + n_budgets=len(budgets), + k_mode=k_mode, + a2_a=a2.a, + a2_b=a2.b, + a2_ab=a2.a + a2.b, + a2_a_int=a2.a_intercept, + a2_b_int=a2.b_intercept, + a3_E=v.E, + a3_A=v.A, + a3_B=v.B, + a3_alpha=v.alpha, + a3_beta=v.beta, + a3_a=v.a, + a3_b=v.b, + grid_res=GRID_RESOLUTION, + a3_rss=sum(r.rss.values()), + pl_x0=r.minima_pl_a2.x0, + pl_x1=r.minima_pl_a2.x1, + pl_x2=r.minima_pl_a2.x2, + pl_rss=r.minima_pl_a2.rss, + budget_table="\n".join(table_lines), + mean_signed=dd.mean_signed, + mean_unsigned=dd.mean_unsigned, + median_signed=dd.median_signed, + median_unsigned=dd.median_unsigned, + ) + ) + return "\n".join(sections) + + +# ============================================================================= +# Main +# ============================================================================= + + +def main(): + OUT_DIR.mkdir(parents=True, exist_ok=True) + + llama3 = load_llama3() + delphi = load_delphi() + + # Figure 1: Forecast sensitivity (Delphi only, E=0 surface for better extrapolation) + delphi_fit_noE = fit_dataset(delphi, fit_asymptote=False) + loo, loo_raw = leave_one_out_sensitivity( + delphi, delphi_fit_noE, fit_asymptote=False + ) + fig1 = plot_forecast_sensitivity(delphi_fit_noE, loo) + save_figure(fig1, OUT_DIR / "forecast_sensitivity.png", dpi=300) + plt.close(fig1) + + # Figure 2: FLOP factors (Delphi only) + fig2 = plot_flop_factors(delphi) + save_figure(fig2, OUT_DIR / "flop_factors.png", dpi=300) + plt.close(fig2) + + # Figure 3: IsoFLOP comparison + llama3_fit = fit_dataset(llama3, fit_asymptote=True) + delphi_fit = fit_dataset(delphi, fit_asymptote=True) + fig3 = plot_comparison([llama3_fit, delphi_fit]) + save_figure(fig3, OUT_DIR / "isoflop_comparison.png", dpi=300) + plt.close(fig3) + + # Reports + report = generate_report([llama3_fit, delphi_fit]) + report_path = OUT_DIR / "isoflop_comparison.md" + report_path.write_text(report) + print(report) + print(f"\nReport saved to {report_path}") + + loo_report = generate_loo_report(delphi_fit_noE, loo, loo_raw) + loo_report_path = OUT_DIR / "forecast_sensitivity.md" + loo_report_path.write_text(loo_report) + print(loo_report) + print(f"\nLOO report saved to {loo_report_path}") + + +if __name__ == "__main__": + main() diff --git a/analysis/results/flop_factors.pdf b/analysis/results/flop_factors.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8a831fdcf215c63fe1d56f1ca7619db65ed17045 GIT binary patch literal 46804 zcmZsCbyQr>vTh&{91`3$_~0%9f+n~J3pNZoxLa^{cMlMpL4w=hZo%CKcMtaXopbJ8 z_rCYm{IS=bmioF^@9L_rs%VuZrCB&wxlw7$mnqAdQ8_5tDQ%4{QH6ym+0@FWg|0?BPHi+2USWD5mbn-#=49jqqU8SfAIe5fP9O&xN}hjSQQ6eYjZ7?T%qV&P)9PRgR0BCt>b{DVlzxQ* za&w|&`)d6PLHs{YiT^ymQhxs*a5(zOLsV{IBvA zKqeMO;nQkA`W{vfjN*!v{asWQHNYip9cH!IO|#Bm%6bv$THT zyK0bl1@hwdyd&+!J4(2Z*f~FLZbUnNT;BLRZ_D(rJss^#UmMu|c-f3G*vzTIbbZ8r zc|1SsS2`R2#)kQFeNq_gRW=$D`SMr#nYr)BA>&)ei_;D__xtP&nMz^`|MwQ5b?WCD*TMNCAWK91}J8xs%CLz z`Nn7Ue;`=A++FBC8n`}A_$jjS5$Jqny#EtJYFmj{_Xt}VjuG*>zv_QJJGpz@Es7cM 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resolution=0.001) + + E = 0.6048 + A = 59.14 + B = 156.22 + alpha = 0.3100 + beta = 0.3140 + a = 0.5032 + b = 0.4968 + RSS = 0.001480 + +### Minima Power Law (L = x1 * D*^x2 + x0) + +Fit to Approach 2 parabola vertices (D*, L_min). + + x0 (offset) = 0.649869 + x1 (coefficient) = 3335.421967 + x2 (exponent) = -0.428627 + RSS = 0.00015275 + +### D* Comparison (Approach 3 vs Approach 2) + +Positive delta means Approach 3 infers more tokens than Approach 2. + + Budget k D* (A2) D* (A3) Delta Delta% + ------------------------------------------------------------------------ + 6.0e18 5.802 4.41e+09 4.31e+09 -9.80e+07 -2.2% + 1.0e19 5.878 5.14e+09 5.52e+09 +3.85e+08 +7.5% + 3.0e19 5.912 7.56e+09 9.50e+09 +1.94e+09 +25.7% + 6.0e19 6.217 1.15e+10 1.31e+10 +1.54e+09 +13.4% + 1.0e20 6.641 1.53e+10 1.63e+10 +9.86e+08 +6.4% + 3.0e20 6.003 2.53e+10 2.96e+10 +4.29e+09 +16.9% + 6.0e20 6.147 4.10e+10 4.13e+10 +3.04e+08 +0.7% + 1.0e21 6.239 5.46e+10 5.28e+10 -1.80e+09 -3.3% + 3.0e21 4.137 9.82e+10 1.12e+11 +1.36e+10 +13.9% + 1.0e22 5.536 2.38e+11 1.76e+11 -6.23e+10 -26.2% + + Mean delta% = +5.3% + Mean |delta%| = 11.6% + Median delta% = +7.0% + Median |delta%| = 10.4% + +## Delphi + +Data: 78 points, 7 budgets +Flop factor mode: learned per-budget (OLS) + +### Approach 2 (Parabolic IsoFLOP Fits) + + a (N* exponent) = 0.3907 + b (D* exponent) = 0.5744 + a + b = 0.9651 + a intercept = 1.3622 + b intercept = -1.4342 + +### Approach 3 (VPNLS Grid, resolution=0.001) + + E = 2.5786 + A = 302423.82 + B = 3928.62 + alpha = 0.6830 + beta = 0.4130 + a = 0.3768 + b = 0.6232 + RSS = 0.010100 + +### Minima Power Law (L = x1 * D*^x2 + x0) + +Fit to Approach 2 parabola vertices (D*, L_min). + + x0 (offset) = 1.784029 + x1 (coefficient) = 88.078799 + x2 (exponent) = -0.184121 + RSS = 0.00013615 + +### D* Comparison (Approach 3 vs Approach 2) + +Positive delta means Approach 3 infers more tokens than Approach 2. + + Budget k D* (A2) D* (A3) Delta Delta% + ------------------------------------------------------------------------ + 2.9e18 3.969 1.48e+09 1.63e+09 +1.46e+08 +9.9% + 9.1e18 5.708 2.90e+09 2.64e+09 -2.55e+08 -8.8% + 1.8e19 6.246 4.20e+09 3.79e+09 -4.15e+08 -9.9% + 3.1e19 6.946 5.70e+09 5.06e+09 -6.35e+08 -11.1% + 8.9e19 6.635 1.02e+10 1.00e+10 -2.34e+08 -2.3% + 1.7e20 6.134 1.59e+10 1.59e+10 +4.52e+07 +0.3% + 3.1e20 5.703 2.19e+10 2.38e+10 +1.96e+09 +8.9% + + Mean delta% = -1.9% + Mean |delta%| = 7.3% + Median delta% = -2.3% + Median |delta%| = 8.9% diff --git a/analysis/results/isoflop_comparison.pdf b/analysis/results/isoflop_comparison.pdf new file mode 100644 index 0000000000000000000000000000000000000000..99b99d6dfc41f5749590356a83db191982ed91a3 GIT binary patch literal 58694 zcmZs>byOX}w)`EcB;-kr*~KP>e|!_qT-Cq05(MGl4Y{uCPZekZ)COx7KnU&WK1e4@QT>oQ&xUCI{jP<_^nAGJBEQ}37WSswLin)R$ zltKC+V=}h?bSUV9K*kO>WbFT%h)l|6`bOq9reqxdJ?daT<|`1W4vyeHy4y7wg<$+-W6@w<(U?R$&)pZ)*L$iLzL 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