docs(kvc): add TTFT probability density figure (KVC v2 vs 4DP)
Adds a two-panel TTFT PDF comparison plot inserted as a new V2_DEEP_ANALYSIS
§3.4 ("TTFT 概率密度对比: bimodal vs unimodal"). Single-percentile numbers
(p50 / p99) hide the qualitative difference between the two distributions;
the figure makes it visible at a glance.
Left panel (linear x in [0, 0.6]s, body):
KVC has a sharp peak at ~40ms (the direct-to-D fast path).
DP has a broad peak around 50-200ms (full prefill per request).
Annotated with p50 and p90 markers for each side.
Right panel (log x in [10ms, 10s], full range):
KVC is visibly bimodal: a tall fast-path peak plus a small reseed tail
around 1-5s.
DP is unimodal: a single broad peak with shorter tail.
Annotated with p99 callouts pointing to each tail.
KDE: scipy.stats.gaussian_kde, bandwidth=0.15 for the body (Scott's rule
oversmooths the sharp fast-path peak), log10-transformed for the full-range
panel so the bimodal structure is visible.
Bundled:
- scripts/analysis/plot_ttft_pdf.py -- rerunable when v2 / DP data change.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
kzlin
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scripts/analysis/plot_ttft_pdf.py
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scripts/analysis/plot_ttft_pdf.py
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#!/usr/bin/env python3
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"""Generate TTFT probability density curves: KVC 1P3D v2 vs 4-way DP CA.
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Inputs:
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outputs/qwen3-30b-tp1-ts1-migration-v2/kvc_1p3d_migration_v2_run1_metrics.jsonl
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outputs/qwen3-30b-tp1-ts1-validation/dp4_metrics.jsonl
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Outputs:
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docs/figures/ttft_pdf_comparison.png -- two-panel figure:
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left panel: linear x in [0, 1.0]s zoomed on the body
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right panel: log x covering full range (0.01 -- 10 s)
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Each KDE curve uses scipy.stats.gaussian_kde with Scott's rule bandwidth.
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Aborted requests are excluded (same filter as metrics.py:_is_failed_request).
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"""
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from __future__ import annotations
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import json
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from pathlib import Path
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import matplotlib.pyplot as plt
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import numpy as np
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from scipy.stats import gaussian_kde
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ROOT = Path(__file__).resolve().parents[2]
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KVC = ROOT / "outputs/qwen3-30b-tp1-ts1-migration-v2/kvc_1p3d_migration_v2_run1_metrics.jsonl"
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DP = ROOT / "outputs/qwen3-30b-tp1-ts1-validation/dp4_metrics.jsonl"
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OUT = ROOT / "docs/figures/ttft_pdf_comparison.png"
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def load(p: Path) -> list[dict]:
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return [json.loads(line) for line in p.open()]
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def is_failed(r: dict) -> bool:
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if r.get("error"):
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return True
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fr = r.get("finish_reason")
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if fr and ("abort" in str(fr).lower() or "badrequest" in str(fr).lower()):
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return True
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return False
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def pct(vals: np.ndarray, q: float) -> float:
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return float(np.quantile(vals, q))
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def main() -> None:
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kvc = [r for r in load(KVC) if not is_failed(r)]
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dp = [r for r in load(DP) if not is_failed(r)]
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kvc_ttft = np.array([r["ttft_s"] for r in kvc if r.get("ttft_s") is not None])
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dp_ttft = np.array([r["ttft_s"] for r in dp if r.get("ttft_s") is not None])
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# Trim absurdly small zeros (rare measurement artifacts) so log KDE behaves.
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kvc_ttft = kvc_ttft[kvc_ttft > 1e-4]
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dp_ttft = dp_ttft[dp_ttft > 1e-4]
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KVC_COLOR = "#1F77B4" # blue
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DP_COLOR = "#D62728" # red
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fig, axes = plt.subplots(1, 2, figsize=(16, 6.5))
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# ------------------------------------------------------------------
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# Left panel: linear x ∈ [0, 0.6]s -- body of the distribution
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# ------------------------------------------------------------------
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ax = axes[0]
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x_body = np.linspace(0.0, 0.6, 600)
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# KDE on linear ttft values, clipped to body
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kde_kvc_lin = gaussian_kde(kvc_ttft, bw_method=0.15)
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kde_dp_lin = gaussian_kde(dp_ttft, bw_method=0.15)
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ax.plot(x_body, kde_kvc_lin(x_body),
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color=KVC_COLOR, lw=2.5, label=f"KVC 1P3D v2 (n={len(kvc_ttft)})")
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ax.fill_between(x_body, kde_kvc_lin(x_body), alpha=0.20, color=KVC_COLOR)
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ax.plot(x_body, kde_dp_lin(x_body),
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color=DP_COLOR, lw=2.5, label=f"4-way DP CA (n={len(dp_ttft)})")
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ax.fill_between(x_body, kde_dp_lin(x_body), alpha=0.20, color=DP_COLOR)
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# Vertical lines for p50, p90
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for q, ls in [(0.50, "-"), (0.90, "--")]:
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ax.axvline(pct(kvc_ttft, q), color=KVC_COLOR, ls=ls, alpha=0.55, lw=1.1)
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ax.axvline(pct(dp_ttft, q), color=DP_COLOR, ls=ls, alpha=0.55, lw=1.1)
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ymax = ax.get_ylim()[1]
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ax.text(pct(kvc_ttft, 0.50), ymax * 0.97,
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f"KVC p50\n{pct(kvc_ttft, 0.50)*1000:.0f}ms",
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color=KVC_COLOR, fontsize=9, va="top", ha="left",
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bbox=dict(facecolor="white", edgecolor="none", alpha=0.7, pad=2))
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ax.text(pct(dp_ttft, 0.50), ymax * 0.50,
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f"DP p50\n{pct(dp_ttft, 0.50)*1000:.0f}ms",
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color=DP_COLOR, fontsize=9, va="top", ha="left",
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bbox=dict(facecolor="white", edgecolor="none", alpha=0.7, pad=2))
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ax.text(pct(kvc_ttft, 0.90), ymax * 0.30,
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f"KVC p90\n{pct(kvc_ttft, 0.90)*1000:.0f}ms",
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color=KVC_COLOR, fontsize=9, va="top", ha="left",
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bbox=dict(facecolor="white", edgecolor="none", alpha=0.7, pad=2))
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ax.text(pct(dp_ttft, 0.90), ymax * 0.18,
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f"DP p90\n{pct(dp_ttft, 0.90)*1000:.0f}ms",
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color=DP_COLOR, fontsize=9, va="top", ha="left",
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bbox=dict(facecolor="white", edgecolor="none", alpha=0.7, pad=2))
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ax.set_xlim(0, 0.6)
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ax.set_xlabel("TTFT (seconds, linear)", fontsize=11)
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ax.set_ylabel("Probability density", fontsize=11)
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ax.set_title("Body of distribution (TTFT ≤ 0.6 s)", fontsize=12, pad=10)
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ax.legend(loc="upper right", fontsize=10, framealpha=0.95)
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ax.grid(True, linestyle=":", alpha=0.4)
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ax.set_axisbelow(True)
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# ------------------------------------------------------------------
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# Right panel: log x ∈ [0.01, 10]s -- full range incl. tail
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# PDF on log-x: we plot density vs log10(t) so the curve integrates
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# to 1 over log space (standard "log-density" presentation).
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# ------------------------------------------------------------------
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ax = axes[1]
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# KDE on log10(ttft) so the resulting curve integrates to 1 over log10 t
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kde_kvc_log = gaussian_kde(np.log10(kvc_ttft), bw_method="scott")
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kde_dp_log = gaussian_kde(np.log10(dp_ttft), bw_method="scott")
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log_x = np.linspace(np.log10(0.01), np.log10(10.0), 600)
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x_full = 10 ** log_x
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y_kvc = kde_kvc_log(log_x)
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y_dp = kde_dp_log(log_x)
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ax.plot(x_full, y_kvc, color=KVC_COLOR, lw=2.5, label=f"KVC 1P3D v2 (n={len(kvc_ttft)})")
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ax.fill_between(x_full, y_kvc, alpha=0.20, color=KVC_COLOR)
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ax.plot(x_full, y_dp, color=DP_COLOR, lw=2.5, label=f"4-way DP CA (n={len(dp_ttft)})")
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ax.fill_between(x_full, y_dp, alpha=0.20, color=DP_COLOR)
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ax.set_xscale("log")
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ax.set_xlim(0.01, 10.0)
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# Percentile markers
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quartile_styles = [(0.50, "-", "p50"), (0.90, "--", "p90"), (0.99, ":", "p99")]
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for q, ls, name in quartile_styles:
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ax.axvline(pct(kvc_ttft, q), color=KVC_COLOR, ls=ls, alpha=0.55, lw=1.1)
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ax.axvline(pct(dp_ttft, q), color=DP_COLOR, ls=ls, alpha=0.55, lw=1.1)
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# Annotate p99 specifically since this is the key reviewer-targeted callout
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ymax = max(y_kvc.max(), y_dp.max())
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kvc_p99 = pct(kvc_ttft, 0.99)
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dp_p99 = pct(dp_ttft, 0.99)
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ax.annotate(f"KVC p99 = {kvc_p99:.2f}s\n(slow-path reseed tail)",
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xy=(kvc_p99, kde_kvc_log(np.log10(kvc_p99))[0]),
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xytext=(2.0, ymax * 0.65),
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fontsize=10, color=KVC_COLOR, fontweight="bold",
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arrowprops=dict(arrowstyle="->", color=KVC_COLOR, lw=1.0))
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ax.annotate(f"DP p99 = {dp_p99*1000:.0f}ms",
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xy=(dp_p99, kde_dp_log(np.log10(dp_p99))[0]),
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xytext=(0.025, ymax * 0.80),
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fontsize=10, color=DP_COLOR, fontweight="bold",
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arrowprops=dict(arrowstyle="->", color=DP_COLOR, lw=1.0))
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# Highlight the KVC bimodal structure
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ax.annotate("KVC fast path\n(direct-to-D, 91.6%)",
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xy=(0.05, y_kvc[np.argmin(np.abs(x_full - 0.05))]),
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xytext=(0.012, ymax * 0.45),
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fontsize=9, color=KVC_COLOR, style="italic",
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arrowprops=dict(arrowstyle="->", color=KVC_COLOR, lw=0.7, alpha=0.6))
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ax.annotate("KVC slow path\n(reseed, ~3.4%)",
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xy=(2.5, y_kvc[np.argmin(np.abs(x_full - 2.5))]),
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xytext=(3.0, ymax * 0.30),
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fontsize=9, color=KVC_COLOR, style="italic",
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arrowprops=dict(arrowstyle="->", color=KVC_COLOR, lw=0.7, alpha=0.6))
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# Custom tick labels in seconds (instead of 10^-2, 10^-1, 10^0, 10^1)
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ax.set_xticks([0.01, 0.05, 0.1, 0.5, 1.0, 5.0, 10.0])
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ax.set_xticklabels(["10ms", "50ms", "100ms", "500ms", "1s", "5s", "10s"])
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ax.set_xlabel("TTFT (log scale)", fontsize=11)
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ax.set_ylabel("Density (per log₁₀ s)", fontsize=11)
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ax.set_title("Full range (TTFT 10 ms – 10 s, log x)", fontsize=12, pad=10)
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ax.legend(loc="upper left", fontsize=10, framealpha=0.95)
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ax.grid(True, which="both", linestyle=":", alpha=0.4)
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ax.set_axisbelow(True)
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fig.suptitle(
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"TTFT probability density: KVC 1P3D v2 vs 4-way DP CA\n"
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"SWE-Bench 50sess trace · ts=1 · 4× H100 80GB · aborted/error requests excluded",
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fontsize=13, y=1.02,
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)
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plt.tight_layout()
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plt.savefig(OUT, dpi=150, bbox_inches="tight")
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print(f"wrote {OUT}")
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plt.close(fig)
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# ------------------------------------------------------------------
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# Print summary stats for doc cross-reference
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# ------------------------------------------------------------------
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print(f"\n=== TTFT distribution summary ===")
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for name, arr in [("KVC v2", kvc_ttft), ("DP 4w", dp_ttft)]:
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print(f" {name} (n={len(arr)})")
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print(f" min={arr.min()*1000:.1f}ms p10={pct(arr,0.10)*1000:.1f}ms "
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f"p50={pct(arr,0.50)*1000:.1f}ms p90={pct(arr,0.90)*1000:.1f}ms "
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f"p99={pct(arr,0.99)*1000:.1f}ms max={arr.max()*1000:.1f}ms")
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if __name__ == "__main__":
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main()
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