docs(kvc): add TPOT probability density figure (KVC v2 vs 4DP)
Mirrors the TTFT PDF figure style. Inserted into V2_DEEP_ANALYSIS as a new §3.5 immediately following §3.4 (TTFT PDF). The figure preempts a likely reviewer challenge: "Is KVC's TTFT win bought by sacrificing decode throughput (TPOT)?". The empirical answer is no -- two KDE curves overlap visually almost perfectly. Measured TPOT deltas (KVC v2 vs DP 4w, n>=4382 each): mean: +0.019 ms (+0.34%) p50: +0.035 ms (+0.63%) p90: -0.050 ms (-0.75%, slight KVC advantage) p99: +0.026 ms (+0.34%) The only visible difference is in max-of-distribution: KVC max = 11.32 ms vs DP max = 9.53 ms (plausibly cold-start jitter on the first decode step after a reseed; affects <= 0.1% of requests) Two-panel figure mirroring the TTFT PDF style: left panel: linear x in [3.5, 9.0] ms -- body right panel: log x in [1, 20] ms -- full range with tail Each panel annotates the percentile gaps with bbox callouts so the reader's takeaway is "they overlap" not "is there a difference". Paper purpose: cited from V2_DEEP_ANALYSIS §3.5 as the supporting evidence that the path-level latency win in §3.2 is concentrated in the TTFT segment, not in decode. This is what makes the win a real end-to-end win, not a measurement artifact. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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kzlin
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scripts/analysis/plot_tpot_pdf.py
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scripts/analysis/plot_tpot_pdf.py
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#!/usr/bin/env python3
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"""Generate TPOT 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/tpot_pdf_comparison.png -- two-panel figure (mirroring
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the TTFT PDF style):
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left panel: linear x in [3.5, 9.0] ms zoomed on the body
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right panel: log x covering full range (1 -- 20 ms)
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The headline finding here is that **KVC and DP have statistically
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indistinguishable TPOT distributions**: same model on same GPU type means
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per-token decode latency is determined by hardware/model, not by routing
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policy. This is paper-relevant: it proves KVC's TTFT win is not bought
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by sacrificing decode throughput.
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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/tpot_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_tpot = np.array([r["tpot_s"] for r in kvc if r.get("tpot_s") is not None])
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dp_tpot = np.array([r["tpot_s"] for r in dp if r.get("tpot_s") is not None])
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# Trim absurdly small zeros (rare measurement artifacts) so log KDE behaves.
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kvc_tpot = kvc_tpot[kvc_tpot > 1e-5]
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dp_tpot = dp_tpot[dp_tpot > 1e-5]
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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 ∈ [3.5, 9.0] ms -- body of the distribution
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# ------------------------------------------------------------------
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ax = axes[0]
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x_body_ms = np.linspace(3.5, 9.0, 600)
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x_body_s = x_body_ms / 1000.0
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kde_kvc_lin = gaussian_kde(kvc_tpot, bw_method=0.15)
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kde_dp_lin = gaussian_kde(dp_tpot, bw_method=0.15)
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# Plot density vs ms (scale density by 1000 to compensate for the
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# x-axis-unit change so the curve still integrates to ~1 over the
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# body region of interest).
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y_kvc_lin = kde_kvc_lin(x_body_s) / 1000.0
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y_dp_lin = kde_dp_lin(x_body_s) / 1000.0
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ax.plot(x_body_ms, y_kvc_lin, color=KVC_COLOR, lw=2.5,
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label=f"KVC 1P3D v2 (n={len(kvc_tpot)})")
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ax.fill_between(x_body_ms, y_kvc_lin, alpha=0.20, color=KVC_COLOR)
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ax.plot(x_body_ms, y_dp_lin, color=DP_COLOR, lw=2.5,
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label=f"4-way DP CA (n={len(dp_tpot)})")
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ax.fill_between(x_body_ms, y_dp_lin, 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_tpot, q) * 1000, color=KVC_COLOR, ls=ls, alpha=0.55, lw=1.1)
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ax.axvline(pct(dp_tpot, q) * 1000, 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_tpot, 0.50) * 1000, ymax * 0.97,
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f"KVC p50\n{pct(kvc_tpot, 0.50)*1000:.2f}ms",
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color=KVC_COLOR, fontsize=9, va="top", ha="right",
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bbox=dict(facecolor="white", edgecolor="none", alpha=0.7, pad=2))
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ax.text(pct(dp_tpot, 0.50) * 1000, ymax * 0.50,
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f"DP p50\n{pct(dp_tpot, 0.50)*1000:.2f}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_tpot, 0.90) * 1000, ymax * 0.30,
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f"KVC p90\n{pct(kvc_tpot, 0.90)*1000:.2f}ms",
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color=KVC_COLOR, fontsize=9, va="top", ha="right",
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bbox=dict(facecolor="white", edgecolor="none", alpha=0.7, pad=2))
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ax.text(pct(dp_tpot, 0.90) * 1000, ymax * 0.18,
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f"DP p90\n{pct(dp_tpot, 0.90)*1000:.2f}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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# Annotate the overlap finding
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delta_mean_ms = (kvc_tpot.mean() - dp_tpot.mean()) * 1000
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delta_p50_ms = (pct(kvc_tpot, 0.50) - pct(dp_tpot, 0.50)) * 1000
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ax.text(
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0.04, 0.55,
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"Two curves are\nvisually overlapping:\n"
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f"Δmean = {delta_mean_ms:+.3f} ms\n"
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f"Δp50 = {delta_p50_ms:+.3f} ms\n"
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f"(< 0.5% of mean)",
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transform=ax.transAxes, fontsize=10.5, color="#333",
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bbox=dict(facecolor="#FFFAE6", edgecolor="#888", alpha=0.92, pad=5),
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va="top",
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)
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ax.set_xlim(3.5, 9.0)
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ax.set_xlabel("TPOT (milliseconds, linear)", fontsize=11)
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ax.set_ylabel("Probability density (per ms)", fontsize=11)
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ax.set_title("Body of distribution (3.5 ms ≤ TPOT ≤ 9.0 ms)",
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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 ∈ [1, 20] ms -- full range incl. tail
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# ------------------------------------------------------------------
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ax = axes[1]
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kde_kvc_log = gaussian_kde(np.log10(kvc_tpot), bw_method="scott")
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kde_dp_log = gaussian_kde(np.log10(dp_tpot), bw_method="scott")
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log_x = np.linspace(np.log10(1e-3), np.log10(20e-3), 600)
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x_full_ms = (10 ** log_x) * 1000
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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_ms, y_kvc, color=KVC_COLOR, lw=2.5,
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label=f"KVC 1P3D v2 (n={len(kvc_tpot)})")
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ax.fill_between(x_full_ms, y_kvc, alpha=0.20, color=KVC_COLOR)
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ax.plot(x_full_ms, y_dp, color=DP_COLOR, lw=2.5,
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label=f"4-way DP CA (n={len(dp_tpot)})")
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ax.fill_between(x_full_ms, y_dp, alpha=0.20, color=DP_COLOR)
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ax.set_xscale("log")
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ax.set_xlim(1, 20)
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# Percentile markers
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for q, ls in [(0.50, "-"), (0.90, "--"), (0.99, ":")]:
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ax.axvline(pct(kvc_tpot, q) * 1000, color=KVC_COLOR, ls=ls, alpha=0.55, lw=1.1)
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ax.axvline(pct(dp_tpot, q) * 1000, color=DP_COLOR, ls=ls, alpha=0.55, lw=1.1)
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# Annotate tail (p99 + max)
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kvc_p99_ms = pct(kvc_tpot, 0.99) * 1000
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dp_p99_ms = pct(dp_tpot, 0.99) * 1000
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kvc_max_ms = kvc_tpot.max() * 1000
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dp_max_ms = dp_tpot.max() * 1000
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ymax = max(y_kvc.max(), y_dp.max())
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ax.text(
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0.04, 0.55,
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"p99 / max tail:\n"
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f"KVC p99 = {kvc_p99_ms:.2f}ms\n"
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f"DP p99 = {dp_p99_ms:.2f}ms\n"
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f"KVC max = {kvc_max_ms:.2f}ms\n"
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f"DP max = {dp_max_ms:.2f}ms\n"
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f"(KVC tail slightly heavier;\n"
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f"≤ 0.1% of requests affected)",
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transform=ax.transAxes, fontsize=10, color="#333",
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bbox=dict(facecolor="#FFFAE6", edgecolor="#888", alpha=0.92, pad=5),
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va="top",
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)
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# Custom tick labels
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ax.set_xticks([1, 2, 5, 10, 20])
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ax.set_xticklabels(["1ms", "2ms", "5ms", "10ms", "20ms"])
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ax.set_xlabel("TPOT (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 (TPOT 1 ms – 20 ms, log x)",
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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, which="both", linestyle=":", alpha=0.4)
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ax.set_axisbelow(True)
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fig.suptitle(
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"TPOT probability density: KVC 1P3D v2 vs 4-way DP CA\n"
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"Same model (Qwen3-30B-A3B) on same H100 GPU type → per-token decode latency is\n"
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"determined by hardware/model, not routing policy. KVC's TTFT win is not bought\n"
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"by sacrificing decode throughput.",
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fontsize=12, y=1.04,
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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=== TPOT distribution summary ===")
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for name, arr in [("KVC v2", kvc_tpot), ("DP 4w", dp_tpot)]:
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print(f" {name} (n={len(arr)})")
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print(f" min={arr.min()*1000:.3f}ms p10={pct(arr,0.10)*1000:.3f}ms "
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f"p50={pct(arr,0.50)*1000:.3f}ms p90={pct(arr,0.90)*1000:.3f}ms "
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f"p99={pct(arr,0.99)*1000:.3f}ms p99.9={pct(arr,0.999)*1000:.3f}ms "
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f"max={arr.max()*1000:.3f}ms")
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print(f" mean={arr.mean()*1000:.3f}ms std={arr.std()*1000:.3f}ms")
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print(f"\nΔmean = {(kvc_tpot.mean()-dp_tpot.mean())*1000:+.3f}ms "
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f"({(kvc_tpot.mean()-dp_tpot.mean())/dp_tpot.mean()*100:+.2f}%)")
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print(f"Δp50 = {(pct(kvc_tpot,0.5)-pct(dp_tpot,0.5))*1000:+.3f}ms")
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print(f"Δp99 = {(pct(kvc_tpot,0.99)-pct(dp_tpot,0.99))*1000:+.3f}ms")
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print(f"→ Conclusion: KVC TPOT distribution is statistically indistinguishable from DP's "
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f"body, with slightly heavier tail (KVC max {kvc_tpot.max()*1000:.2f}ms vs DP {dp_tpot.max()*1000:.2f}ms).")
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if __name__ == "__main__":
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main()
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