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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>FlashLib: Bringing Flash Magic to Classical Machine Learning Operators</title>
<meta name="description" content="FlashLib is a GPU library for classical machine learning operators on modern hardware, rebuilt for today's ML workloads and emerging agentic AI systems.">
<meta name="color-scheme" content="light dark">
<style>
:root{
--bg:#FAF9F6;
--surface:#FFFFFF;
--surface-2:#F4F2EC;
--text:#3D3D3A;
--text-strong:#1F1F1D;
--text-muted:#6E6D67;
--text-faint:#A6A59E;
--rule:rgba(115,114,108,0.18);
--rule-strong:rgba(115,114,108,0.40);
--accent:#185FA5;
--link:#185FA5;
--link-visited:#534AB7;
--code-bg:#F2F0EA;
--code-border:rgba(115,114,108,0.18);
/* per-primitive identity colors, lifted from Figure 1's palette */
--c-kmeans:#D85A30;
--c-knn:#1D9E75;
--c-tsvd:#534AB7;
--c-pca:#185FA5;
--c-hdbscan:#D4537E;
--c-tsne:#C99540;
--c-mnb:#2C8EA0;
--c-ridge:#6B7A2C;
--c-dbscan:#B5722A;
--c-umap:#884B91;
--c-rf:#2A7757;
--c-linreg:#3D5E8C;
--c-logreg:#7A3D52;
--font-serif:"Charter","Iowan Old Style","Source Serif Pro","Source Serif",Georgia,"Times New Roman",serif;
--font-sans:-apple-system,BlinkMacSystemFont,"Inter","Segoe UI","Helvetica Neue",Arial,sans-serif;
--font-mono:"JetBrains Mono","SF Mono","Fira Code",ui-monospace,Menlo,Consolas,monospace;
--w:720px;
}
@media (prefers-color-scheme: dark){
:root{
--bg:#1C1B19;
--surface:#222120;
--surface-2:#2A2926;
--text:#E2E1DC;
--text-strong:#F4F3EE;
--text-muted:#A6A59E;
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--rule:rgba(168,167,161,0.20);
--rule-strong:rgba(168,167,161,0.40);
--accent:#8FB6DC;
--link:#8FB6DC;
--link-visited:#B0A6E0;
--code-bg:#1F1E1C;
--code-border:rgba(168,167,161,0.16);
/* slightly lighter / more saturated for dark backgrounds */
--c-kmeans:#E58060;
--c-knn:#4BC59A;
--c-tsvd:#8E84E0;
--c-pca:#7DB3E8;
--c-hdbscan:#E68AAA;
--c-tsne:#DDB46E;
--c-mnb:#5BB3C5;
--c-ridge:#A2B056;
--c-dbscan:#D89B5C;
--c-umap:#B98ABF;
--c-rf:#5AB28C;
--c-linreg:#7896C4;
--c-logreg:#B57588;
}
}
*,*::before,*::after{box-sizing:border-box;margin:0;padding:0}
html{font-size:17px;-webkit-text-size-adjust:100%}
body{
background:var(--bg);
color:var(--text);
font-family:var(--font-serif);
line-height:1.65;
font-feature-settings:"kern","liga","clig","onum";
-webkit-font-smoothing:antialiased;
-moz-osx-font-smoothing:grayscale;
}
article{
max-width:var(--w);
margin:0 auto;
padding:4.5rem 1.5rem 5rem;
}
@media (max-width:640px){
article{padding:2.5rem 1.1rem 3.5rem}
html{font-size:16px}
}
h1,h2,h3,h4{
font-family:var(--font-sans);
color:var(--text-strong);
font-weight:600;
letter-spacing:-0.012em;
line-height:1.2;
}
h1{
font-size:2.15rem;
letter-spacing:-0.018em;
font-weight:700;
line-height:1.15;
margin-bottom:0.5rem;
}
h2{
font-size:1.35rem;
margin:3.2rem 0 0.9rem;
font-weight:600;
}
h3{font-size:1.08rem;margin:2rem 0 0.6rem;font-weight:600}
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em{font-style:italic}
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text-decoration:none;
border-bottom:1px solid var(--rule-strong);
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a:visited{color:var(--link-visited);border-bottom-color:rgba(83,74,183,0.30)}
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color:var(--text-strong);
}
.byline{
font-family:var(--font-sans);
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margin:0 0 1.6rem;
padding-bottom:1.4rem;
border-bottom:1px solid var(--rule);
}
.byline-authors{
font-size:0.92rem;
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margin-bottom:0.4rem;
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border-bottom:none;
}
.byline-authors sup{
font-size:0.65em;
color:var(--text-muted);
margin-left:0.06em;
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font-weight:400;
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.byline-affil sup{
font-size:0.78em;
margin-right:0.2em;
vertical-align:0.4em;
}
/* Hero stat grid: 2×4 with 7 cards + 1 empty corner.
Cells use the negative-margin trick so the empty position has no border. */
.hero-stats{
display:grid;
grid-template-columns:repeat(4,1fr);
background:var(--surface);
border:1px solid var(--rule);
border-radius:8px;
overflow:hidden;
margin:0 0 2.4rem;
}
.hero-stats .stat{
padding:1rem 1.05rem 0.95rem;
border-left:1px solid var(--rule);
border-top:1px solid var(--rule);
margin:-1px 0 0 -1px;
display:flex;
flex-direction:column;
gap:0.12rem;
min-height:106px;
background:var(--surface);
transition:background .12s;
}
.hero-stats .stat:hover{background:var(--surface-2)}
.hero-stats .num{
font-family:var(--font-sans);
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font-weight:600;
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}
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}
.hero-stats .meta{
font-family:var(--font-sans);
font-size:0.74rem;
color:var(--text-muted);
margin-top:0.1rem;
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@media (max-width:720px){
.hero-stats{grid-template-columns:repeat(2,1fr)}
}
@media (max-width:380px){
.hero-stats{grid-template-columns:1fr}
}
/* Inline math: keeps a multi-symbol expression on one line and gives variables
a faintly mathematical look without pulling in a typesetter. */
.math{
font-family:var(--font-serif);
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letter-spacing:0.01em;
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.math em{font-style:italic}
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/* Code block: rounded card, syntax-highlighted Python. */
.codeblock{
background:var(--code-bg);
border:1px solid var(--code-border);
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-webkit-text-size-adjust:100%;
tab-size:4;
}
/* Reset the inline-code box treatment for <code> INSIDE a .codeblock.
Without this, the inline <code>'s background+border would render around
every line of the preformatted text. */
.codeblock code{
background:transparent;
border:0;
padding:0;
border-radius:0;
font-size:inherit;
color:inherit;
display:block;
}
/* Syntax tokens. Colors borrow from the primitive palette so the highlighting
stays consistent with the rest of the page. */
.codeblock .c {color:var(--text-muted); font-style:italic} /* comment */
.codeblock .k {color:var(--c-tsvd); font-weight:500} /* keyword: import/from/as/for/in */
.codeblock .mod {color:var(--c-pca)} /* module reference */
.codeblock .fn {color:var(--c-tsne); font-weight:500} /* function/attribute call */
.codeblock .kw {color:var(--c-mnb)} /* kwarg name */
.codeblock .num {color:var(--c-kmeans)} /* numeric literal */
.codeblock .str {color:var(--c-knn)} /* string literal */
.codeblock .b {color:var(--c-hdbscan); font-weight:500} /* builtin: None/True/False */
/* "Principle 01 / 04 -- xxx" eyebrow above each principle heading. */
.eyebrow{
font-family:var(--font-sans);
font-size:0.7rem;
font-weight:600;
letter-spacing:0.14em;
text-transform:uppercase;
color:var(--accent);
margin:3.4rem 0 0.45rem;
display:flex;
align-items:center;
gap:0.7rem;
}
.eyebrow::after{
content:"";
display:block;
height:1px;
flex:1 1 auto;
background:var(--rule);
}
.eyebrow + h2{margin-top:0.15rem}
.eyebrow .num{
display:inline-block;
min-width:1.4em;
color:var(--text-faint);
font-weight:500;
letter-spacing:0.08em;
}
figure.fig{
margin:2.2rem 0;
}
figure.fig .figbody{
background:var(--surface);
border:1px solid var(--rule);
border-radius:8px;
padding:1.2rem;
}
figure.fig img,
figure.fig svg{display:block;width:100%;height:auto}
/* ── Interactive Figure 1 hover-to-cite tooltip ── */
figure.fig-latency-chart svg{overflow:visible}
figure.fig-interactive .figbody.fig-host{position:relative}
.fig-tip-target{cursor:pointer; outline:none}
.fig-tip-target circle{transition:r 120ms ease, stroke-width 120ms ease}
.fig-tip-target:hover circle,
.fig-tip-target:focus-visible circle,
.fig-tip-target.is-active circle{filter:brightness(1.08)}
.fig-tip-target:hover circle[r="5"],
.fig-tip-target:focus-visible circle[r="5"],
.fig-tip-target.is-active circle[r="5"]{r:7}
.fig-tip-target:focus-visible{
outline:2px solid var(--accent);
outline-offset:2px;
border-radius:50%;
}
.fig-tip-target.is-active text{font-weight:600}
.fig-tip{
position:absolute;
display:none;
max-width:360px;
min-width:260px;
background:var(--surface);
border:1px solid var(--rule-strong);
border-radius:6px;
box-shadow:0 6px 24px rgba(0,0,0,0.14);
padding:10px 12px 11px;
font-family:var(--font-sans);
font-size:0.82rem;
color:var(--text-strong);
line-height:1.5;
z-index:20;
pointer-events:none;
}
.fig-tip[data-shown="true"]{display:block}
.fig-tip .tip-era{
font-family:var(--font-mono);
font-size:0.66rem;
letter-spacing:0.05em;
text-transform:uppercase;
color:var(--text-muted);
margin-bottom:3px;
}
.fig-tip .tip-title{
font-weight:600;
font-size:0.9rem;
color:var(--text-strong);
margin-bottom:5px;
line-height:1.3;
}
.fig-tip .tip-body{color:var(--text-strong); font-weight:400}
.fig-tip .tip-body code{
font-family:var(--font-mono);
font-size:0.78rem;
background:var(--surface-2);
border:1px solid var(--rule);
border-radius:3px;
padding:0 4px;
}
.fig-tip .tip-refs{
margin-top:7px;
padding-top:6px;
border-top:1px solid var(--rule);
font-size:0.74rem;
color:var(--text-muted);
line-height:1.45;
display:flex;
flex-direction:column;
gap:2px;
}
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display:inline-block;
font-family:var(--font-mono);
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text-transform:uppercase;
color:var(--text-muted);
background:var(--surface-2);
border:1px solid var(--rule);
border-radius:3px;
padding:0 4px;
margin-right:5px;
vertical-align:0.1em;
}
.fig-tip .tip-ref a{color:var(--accent); text-decoration:none}
.fig-tip .tip-ref a:hover{text-decoration:underline}
.fig-tip .tip-note{
margin-top:6px;
font-size:0.72rem;
font-style:italic;
color:var(--text-muted);
line-height:1.4;
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@media (prefers-color-scheme: dark){
figure.fig-latency-chart svg text{
fill:var(--text) !important;
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figure.fig-latency-chart svg .fig-tip-target.is-active text{
fill:var(--text-strong) !important;
}
figure.fig-latency-chart svg line{
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<article>
<h1>FlashLib: Bringing Flash Magic to Classical Machine Learning Operators</h1>
<p class="byline byline-authors">Shuo Yang<sup>1</sup>, Haocheng Xi<sup>1</sup>, Yilong Zhao<sup>1</sup>, Qiuyang Mang<sup>1</sup>, Zhe Wang<sup>2</sup>, Shanlin Sun<sup>2</sup>, Kurt Keutzer<sup>1</sup>, Joseph E. Gonzalez<sup>1</sup>, Song Han<sup>3</sup>, Chenfeng Xu<sup>4,*</sup>, Ion Stoica<sup>1,*</sup></p>
<p class="byline byline-affil" style="border-bottom:none; padding-bottom:0; margin-bottom:0.4rem"><sup>1</sup>UC Berkeley · <sup>2</sup>UC Irvine · <sup>3</sup>MIT · <sup>4</sup>UT Austin · <sup>*</sup>Co-advising</p>
<p class="byline byline-links">Code: <a href="https://github.com/FlashML-org/flashlib" target="_blank" rel="noopener">github.com/FlashML-org/flashlib</a></p>
<div class="hero-stats" aria-label="Headline speedups over cuML 25.10 on H200">
<div class="stat" style="--swatch:var(--c-kmeans)">
<span class="num">26<span class="x">×</span></span>
<span class="name">KMeans</span>
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<span class="num">19<span class="x">×</span></span>
<span class="name">KNN</span>
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<div class="stat" style="--swatch:var(--c-tsvd)">
<span class="num">208<span class="x">×</span></span>
<span class="name">TruncatedSVD</span>
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<div class="stat" style="--swatch:var(--c-pca)">
<span class="num">47<span class="x">×</span></span>
<span class="name">PCA</span>
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<div class="stat" style="--swatch:var(--c-umap)">
<span class="num">7<span class="x">×</span></span>
<span class="name">UMAP</span>
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<div class="stat" style="--swatch:var(--c-hdbscan)">
<span class="num">40<span class="x">×</span></span>
<span class="name">HDBSCAN</span>
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<div class="stat" style="--swatch:var(--c-tsne)">
<span class="num">147<span class="x">×</span></span>
<span class="name">t-SNE (exact)</span>
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<div class="stat" style="--swatch:var(--c-mnb)">
<span class="num">49<span class="x">×</span></span>
<span class="name">MultinomialNB</span>
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<p>Introducing <strong>FlashLib</strong> — a GPU library for classical machine learning operators on modern hardwares, rebuilt for today's ML workloads and emerging agentic AI systems. Here are a few headline results from the first release:</p>
<ul>
<li>Significant wins over cuML on Hopper GPUs: up to <strong>26×</strong> on KMeans, <strong>19×</strong> on KNN, <strong>40×</strong> on HDBSCAN, <strong>208×</strong> on TruncatedSVD, <strong>47×</strong> on PCA, <strong>147×</strong> on exact t-SNE, and <strong>49×</strong> on MultinomialNB.</li>
<li>Flash informative API: Predict runtime, memory footprint, and overhead for any workload in <strong>~5 µs on pure CPU</strong>, with no GPU profiling required.</li>
<li>Fast cold start, built to scale: FlashLib uses heuristic kernel selection to avoid long autotune loops, and already supports multi-GPU execution for large workloads.</li>
<li>Toward optimal hardware utilization: FlashLib drives kernels much closer to the limits of modern GPUs, with Flash-KMeans reaching up to <strong>61% of peak FLOPs</strong> and Flash-KNN reaching up to <strong>85.2% of peak HBM bandwidth</strong> on H200.</li>
</ul>
<p>The next frontier of AI efficiency is not just faster LLM inference. It is faster intelligence assembly. For the past few years, MLsys work largely followed a model-centric view of intelligence. As LLMs became stronger through better reasoning, larger-scale test-time compute, and more capable inference, the systems community focused on making the transformer core faster: FlashAttention, FlashDecoding, KV-cache management, and LLM serving systems etc.</p>
<p>But the rise of agentic AI is changing the bottleneck. Modern intelligence is increasingly built around the base model through tools, harnesses, retrieval, verification, search, and orchestration. The LLM is no longer merely a standalone reasoner; it becomes a controller over a broader computational system. As a result, the performance bottleneck is no longer confined to transformer inference. It extends to the entire computational substrate surrounding the model. For example, in Agentic AI for Science, LLM agents may generate hypotheses or candidate solutions, but the surrounding loop often depends on search, clustering, nearest-neighbor retrieval, PCA, SVD, and other classical ML operators for verification and feedback. In multimodal generation and physical AI, models must increasingly process, compress, retrieve, and reorganize streaming features on the fly before they enter the model. These examples point to a broader shift: classical ML operators are becoming core primitives around the LLM model. We envision future agentic workflows where clustering, retrieval, dimensionality reduction, verification, and linear algebra are no longer offline utilities, but online primitives in the critical path of intelligence assembly. Figure 1 illustrates this shift.</p>
<figure class="fig fig-interactive fig-latency-chart">
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<text x="340" y="4" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:start;dominant-baseline:auto">HDBSCAN</text>
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<line x1="70" y1="60" x2="70" y2="470" stroke="var(--t)" stroke-width="0.5" style="fill:rgb(0, 0, 0);stroke:rgb(115, 114, 108);color:rgb(0, 0, 0);stroke-width:0.5px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/>
<line x1="70" y1="470" x2="640" y2="470" stroke="var(--t)" stroke-width="0.5" style="fill:rgb(0, 0, 0);stroke:rgb(115, 114, 108);color:rgb(0, 0, 0);stroke-width:0.5px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/>
<text x="62" y="60" text-anchor="end" dominant-baseline="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:middle">1 ms</text>
<text x="62" y="110" text-anchor="end" dominant-baseline="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:middle">10 ms</text>
<text x="62" y="160" text-anchor="end" dominant-baseline="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:middle">100 ms</text>
<text x="62" y="210" text-anchor="end" dominant-baseline="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:middle">1 s</text>
<text x="62" y="300" text-anchor="end" dominant-baseline="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:middle">1 min</text>
<text x="62" y="390" text-anchor="end" dominant-baseline="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:middle">1 hr</text>
<text x="80" y="488" text-anchor="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:middle;dominant-baseline:auto">2015</text>
<text x="220" y="488" text-anchor="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:middle;dominant-baseline:auto">2018</text>
<text x="360" y="488" text-anchor="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:middle;dominant-baseline:auto">2021</text>
<text x="500" y="488" text-anchor="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:middle;dominant-baseline:auto">2024</text>
<text x="640" y="488" text-anchor="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:middle;dominant-baseline:auto">2027</text>
<text x="355" y="525" text-anchor="middle" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:middle;dominant-baseline:auto">Year operator entered this latency tier</text>
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<g class="fig-tip-target" data-tip-key="user-segmentation" tabindex="0" role="button" aria-label="User segmentation (K-means)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="140" cy="340" r="5" fill="#D85A30" style="fill:rgb(216, 90, 48);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="146" y="357" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:start;dominant-baseline:auto">User segmentation</text></g>
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<g class="fig-tip-target" data-tip-key="topic-discovery" tabindex="0" role="button" aria-label="BERTopic (HDBSCAN)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="360" cy="220" r="5" fill="#D4537E" style="fill:rgb(212, 83, 126);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="354" y="216" text-anchor="end" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:auto">Topic discovery</text></g>
<g class="fig-tip-target" data-tip-key="rag-retrieval" tabindex="0" role="button" aria-label="RAG retrieval (k-NN)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="407" cy="180" r="5" fill="#1D9E75" style="fill:rgb(29, 158, 117);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="413" y="172" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:start;dominant-baseline:auto">RAG retrieval</text></g>
<g class="fig-tip-target" data-tip-key="semantic-cache" tabindex="0" role="button" aria-label="Semantic cache (K-means)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="453" cy="270" r="5" fill="#D85A30" style="fill:rgb(216, 90, 48);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="459" y="266" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:start;dominant-baseline:auto">Semantic cache</text></g>
<g class="fig-tip-target" data-tip-key="pca-compression" tabindex="0" role="button" aria-label="PCA-based compression (PCA)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="500" cy="150" r="5" fill="#185FA5" style="fill:rgb(24, 95, 165);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="494" y="139" text-anchor="end" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:auto">PCA-based compression</text></g>
<g class="fig-tip-target" data-tip-key="svd-compression" tabindex="0" role="button" aria-label="SVD-based compression (TruncatedSVD)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="523" cy="180" r="5" fill="#534AB7" style="fill:rgb(83, 74, 183);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="529" y="200" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:start;dominant-baseline:auto">SVD-based compression</text></g>
<g class="fig-tip-target" data-tip-key="streaming-video" tabindex="0" role="button" aria-label="Streaming video generation (K-means)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="547" cy="110" r="5" fill="#D85A30" style="fill:rgb(216, 90, 48);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="541" y="100" text-anchor="end" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:auto">Streaming video generation</text></g>
<g class="fig-tip-target" data-tip-key="kv-clustering" tabindex="0" role="button" aria-label="KV-cache clustering (HDBSCAN)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="570" cy="130" r="5" fill="#D4537E" style="fill:rgb(212, 83, 126);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="567.8" y="146" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:start;dominant-baseline:auto">KV cache clustering</text></g>
<g class="fig-tip-target" data-tip-key="agent-tool-routing" tabindex="0" role="button" aria-label="Agent tool routing (k-NN)" style="fill:rgb(0, 0, 0);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"><circle cx="593" cy="80" r="5" fill="#1D9E75" style="fill:rgb(29, 158, 117);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:16px;font-weight:400;text-anchor:start;dominant-baseline:auto"/><text x="587" y="76" text-anchor="end" style="fill:rgb(61, 61, 58);stroke:none;color:rgb(0, 0, 0);stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;opacity:1;font-family:"Anthropic Sans", -apple-system, "system-ui", "Segoe UI", sans-serif;font-size:12px;font-weight:400;text-anchor:end;dominant-baseline:auto">Agent tool routing</text></g>
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<script type="application/json" class="fig-tip-data">{"user-segmentation": {"era": "2015 · batch tier", "title": "User segmentation (K-means)", "body": "Marketing teams cluster millions of users by purchase and behaviour features into a handful of personas. A nightly Spark / scikit-learn K-means job is the textbook example; latency budget is the next morning's dashboard.", "refs": [{"text": "Meng et al., MLlib · JMLR 17, 2016", "url": "https://www.jmlr.org/papers/v17/15-237.html"}, {"prefix": "Foundational", "text": "Lloyd, Least-squares quantization in PCM · IEEE TIT 28(2), 1982", "url": null}], "note": null}, "feature-reduction": {"era": "2015 · batch tier", "title": "Feature reduction (PCA)", "body": "Pre-processing step in tabular ML pipelines: project hundreds of correlated features down to a handful of principal components before fitting a regressor or tree model. Runs once per data refresh on a single CPU box.", "refs": [{"text": "Halko, Martinsson, Tropp · SIAM Review 53(2), 2011", "url": "https://arxiv.org/abs/0909.4061"}], "note": null}, "topic-modeling": {"era": "1990–2015 · batch tier", "title": "Topic modelling / LSA (TruncatedSVD)", "body": "Latent Semantic Analysis on a term–document matrix is the textbook offline application of TruncatedSVD. Still the default in gensim's <code>LsiModel</code>; runtime measured in hours on Wikipedia-scale corpora.", "refs": [{"text": "Deerwester et al., Indexing by Latent Semantic Analysis · JASIS 41(6), 1990", "url": null}], "note": null}, "doc-clustering": {"era": "2013 · batch tier", "title": "Document clustering (HDBSCAN)", "body": "Campello, Moulavi & Sander introduced HDBSCAN as a density-based replacement for DBSCAN that picks the cluster count automatically and labels noise. Standard offline pipeline for grouping unstructured documents and log lines.", "refs": [{"text": "Campello, Moulavi, Sander · PAKDD 2013", "url": "https://link.springer.com/chapter/10.1007/978-3-642-37456-2_14"}], "note": null}, "item-item-recsys": {"era": "2001–2003 · batch tier", "title": "Item-to-item recommendations (k-NN)", "body": "For every item, precompute the k nearest neighbours by co-purchase / cosine similarity and serve from a lookup table. The k-NN build runs offline over hours; only the lookup is online.", "refs": [{"text": "Sarwar et al., Item-based collaborative filtering · WWW 2001", "url": "https://dl.acm.org/doi/10.1145/371920.372071"}, {"prefix": "Industrial", "text": "Linden, Smith, York · IEEE Internet Computing 7(1), 2003", "url": "https://www.cs.umd.edu/~samir/498/Amazon-Recommendations.pdf"}], "note": null}, "pipeline-pca": {"era": "~2019 · pipeline tier", "title": "PCA inside an ML pipeline", "body": "By the late 2010s, PCA migrated into the inference pipeline itself: <code>sklearn.Pipeline([PCA(...), Classifier(...)])</code> at request time, Kaggle-era feature engineering, real-time anomaly detection on streaming telemetry.", "refs": [{"prefix": "Implementation", "text": "Pedregosa et al., scikit-learn · JMLR 12, 2011", "url": "https://www.jmlr.org/papers/v12/pedregosa11a.html"}], "note": "General MLOps practice; no single canonical paper."}, "embedding-compress": {"era": "~2019 · pipeline tier", "title": "Embedding compression (TruncatedSVD)", "body": "Once dense 384–1024-d transformer embeddings became the default for search and recommendation, libraries started shipping per-query compression to shrink them for downstream vector indexes.", "refs": [{"prefix": "Closest fit", "text": "Jégou, Douze, Schmid, Product Quantization · IEEE TPAMI 33(1), 2011", "url": "https://hal.inria.fr/inria-00514462v2/document"}], "note": "Product Quantization is the dominant embedding-compression primitive but is K-means-based, not strictly SVD; SVD-on-embeddings has no canonical modern paper."}, "topic-discovery": {"era": "2022 · pipeline tier", "title": "BERTopic (HDBSCAN)", "body": "Grootendorst's <b>BERTopic</b> pipeline is the canonical modern topic-discovery stack: <i>sentence-transformers → UMAP → HDBSCAN → c-TF-IDF</i>. HDBSCAN sits inside the request — the cluster step has to finish in seconds for the dashboard to feel interactive.", "refs": [{"text": "Grootendorst · arXiv 2203.05794, 2022", "url": "https://arxiv.org/abs/2203.05794"}], "note": null}, "rag-retrieval": {"era": "2019–2020 · pipeline tier", "title": "RAG retrieval (k-NN)", "body": "Lewis et al.'s RAG made dense top-k vector search a hard dependency of every modern LLM stack; one RAG turn now spends tens of ms inside k-NN, on top of GPU-accelerated indexes like FAISS.", "refs": [{"text": "Lewis et al., RAG · NeurIPS 2020 (arXiv 2005.11401)", "url": "https://arxiv.org/abs/2005.11401"}, {"prefix": "Infrastructure", "text": "Johnson, Douze, Jégou, FAISS-GPU · IEEE Trans. Big Data 7(3), 2019", "url": "https://arxiv.org/abs/1702.08734"}], "note": null}, "semantic-cache": {"era": "2023 · pipeline tier", "title": "Semantic cache (K-means)", "body": "<b>GPTCache</b> embeds each LLM prompt, runs a top-k similarity search against cached responses, and short-circuits the model when the cluster centroid is close enough. Hit-or-miss in < 100 ms or you've blown the latency saved by skipping inference.", "refs": [{"text": "Bang, GPTCache · EMNLP NLP-OSS 2023", "url": "https://aclanthology.org/2023.nlposs-1.24/"}], "note": "GPTCache uses similarity search, not strict K-means; tighter K-means semantic-cache work is SAFE-CACHE (Scientific Reports, 2026)."}, "pca-compression": {"era": "2024–2025 · serving tier", "title": "PCA-based compression (PCA)", "body": "Project the KV cache (or activations) into a low-rank subspace at inference time, cutting both memory and attention FLOPs. NVIDIA's <b>ESPACE</b> and <b>MatryoshkaKV</b>'s trainable orthogonal projections are the recent canonical entries.", "refs": [{"text": "Sakr & Khailany, ESPACE · NeurIPS 2024 (arXiv 2410.05437)", "url": "https://arxiv.org/abs/2410.05437"}, {"text": "Lin et al., MatryoshkaKV · ICLR 2025 (arXiv 2410.14731)", "url": "https://arxiv.org/abs/2410.14731"}], "note": null}, "svd-compression": {"era": "2024–2025 · serving tier", "title": "SVD-based compression (TruncatedSVD)", "body": "Factor LLM weight matrices into low-rank pieces via truncation-aware SVD; the decomposition runs at load time and the cheaper matmuls happen every token. <b>SVD-LLM</b> and the differentiable <b>Dobi-SVD</b> are the recent leaders on the perplexity-vs-compression frontier.", "refs": [{"text": "Wang et al., Dobi-SVD · ICLR 2025 (arXiv 2502.02723)", "url": "https://arxiv.org/abs/2502.02723"}, {"text": "Wang et al., SVD-LLM · NeurIPS 2024 (arXiv 2403.07378)", "url": "https://arxiv.org/abs/2403.07378"}], "note": null}, "streaming-video": {"era": "2025 · serving tier", "title": "Streaming video generation (K-means)", "body": "Real-time video diffusion lives or dies by per-frame budget. <b>Sparse VideoGen2</b> uses semantic-aware permutation — K-means on token features — to drive sparse attention while keeping quality.", "refs": [{"text": "Yang et al., Sparse VideoGen2 · NeurIPS 2025 (arXiv 2505.18875)", "url": "https://arxiv.org/abs/2505.18875"}], "note": null}, "kv-clustering": {"era": "2025 · serving tier", "title": "KV-cache clustering (HDBSCAN)", "body": "Group KV-cache tokens by the density of their attention patterns, then keep only one representative per cluster. <b>ClusterAttn</b> exploits the intrinsic clustering of attention weights to compress the cache without dropping context.", "refs": [{"text": "Zhang et al., ClusterAttn · ACL 2025", "url": "https://aclanthology.org/2025.acl-long.703"}], "note": "ClusterAttn uses DBSCAN — the same density-based clustering family as HDBSCAN."}, "agent-tool-routing": {"era": "2024 · serving tier", "title": "Agent tool routing (k-NN)", "body": "Every agent turn now starts with a top-k vector retrieval over tool / agent embeddings to pick the right tool from a thousand-tool catalogue. <b>Re-Invoke</b> rewrites the user query first to lift zero-shot retrieval recall.", "refs": [{"text": "Chen et al., Re-Invoke · arXiv 2408.01875, 2024 (Google Cloud AI Research)", "url": "https://arxiv.org/abs/2408.01875"}], "note": null}}</script>
</div>
<figcaption><span class="label">Figure 1.</span> The latency budget for classical ML operators (KMeans, k-NN, TruncatedSVD, PCA, HDBSCAN) has been falling steadily over the past decade, on a log scale. The same primitives that used to run offline at the minute-to-hour tier (user segmentation, topic modeling, batch feature reduction) are now being called inside online serving paths (RAG retrieval, semantic cache, KV-cache clustering, agent tool routing) where the budget is measured in milliseconds. As this trend continues, the systems community needs implementations of these operators that are fast, hardware-efficient, reliable, and numerically faithful enough to sit in the critical path. <em>Hover (or tap) any point to see the specific work it represents.</em></figcaption>
</figure>
<p>However, the underlying implementations of these classical operators have not kept pace with this shift. Their core design assumptions still come from the pre-FlashAttention, pre-Hopper, pre-agent era, which creates a four-way mismatch. First, many operators carry natural implementations that are unfriendly to GPUs. Second, many libraries ship one static kernel implementation across all workloads and hardware tiers, leaving modern GPU hardware features unexploited. Third, many libraries are unaware of the user's precision needs: they expose no way to declare a precision budget, leaving users unable to ask for the fastest algorithm that meets their tolerance. Fourth, the performance is black box: costly to profile, hard to modify, and impossible to budget without first reading the codebase, which leaves both developers and LLM-based agents in the dark.</p>
<p>FlashLib is our attempt to close these gaps and accelerate this emerging substrate, making it fast enough to sit inside the loop of agentic AI. It transforms classical ML operators from slow, offline utilities into fast, online ML primitives. Moreover, FlashLib exposes flash-informative APIs that reveal the cost, tolerance, and execution behavior of these primitives to higher-level agentic pipelines, thus enabling better scheduling and orchestration. We would also like to point out that while FlashLib is motivated by the emerging needs of LLM-centric and agentic AI systems, we also recognize that classical ML algorithms remain widely used across today's machine learning stacks. Beyond generative AI, operators such as KMeans, KNN, PCA, SVD, t-SNE, and HDBSCAN etc are still core building blocks for recommendation systems, retrieval pipelines, scientific computing, anomaly detection, visualization, and preprocessing for downstream ML models. FlashLib provides a fast, easy-to-use, and adaptive software stack that covers these diverse applications with plug-and-play GPU acceleration.</p>
<p>We built FlashLib around four design principles. First, we reshape the algorithm to fit the hardware while achieving mathematical equivalence. Second, we build kernel variants per operator to fully exploit different workloads on different hardwares using modern hardware features. Third, we let users declare a precision budget and route to the fastest algorithm that meets it. Fourth, we keep the entire library transparent enough that users and LLM agents can easily read, compose, and modify the kernels.</p>
<div class="eyebrow"><span class="num">01 / 04</span><span>Reformulation</span></div>
<h2>Mathematically Equivalent Reformulation: Rewriting Operators to Be GPU-Friendly</h2>
<p>Many classical ML operators have natural implementations that are unfriendly to GPUs: they materialize large intermediates in HBM, introduce atomic contention, or run reductions along dimensions that don't tile well. FlashLib's first principle is to rewrite these into mathematically equivalent forms that are friendly to modern accelerators. KMeans assign is the clearest example: the natural implementation forms an <span class="math"><em>N</em>×<em>K</em></span> distance matrix in HBM and runs an <code>argmin</code> per row, but the streaming-fused version keeps the running local minima in registers and never materializes the matrix. The same pattern recurs across the library: KNN's fused top-K skips the <span class="math">‖<em>x</em>‖<sup>2</sup></span> term in <span class="math">‖<em>x</em> − <em>y</em>‖<sup>2</sup> = ‖<em>x</em>‖<sup>2</sup> + ‖<em>y</em>‖<sup>2</sup> − 2⟨<em>x</em>, <em>y</em>⟩</span>, PCA's dual-Gram routing picks the smaller of <span class="math"><em>X</em><sup>⊤</sup><em>X</em> (<em>D</em>×<em>D</em>)</span> and <span class="math"><em>X X</em><sup>⊤</sup> (<em>N</em>×<em>N</em>)</span>, avoiding the wasted <span class="math">O(max(<em>N</em>,<em>D</em>)<sup>3</sup>)</span> <code>eigh</code> that cuML's fixed <span class="math"><em>D</em>×<em>D</em></span> path runs on wide data, MultinomialNB changes atomic scatter for segment-level reduction, and t-SNE's gradient never materializes the <span class="math"><em>N</em>×<em>N</em></span> Q matrix.</p>
<div class="eyebrow"><span class="num">02 / 04</span><span>Hardware-Aware Kernels</span></div>
<h2>Hardware-Aware Implementation: Kernel Variants for Different Hardware and Workloads</h2>
<p>To map these mathematical formulations directly to silicon, FlashLib builds multiple kernel variants that adapt to both the hardware and the workload. Flash-KNN illustrates this approach. First, at the backend layer, we ship a portable Triton implementation for both Ampere and Hopper. For Hopper, an opt-in CuteDSL FA3 backend additionally unlocks modern features like TMA fetching and warp-specialized pipelines. Second, at the kernel layer, the design adapts to the workload. For large queries, the kernel mirrors standard FlashAttention to maximize TensorCore utilization. For small queries against a huge corpus, it mirrors Flash-Decoding: a split-k layout distributes work across the corpus dimension to prevent SM idling. Third, at the heuristic layer, we choose hyperparameters like tile sizes and warp counts based on hardware characteristics such as cache size and register capacity. As a result, even a <span class="math"><em>Q</em>=1</span> query against a 100M-vector corpus holds the kernel at <strong>85.2% of the H200's peak HBM bandwidth</strong>.</p>
<div class="eyebrow"><span class="num">03 / 04</span><span>Tolerance Routing</span></div>
<h2>Tolerance-Driven Dispatch: Routing to the Fastest Algorithm within a Precision Budget</h2>
<p>FlashLib also exposes the speed-accuracy tradeoff as a user choice. Classical scientific computing often demands high precision in FP32 or even FP64 — for solving PDEs, certifying numerical methods, or anywhere a small error cascades into a wrong answer. Many AI workloads have no such requirement: a clustering pass over embedding vectors, a top-K retrieval, or a regression on noisy data can absorb a small declared residual for a substantial speedup. FlashLib makes that distinction the user's to draw, through a single per-call argument, <code>tol</code>. At <code>tol=None</code>, reductions stay in exact precision and the call rides the kernel-fusion wins from above. At <code>tol > 0</code>, the dispatcher routes through a Pareto frontier of precision emulation (fused variants like <code>3xbf16</code> and Ozaki-II INT8) and algorithm substitution (Halko subspace iteration), picking whichever has the highest throughput within the declared residual.</p>
<pre class="codeblock"><code><span class="c"># GEMM: same call, different tol -> different variant.</span>
<span class="mod">flashlib</span>.<span class="fn">gemm</span>(A, B) <span class="c"># exact fp32</span>
<span class="mod">flashlib</span>.<span class="fn">gemm</span>(A, B, <span class="kw">tol</span>=<span class="num">1e-3</span>) <span class="c"># bf16</span>
<span class="mod">flashlib</span>.<span class="fn">gemm</span>(A, B, <span class="kw">tol</span>=<span class="num">1e-5</span>) <span class="c"># 3xbf16 (cute-fused)</span>
<span class="mod">flashlib</span>.<span class="fn">gemm</span>(A, B, <span class="kw">tol</span>=<span class="num">1e-7</span>) <span class="c"># ozaki2_cute(s=8): tighter AND faster</span>
<span class="mod">flashlib</span>.<span class="fn">gemm</span>(A, B, <span class="kw">tol</span>=<span class="num">1e-12</span>) <span class="c"># ozaki2_int8(s=14): FP64-grade</span>
<span class="c"># PCA: tol unlocks an algorithm substitution, not just precision.</span>
<span class="mod">flashlib</span>.<span class="fn">flash_pca</span>(X, <span class="kw">K</span>=<span class="num">32</span>) <span class="c"># exact eigh on Gram / cov matrix</span>
<span class="mod">flashlib</span>.<span class="fn">flash_pca</span>(X, <span class="kw">K</span>=<span class="num">32</span>, <span class="kw">tol</span>=<span class="num">1e-4</span>) <span class="c"># Halko subspace: ~30x faster</span></code></pre>
<div class="eyebrow"><span class="num">04 / 04</span><span>Cost-Predictable API</span></div>
<h2>Agent-Native API: Transparent Source and Predictable Cost for Users and Agents</h2>
<p>In an era when LLM-based agents increasingly read, call, and modify performance code, the cost of a library is not just its kernel throughput but how legible its cost model and source are. FlashLib is written in Triton and CuteDSL with no opaque binaries — every kernel from <code>flash_kmeans(...)</code> down to the <code>tl.dot</code> call is editable. And every primitive ships a GPU-free cost-prediction surface: <code>flashlib.info.estimate(...)</code> takes a shape and a tolerance and returns a recursive tree of runtime, FLOPs, HBM bytes, and bound regime in ~5 microseconds on pure CPU, never importing torch, triton, or cutlass. An LLM agent can compose a pipeline of ten primitives, walk that cost tree, and decide whether the budget fits before spending a single FLOP.</p>
<pre class="codeblock"><code><span class="k">import</span> <span class="mod">flashlib.info</span> <span class="k">as</span> <span class="mod">info</span> <span class="c"># pure stdlib -- no torch/triton/cutlass.</span>
<span class="c"># Predict cost without touching the GPU -- ~5 microseconds on pure CPU.</span>
est = <span class="mod">info</span>.<span class="fn">estimate</span>(<span class="str">"pca"</span>, <span class="kw">shape</span>=(<span class="num">1_000_000</span>, <span class="num">512</span>), <span class="kw">params</span>={<span class="str">"K"</span>: <span class="num">32</span>}, <span class="kw">device</span>=<span class="str">"H200"</span>)
<span class="fn">print</span>(est.<span class="fn">summary_line</span>())
<span class="c"># pca 13.18 ms bound=compute 42 TF (83% peak) res~1e-7 [roofline]</span>
est.<span class="fn">print_tree</span>() <span class="c"># walk the recursive call-stack tree</span>
<span class="c"># pca 13.18 ms 2.18 GB compute 42 TF res~1e-7</span>
<span class="c"># ├── cov_gemm 10.49 ms 2.05 GB compute 50 TF</span>
<span class="c"># ├── eigh 0.12 ms 0.00 GB compute 3 TF</span>
<span class="c"># └── transform 2.57 ms 2.18 GB compute 13 TF</span>
<span class="c"># Pareto-optimal GEMM variants for a 4Kx4Kx4K matmul on H200:</span>
<span class="k">for</span> v <span class="k">in</span> <span class="mod">info</span>.<span class="fn">pareto</span>(<span class="str">"gemm"</span>, <span class="kw">shape</span>=(<span class="num">4096</span>, <span class="num">4096</span>, <span class="num">4096</span>), <span class="kw">device</span>=<span class="str">"H200"</span>):
<span class="fn">print</span>(v)
<span class="c"># Variant('gemm_fp16' : 0.2 ms residual~8e-04)</span>
<span class="c"># Variant('gemm_tf32' : 0.4 ms residual~3e-04)</span>
<span class="c"># Variant('gemm_3xfp16' : 0.5 ms residual~2e-04)</span>
<span class="c"># Variant('gemm_fp16_x3_kahan' : 0.6 ms residual~5e-07)</span>
<span class="c"># Variant('gemm_ozaki2_cute' : 0.8 ms residual~2e-15)</span></code></pre>
<h2>Benchmarks</h2>
<p>All results below are measured on a single NVIDIA H200 (SM90, 150 GB HBM3e) with <code>CUDA 13.0</code>, driver <code>580.126</code>, <code>PyTorch 2.11</code>, <code>Triton 3.6</code>, against <code>cuML 25.10</code>. Every cell is the median over 5 iterations with the first call discarded for JIT amortization; inputs are GPU-resident on both sides; matched-algorithm rows (same <code>algorithm</code>, <code>method</code>, <code>svd_solver</code>) are paired with reduced-precision and algorithmic-shortcut rows so the comparison is fair at every shape.</p>
<h3>1. Breadth: speedup over cuML across 13 primitives</h3>
<p>The first benchmark is a broad sweep: 13 primitives × 194 (shape, dtype, hyperparameter) cells, all run against <code>cuml 25.10</code> on the same H200. <strong>Every cell here is an apples-to-apples comparison: matched algorithm, matched precision, matched hyperparameters — FlashLib is forbidden from using any reduced-precision GEMM (no bf16/fp16/Ozaki) or algorithmic shortcut (no Halko, no FFT t-SNE, no NN-Descent KNN).</strong> Because of this, the bars below are strictly <em>lower</em> than the headline numbers at the top of the post: the hero stats are FlashLib's best ceiling speedups on each primitive (which, where applicable, do let the user trade precision or algorithmic exactness for throughput via the <code>tol</code> knob from Principle 03), whereas the broad sweep deliberately removes those degrees of freedom to isolate the pure kernel-engineering win. The bar chart below collapses each primitive's 8–34 cells into a single bar — <strong>Geomean</strong> shows the geometric-mean speedup across all of that primitive's cells, and <strong>Max</strong> shows the per-primitive ceiling on the most favourable cell. FlashLib is at least as fast as cuML on <strong>193 / 194</strong> cells; <strong>126</strong> cells cross 5×, and <strong>11</strong> cross 50×.</p>
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<div class="chart-title">Speedup over cuML 25.10, per primitive</div>
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<span class="show-geomean">Geometric mean across 194 workload cells, exact-to-exact (no reduced precision, no algorithmic shortcut) · log-scale x-axis.</span>
<span class="show-max">Maximum win across the same 194 cells, exact-to-exact · log-scale x-axis.</span>
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<span class="speedup-summary-copy">Click one of the five primitive buttons to pin it to the top, then switch between geomean and max to watch the ordering and bar lengths move smoothly.</span>
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<h3>2. Depth: precision × runtime trade-off inside one primitive (GEMM)</h3>
<p>The second benchmark zooms into a single primitive, GEMM at 4096³ on H200, to show what tolerance routing looks like in practice. FlashLib ships ~10 GEMM variants in <code>flashlib.linalg.gemm</code> — bf16, fp16, tf32, fused multi-pass (<code>3xbf16</code>, <code>fp16_x3_kahan</code>), and the Ozaki-II INT8 family (<code>ozaki2_cute</code>, <code>ozaki2_int8</code>) — all behind the single <code>tol</code>-routed dispatcher from Principle 03. The scatter below plots each variant on RMS relative error (vs an FP64 reference) against per-call runtime. The dashed curve is the <em>Pareto frontier</em>: variants below it dominate the rest. The interesting point is <code>ozaki2_cute(s=8)</code>: it sits below <em>and</em> to the left of <code>fp32</code>, meaning it is simultaneously tighter and ~2× faster than the native fp32 path on this shape.</p>
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