index.html

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>InKAN — Fast B-Spline KAN Layers for PyTorch</title>
    <meta name="description" content="InKAN: Fast uniform cubic B-spline Kolmogorov-Arnold Network (KAN) layers for PyTorch. 2.8-5.4x faster than Cox-de Boor recursion. Drop-in nn.Linear replacement with learnable spline activations.">
    <meta name="keywords" content="inkan, KAN, Kolmogorov-Arnold Network, B-spline, PyTorch, neural network, deep learning, machine learning, learnable activation, spline, interpretable ML">
    <meta name="author" content="Naveen Mysore">
    <link rel="canonical" href="https://pypi.org/project/inkan/">
    <style>
        * { box-sizing: border-box; margin: 0; padding: 0; }
        body {
            font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Helvetica, Arial, sans-serif;
            background: #0d1117; color: #c9d1d9;
            line-height: 1.6; padding: 0;
        }
        .hero {
            background: linear-gradient(135deg, #1a1a2e 0%, #16213e 50%, #0f3460 100%);
            padding: 60px 20px; text-align: center;
        }
        .hero h1 { font-size: 3em; color: #58a6ff; margin-bottom: 10px; }
        .hero h1 span { color: #f0883e; }
        .hero p { font-size: 1.2em; color: #8b949e; max-width: 700px; margin: 0 auto 30px; }
        .install {
            background: #161b22; border: 1px solid #30363d; border-radius: 8px;
            padding: 15px 25px; display: inline-block; font-family: monospace;
            font-size: 1.1em; color: #7ee787; cursor: pointer;
        }
        .install:hover { border-color: #58a6ff; }
        .badges { margin: 20px 0; }
        .badges img { margin: 0 4px; }
        .container { max-width: 900px; margin: 0 auto; padding: 40px 20px; }
        h2 { color: #58a6ff; font-size: 1.5em; margin: 40px 0 15px; border-bottom: 1px solid #21262d; padding-bottom: 8px; }
        .feature-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 20px; margin: 20px 0; }
        .feature {
            background: #161b22; border: 1px solid #30363d; border-radius: 8px;
            padding: 20px;
        }
        .feature h3 { color: #f0883e; margin-bottom: 8px; }
        .feature p { color: #8b949e; font-size: 0.95em; }
        pre {
            background: #161b22; border: 1px solid #30363d; border-radius: 8px;
            padding: 20px; overflow-x: auto; font-size: 0.9em;
        }
        code { color: #7ee787; }
        .kw { color: #ff7b72; }
        .fn { color: #d2a8ff; }
        .str { color: #a5d6ff; }
        .cmt { color: #8b949e; }
        .num { color: #79c0ff; }
        a { color: #58a6ff; text-decoration: none; }
        a:hover { text-decoration: underline; }
        .links { display: flex; gap: 15px; justify-content: center; margin: 30px 0; flex-wrap: wrap; }
        .links a {
            background: #21262d; border: 1px solid #30363d; border-radius: 8px;
            padding: 12px 24px; font-size: 1em; transition: 0.2s;
        }
        .links a:hover { border-color: #58a6ff; background: #161b22; text-decoration: none; }
        .comparison { width: 100%; border-collapse: collapse; margin: 20px 0; }
        .comparison th, .comparison td { padding: 10px 15px; border: 1px solid #30363d; text-align: left; }
        .comparison th { background: #161b22; color: #58a6ff; }
        .comparison td { color: #c9d1d9; }
        .highlight { color: #7ee787; font-weight: bold; }
        .math {
            background: #161b22; border: 1px solid #30363d; border-radius: 8px;
            padding: 20px; margin: 15px 0; text-align: center;
            font-family: 'Times New Roman', serif; font-size: 1.2em; color: #c9d1d9;
        }
        footer { text-align: center; padding: 40px; color: #484f58; font-size: 0.9em; }
        @media (max-width: 600px) {
            .feature-grid { grid-template-columns: 1fr; }
            .hero h1 { font-size: 2em; }
        }
    </style>
</head>
<body>

<div class="hero">
    <h1>In<span>KAN</span></h1>
    <p>Fast B-spline Kolmogorov-Arnold Network layers for PyTorch.<br>
    Drop-in <code>nn.Linear</code> replacement with learnable spline activations.</p>

    <div class="badges">
        <a href="https://pypi.org/project/inkan/"><img src="https://img.shields.io/pypi/v/inkan" alt="PyPI"></a>
        <a href="https://pypi.org/project/inkan/"><img src="https://img.shields.io/pypi/dm/inkan" alt="Downloads"></a>
        <img src="https://img.shields.io/pypi/pyversions/inkan" alt="Python">
        <img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="MIT">
    </div>

    <div class="install" onclick="navigator.clipboard.writeText('pip install inkan')">
        pip install inkan
    </div>
    <p style="font-size: 0.8em; color: #484f58; margin-top: 8px;">click to copy</p>
</div>

<div class="container">

    <h2>What is a KAN?</h2>
    <p>In a standard MLP, each connection has a fixed weight and a shared activation function.
    In a <strong>Kolmogorov-Arnold Network</strong>, each edge has its own learnable univariate function
    &phi;(x) &mdash; a B-spline curve that transforms the scalar flowing along that edge.</p>

    <div class="math">
        MLP: &ensp; y = &sigma;(W&middot;x + b) &emsp;&emsp;&emsp;
        KAN: &ensp; y<sub>j</sub> = &sum;<sub>i</sub> &phi;<sub>ji</sub>(x<sub>i</sub>)
    </div>

    <p>Each &phi;<sub>ji</sub> is a learned cubic B-spline with <strong>local support</strong>:
    changing one coefficient affects the function over only ~4 knot intervals.
    This makes KANs inherently more interpretable and editable than MLPs.</p>

    <h2>Why InKAN?</h2>

    <div class="feature-grid">
        <div class="feature">
            <h3>2.8&ndash;5.4x Faster</h3>
            <p>Stable piecewise polynomial evaluation instead of recursive Cox-de Boor.
            Local 4-basis lookup instead of dense K-basis computation.</p>
        </div>
        <div class="feature">
            <h3>Drop-in Replacement</h3>
            <p><code>KANLayer(in, out)</code> replaces <code>nn.Linear(in, out)</code>.
            Same interface, same optimizer, same training loop.</p>
        </div>
        <div class="feature">
            <h3>Numerically Stable</h3>
            <p>Guaranteed non-negative basis output. Float32 accuracy ~1.2e-7.
            No catastrophic cancellation from alternating sums.</p>
        </div>
        <div class="feature">
            <h3>1D and 2D Splines</h3>
            <p>Univariate spline layers plus tensor-product B-spline surfaces
            for joint function approximation.</p>
        </div>
    </div>

    <h2>Quick Start</h2>
    <pre><code><span class="kw">import</span> torch
<span class="kw">from</span> inkan <span class="kw">import</span> KANLayer, KANNetwork

<span class="cmt"># Single layer — drop-in for nn.Linear</span>
layer = <span class="fn">KANLayer</span>(<span class="num">8</span>, <span class="num">4</span>)
x = torch.<span class="fn">randn</span>(<span class="num">32</span>, <span class="num">8</span>)
y = <span class="fn">layer</span>(x)  <span class="cmt"># [32, 4]</span>

<span class="cmt"># Multi-layer network</span>
net = <span class="fn">KANNetwork</span>([<span class="num">784</span>, <span class="num">64</span>, <span class="num">10</span>])
x = torch.<span class="fn">randn</span>(<span class="num">32</span>, <span class="num">784</span>)
y = <span class="fn">net</span>(x)  <span class="cmt"># [32, 10]</span>

<span class="cmt"># Standard PyTorch training</span>
optimizer = torch.optim.<span class="fn">Adam</span>(net.<span class="fn">parameters</span>(), lr=<span class="num">1e-3</span>)
loss = y.<span class="fn">sum</span>()
loss.<span class="fn">backward</span>()
optimizer.<span class="fn">step</span>()</code></pre>

    <h2>Performance</h2>
    <table class="comparison">
        <tr>
            <th>Method</th><th>Grid Size 8</th><th>Grid Size 20</th><th>Grid Size 50</th>
        </tr>
        <tr>
            <td>Cox-de Boor (recursive)</td><td>1.0x</td><td>1.0x</td><td>1.0x</td>
        </tr>
        <tr>
            <td><strong>InKAN (piecewise + local)</strong></td>
            <td class="highlight">2.8x faster</td>
            <td class="highlight">3.9x faster</td>
            <td class="highlight">5.4x faster</td>
        </tr>
    </table>

    <h2>Used In</h2>
    <p><a href="https://github.com/NAVEENMN/attention_manifolds">Attention Manifolds</a> &mdash;
    Learned B-spline coordinate curves for AI safety and mechanistic interpretability in transformer attention.
    Per-coordinate spline curves on Q/K projections, trained on Llama-3.2-1B and 3B.</p>

    <div class="links">
        <a href="https://pypi.org/project/inkan/">📦 PyPI</a>
        <a href="https://github.com/NAVEENMN/inkan">💻 GitHub</a>
        <a href="https://arxiv.org/abs/2609.01956">📄 Paper</a>
        <a href="https://naveenmn.github.io/inkan/">📖 Docs</a>
    </div>

</div>

<footer>
    InKAN &copy; 2026 Naveen Mysore &middot; MIT License
</footer>

</body>
</html>