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</html>
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>InKAN β Fast B-Spline KAN Layers for PyTorch</title>
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<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.">
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<meta name="keywords" content="inkan, KAN, Kolmogorov-Arnold Network, B-spline, PyTorch, neural network, deep learning, machine learning, learnable activation, spline, interpretable ML">
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<meta name="author" content="Naveen Mysore">
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<link rel="canonical" href="https://pypi.org/project/inkan/">
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<style>
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* { box-sizing: border-box; margin: 0; padding: 0; }
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body {
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font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Helvetica, Arial, sans-serif;
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background: #0d1117; color: #c9d1d9;
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line-height: 1.6; padding: 0;
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}
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.hero {
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background: linear-gradient(135deg, #1a1a2e 0%, #16213e 50%, #0f3460 100%);
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padding: 60px 20px; text-align: center;
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}
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.hero h1 { font-size: 3em; color: #58a6ff; margin-bottom: 10px; }
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.hero h1 span { color: #f0883e; }
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.hero p { font-size: 1.2em; color: #8b949e; max-width: 700px; margin: 0 auto 30px; }
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.install {
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background: #161b22; border: 1px solid #30363d; border-radius: 8px;
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padding: 15px 25px; display: inline-block; font-family: monospace;
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font-size: 1.1em; color: #7ee787; cursor: pointer;
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}
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.install:hover { border-color: #58a6ff; }
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.badges { margin: 20px 0; }
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.badges img { margin: 0 4px; }
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.container { max-width: 900px; margin: 0 auto; padding: 40px 20px; }
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h2 { color: #58a6ff; font-size: 1.5em; margin: 40px 0 15px; border-bottom: 1px solid #21262d; padding-bottom: 8px; }
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.feature-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 20px; margin: 20px 0; }
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.feature {
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background: #161b22; border: 1px solid #30363d; border-radius: 8px;
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padding: 20px;
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}
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.feature h3 { color: #f0883e; margin-bottom: 8px; }
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.feature p { color: #8b949e; font-size: 0.95em; }
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pre {
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background: #161b22; border: 1px solid #30363d; border-radius: 8px;
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padding: 20px; overflow-x: auto; font-size: 0.9em;
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}
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code { color: #7ee787; }
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.kw { color: #ff7b72; }
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.fn { color: #d2a8ff; }
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.str { color: #a5d6ff; }
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.cmt { color: #8b949e; }
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.num { color: #79c0ff; }
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a { color: #58a6ff; text-decoration: none; }
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a:hover { text-decoration: underline; }
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.links { display: flex; gap: 15px; justify-content: center; margin: 30px 0; flex-wrap: wrap; }
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.links a {
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background: #21262d; border: 1px solid #30363d; border-radius: 8px;
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padding: 12px 24px; font-size: 1em; transition: 0.2s;
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}
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.links a:hover { border-color: #58a6ff; background: #161b22; text-decoration: none; }
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.comparison { width: 100%; border-collapse: collapse; margin: 20px 0; }
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.comparison th, .comparison td { padding: 10px 15px; border: 1px solid #30363d; text-align: left; }
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.comparison th { background: #161b22; color: #58a6ff; }
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.comparison td { color: #c9d1d9; }
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.highlight { color: #7ee787; font-weight: bold; }
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.math {
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background: #161b22; border: 1px solid #30363d; border-radius: 8px;
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padding: 20px; margin: 15px 0; text-align: center;
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font-family: 'Times New Roman', serif; font-size: 1.2em; color: #c9d1d9;
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}
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footer { text-align: center; padding: 40px; color: #484f58; font-size: 0.9em; }
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@media (max-width: 600px) {
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.feature-grid { grid-template-columns: 1fr; }
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.hero h1 { font-size: 2em; }
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}
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</style>
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</head>
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<body>
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<div class="hero">
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<h1>In<span>KAN</span></h1>
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<p>Fast B-spline Kolmogorov-Arnold Network layers for PyTorch.<br>
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Drop-in <code>nn.Linear</code> replacement with learnable spline activations.</p>
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<div class="badges">
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<a href="https://pypi.org/project/inkan/"><img src="https://img.shields.io/pypi/v/inkan" alt="PyPI"></a>
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<a href="https://pypi.org/project/inkan/"><img src="https://img.shields.io/pypi/dm/inkan" alt="Downloads"></a>
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<img src="https://img.shields.io/pypi/pyversions/inkan" alt="Python">
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<img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="MIT">
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</div>
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<div class="install" onclick="navigator.clipboard.writeText('pip install inkan')">
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pip install inkan
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</div>
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<p style="font-size: 0.8em; color: #484f58; margin-top: 8px;">click to copy</p>
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</div>
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<div class="container">
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<h2>What is a KAN?</h2>
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<p>In a standard MLP, each connection has a fixed weight and a shared activation function.
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In a <strong>Kolmogorov-Arnold Network</strong>, each edge has its own learnable univariate function
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φ(x) — a B-spline curve that transforms the scalar flowing along that edge.</p>
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<div class="math">
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MLP:   y = σ(W·x + b)    
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KAN:   y<sub>j</sub> = ∑<sub>i</sub> φ<sub>ji</sub>(x<sub>i</sub>)
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</div>
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<p>Each φ<sub>ji</sub> is a learned cubic B-spline with <strong>local support</strong>:
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changing one coefficient affects the function over only ~4 knot intervals.
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This makes KANs inherently more interpretable and editable than MLPs.</p>
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<h2>Why InKAN?</h2>
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<div class="feature-grid">
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<div class="feature">
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<h3>2.8–5.4x Faster</h3>
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<p>Stable piecewise polynomial evaluation instead of recursive Cox-de Boor.
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Local 4-basis lookup instead of dense K-basis computation.</p>
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</div>
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<div class="feature">
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<h3>Drop-in Replacement</h3>
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<p><code>KANLayer(in, out)</code> replaces <code>nn.Linear(in, out)</code>.
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Same interface, same optimizer, same training loop.</p>
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</div>
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<div class="feature">
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<h3>Numerically Stable</h3>
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<p>Guaranteed non-negative basis output. Float32 accuracy ~1.2e-7.
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No catastrophic cancellation from alternating sums.</p>
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</div>
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<div class="feature">
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<h3>1D and 2D Splines</h3>
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<p>Univariate spline layers plus tensor-product B-spline surfaces
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for joint function approximation.</p>
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</div>
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</div>
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<h2>Quick Start</h2>
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<pre><code><span class="kw">import</span> torch
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<span class="kw">from</span> inkan <span class="kw">import</span> KANLayer, KANNetwork
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<span class="cmt"># Single layer β drop-in for nn.Linear</span>
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layer = <span class="fn">KANLayer</span>(<span class="num">8</span>, <span class="num">4</span>)
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x = torch.<span class="fn">randn</span>(<span class="num">32</span>, <span class="num">8</span>)
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y = <span class="fn">layer</span>(x) <span class="cmt"># [32, 4]</span>
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<span class="cmt"># Multi-layer network</span>
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net = <span class="fn">KANNetwork</span>([<span class="num">784</span>, <span class="num">64</span>, <span class="num">10</span>])
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x = torch.<span class="fn">randn</span>(<span class="num">32</span>, <span class="num">784</span>)
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y = <span class="fn">net</span>(x) <span class="cmt"># [32, 10]</span>
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<span class="cmt"># Standard PyTorch training</span>
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optimizer = torch.optim.<span class="fn">Adam</span>(net.<span class="fn">parameters</span>(), lr=<span class="num">1e-3</span>)
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loss = y.<span class="fn">sum</span>()
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loss.<span class="fn">backward</span>()
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optimizer.<span class="fn">step</span>()</code></pre>
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<h2>Performance</h2>
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<table class="comparison">
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<tr>
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<th>Method</th><th>Grid Size 8</th><th>Grid Size 20</th><th>Grid Size 50</th>
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</tr>
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<tr>
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<td>Cox-de Boor (recursive)</td><td>1.0x</td><td>1.0x</td><td>1.0x</td>
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</tr>
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<tr>
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<td><strong>InKAN (piecewise + local)</strong></td>
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<td class="highlight">2.8x faster</td>
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<td class="highlight">3.9x faster</td>
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<td class="highlight">5.4x faster</td>
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</tr>
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</table>
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<h2>Used In</h2>
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<p><a href="https://github.com/NAVEENMN/attention_manifolds">Attention Manifolds</a> —
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Learned B-spline coordinate curves for AI safety and mechanistic interpretability in transformer attention.
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Per-coordinate spline curves on Q/K projections, trained on Llama-3.2-1B and 3B.</p>
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<div class="links">
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<a href="https://pypi.org/project/inkan/">π¦ PyPI</a>
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<a href="https://github.com/NAVEENMN/inkan">π» GitHub</a>
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<a href="https://arxiv.org/abs/2609.01956">π Paper</a>
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<a href="https://naveenmn.github.io/inkan/">π Docs</a>
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</div>
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</div>
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<footer>
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InKAN © 2026 Naveen Mysore · MIT License
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</footer>
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</body>
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</html>
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