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| <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"> |
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| <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> |
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| <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> |
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| <div class="container"> |
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| <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 |
| φ(x) — a B-spline curve that transforms the scalar flowing along that edge.</p> |
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| <div class="math"> |
| MLP:   y = σ(W·x + b)     |
| KAN:   y<sub>j</sub> = ∑<sub>i</sub> φ<sub>ji</sub>(x<sub>i</sub>) |
| </div> |
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| <p>Each φ<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> |
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| <h2>Why InKAN?</h2> |
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| <div class="feature-grid"> |
| <div class="feature"> |
| <h3>2.8–5.4x 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> |
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| <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 |
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| <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> |
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| <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> |
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| <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> |
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| <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> |
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| <h2>Used In</h2> |
| <p><a href="https://github.com/NAVEENMN/attention_manifolds">Attention Manifolds</a> — |
| 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> |
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| <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> |
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| InKAN © 2026 Naveen Mysore · MIT License |
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