CliffordNet All You Need is Geometric Algebra

C3P0 (C3P0) • 2026年02月04日 12:10
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<body>

<div class="poster-container">
    <div class="bg-shape shape-1"></div>
    <div class="bg-shape shape-2"></div>

    <header>
        <h1>CliffordNet</h1>
        <div class="subtitle">
            All You Need is Geometric Algebra
            <span class="tag">CV Architecture</span>
            <span class="tag">Math First Principles</span>
        </div>
        <p style="margin-top: 15px; color: #cbd5e1;">
            一种回归数学第一性原理的新型视觉骨干网络，挑战了现代网络依赖堆叠复杂模块（Attention/Conv + FFN）的传统范式。
        </p>
    </header>

    <div class="content-grid">
        <!-- Section 1: The Core Math -->
        <div class="card">
            <div class="card-title">
                <i class="material-icons">functions</i>
                核心原理：几何乘积
            </div>
            <div class="image-container">
                <img src="https://sfile.chatglm.cn/image/9a/9a0e2033.jpg" alt="Geometric Algebra Visualization">
                <div class="image-caption">Geometric Algebra & Vector Space</div>
            </div>
            <p>
                CliffordNet 利用 Clifford 几何乘积 (<span style="font-family:serif; font-style:italic;">uv</span>) 统一了特征的交互。它不仅包含相似性对齐，还包含结构化差异提取。
            </p>
            <div class="math-container">
                <div class="formula">
                    uv = <span>u · v</span> + <span style="color:var(--accent-purple)">u ∧ v</span>
                </div>
                <div class="formula-desc">
                    <div class="desc-item">
                        <span class="dot">Dot (内积)</span>
                        <span>特征对齐</span>
                    </div>
                    <div class="desc-item">
                        <span class="wedge">Wedge (外积)</span>
                        <span>结构/边缘</span>
                    </div>
                </div>
            </div>
            <p>
                <strong style="color:var(--text-light)">代数完备性：</strong> 几何乘积不仅捕获点积（标量相似性），还通过外积捕获正交性和结构变异（双向量），使网络能够直接"看到"几何结构。
            </p>
        </div>

        <!-- Section 2: Architecture Innovation -->
        <div class="card">
            <div class="card-title">
                <i class="material-icons">architecture</i>
                架构创新：稀疏滚动交互
            </div>
            <p>
                摒弃了标准的 Feed-Forward Networks (FFN) 和全局 Attention，采用高效的 <strong>Sparse Rolling Interaction</strong>。
            </p>
            <div class="arch-diagram">
                <div class="arch-block block-input">State H</div>
                <div class="arrow-down">↓</div>
                <div class="arch-block" style="justify-content: center; gap: 10px;">
                    <span style="font-size: 10px; color: #94a3b8;">Shifted Context C</span>
                </div>
                <div class="arrow-down">↓</div>
                <div class="arch-block block-geo">
                    Clifford Product (Linear O(N))
                </div>
                <div class="arrow-down">↓</div>
                <div class="arch-block block-output">Output</div>
            </div>
            <div class="highlight-box" style="border-color: var(--accent-purple); background: rgba(139, 92, 246, 0.1);">
                <strong>NO FFN Design:</strong><br>
                实验证明，Clifford 交互层本身具有极强的表达能力，使得传统 Transformer 中昂贵的 FFN 模块变得多余。
            </div>
        </div>

        <!-- Section 3: 2D Topology & Mechanism -->
        <div class="card">
            <div class="card-title">
                <i class="material-icons">grid_on</i>
                保留二维拓扑特征
            </div>
            <div class="image-container">
                <img src="https://sfile.chatglm.cn/image/82/8219ef9c.jpg" alt="Vector Projection">
                <div class="image-caption">Interaction Mechanics</div>
            </div>
            <p>
                通过稀疏滚动机制（<span style="font-family:serif">T_s</span>），模型在不增加随机内存访问成本的情况下，捕获了通道间的远距离上下文。
            </p>
            <ul style="font-size: 13px; color: var(--text-dim); padding-left: 20px; margin: 0;">
                <li><strong style="color:var(--accent-cyan)">线性复杂度 O(N)：</strong> 避免了标准 Self-Attention 的二次成本。</li>
                <li><strong style="color:var(--accent-cyan)">参数效率：</strong> 极致精简的模型参数。</li>
                <li><strong>几何严谨性：</strong> 基于严格的数学代数而非启发式堆叠。</li>
            </ul>
        </div>

        <!-- Section 4: Experimental Results -->
        <div class="card">
            <div class="card-title">
                <i class="material-icons">bar_chart</i>
                实验结果：新帕累托前沿
            </div>
            <p>
                在 CIFAR-100 数据集上，CliffordNet 以极少的参数达到了媲美重型模型的效果。
            </p>
            <div class="chart-container">
                <div class="bar-group">
                    <div class="bar-label">
                        <span>CliffordNet-Nano (Ours)</span>
                        <span style="color:var(--accent-cyan)">1.4M Params</span>
                    </div>
                    <div class="bar-bg">
                        <div class="bar-fill fill-cyan" style="width: 12%;">1.4M</div>
                    </div>
                    <div style="font-size: 11px; color: #fff; text-align: right;">Accuracy: 76.41%</div>
                </div>

                <div class="bar-group">
                    <div class="bar-label">
                        <span>ResNet-18 (Baseline)</span>
                        <span style="color:var(--accent-purple)">11.2M Params</span>
                    </div>
                    <div class="bar-bg">
                        <div class="bar-fill fill-purple" style="width: 90%;">11.2M</div>
                    </div>
                    <div style="font-size: 11px; color: #fff; text-align: right;">Accuracy: 76.63%</div>
                </div>
            </div>
            <div class="highlight-box">
                <strong>结论：</strong> 参数减少 <strong>8倍</strong>，性能持平。
                <br>Base 变体 (3.0M) 更是创造了小模型的 SOTA (78.05%)。
            </div>
        </div>

        <!-- Section 5: Full Width Summary -->
        <div class="card full-width" style="flex-direction: row; align-items: center; justify-content: space-between;">
            <div style="flex: 2;">
                <div class="card-title" style="border: none; margin-bottom: 5px;">
                    未来展望
                </div>
                <p style="margin-bottom: 0;">
                    CliffordNet 为开发极度精简且具有数学严谨性的视觉骨干网开辟了新路径。未来将扩展至 ImageNet、密集预测任务（分割/检测）以及更高阶的几何代数应用。
                </p>
            </div>
            <div style="flex: 1; text-align: right; display: flex; gap: 10px; justify-content: flex-end;">
                <div class="icon-box"><i class="material-icons">check_circle</i> No FFN</div>
                <div class="icon-box"><i class="material-icons">check_circle</i> O(N)</div>
                <div class="icon-box"><i class="material-icons">check_circle</i> Geometry</div>
            </div>
        </div>
    </div>

    <footer>
        <div>Source: arXiv:2601.06793 (CliffordNet: All You Need is Geometric Algebra)</div>
        <div>Generated by NotebookLM Assistant</div>
    </footer>
</div>

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