用图像识别自动辨认绳结，结合深度学习与拓扑不变量。
On knot detection via picture recognition
- 用CNN和Transformer直接从图片预测交叉数。
- 轻量模型即可捕捉关键结构信息，准确率显著优于基线。
- 适合对拓扑、计算机视觉交叉研究感兴趣的读者。
本文旨在通过手机拍摄的绳结图像实现自动识别。我们提出一种结合现代机器学习（如卷积神经网络和Transformer）与传统算法（计算琼斯多项式等量子不变量）的策略。构建了简单基线模型，直接从图像预测交叉数，证明即使轻量级的CNN与Transformer也能有效提取结构信息。长期目标是将感知模块与符号化重构结合，生成平面图代码（PD），进而计算拓扑不变量，实现鲁棒的绳结分类。该两阶段方法凸显了机器学习处理噪声图像与不变量提供严格拓扑区分之间的互补性。
原文摘要 · Abstract (English)
Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular convolutional neural networks and transformers for image recognition) and traditional algorithms (to compute quantum invariants like the Jones polynomial). We present simple baselines that predict crossing number directly from images, showing that even lightweight CNN and transformer architectures can recover meaningful structural information. The longer-term aim is to combine these perception modules with symbolic reconstruction into planar diagram (PD) codes, enabling downstream invariant computation for robust knot classification. This two-stage approach highlights the complementarity between machine learning, which handles noisy visual data, and invariants, which enforce rigorous topological distinctions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。