Ananke：收缩环面吸引子网络
Ananke: Contractive Torus Attractor Networks
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中文总结 AI 辅助
提出Ananke框架及CTAN骨干，通过乘积环面先验和双相连续流实现高效表示学习，以0.27M参数在Kvasir-v2达90.52%准确率，超越大容量基线。
中文摘要 AI 辅助
我们提出了Ananke，一个表示学习框架，将潜在表示构建在结构化的乘积环面先验之上，以及其旗舰视觉骨干实现——收缩环面吸引子网络（CTAN）。通过将高维潜在空间分解为二维相平面的正交直和（$\bigoplus_{k=1}^K \R^2$），Ananke通过解耦的双相连续流协调特征更新：斜对称哈密顿传输沿能量水平集切向移动特征以保持语义相位不变量，而有符号梯度耗散将横向扰动法向收缩至目标不变流形。对于具有冻结参数的圆形势函数族，对数径向反馈产生精确对数辛流（ELSF），这是一种解析闭式映射，具有对数半径误差的精确指数衰减，且无需数值积分即可在单次前向传播中计算。我们建立了水平集偏差和对数半径误差的局部输入到状态界，并刻画了理想乘积环面在有界扰动下的法向双曲性和持续性。我们进一步通过Lie--Trotter算子分裂来构建该架构，统一了空间深度扩散与局部流形收缩，并分析了精确三角流和硬件友好的辛双剪切变体。在自然图像基准（CIFAR-100）和临床挑战性内窥镜数据集（Kvasir-v2）上，CTAN展现了卓越的参数效率：一个仅含0.27M参数的超紧凑分层模型在Kvasir-v2上达到90.52%的准确率，在容量上以近两个数量级的优势超越25M+参数的基线（ResNet-50、DenseNet-161），而扩展变体在CIFAR-100上达到80.32%的top-1准确率。
英文摘要
We introduce Ananke, a representation-learning framework that scaffolds latent representations onto a structured product-torus prior, and its flagship visual backbone realization, Contractive Torus Attractor Networks (CTAN). By factorizing high-dimensional latent spaces into an orthogonal direct sum of two-dimensional phase planes ($\bigoplus_{k=1}^K \R^2$), Ananke coordinates feature updates via a decoupled dual-phase continuous flow: skew-symmetric Hamiltonian transport moves features tangentially along energy level sets to preserve semantic phase invariants, while signed gradient dissipation contracts transverse perturbations normally toward target invariant manifolds. For circular potential families with frozen parameters, logarithmic radial feedback yields the Exact Log-Symplectic Flow (ELSF), an analytical closed-form mapping with exact exponential decay of log-radius error that evaluates in a single forward pass without numerical integration. We establish local input-to-state bounds for level-set deviations and log-radius errors, and characterize the normal hyperbolicity and persistence of the ideal product torus under bounded perturbations. We further formulate the architecture through Lie--Trotter operator splitting, unifying spatial depthwise diffusion with local manifold contraction, and analyze both exact trigonometric flows and hardware-friendly symplectic dual-shear variants. Across natural image benchmarks (CIFAR-100) and clinically challenging endoscopy datasets (Kvasir-v2), CTAN demonstrates exceptional parameter efficiency: an ultra-compact hierarchical model with merely 0.27M parameters achieves 90.52\% accuracy on Kvasir-v2, outperforming 25M+ baselines (ResNet-50, DenseNet-161) by nearly two orders of magnitude in capacity, while scaled variants attain 80.32\% top-1 accuracy on CIFAR-100.
