Ananke framework enables compact and efficient visual models
Ananke: Contractive Torus Attractor Networks
Computer Vision and Pattern Recognition
Summary
Representing complex visual data in simpler, structured ways helps computers understand images better. The authors created Ananke, a system that organizes information in a special circular pattern to preserve important features. Their design, CTAN, uses mathematical flows to keep key details stable while improving learning. This approach led to very small models that perform well on both medical images and common picture datasets.
What this means in practice
- •For medical imaging engineers: Build compact models for medical image classification that maintain high accuracy with fewer parameters on datasets like endoscopy images.
- •For machine learning practitioners: Create efficient visual recognition models using structured latent spaces to reduce model size without sacrificing accuracy.
Authors
Zhongping Ji
Abstract
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.