Title: hZACH-ViT: Leveraging Curved Latent Geometry for Efficient Vision Transformers in Data-Scarce Medical Imaging

Abstract:

While Compact Vision Transformers (ViTs) offer significant promise for medical imaging applications where data and computational resources are limited, current variants predominantly rely on the assumption that Euclidean latent geometry adequately organizes image representations. To address this, we present hZACH-ViT, a series of extensions that apply curved-geometry principles to ZACH-ViT. ZACH-ViT is a streamlined, zero-token Vision Transformer architecture that eliminates the need for positional embeddings and class tokens, instead utilizing global average pooling on patch representations.

To strictly isolate the impact of geometric structure, we retained the validated ZACH-ViT backbone and altered only the final representation space and the prototype-based classifier head. This approach facilitates a rigorous, controlled comparison among Euclidean, hyperbolic, and spherical latent spaces. Our evaluation involved testing Poincaré, Klein, and spherical variants of hZACH-ViT across seven MedMNIST datasets. The experimental design adhered to a consistent few-shot protocol, employing five random seeds and 50 samples per class.

The resulting benchmark comprises 770 training runs, covering seven datasets, three non-Euclidean geometries, a Euclidean baseline, and seven distinct curvature magnitudes. Our findings indicate that the optimal non-Euclidean hZACH-ViT configuration consistently outperforms the Euclidean ZACH-ViT baseline across all seven datasets. On average, the non-Euclidean models achieved a +0.021 improvement in the primary dataset-specific metric, with the most substantial gain observed on OCTMNIST (+0.055 MacroF1).

Notably, fixed low-curvature configurations maintained positive performance gains across the majority of datasets. Specifically, curvature values of c = 0.1 or 0.2 were associated with victory in six of the seven datasets. Rather than pointing to a single universally optimal manifold, our results identify geometry and curvature as variables dependent on the specific dataset. Furthermore, fixed low-curvature analyses demonstrate that these performance benefits endure even without exhaustive, per-dataset hyperparameter tuning.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC