Mind the Gap: Continuous Magnification Sampling for Pathology Foundation Models

TL;DR

This work reframes magnification sampling in pathology foundation models as a multi-source domain adaptation problem and demonstrates that standard discrete uniform sampling degrades representations at intermediate scales. It introduces continuous magnification training via crop-and-resize, along with principled optimization of sampling distributions under average- and worst-case criteria, to achieve smoother, more robust embeddings across the magnification spectrum. The authors validate their theory with RankMe-based profiling and two new multi-scale benchmarks (TCGA-MS, BRACS-MS), showing improvements of up to about 4 percentage points in intermediate magnifications and revealing magnification as a major driver of model performance. The findings have practical implications for evaluating and constructing pathology foundation models that perform reliably across scales, and point to future directions in cross-scale analysis and multi-scale benchmark development.

Abstract

In histopathology, pathologists examine both tissue architecture at low magnification and fine-grained morphology at high magnification. Yet, the performance of pathology foundation models across magnifications and the effect of magnification sampling during training remain poorly understood. We model magnification sampling as a multi-source domain adaptation problem and develop a simple theoretical framework that reveals systematic trade-offs between sampling strategies. We show that the widely used discrete uniform sampling of magnifications (0.25, 0.5, 1.0, 2.0 mpp) leads to degradation at intermediate magnifications. We introduce continuous magnification sampling, which removes gaps in magnification coverage while preserving performance at standard scales. Further, we derive sampling distributions that optimize representation quality across magnification scales. To evaluate these strategies, we introduce two new benchmarks (TCGA-MS, BRACS-MS) with appropriate metrics. Our experiments show that continuous sampling substantially improves over discrete sampling at intermediate magnifications, with gains of up to 4 percentage points in balanced classification accuracy, and that optimized distributions can further improve performance. Finally, we evaluate current histopathology foundation models, finding that magnification is a primary driver of performance variation across models. Our work paves the way towards future pathology foundation models that perform reliably across magnifications.

Figures (23)

• Figure 1: Overview of our approach. We derive novel, principled magnification sampling strategies to pretrain vision foundation models (FMs) from multi-scale histopathology data and compare them to established discrete magnification sampling protocols (MPP = microns per pixel). For evaluation, we introduce three techniques to measure FM embedding quality across magnifications: (1) a data-free theoretical domain adaptation framework for magnification sampling, (2) a RankMe score to quantify the information richness of a model’s embedding space, and (3) a multi-scale predictive performance benchmark for FM-derived downstream models. Together, these evaluations provide a comprehensive view of the magnification performance profile of new and established pathology foundation models.
• Figure 2: Properties of the domain adaptation framework. (a) Transfer potential $\bar{K}(x)$ for three similarity kernels across the magnification range. Central magnifications exhibit higher transfer potential due to shared visual features with neighboring scales, while boundary magnifications show reduced potential. (b) Accumulated Training Signal $S(y)$ for the "Information-Based Kernel" for the continuous uniform and discrete sampling distributions. Continuous uniform sampling leads to systematic degradation at boundaries (Proposition \ref{['prop:mag_prototypes']}), while discrete sampling creates gaps at intermediate magnifications.
• Figure 3: Optimized magnification sampling distributions. (a) Sampling distributions from max-average optimization with entropy regularization for the information-based kernel. As the regularization parameter $\lambda$ increases, the optimal distribution shifts from sampling more prototypical magnifications near the center to near-uniform. (b) Max-min optimization oversamples boundary magnifications for both kernels.
• Figure 4: Representation quality across magnifications for single-scale models trained on different magnifications. Each line represents a model trained at the magnification indicated in the legend. Models exhibit smooth degradation in RankMe scores as evaluation magnification moves away from training magnification.
• Figure 5: Representation quality and embedding space organization in multi-scale models. (A) RankMe profiles across magnifications: discrete uniform sampling (DU) shows dips at intermediate scales, while continuous strategies produce smooth profiles. (B) Minimal and overall theoretical training signal and normalized RankMe scores across sampling strategies. The close alignment between theoretical predictions and measured embedding quality validates our domain adaptation framework. (C) Cosine similarities between embedding centroids at standard magnifications (DU model). Patches from similar magnifications cluster more closely, while larger magnification differences correspond to greater separation in the learned feature space. (D) t-SNE projection of patch embeddings colored by magnification (DU model), showing that scale acts as a continuous organizing dimension.

Theorems & Definitions (1)

• Proposition 1: Magnification Prototypes