Graph Laplacian Transformer with Progressive Sampling for Prostate Cancer Grading

Prostate cancer grading from whole-slide images (WSIs) remains a challenging task due to the large-scale nature of WSIs, the presence of heterogeneous tissue structures, and difficulty of selecting diagnostically relevant regions. Existing approaches often rely on random or static patch selection, leading to the inclusion of redundant or non-informative regions that degrade performance. To address this, we propose a Graph Laplacian Attention-Based Transformer (GLAT) integrated with an Iterative Refinement Module (IRM) to enhance both feature learning and spatial consistency. The IRM iteratively refines patch selection by leveraging a pretrained ResNet50 for local feature extraction and a foundation model in no-gradient mode for importance scoring, ensuring only the most relevant tissue regions are preserved. The GLAT models tissue-level connectivity by constructing a graph where patches serve as nodes, ensuring spatial consistency through graph Laplacian constraints and refining feature representations via a learnable filtering mechanism that enhances discriminative histological structures. Additionally, a convex aggregation mechanism dynamically adjusts patch importance to generate a robust WSI-level representation. Extensive experiments on five public and one private dataset demonstrate that our model outperforms state-of-the-art methods, achieving higher performance and spatial consistency while maintaining computational efficiency.

💡 Research Summary

Prostate cancer grading from whole‑slide images (WSIs) is hampered by the massive size of the images, heterogeneous tissue patterns, and the difficulty of pinpointing diagnostically relevant regions. Existing multiple‑instance learning (MIL) pipelines either treat all patches equally or rely on static attention mechanisms, which often include redundant or non‑informative patches and consequently degrade performance. Graph‑based methods capture local connectivity but are computationally expensive, while transformer‑based approaches model long‑range dependencies yet still suffer from random patch selection.

To address these challenges, the authors propose a two‑stage framework consisting of an Iterative Refinement Module (IRM) and a Graph Laplacian Attention‑based Transformer (GLAT).

Iterative Refinement Module (IRM)

1. Local feature extraction – A pretrained ResNet‑50 converts each 224 × 224 patch into a 512‑dimensional embedding.
2. Contextual importance scoring – A frozen foundation model (the UNI model) computes self‑attention across all patches. The average attention weight for each patch serves as an importance score.
3. Progressive sampling – The whole set of patches is split into T non‑overlapping subsets. After each iteration, the FM re‑evaluates the importance scores of the currently retained patches together with the next subset, and only the top‑M patches are kept. After T iterations, a compact, high‑informative patch set (P^{(T)}_{selected}) is produced. Because the FM operates in no‑gradient mode, global contextual reasoning is obtained without additional training cost.

Graph Laplacian Attention Transformer (GLAT)

1. Graph construction – Selected patches become nodes; edges are defined by a Gaussian kernel on the refined embeddings (E’i), yielding an adjacency matrix (W{ij}= \exp(-|E’_i-E’_j|^2/2\sigma^2)).
2. Laplacian regularization – The degree matrix (D) and global Laplacian (L_{global}=D-W) are computed. A learnable filter (L_{\theta}) is applied to the query, key and value matrices: (Q’ = L_{\theta}Q), (K’ = L_{\theta}K), (V’ = L_{\theta}V).
3. Graph‑augmented attention – The attention scores are modified as
   \