Beer-Lambert Autoencoder for Unsupervised Stain Representation Learning and Deconvolution in Multi-immunohistochemical Brightfield Histology Images

Separating the contributions of individual chromogenic stains in RGB histology whole slide images (WSIs) is essential for stain normalization, quantitative assessment of marker expression, and cell-level readouts in immunohistochemistry (IHC). Classical Beer-Lambert (BL) color deconvolution is well-established for two- or three-stain settings, but becomes under-determined and unstable for multiplex IHC (mIHC) with K>3 chromogens. We present a simple, data-driven encoder-decoder architecture that learns cohort-specific stain characteristics for mIHC RGB WSIs and yields crisp, well-separated per-stain concentration maps. The encoder is a compact U-Net that predicts K nonnegative concentration channels; the decoder is a differentiable BL forward model with a learnable stain matrix initialized from typical chromogen hues. Training is unsupervised with a perceptual reconstruction objective augmented by loss terms that discourage unnecessary stain mixing. On a colorectal mIHC panel comprising 5 stains (H, CDX2, MUC2, MUC5, CD8) we show excellent RGB reconstruction, and significantly reduced inter-channel bleed-through compared with matrix-based deconvolution. Code and model are available at https://github.com/measty/StainQuant.git.

INSIGHT: Spatially resolved survival modelling from routine histology crosslinked with molecular profiling reveals prognostic epithelial-immune axes in stage II/III colorectal cancer

Routine histology contains rich prognostic information in stage II/III colorectal cancer, much of which is embedded in complex spatial tissue organisation. We present INSIGHT, a graph neural network that predicts survival directly from routine histology images. Trained and cross-validated on TCGA (n=342) and SURGEN (n=336), INSIGHT produces patient-level spatially resolved risk scores. Large independent validation showed superior prognostic performance compared with pTNM staging (C-index 0.68-0.69 vs 0.44-0.58). INSIGHT spatial risk maps recapitulated canonical prognostic histopathology and identified nuclear solidity and circularity as quantitative risk correlates. Integrating spatial risk with data-driven spatial transcriptomic signatures, spatial proteomics, bulk RNA-seq, and single-cell references revealed an epithelium-immune risk manifold capturing epithelial dedifferentiation and fetal programs, myeloid-driven stromal states including $\mathrm{SPP1}^{+}$ macrophages and $\mathrm{LAMP3}^{+}$ dendritic cells, and adaptive immune dysfunction. This analysis exposed patient-specific epithelial heterogeneity, stratification within MSI-High tumours, and high-risk routes of CDX2/HNF4A loss and CEACAM5/6-associated proliferative programs, highlighting coordinated therapeutic vulnerabilities.