\section{Introduction}
\label{sec:intro}


\begin{figure}[!t]
    \centering
    \subfigure[\normalsize Original \textcolor{white}{\LARGE\smiley}]{
    % \subfigure[\normalsize original ]{
        \includegraphics[width=0.222\textwidth]{figures/retrained/58_000450_input.png}
    }
    % \subfigure[\LARGE{\frownie} \normalsize StainGAN \protect\citep{shaban2019staingan}]{
    \subfigure[\LARGE{\frownie} \normalsize StainGAN]{
        \includegraphics[width=0.222\textwidth]{figures/retrained/58_000450_output.png}
    }
    % \subfigure[\LARGE{\frownie} \normalsize StainNet \protect\citep{stainnet}]{
    \subfigure[\LARGE{\frownie} \normalsize StainNet]{
        \includegraphics[width=0.222\textwidth]{figures/retrained/58_000450_stainNet.png}
    }
    \subfigure[\LARGE{\smiley} \normalsize  Ours]{
        \includegraphics[width=0.222\textwidth]{figures/retrained/2025-09-05__11_05_11__grid_breast2breast_899950_step_00048_58_000450_input.png}
    }
    \caption{ 
        Stain normalization enables consistent visual appearance across histology images from different institutes, enhancing interoperability for downstream models and pathologists. 
        Unlike prior methods that risk hallucinations or structural degradation, our approach preserves tissue integrity and is explicitly designed to be hallucination resilient.
    }
    \label{fig:retrained}
\end{figure}


\begin{table*}[!b]
\centering
\caption{A comparison of normalization methods with respect to desirable properties for their practical use. For a description of the properties and an elaboration on StainNet, see section~\ref{sec:prop}.}
\label{tab:prop}
\begin{tabular}{lccccc}
% \hline
% \textbf{} & \textbf{\rotatebox{45}{StainGAN}} & \textbf{StainFuser} & \textbf{ContriMix} & \textbf{StainNet} & \textbf{Ours} \\
% \textbf{} & \textbf{\rotatebox{45}{StainGAN}} & \textbf{StainFuser} & \textbf{ContriMix} & \textbf{StainNet} & \textbf{Ours} \\
% \fontsize{6pt}{8pt}\selectfont
\multicolumn{1}{c}{}&\multicolumn{1}{c}{\textbf{\rotatebox{30}{StainGAN}}}&\multicolumn{1}{c}{\textbf{\rotatebox{30}{StainFuser}}}&\multicolumn{1}{c}{\textbf{\rotatebox{30}{ContriMix}}}&\multicolumn{1}{c}{\textbf{\rotatebox{30}{StainNet}}}&\multicolumn{1}{c}{\textbf{\rotatebox{30}{ours}}}\\
\hline
% \fontsize{12pt}{14pt}\selectfont
Retroactively applicable & \cmark & \cmark & \xmark & \cmark & \cmark \\
Retention of infrequent colors & \xmark & \xmark & \cmark & \xmark & \cmark \\
Resilient to hallucination & \xmark & \xmark & \xmark & \dmark & \cmark \\
Scale independent & \xmark & \xmark & \xmark & \cmark & \cmark \\
Structure independent & \xmark & \xmark & \xmark & \dmark & \cmark \\
\hline
\end{tabular}
\end{table*}

Histopathology plays a critical role in clinical diagnostics, yet it faces persistent challenges in the application of machine learning due to domain shift and data drift.
Variability in staining protocols, scanner hardware, and tissue preparation introduces significant heterogeneity across datasets, which can degrade the performance of deep learning models trained on limited or homogeneous data.


% This variability is not merely a technical nuisance, it has real clinical implications.
% Even experienced pathologists may struggle to reach consensus on ambiguous cases.
% As workloads continue to rise, the potential of telepathology to alleviate pressure by enabling remote collaboration and diagnosis becomes increasingly relevant.
% Encountering images that exhibit unfamiliar characteristics, such as unexpected color profiles or staining artifacts, poses an additional hurdle to telepathology.
% This visual inconsistency can impede rapid and accurate interpretation, especially when pathologists must adapt to data distributions outside their routine experience.
% In such scenarios, normalization techniques can offer immediate visual consistency, aiding human interpretation.
% Unlike augmentations, normalization can be applied retroactively, making it particularly useful when dealing with third-party models or archived data.


As \citet{tellez2019quantifying} emphasize, addressing the variability issues for machine learning requires either data augmentation, normalization, or a combination of both.
% Numerous studies have demonstrated the benefits of augmentations in improving generalization across domains.
% These techniques simulate variability during training, allowing models to become more robust to unseen data.
\citet{vasiljevic2022cyclegan} caution the use of deep learning methods as they produce varying results and can be prone to hallucinations.
This risk is exacerbated with the trend towards larger models with more capacity \citep{wang2022transformer, stegmuller2023scorenet, alber2025novel}.
These models often function as `black boxes', prone to regressing toward the most probable modes in the data distribution, potentially overwriting rare but clinically significant features.
On the other hand, \citet{swiderska2020impact} demonstrate that simple color normalization alone is insufficient to bridge the performance gap across domains.
Their findings suggest that more expressive, non-linear models are necessary to capture complex variations such as scanner-specific artifacts and staining concentration differences.


% In summary, while normalization may not be a panacea, it remains a practical tool—especially in scenarios where augmentations are infeasible.
% As telepathology becomes more viable and workloads increase, ensuring visual consistency across institutions will be critical for both human and machine decision-making.



In this work, we propose a lightweight, non-adversarial domain adaptation framework, $1\times1$ Stainer, that mitigates hallucination risk and preserves critical histological information. 
Our method introduces a novel color distribution dissimilarity loss to guide a non-linear color mapping without relying on generative adversarial networks (GANs), cycle consistency or diffusion models. 
% Such a color mapping focuses on bridging the gap introduced by slide preparation, scanner, settings, and digitization.
We aim to strike a balance between model expressiveness and interpretability, offering a practical solution for robust histopathological analysis across diverse clinical settings.
Our contributions to domain adaptation for histopathology are as follows:
\begin{itemize}
   \item We propose a method to directly train light-weight domain adaptation models on unlabeled data that are free of  hallucinations.
   % \item We propose a stopping criterion for adversarial training based on a discriminator that is trained until convergence on the target domain and random color augmentations.
   \item We propose a color distribution dissimilarity loss function for distribution matching.
   \item We illustrate the risk of hallucinations in several state-of-the-art deep learning models with examples, and offer an approach to mitigate this risk.
\end{itemize}



% \todo{Rewrite}
% %What do I want to talk about in this section?
% %First I want to answer the why of this work.
% AI for medicine has made great advances in recent years.
% However, the scarcity of labeled data, especially for rare diseases, and data variability remain significant challenges.
% Limited digitization within the field of histopathology exacerbates this issue.
% % Collecting sufficient labeled data to capture the full distribution over diseases and technical setups can seem infeasible.
% % Normalization addresses these challenges by enabling models to generalize across different data sources \citep{stacke2020measuring,Legala2025,Gangeh2025}.
% Normalization addresses these challenges by enabling models to generalize across different data sources \citep{stacke2020measuring, Legala2025, Gangeh2025}.
% It allows the occurrences of rare cases to be pooled across domains.
% For models trained on the data, it enhances robustness and applicability in clinical diagnostics.
% %Then I want to talk about the challenges in the field.
% However, in addition to the challenge of matching the target domain distribution, domain adaptation also introduces the difficult-to-quantify risk of information loss.
% Some sort of cycle consistency loss or comparison to the input image is introduced by some works to mitigate this risk \citep{tellez2019quantifying, bai2023deep,shaban2019staingan, lee2022stain, wagner2021structure, nguyencontrimix}.
% Such losses are insufficient, especially for rare pixel structures, as summing over batches incentivizes neural networks to have their outputs converge to the mean.
% With the current trend towards larger models and larger, uncurated datasets, this becomes more of an issue \citep{alber2025novel, wang2022transformer, stegmuller2023scorenet}.
% Instead, the method proposed in this work follows the example of StainNet \citep{stainnet} to smaller neural networks that are far less prone to hallucinations and information loss.
% To fit its models, StainNet still relies on Generative Adversarial Network (GAN) based methods for direct supervision and therefore risks transferring their biases.
% Finally, offering an alternative to GANs for image generation, diffusion models are becoming more widespread \citep{moghadam2023morphology, shen2023staindiff, jewsbury2024stainfuser}.
% As diffusion models characteristically start their generation from noise, they are required to generate image structure.
% This puts them at risk of overwriting crucial information for downstream tasks.
% %I want to go over some of the related work that attempted to address these challenges.
% % Domain shift has been recognized as a problem for histopathology.  \citep{stacke2020measuring}
% % Other virtual stain modifying models also adopt cycle consistency loss as a way to avoid the loss of information \citep{bai2023deep}.
% % A trend towards larger models, such as transformer based models \citep{alber2025novel,wang2022transformer,stegmuller2023scorenet}.
% % Also more and more diffusion models, have to let them generate structure \citep{moghadam2023morphology}.
% % Using a U-Net like architecture and heavy augmentations \citep{tellez2019quantifying}, similar freedom as GANs.
% %Finally, I want to introduce the approach that I will take in this work.
% %I'll finish this section with our contributions.
% Our contributions to domain adaptation for histopathology are as follows:
% \begin{itemize}
   % \item We propose a method to directly train light-weight domain adaptation models on unlabeled data that limit hallucinations.
   % % \item We propose a stopping criterion for adversarial training based on a discriminator that is trained until convergence on the target domain and random color augmentations.
   % \item We propose a color distribution dissimilarity loss function for distribution matching.
   % \item We illustrate the risk of hallucinations in several deep learning models with examples, and propose an approach to mitigate this risk.
% \end{itemize}

