Proto4DME: Interpretable Cell Counting via Additive Prototype Density Decomposition and Optimal-Transport Coverage

Abdurahman Ali Mohammed, Wallapak Tavanapong
Proceedings of the 7th Conference on Health, Inference, and Learning, PMLR 333:688-702, 2026.

Abstract

Cell counting via density map estimation predicts a per-pixel density. Summing the density yields the final count, a common readout in clinical diagnostics and disease monitoring. Yet these models are often hard to audit when errors occur. We present Proto4DME, an interpretable density map estimator with faithful explanations by construction. The predicted density (and thus the count) is an additive, non-negative combination of contributions from learned visual patterns (prototypes). Prior prototype-based counting uses signed aggregation, which permits cancellation. In contrast, Proto4DME provides non-canceling attributions, in which increasing a prototype’s activation can only increase the predicted density. So prototype heatmaps correspond to positive contributions for the count. Proto4DME learns spatial prototype activation maps from backbone features and selects a compact set of prototypes using sparsity-inducing Hard-Concrete gates. To encourage diverse foreground coverage and prevent prototype collapse, we introduce an entropically-regularized optimal-transport coverage objective. It allocates ground-truth density mass across prototypes under capacity constraints and induces competition among prototypes. Across three microscopy benchmarks (MBM, ADI, and DCC), Proto4DME achieves competitive mean absolute error (MAE) while producing compact, auditable explanations that support error analysis and model debugging.

Cite this Paper

BibTeX
@InProceedings{pmlr-v333-mohammed26a, title = {Proto4DME: Interpretable Cell Counting via Additive Prototype Density Decomposition and Optimal-Transport Coverage}, author = {Mohammed, Abdurahman Ali and Tavanapong, Wallapak}, booktitle = {Proceedings of the 7th Conference on Health, Inference, and Learning}, pages = {688--702}, year = {2026}, editor = {Healey, Elizabeth and Fries, Jason and Pollard, Tom and Tang, Shengpu and Zink, Anna and Hartvigsen, Tom and Agrawal, Monica and Finlayson, Sam and Glicksberg, Benjamin and Beaulieu-Jones, Brett and Wang, Kai and Fontalvo, Daseyra and Sarker, Tasmie and Chen, Irene and Alsentzer, Emily}, volume = {333}, series = {Proceedings of Machine Learning Research}, month = {29--30 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v333/main/assets/mohammed26a/mohammed26a.pdf}, url = {https://proceedings.mlr.press/v333/mohammed26a.html}, abstract = {Cell counting via density map estimation predicts a per-pixel density. Summing the density yields the final count, a common readout in clinical diagnostics and disease monitoring. Yet these models are often hard to audit when errors occur. We present Proto4DME, an interpretable density map estimator with faithful explanations by construction. The predicted density (and thus the count) is an additive, non-negative combination of contributions from learned visual patterns (prototypes). Prior prototype-based counting uses signed aggregation, which permits cancellation. In contrast, Proto4DME provides non-canceling attributions, in which increasing a prototype’s activation can only increase the predicted density. So prototype heatmaps correspond to positive contributions for the count. Proto4DME learns spatial prototype activation maps from backbone features and selects a compact set of prototypes using sparsity-inducing Hard-Concrete gates. To encourage diverse foreground coverage and prevent prototype collapse, we introduce an entropically-regularized optimal-transport coverage objective. It allocates ground-truth density mass across prototypes under capacity constraints and induces competition among prototypes. Across three microscopy benchmarks (MBM, ADI, and DCC), Proto4DME achieves competitive mean absolute error (MAE) while producing compact, auditable explanations that support error analysis and model debugging.} }
Endnote
%0 Conference Paper %T Proto4DME: Interpretable Cell Counting via Additive Prototype Density Decomposition and Optimal-Transport Coverage %A Abdurahman Ali Mohammed %A Wallapak Tavanapong %B Proceedings of the 7th Conference on Health, Inference, and Learning %C Proceedings of Machine Learning Research %D 2026 %E Elizabeth Healey %E Jason Fries %E Tom Pollard %E Shengpu Tang %E Anna Zink %E Tom Hartvigsen %E Monica Agrawal %E Sam Finlayson %E Benjamin Glicksberg %E Brett Beaulieu-Jones %E Kai Wang %E Daseyra Fontalvo %E Tasmie Sarker %E Irene Chen %E Emily Alsentzer %F pmlr-v333-mohammed26a %I PMLR %P 688--702 %U https://proceedings.mlr.press/v333/mohammed26a.html %V 333 %X Cell counting via density map estimation predicts a per-pixel density. Summing the density yields the final count, a common readout in clinical diagnostics and disease monitoring. Yet these models are often hard to audit when errors occur. We present Proto4DME, an interpretable density map estimator with faithful explanations by construction. The predicted density (and thus the count) is an additive, non-negative combination of contributions from learned visual patterns (prototypes). Prior prototype-based counting uses signed aggregation, which permits cancellation. In contrast, Proto4DME provides non-canceling attributions, in which increasing a prototype’s activation can only increase the predicted density. So prototype heatmaps correspond to positive contributions for the count. Proto4DME learns spatial prototype activation maps from backbone features and selects a compact set of prototypes using sparsity-inducing Hard-Concrete gates. To encourage diverse foreground coverage and prevent prototype collapse, we introduce an entropically-regularized optimal-transport coverage objective. It allocates ground-truth density mass across prototypes under capacity constraints and induces competition among prototypes. Across three microscopy benchmarks (MBM, ADI, and DCC), Proto4DME achieves competitive mean absolute error (MAE) while producing compact, auditable explanations that support error analysis and model debugging.
APA
Mohammed, A.A. & Tavanapong, W.. (2026). Proto4DME: Interpretable Cell Counting via Additive Prototype Density Decomposition and Optimal-Transport Coverage. Proceedings of the 7th Conference on Health, Inference, and Learning, in Proceedings of Machine Learning Research 333:688-702 Available from https://proceedings.mlr.press/v333/mohammed26a.html.

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