WHY MATHEMATICS?

Why Mathematics? | MARS for Meta-Learning Cell Types: Neural Embeddings, Landmarks, Heterogeneous Datasets and Novel-Class Discovery

How MARS learns across heterogeneous single-cell experiments without requiring the target to share their types: a neural map projects every experiment into a common space, experiment-specific landmarks organise clusters, and annotated studies teach a transferable distance geometry.

Why mathematics is important becomes easier to see when a real decision depends on it. This guide follows the mechanism from definitions and dimensions to a worked calculation, validation, practical learning and responsible use. It keeps factual evidence separate from interpretation and treats every illustrative scenario as an example rather than a promise of results.

Choose a reading route

Build a meta-dataset of labelled and unlabelled experiments
Pretrain and initialise an experiment-shared embedding
Optimise compact cells and separated landmarks
Discover target clusters, name cautiously and test cluster count

Chapter map

1. Why meta-learning fits heterogeneous experiments
2. Meta-dataset definition
3. Normalised expression vectors
4. Autoencoder pretraining
5. Low-dimensional embedding function
6. Landmark initialisation
7. Labelled compactness loss
8. Target nearest-landmark loss
9. Landmark separation term
10. Joint objective and tau
11. End-to-end alternating updates
12. Nearest-landmark inference
13. Probabilistic post-hoc naming
14. Number of target clusters
15. No automatic batch correction
16. Governance and careers

Visit the How Mathematics Works hub for the wider series and its connections to education, reasoning, science, computing, design and careers.

1. Why meta-learning fits heterogeneous experiments

This is where modelling choices begin to affect evidence. The model learns how to build a useful distance space across tasks rather than copying a fixed list of source labels.

A concrete situation

Pancreas and lung studies help organise an unlabelled brain study.

What the mathematics does not license

Transfer can import irrelevant structure. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Describe every experiment and task. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

2. Meta-dataset definition

The central mathematical idea is concrete. The input combines M labelled experiments with one unlabelled experiment U.

A concrete situation

Three tissues have labels; a fourth has none.

What the mathematics does not license

Different gene panels reduce shared information. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Audit common genes and preprocessing. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

3. Normalised expression vectors

Here the geometry becomes operational. Each cell begins as a high-dimensional vector over genes.

A concrete situation

Twenty thousand values describe one cell.

What the mathematics does not license

Normalisation can preserve technical effects. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Compare distributions across experiments. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

4. Autoencoder pretraining

This step deserves a careful pause. An encoder compresses target expression and a decoder reconstructs it; mean-squared error measures reconstruction.

A concrete situation

Lower reconstruction error preserves common variation.

What the mathematics does not license

Reconstruction can favour abundant technical signals. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Inspect gene- and cell-level residuals. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

Did You Know? In this chapter, the most important number is useful only together with its construction rule. Changing scaling, sample membership or validation design can change the numerical answer without changing the arithmetic.

5. Low-dimensional embedding function

The useful question is not only how to calculate, but what the calculation assumes. A shared neural function f maps cells from every experiment into Z-dimensional coordinates.

A concrete situation

A cell becomes a 100-number embedding.

What the mathematics does not license

Coordinates are learned, not direct measurements. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Test seed and architecture stability. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

6. Landmark initialisation

A small example makes the mechanism visible. After pretraining, K-means runs separately in each experiment’s embedding; multiple starts select the smallest within-cluster sum of squares.

A concrete situation

Ten starts initialise target landmarks.

What the mathematics does not license

K-means assumes a chosen cluster count. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Record starts and costs. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

7. Labelled compactness loss

This is where modelling choices begin to affect evidence. For labelled cells, squared Euclidean distance to the ground-truth type landmark is minimised.

A concrete situation

A labelled B cell moves toward the B landmark.

What the mathematics does not license

Wrong labels teach the wrong geometry. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Audit label conflicts. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

8. Target nearest-landmark loss

The central mathematical idea is concrete. For unlabelled cells, distance to the nearest target landmark is minimised because true labels are unavailable.

A concrete situation

A target cell chooses the closest of K points.

What the mathematics does not license

Early nearest choices can reinforce themselves. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Track assignment switches. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

9. Landmark separation term

Here the geometry becomes operational. Pairwise distances among landmarks within each experiment are maximised, weighted by a regularisation constant.

A concrete situation

Two type landmarks move apart.

What the mathematics does not license

Too much separation can distort nearby biology. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Plot compactness and separation separately. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

10. Joint objective and tau

This step deserves a careful pause. Losses across annotated experiments are added to the target loss multiplied by tau, balancing prior tasks with the target.

A concrete situation

Tau one gives the published balance.

What the mathematics does not license

One setting may not fit every meta-dataset. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Run sensitivity analysis. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

11. End-to-end alternating updates

The useful question is not only how to calculate, but what the calculation assumes. Network parameters and landmarks are optimised together; annotated landmarks have a closed-form update while target landmarks use gradient optimisation.

A concrete situation

Cells and representatives co-adapt.

What the mathematics does not license

Optimisation order and learning rate matter. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Archive loss traces and landmarks. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

12. Nearest-landmark inference

A small example makes the mechanism visible. At inference, each target cell is assigned to the cluster of its closest target landmark.

A concrete situation

A cell is 0.4 units from landmark 2.

What the mathematics does not license

Distance has meaning only in the learned space. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Compare margins and neighbourhoods. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

13. Probabilistic post-hoc naming

This is where modelling choices begin to affect evidence. Distances from a discovered target cluster to annotated landmarks are converted through Gaussian-density weights into name suggestions.

A concrete situation

A target cluster is close to stromal landmarks.

What the mathematics does not license

The naming step needs comparable, batch-corrected embeddings. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Report full name probabilities. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

14. Number of target clusters

The central mathematical idea is concrete. MARS requires a target cluster count K; unused landmarks can remain empty when K is somewhat high.

A concrete situation

Eight proposed landmarks yield six occupied ones.

What the mathematics does not license

A poor K can merge or split biology. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Explore several resolutions. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

15. No automatic batch correction

Here the geometry becomes operational. The paper states that MARS does not explicitly correct batch effects, although it can follow suitable integration methods.

A concrete situation

A platform shift persists in embedding.

What the mathematics does not license

Aggressive correction can erase condition signal. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Measure batch and biology together. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

16. Governance and careers

This step deserves a careful pause. Version meta-dataset, network, reconstruction, K, landmarks, losses and name probabilities. This connects geometry, optimisation and AI.

A concrete situation

Students can begin with K-means and squared distance.

What the mathematics does not license

Novel-class discovery requires biological validation. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Write a landmark-learning model card. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

A seven-day practice lab

Day 1: define the decision, observation unit, X variables and Y or reference condition.
Day 2: reproduce the smallest worked example and check every dimension, unit and sign.
Day 3: build a transparent baseline and write what it assumes.
Day 4: fit the main method inside a training-only pipeline; record every parameter.
Day 5: challenge one assumption with a deliberately difficult dataset or operating regime.
Day 6: compare validation metrics with the practical workload created by errors.
Day 7: present one supported conclusion, one unresolved uncertainty and one safe next experiment.

Questions for a student, parent or mentor

Which part of the model is a mathematical definition, and which part is a choice?
What small calculation would catch a sign, scale or dimension error?
What evidence comes from training, validation and the untouched test?
What benign condition could look like a fault or prediction failure?
How would the answer change for another response, asset, school project or time period?
What should a human review before acting on the score?

A method-specific audit before deployment

A MARS audit constructs a meta-dataset from any number of labelled experiments and one unlabelled target experiment. It pretrains an autoencoder, initialises experiment-specific landmarks and then jointly learns a shared neural embedding in which labelled cells approach their ground-truth landmarks, target cells approach their nearest target landmark and landmarks within each experiment separate.

Record genes, normalisation, experiments, labels, autoencoder reconstruction, embedding architecture, K-means starts, target cluster count, every landmark, squared distances, loss terms, regularisation weights, optimiser path and empty landmarks. The target receives its own landmarks, so cluster discovery is separate from the optional post-hoc naming step based on nearby labelled landmarks.

Validate with whole tissues, ages, species or technologies withheld, target cluster counts above and below plausible values, ablations of pretraining and labelled experiments, and repeated landmark initialisation. Report cluster agreement, stability, naming probabilities and failure under batch effects. A newly separated cluster is a hypothesis for biological study, not automatic proof of a novel cell type.

Frequently asked questions

What is MARS?

MARS is a meta-learning method that learns a shared neural embedding and experiment-specific cell-type landmarks from labelled experiments plus a completely unlabelled target experiment.

Must the target share cell types with the labelled experiments?

No. The method is designed so the unlabelled experiment need not share any cell type with the annotated experiments.

What is a landmark?

A landmark is a learned representative point for one cell-type cluster in the low-dimensional embedding of a particular experiment.

What does pretraining do?

An autoencoder reconstructs normalised target expression. Its encoder weights initialise the embedding network, giving the model a target-aware starting point.

How does MARS train?

It minimises cell-to-correct-landmark distance in labelled experiments, minimises cell-to-nearest-landmark distance in the target and rewards separation among landmarks within each experiment.

Does a new MARS cluster prove a new cell type?

No. A separated cluster is a computational hypothesis. Marker evidence, replication, experimental validation and alternative explanations such as state or batch remain necessary.

Primary source and fact-check note

Maria Brbić, Marinka Zitnik, Sheng Wang et al., “MARS: discovering novel cell types across heterogeneous single-cell experiments,” Nature Methods 17, 1200–1206 (2020), DOI 10.1038/s41592-020-00979-3. Definitions and core claims in this article were checked against this primary publication. Calculations shown here were independently recomputed. Examples are educational illustrations; they are not reported industrial performance results.

Useful next reading

Keep the options open. Mathematics education supports clearer questions, transferable problem-solving skills and informed choices across science, engineering, computing, AI, statistics, design and many other careers. It does not guarantee intelligence, income, admission or employment; those outcomes depend on far more than one subject or model.

Extended laboratory: topic-specific validation and responsible use

Meta-dataset ledger

Record each experiment, labels, gene coverage, preprocessing and relationship to the target. More tasks are helpful only when transfer is relevant.

Reconstruction audit

Compare target autoencoder errors by gene, cell and donor. A good average can hide rare-population loss.

Landmark-stability audit

Repeat autoencoder and K-means seeds. Align landmarks between runs and report occupancy, movement and cluster agreement.

Loss-decomposition audit

Track labelled compactness, target compactness and landmark separation separately. A falling total can hide one failing term.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

K-resolution challenge

Fit several target cluster counts and report occupied landmarks, stability, marker coherence and split/merge paths.

Naming-probability audit

Preserve probabilities over annotated landmarks and do not convert a weak nearest neighbour into a definitive biological name.

Batch challenge

Measure whether experiment origin remains predictable from embeddings, then compare appropriate upstream integration without erasing biology.

Final claim

Name meta-dataset, pretraining, architecture, K, landmarks, losses and name probabilities. Discovery is a testable hypothesis.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Why meta-learning fits heterogeneous experiments

Start with the mechanism: The model learns how to build a useful distance space across tasks rather than copying a fixed list of source labels. The worked case is concrete: Pancreas and lung studies help organise an unlabelled brain study. Expose the boundary: Transfer can import irrelevant structure. Complete this evidence step: Describe every experiment and task. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 2: Meta-dataset definition

Start with the mechanism: The input combines M labelled experiments with one unlabelled experiment U. The worked case is concrete: Three tissues have labels; a fourth has none. Expose the boundary: Different gene panels reduce shared information. Complete this evidence step: Audit common genes and preprocessing. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 3: Normalised expression vectors

Start with the mechanism: Each cell begins as a high-dimensional vector over genes. The worked case is concrete: Twenty thousand values describe one cell. Expose the boundary: Normalisation can preserve technical effects. Complete this evidence step: Compare distributions across experiments. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 4: Autoencoder pretraining

Start with the mechanism: An encoder compresses target expression and a decoder reconstructs it; mean-squared error measures reconstruction. The worked case is concrete: Lower reconstruction error preserves common variation. Expose the boundary: Reconstruction can favour abundant technical signals. Complete this evidence step: Inspect gene- and cell-level residuals. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 5: Low-dimensional embedding function

Start with the mechanism: A shared neural function f maps cells from every experiment into Z-dimensional coordinates. The worked case is concrete: A cell becomes a 100-number embedding. Expose the boundary: Coordinates are learned, not direct measurements. Complete this evidence step: Test seed and architecture stability. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 6: Landmark initialisation

Start with the mechanism: After pretraining, K-means runs separately in each experiment’s embedding; multiple starts select the smallest within-cluster sum of squares. The worked case is concrete: Ten starts initialise target landmarks. Expose the boundary: K-means assumes a chosen cluster count. Complete this evidence step: Record starts and costs. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 7: Labelled compactness loss

Start with the mechanism: For labelled cells, squared Euclidean distance to the ground-truth type landmark is minimised. The worked case is concrete: A labelled B cell moves toward the B landmark. Expose the boundary: Wrong labels teach the wrong geometry. Complete this evidence step: Audit label conflicts. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 8: Target nearest-landmark loss

Start with the mechanism: For unlabelled cells, distance to the nearest target landmark is minimised because true labels are unavailable. The worked case is concrete: A target cell chooses the closest of K points. Expose the boundary: Early nearest choices can reinforce themselves. Complete this evidence step: Track assignment switches. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 9: Landmark separation term

Start with the mechanism: Pairwise distances among landmarks within each experiment are maximised, weighted by a regularisation constant. The worked case is concrete: Two type landmarks move apart. Expose the boundary: Too much separation can distort nearby biology. Complete this evidence step: Plot compactness and separation separately. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 10: Joint objective and tau

Start with the mechanism: Losses across annotated experiments are added to the target loss multiplied by tau, balancing prior tasks with the target. The worked case is concrete: Tau one gives the published balance. Expose the boundary: One setting may not fit every meta-dataset. Complete this evidence step: Run sensitivity analysis. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 11: End-to-end alternating updates

Start with the mechanism: Network parameters and landmarks are optimised together; annotated landmarks have a closed-form update while target landmarks use gradient optimisation. The worked case is concrete: Cells and representatives co-adapt. Expose the boundary: Optimisation order and learning rate matter. Complete this evidence step: Archive loss traces and landmarks. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 12: Nearest-landmark inference

Start with the mechanism: At inference, each target cell is assigned to the cluster of its closest target landmark. The worked case is concrete: A cell is 0.4 units from landmark 2. Expose the boundary: Distance has meaning only in the learned space. Complete this evidence step: Compare margins and neighbourhoods. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 13: Probabilistic post-hoc naming

Start with the mechanism: Distances from a discovered target cluster to annotated landmarks are converted through Gaussian-density weights into name suggestions. The worked case is concrete: A target cluster is close to stromal landmarks. Expose the boundary: The naming step needs comparable, batch-corrected embeddings. Complete this evidence step: Report full name probabilities. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 14: Number of target clusters

Start with the mechanism: MARS requires a target cluster count K; unused landmarks can remain empty when K is somewhat high. The worked case is concrete: Eight proposed landmarks yield six occupied ones. Expose the boundary: A poor K can merge or split biology. Complete this evidence step: Explore several resolutions. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 15: No automatic batch correction

Start with the mechanism: The paper states that MARS does not explicitly correct batch effects, although it can follow suitable integration methods. The worked case is concrete: A platform shift persists in embedding. Expose the boundary: Aggressive correction can erase condition signal. Complete this evidence step: Measure batch and biology together. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 16: Governance and careers

Start with the mechanism: Version meta-dataset, network, reconstruction, K, landmarks, losses and name probabilities. This connects geometry, optimisation and AI. The worked case is concrete: Students can begin with K-means and squared distance. Expose the boundary: Novel-class discovery requires biological validation. Complete this evidence step: Write a landmark-learning model card. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare marker modes, responsibilities, objective terms, centroids, landmarks, soft assignments, losses or unknown outcomes. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.