WHY MATHEMATICS?

Why Mathematics? | ItClust for Transfer-Learned Clustering: Source Pretraining, Target Fine-Tuning, Cluster Centres and Target-Only Cell Types

How ItClust transfers a labelled source network into an unlabelled target study, then lets target evidence reshape the embedding and cluster centres: soft Student-t assignments are sharpened into an auxiliary objective, and unused source centres can move toward target-only populations.

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

Choose target-variable genes and learn a source embedding
Initialise labelled source cluster centres
Refine soft assignments with KL divergence
Fine-tune on target data and audit free-centre behaviour

Chapter map

1. Why transfer then fine-tune
2. Two-dataset contract
3. Target highly variable genes
4. Stacked denoising autoencoder
5. Encoder as nonlinear map
6. Labelled source centroids
7. Student-t similarity kernel
8. Soft assignments q
9. Auxiliary target distribution p
10. KL-divergence clustering loss
11. Source-network optimisation
12. Target-network initialisation
13. Iterative target fine-tuning
14. Free centroids and target-only types
15. Empty-centroid deletion and cluster count
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 transfer then fine-tune

This step deserves a careful pause. Source labels give a useful initial geometry, while target expression corrects for batch shift and target-only structure.

A concrete situation

A mouse source helps organise a human target.

What the mathematics does not license

Poor source labels can create a bad start. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Compare source-only and fine-tuned models. 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. Two-dataset contract

The useful question is not only how to calculate, but what the calculation assumes. The source has expression and trusted type labels; the target has expression but needs clustering and annotation.

A concrete situation

Source and target are different protocols.

What the mathematics does not license

The studies may not be biologically comparable. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Document species, tissue and protocol. 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. Target highly variable genes

A small example makes the mechanism visible. ItClust selects top variable genes in the target, then keeps those present in the source.

A concrete situation

Two thousand target genes overlap 1,700 source genes.

What the mathematics does not license

Target-only variation may be technical. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Repeat selection by donor. 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. Stacked denoising autoencoder

This is where modelling choices begin to affect evidence. Layers learn to reconstruct previous representations after random corruption, then combine into a multilayer autoencoder.

A concrete situation

Noise is added and the clean vector is reconstructed.

What the mathematics does not license

Reconstruction quality is not label quality. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Plot corruption sensitivity. 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. Encoder as nonlinear map

The central mathematical idea is concrete. After autoencoder training, decoder layers are removed and the encoder maps expression x to latent z.

A concrete situation

Ten thousand genes become low-dimensional features.

What the mathematics does not license

Latent axes can encode batch. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Probe donor prediction from z. 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. Labelled source centroids

Here the geometry becomes operational. For each known source type, the initial centroid is the mean embedding of its labelled cells.

A concrete situation

All source B cells define one mean point.

What the mathematics does not license

A multimodal type is poorly represented by one mean. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Inspect within-type structure. 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. Student-t similarity kernel

This step deserves a careful pause. For cell i and centroid j, one plus squared distance divided by alpha is inverted and normalised across centroids; alpha is one in the implementation described.

A concrete situation

Closer centres receive larger q.

What the mathematics does not license

q is model-based similarity, not calibrated truth. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Hand-calculate a two-centre example. 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. Soft assignments q

The useful question is not only how to calculate, but what the calculation assumes. Every cell receives a probability-like vector whose entries sum to one.

A concrete situation

q equals 0.70, 0.20 and 0.10.

What the mathematics does not license

A closed set always distributes all mass. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Track entropy and maximum q. 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. Auxiliary target distribution p

A small example makes the mechanism visible. The algorithm derives p from q to strengthen high-confidence assignments and rebalance cluster influence during refinement.

A concrete situation

A dominant q entry becomes more influential.

What the mathematics does not license

Sharpening can reinforce early mistakes. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Compare q and p each iteration. 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. KL-divergence clustering loss

This is where modelling choices begin to affect evidence. The loss sums p times log(p divided by q), penalising disagreement between target assignments and current network predictions.

A concrete situation

When p equals q the term is zero.

What the mathematics does not license

A self-training objective can converge confidently to a wrong partition. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Use external and stability tests. 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. Source-network optimisation

The central mathematical idea is concrete. The labelled source centres and embedding are refined so the source structure yields cell-type-specific expression representation.

A concrete situation

Same-label cells move toward their centroid.

What the mathematics does not license

Optimised source accuracy may not transfer. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Hold out entire source studies. 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. Target-network initialisation

Here the geometry becomes operational. The target network begins from learned source parameters and the corresponding centroids.

A concrete situation

Target training starts near a useful solution.

What the mathematics does not license

Strong batch shift can make the initial geometry misleading. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Measure before and after fine-tuning. 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. Iterative target fine-tuning

This step deserves a careful pause. Target q, p, embeddings and centroids are repeatedly updated until assignments stabilise or the stopping rule is met.

A concrete situation

Centres shift toward target populations.

What the mathematics does not license

Iteration count and learning rate affect the result. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Archive assignment-change curves. 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. Free centroids and target-only types

The useful question is not only how to calculate, but what the calculation assumes. Centres for source-only types may receive no target cells; these free centres can migrate and help capture cell types found only in the target.

A concrete situation

A source-only centre moves toward a target-only stromal group.

What the mathematics does not license

Too few spare centres limit this behaviour. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Count free and repurposed centres. 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. Empty-centroid deletion and cluster count

A small example makes the mechanism visible. The initial target centroid count equals the number of source types; a centroid with no assigned target cells can be removed.

A concrete situation

Five source types yield four occupied target clusters.

What the mathematics does not license

The resulting count depends on source coverage and dynamics. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Compare with independent cluster-resolution evidence. 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 is where modelling choices begin to affect evidence. Version genes, corruption, encoder, centroids, q, p, KL loss, fine-tuning and free centres. This connects transfer learning and clustering.

A concrete situation

Students can begin with distances and KL divergence.

What the mathematics does not license

A transferred cluster proves no diagnosis or mechanism. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Write an iterative-transfer 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

An ItClust audit starts with a labelled source dataset and an unlabelled target dataset. Target-variable genes define the shared input, a stacked denoising autoencoder learns a source embedding, labelled source means initialise cluster centroids and a Student-t kernel converts cell-to-centroid distances into soft assignments.

Record overlapping genes, corruption and reconstruction settings, network weights, source centroids, every soft assignment q, auxiliary target distribution p, KL-divergence loss, target-network initialisation, centroid movement, empty-centroid deletion and stopping rule. Free centroids can move toward target-only populations, but that opportunity depends on source composition and the initial number of centroids.

Validate source quality, source–target batch shift, missing source classes, target-only classes, cluster-number mismatch, several seeds and target fine-tuning ablations. Report clustering as well as label-transfer accuracy, cluster confidence and empty-centroid behaviour. Transfer learning can provide a strong start while still requiring target evidence and biological review.

Frequently asked questions

What is ItClust?

ItClust is an iterative transfer-learning method for clustering and cell-type classification. It learns from a labelled source dataset, transfers the network to an unlabelled target dataset and fine-tunes using target structure.

Which genes are used?

The published method first selects highly variable genes in the target and then uses the genes that overlap the source, making the input explicitly target-aware.

What is transferred?

Encoder parameters and source-derived cluster-centre information initialise the target network; target training then adjusts them.

How are soft cluster assignments calculated?

A Student-t kernel converts squared distance between an embedded cell and each centroid into normalised q probabilities.

What is the KL objective?

An auxiliary distribution p is derived from current q values to emphasise confident assignments, and the network minimises KL divergence from p to q while refining embeddings and centroids.

How can ItClust represent a target-only type?

A centroid belonging to a source-only type may receive few target cells and become free to move during target fine-tuning, allowing it to capture a target-only cluster; this is an opportunity rather than a guarantee.

Primary source and fact-check note

Jian Hu, Xiangjie Li, Gang Hu et al., “Iterative transfer learning with neural network for clustering and cell type classification in single-cell RNA-seq analysis,” Nature Machine Intelligence 2, 607–618 (2020), DOI 10.1038/s42256-020-00233-7. 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

Source-quality audit

Review source labels, class sizes and within-type heterogeneity. Repeat after removing questionable source cells.

Gene-overlap audit

Store target-variable genes, shared input genes and selection frequency across target donor resamples.

Autoencoder audit

Record corruption, reconstruction loss, layer sizes and latent batch predictability before clustering.

q–p trajectory audit

Save soft q, sharpened p, KL loss and assignment entropy through source and target optimisation.

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.

Free-centre ledger

Track target occupancy and movement for every source centroid. Identify empty, stable, shifted and repurposed centres.

Target-only challenge

Add or withhold a known target-only type and measure whether a free centroid recovers it rather than merging it.

Fine-tuning ablation

Compare source-only transfer with successive target fine-tuning stages under untouched biological labels.

Final claim

Name genes, network, source centres, q, p, KL loss, fine-tuning and free-centre behaviour. Transfer is conditional on both datasets.

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 transfer then fine-tune

Start with the mechanism: Source labels give a useful initial geometry, while target expression corrects for batch shift and target-only structure. The worked case is concrete: A mouse source helps organise a human target. Expose the boundary: Poor source labels can create a bad start. Complete this evidence step: Compare source-only and fine-tuned models. 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: Two-dataset contract

Start with the mechanism: The source has expression and trusted type labels; the target has expression but needs clustering and annotation. The worked case is concrete: Source and target are different protocols. Expose the boundary: The studies may not be biologically comparable. Complete this evidence step: Document species, tissue and protocol. 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: Target highly variable genes

Start with the mechanism: ItClust selects top variable genes in the target, then keeps those present in the source. The worked case is concrete: Two thousand target genes overlap 1,700 source genes. Expose the boundary: Target-only variation may be technical. Complete this evidence step: Repeat selection by donor. 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: Stacked denoising autoencoder

Start with the mechanism: Layers learn to reconstruct previous representations after random corruption, then combine into a multilayer autoencoder. The worked case is concrete: Noise is added and the clean vector is reconstructed. Expose the boundary: Reconstruction quality is not label quality. Complete this evidence step: Plot corruption sensitivity. 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: Encoder as nonlinear map

Start with the mechanism: After autoencoder training, decoder layers are removed and the encoder maps expression x to latent z. The worked case is concrete: Ten thousand genes become low-dimensional features. Expose the boundary: Latent axes can encode batch. Complete this evidence step: Probe donor prediction from z. 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: Labelled source centroids

Start with the mechanism: For each known source type, the initial centroid is the mean embedding of its labelled cells. The worked case is concrete: All source B cells define one mean point. Expose the boundary: A multimodal type is poorly represented by one mean. Complete this evidence step: Inspect within-type structure. 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: Student-t similarity kernel

Start with the mechanism: For cell i and centroid j, one plus squared distance divided by alpha is inverted and normalised across centroids; alpha is one in the implementation described. The worked case is concrete: Closer centres receive larger q. Expose the boundary: q is model-based similarity, not calibrated truth. Complete this evidence step: Hand-calculate a two-centre example. 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: Soft assignments q

Start with the mechanism: Every cell receives a probability-like vector whose entries sum to one. The worked case is concrete: q equals 0.70, 0.20 and 0.10. Expose the boundary: A closed set always distributes all mass. Complete this evidence step: Track entropy and maximum q. 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: Auxiliary target distribution p

Start with the mechanism: The algorithm derives p from q to strengthen high-confidence assignments and rebalance cluster influence during refinement. The worked case is concrete: A dominant q entry becomes more influential. Expose the boundary: Sharpening can reinforce early mistakes. Complete this evidence step: Compare q and p each iteration. 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: KL-divergence clustering loss

Start with the mechanism: The loss sums p times log(p divided by q), penalising disagreement between target assignments and current network predictions. The worked case is concrete: When p equals q the term is zero. Expose the boundary: A self-training objective can converge confidently to a wrong partition. Complete this evidence step: Use external and stability tests. 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: Source-network optimisation

Start with the mechanism: The labelled source centres and embedding are refined so the source structure yields cell-type-specific expression representation. The worked case is concrete: Same-label cells move toward their centroid. Expose the boundary: Optimised source accuracy may not transfer. Complete this evidence step: Hold out entire source studies. 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: Target-network initialisation

Start with the mechanism: The target network begins from learned source parameters and the corresponding centroids. The worked case is concrete: Target training starts near a useful solution. Expose the boundary: Strong batch shift can make the initial geometry misleading. Complete this evidence step: Measure before and after fine-tuning. 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: Iterative target fine-tuning

Start with the mechanism: Target q, p, embeddings and centroids are repeatedly updated until assignments stabilise or the stopping rule is met. The worked case is concrete: Centres shift toward target populations. Expose the boundary: Iteration count and learning rate affect the result. Complete this evidence step: Archive assignment-change curves. 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: Free centroids and target-only types

Start with the mechanism: Centres for source-only types may receive no target cells; these free centres can migrate and help capture cell types found only in the target. The worked case is concrete: A source-only centre moves toward a target-only stromal group. Expose the boundary: Too few spare centres limit this behaviour. Complete this evidence step: Count free and repurposed centres. 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: Empty-centroid deletion and cluster count

Start with the mechanism: The initial target centroid count equals the number of source types; a centroid with no assigned target cells can be removed. The worked case is concrete: Five source types yield four occupied target clusters. Expose the boundary: The resulting count depends on source coverage and dynamics. Complete this evidence step: Compare with independent cluster-resolution evidence. 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 genes, corruption, encoder, centroids, q, p, KL loss, fine-tuning and free centres. This connects transfer learning and clustering. The worked case is concrete: Students can begin with distances and KL divergence. Expose the boundary: A transferred cluster proves no diagnosis or mechanism. Complete this evidence step: Write an iterative-transfer 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.