WHY MATHEMATICS?

Why Mathematics? | scGPT for Single-Cell Foundation Models: Gene Tokens, Expression Bins, Masked Generation and Transfer Learning

How scGPT adapts generative Transformer mathematics to unordered single-cell measurements: gene identities and expression values become paired embeddings, a specialised attention mask supports prediction of withheld expression, and large-scale pretraining supplies a starting representation for annotation, integration and perturbation tasks.

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

Tokenise genes, expression values and conditions
Pretrain by masked generative prediction
Learn gene and cell representations through attention
Fine-tune cautiously and test transfer against baselines

Chapter map

1. Why foundation pretraining is attractive
2. Cell as an unordered gene set
3. Gene vocabulary
4. Expression normalisation
5. Within-cell value bins
6. Combined input embeddings
7. Special cell token
8. Masked positions
9. Generative attention mask
10. Multi-head self-attention
11. Gene-expression prediction loss
12. Cell-conditioned prediction
13. Large-scale pretraining
14. Fine-tuning for annotation
15. Beyond annotation
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 foundation pretraining is attractive

The central mathematical idea is concrete. Large unlabelled cell collections contain recurring gene relationships that may help smaller downstream studies.

A concrete situation

A rare labelled study starts from a pretrained checkpoint.

What the mathematics does not license

Corpus scale can amplify bias and batch structure. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Document corpus and checkpoint. 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. Cell as an unordered gene set

Here the geometry becomes operational. Unlike a sentence, a cell’s genes have no natural word order, so architecture and attention masking must avoid pretending order is biological syntax.

A concrete situation

Gene A need not precede gene B.

What the mathematics does not license

Implementation order can still affect computation. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Test permutation handling. 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. Gene vocabulary

This step deserves a careful pause. Each recognised gene maps to an integer token ID and trainable vector.

A concrete situation

TP53 receives one embedding index.

What the mathematics does not license

Aliases and missing genes create out-of-vocabulary problems. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Freeze a gene-ID crosswalk. 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. Expression normalisation

The useful question is not only how to calculate, but what the calculation assumes. Counts are filtered and normalised under a declared preprocessing contract before token values are formed.

A concrete situation

Library-size normalisation precedes binning.

What the mathematics does not license

A new pipeline can mismatch the checkpoint. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Checksum every transformation. 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. Within-cell value bins

A small example makes the mechanism visible. Nonzero expression values are divided by cell-specific quantile edges into ordered bins, while zeros retain their own value.

A concrete situation

The top quantile gets a high bin index.

What the mathematics does not license

Bins discard exact magnitude and depend on cell composition. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Compare bins with continuous values. 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. Combined input embeddings

This is where modelling choices begin to affect evidence. Gene, value and optional condition embeddings are combined so identity, abundance and context enter the model.

A concrete situation

The same gene changes when its value bin changes.

What the mathematics does not license

Condition tokens can encode confounding. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Ablate metadata embeddings. 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. Special cell token

The central mathematical idea is concrete. A CLS-like token participates in attention and learns a vector intended to summarise the whole cell.

A concrete situation

The cell token becomes a 512-dimensional embedding.

What the mathematics does not license

One vector may blur mixed biological programmes. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Inspect task-specific separability. 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. Masked positions

Here the geometry becomes operational. A subset of expression values is replaced with a mask value and becomes the prediction target.

A concrete situation

Twenty percent of selected genes are hidden.

What the mathematics does not license

Mask rate changes task difficulty. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Plot validation loss across rates. 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. Generative attention mask

This step deserves a careful pause. The specialised mask controls which observed and generated positions can exchange information, supporting iterative prediction on non-sequential data.

A concrete situation

Known genes inform the next withheld group.

What the mathematics does not license

Leakage would make pretraining trivial. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Unit-test allowed attention paths. 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. Multi-head self-attention

The useful question is not only how to calculate, but what the calculation assumes. Each head computes scaled query–key similarities and value mixtures, allowing several gene-context patterns to be learned.

A concrete situation

One head tracks a coexpression module.

What the mathematics does not license

Attention weights are not causal networks. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Validate edges with held-out perturbations. 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. Gene-expression prediction loss

A small example makes the mechanism visible. Predicted masked values are compared with true expression using mean-squared error in the reported objective.

A concrete situation

Prediction 2.5 versus truth 3 gives squared error 0.25.

What the mathematics does not license

MSE emphasises large numeric errors. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Report performance by expression range. 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. Cell-conditioned prediction

This is where modelling choices begin to affect evidence. A second objective uses the cell representation with gene identity to predict masked expression, tying whole-cell context to gene values.

A concrete situation

The same gene receives different predictions in two cell contexts.

What the mathematics does not license

A compressed cell token can retain shortcuts. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Probe batch information in embeddings. 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. Large-scale pretraining

The central mathematical idea is concrete. The 2024 paper reports a repository of more than 33 million cells used to learn general representations before downstream adaptation.

A concrete situation

Many tissues contribute repeated gene contexts.

What the mathematics does not license

Training scale is not proof of universal coverage. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

List tissues, species and conditions. 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. Fine-tuning for annotation

Here the geometry becomes operational. A classification head and labelled target data update some or all parameters for cell-type prediction.

A concrete situation

Softmax maps a cell token to label scores.

What the mathematics does not license

Small data can overfit millions of parameters. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Compare frozen, partial and full 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.

15. Beyond annotation

This step deserves a careful pause. The paper evaluates batch integration, multi-omic integration, perturbation response and gene-network inference with task-specific objectives.

A concrete situation

A condition token represents modality or batch.

What the mathematics does not license

One checkpoint can excel at one task and fail another. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Use task-specific baselines and metrics. 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

The useful question is not only how to calculate, but what the calculation assumes. Version vocabulary, bins, masks, checkpoint, losses, tuning and evaluation. This joins statistics, Transformers and computational biology.

A concrete situation

Students can begin with embeddings and masked prediction.

What the mathematics does not license

A foundation model is a reusable prior, not an oracle. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Write a foundation-model factsheet. 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 scGPT audit starts with a precise tokenisation contract for gene identity, expression values and optional condition metadata. The 2024 paper reports generative pretraining across more than 33 million cells: a masked-attention transformer predicts withheld expression from observed genes while learning gene representations and a cell token that can be adapted to downstream tasks.

Record vocabulary, gene mapping, normalisation, within-cell expression bins, masked positions, attention mask, transformer checkpoint, cell embeddings, pretraining objectives, fine-tuning split, frozen and updated parameters, loss curves and task outputs. A large pretrained model carries statistical regularities from its corpus; it does not guarantee biological truth, causal mechanism or equal performance outside that corpus.

Validate against simple and task-specific baselines, freeze-versus-fine-tune choices, donor and study holdouts, unseen tissues, batch confounding, calibration and input perturbations. Foundation models are valuable mathematical starting points when every transfer claim remains tied to evidence.

Frequently asked questions

What is scGPT?

scGPT is a generative pretrained Transformer for single-cell data. The Nature Methods paper reports pretraining across more than 33 million cells and adaptation to annotation, batch integration, multi-omic integration, perturbation prediction and gene-network inference.

What is a gene token?

A gene identifier is mapped through a learned embedding table. Its expression value is represented separately and combined with the gene embedding for Transformer input.

Why bin expression values?

Quantile-based within-cell bins convert nonzero expression magnitudes into discrete value indices, reducing scale complexity while preserving relative expression information.

What is masked generative pretraining?

Some gene-expression values are withheld and the model predicts them from observed genes under a specialised attention mask, creating a self-supervised learning signal without cell-type labels.

What is the cell token?

A special token learns a whole-cell representation through attention to gene tokens. It can feed downstream classification or other task heads.

Does a foundation model always beat a smaller model?

No. Performance depends on corpus coverage, preprocessing, checkpoint, fine-tuning, task and evaluation. Strong simple baselines and external biological validation remain necessary.

Primary source and fact-check note

Haotian Cui, Chloe Wang, Hassaan Maan et al., “scGPT: toward building a foundation model for single-cell multi-omics using generative AI,” Nature Methods 21, 1470–1480 (2024), DOI 10.1038/s41592-024-02201-0. 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

Vocabulary checksum

Record gene IDs, aliases, unknown genes, value-bin edges and optional condition tokens for every dataset.

Mask-leakage audit

Verify that predicted positions cannot access their true values through attention or auxiliary inputs.

Checkpoint ledger

Store checkpoint identity, corpus description, parameter count, code version and licence with every downstream result.

Fine-tuning ablation

Compare frozen embeddings, linear probing, partial tuning, full tuning and a task-specific model under identical folds.

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.

Simple-baseline challenge

Benchmark against PCA plus logistic regression, nearest neighbours or established domain methods before claiming foundation-model value.

Calibration and shift audit

Report reliability, entropy and error by tissue, donor, disease, technology and distance from pretraining coverage.

Representation perturbation

Mask, permute and alter gene values to test whether predictions depend on coherent biology rather than shortcuts.

Final claim

Name vocabulary, bins, mask, checkpoint, tuning and external tests. Scale supports reuse; it does not guarantee validity.

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 foundation pretraining is attractive

Start with the mechanism: Large unlabelled cell collections contain recurring gene relationships that may help smaller downstream studies. The worked case is concrete: A rare labelled study starts from a pretrained checkpoint. Expose the boundary: Corpus scale can amplify bias and batch structure. Complete this evidence step: Document corpus and checkpoint. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Cell as an unordered gene set

Start with the mechanism: Unlike a sentence, a cell’s genes have no natural word order, so architecture and attention masking must avoid pretending order is biological syntax. The worked case is concrete: Gene A need not precede gene B. Expose the boundary: Implementation order can still affect computation. Complete this evidence step: Test permutation handling. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Gene vocabulary

Start with the mechanism: Each recognised gene maps to an integer token ID and trainable vector. The worked case is concrete: TP53 receives one embedding index. Expose the boundary: Aliases and missing genes create out-of-vocabulary problems. Complete this evidence step: Freeze a gene-ID crosswalk. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Expression normalisation

Start with the mechanism: Counts are filtered and normalised under a declared preprocessing contract before token values are formed. The worked case is concrete: Library-size normalisation precedes binning. Expose the boundary: A new pipeline can mismatch the checkpoint. Complete this evidence step: Checksum every transformation. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Within-cell value bins

Start with the mechanism: Nonzero expression values are divided by cell-specific quantile edges into ordered bins, while zeros retain their own value. The worked case is concrete: The top quantile gets a high bin index. Expose the boundary: Bins discard exact magnitude and depend on cell composition. Complete this evidence step: Compare bins with continuous values. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Combined input embeddings

Start with the mechanism: Gene, value and optional condition embeddings are combined so identity, abundance and context enter the model. The worked case is concrete: The same gene changes when its value bin changes. Expose the boundary: Condition tokens can encode confounding. Complete this evidence step: Ablate metadata embeddings. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Special cell token

Start with the mechanism: A CLS-like token participates in attention and learns a vector intended to summarise the whole cell. The worked case is concrete: The cell token becomes a 512-dimensional embedding. Expose the boundary: One vector may blur mixed biological programmes. Complete this evidence step: Inspect task-specific separability. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Masked positions

Start with the mechanism: A subset of expression values is replaced with a mask value and becomes the prediction target. The worked case is concrete: Twenty percent of selected genes are hidden. Expose the boundary: Mask rate changes task difficulty. Complete this evidence step: Plot validation loss across rates. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Generative attention mask

Start with the mechanism: The specialised mask controls which observed and generated positions can exchange information, supporting iterative prediction on non-sequential data. The worked case is concrete: Known genes inform the next withheld group. Expose the boundary: Leakage would make pretraining trivial. Complete this evidence step: Unit-test allowed attention paths. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Multi-head self-attention

Start with the mechanism: Each head computes scaled query–key similarities and value mixtures, allowing several gene-context patterns to be learned. The worked case is concrete: One head tracks a coexpression module. Expose the boundary: Attention weights are not causal networks. Complete this evidence step: Validate edges with held-out perturbations. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Gene-expression prediction loss

Start with the mechanism: Predicted masked values are compared with true expression using mean-squared error in the reported objective. The worked case is concrete: Prediction 2.5 versus truth 3 gives squared error 0.25. Expose the boundary: MSE emphasises large numeric errors. Complete this evidence step: Report performance by expression range. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Cell-conditioned prediction

Start with the mechanism: A second objective uses the cell representation with gene identity to predict masked expression, tying whole-cell context to gene values. The worked case is concrete: The same gene receives different predictions in two cell contexts. Expose the boundary: A compressed cell token can retain shortcuts. Complete this evidence step: Probe batch information in embeddings. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Large-scale pretraining

Start with the mechanism: The 2024 paper reports a repository of more than 33 million cells used to learn general representations before downstream adaptation. The worked case is concrete: Many tissues contribute repeated gene contexts. Expose the boundary: Training scale is not proof of universal coverage. Complete this evidence step: List tissues, species and conditions. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Fine-tuning for annotation

Start with the mechanism: A classification head and labelled target data update some or all parameters for cell-type prediction. The worked case is concrete: Softmax maps a cell token to label scores. Expose the boundary: Small data can overfit millions of parameters. Complete this evidence step: Compare frozen, partial and full 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 graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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: Beyond annotation

Start with the mechanism: The paper evaluates batch integration, multi-omic integration, perturbation response and gene-network inference with task-specific objectives. The worked case is concrete: A condition token represents modality or batch. Expose the boundary: One checkpoint can excel at one task and fail another. Complete this evidence step: Use task-specific baselines and metrics. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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 vocabulary, bins, masks, checkpoint, losses, tuning and evaluation. This joins statistics, Transformers and computational biology. The worked case is concrete: Students can begin with embeddings and masked prediction. Expose the boundary: A foundation model is a reusable prior, not an oracle. Complete this evidence step: Write a foundation-model factsheet. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. 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.