WHY MATHEMATICS?

Why Mathematics? | scMulan for Prompted Cell Analysis: Structured Cell Sentences, Metadata Tokens, Autoregressive Tasks and Zero-Shot Generation

How scMulan serializes genes, values, metadata and task requests into one cell sentence, then uses decoder-only Transformer probability to perform several single-cell tasks through prompts and conditional generation.

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 precise c-sentence from genes, values and metadata
Use causal probability to generate the next tuple
Turn annotation, metadata prediction and generation into prompts
Test zero-shot results, prompt sensitivity and synthetic-cell limits

Chapter map

1. Why serialize a cell
2. Gene–expression tuple
3. Metadata–value tuple
4. Task placeholder tuple
5. Vocabulary and token IDs
6. Position and field structure
7. Causal attention mask
8. Next-token probability
9. Autoregressive cross-entropy
10. Microscopic reconstruction task
11. Macroscopic prediction task
12. Conditional cell generation
13. Prompted batch integration
14. Worked tiny c-sentence
15. Zero-shot evaluation
16. Governance and learning

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

1. Why serialize a cell

This step deserves a careful pause. A decoder predicts sequences, so a matrix row must become a declared sequence of typed fields.

A concrete situation

One cell becomes a list of gene and metadata tuples.

What the mathematics does not license

Serialization imposes an order. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Record the exact grammar. 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. Gene–expression tuple

The useful question is not only how to calculate, but what the calculation assumes. Each gene entity is paired with its encoded expression value so identity and abundance travel together.

A concrete situation

The tuple for gene A includes value 4.

What the mathematics does not license

Discretization loses some numeric detail. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Publish bins or value encoding. 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. Metadata–value tuple

A small example makes the mechanism visible. Organ, donor attributes, batch and labels can be represented with named fields and values.

A concrete situation

An organ tuple says lung.

What the mathematics does not license

Metadata can be missing, wrong or confounded. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Audit completeness and provenance. 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. Task placeholder tuple

This is where modelling choices begin to affect evidence. A special field tells the model which supported continuation it should generate.

A concrete situation

The prompt requests cell-type annotation.

What the mathematics does not license

A token name does not guarantee task competence. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Evaluate every prompt 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.

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. Vocabulary and token IDs

The central mathematical idea is concrete. Entities and values map to integer tokens and learned vectors before entering the decoder.

A concrete situation

A gene symbol and an organ value get distinct IDs.

What the mathematics does not license

Unknown terms need a fallback rule. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Freeze vocabulary and aliases. 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. Position and field structure

Here the geometry becomes operational. Position and tuple roles help the model distinguish entity from value and context from target.

A concrete situation

Gene ID precedes its expression token.

What the mathematics does not license

Changing order can change likelihood. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Run order and shuffle controls. 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. Causal attention mask

This step deserves a careful pause. At position i, attention can use earlier tokens but cannot see the future target token.

A concrete situation

A cell-type value is predicted from preceding genes and metadata.

What the mathematics does not license

Target leakage makes a task trivial. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Unit-test every allowed edge. 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. Next-token probability

The useful question is not only how to calculate, but what the calculation assumes. A softmax over vocabulary estimates P(token_i given the prefix).

A concrete situation

One label token receives probability 0.72.

What the mathematics does not license

Probability is relative to candidate vocabulary. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Inspect top alternatives and entropy. 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. Autoregressive cross-entropy

A small example makes the mechanism visible. Negative log probability of each true next token is summed or averaged across the c-sentence.

A concrete situation

Probability 0.8 gives loss minus log 0.8.

What the mathematics does not license

Long fields can dominate total loss. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Report loss by field type. 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. Microscopic reconstruction task

This is where modelling choices begin to affect evidence. Gene and expression continuations force the model to learn local and global expression structure.

A concrete situation

Given a prefix, the model predicts later gene tuples.

What the mathematics does not license

Generated genes need not be regulatory consequences. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Compare with held-out measured profiles. 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. Macroscopic prediction task

The central mathematical idea is concrete. The model predicts cell-level metadata values from gene context and other declared fields.

A concrete situation

A cell-type token follows the transcriptome prefix.

What the mathematics does not license

Dataset labels can encode curator bias. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Use independent relabelling and rejection. 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. Conditional cell generation

Here the geometry becomes operational. Metadata and a generation prompt condition a sequence of gene-expression tuples.

A concrete situation

Request a profile for a declared cell type.

What the mathematics does not license

A plausible profile may be biologically impossible. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Check distributions and pathway constraints. 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. Prompted batch integration

This step deserves a careful pause. Cell representations or outputs conditioned on task tokens can support alignment across batches.

A concrete situation

Two technologies map into a shared representation.

What the mathematics does not license

Integration may erase real condition effects. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Measure batch removal and biology preservation. 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. Worked tiny c-sentence

The useful question is not only how to calculate, but what the calculation assumes. Serialize three genes, one organ field and one task prompt; calculate a two-step softmax and cross-entropy.

A concrete situation

The correct label follows a high-probability gene programme.

What the mathematics does not license

A tiny vocabulary exaggerates certainty. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Swap metadata and recompute. 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. Zero-shot evaluation

A small example makes the mechanism visible. Hold out labels, studies and batches from any task-specific fitting and measure accuracy, calibration and rejection.

A concrete situation

A new study uses the pretrained prompt directly.

What the mathematics does not license

Corpus overlap can mimic zero-shot transfer. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Audit dataset lineage. 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 learning

This is where modelling choices begin to affect evidence. Version grammar, tuples, prompts, masks, checkpoint and decoding. This links probability, data modelling and language AI.

A concrete situation

Students can start with conditional probability.

What the mathematics does not license

A fluent continuation is still a model output. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Write a scMulan prompt 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 scMulan audit treats a cell as a structured sentence rather than a bare list of genes. Gene–expression tuples, metadata–value tuples and a task prompt are serialized into one c-sentence. A decoder-only Transformer then learns autoregressively across microscopic gene information and macroscopic attributes, turning cell-type annotation, metadata prediction and conditional generation into prompted generation tasks.

Record the gene vocabulary, expression discretization, highly variable gene set, metadata fields, tuple syntax, order or shuffling rule, task token, causal mask, positive targets, checkpoint and decoding settings. The 2024 work reports a 368-million-parameter model pretrained on about 10 million cells with metadata; missing or imbalanced metadata can become a modelling bias.

Validate with prompt paraphrases, metadata ablations, unseen cell types, donor and study holdouts, generation checks and expression-only baselines. A generated profile or zero-shot label is a conditional model output, not a measured cell or experimental perturbation result.

Frequently asked questions

What is scMulan?

scMulan is a prompt-driven, decoder-only model for single-cell analysis. Its 2024 report describes 368 million parameters pretrained on about 10 million transcriptomes and associated metadata.

What is a c-sentence?

A structured cell sentence serializes gene–expression tuples, metadata–value tuples and a task placeholder into one sequence that a language-model objective can process.

What are microscopic and macroscopic information?

Microscopic information refers to gene-level expression patterns. Macroscopic information refers to cell type, organ, donor or other declared metadata describing the whole cell and its context.

How does a task prompt work?

A special task tuple specifies the requested output, such as cell-type annotation, metadata prediction or conditional cell generation. The same model then generates the appropriate continuation.

What does zero-shot mean in scMulan?

It means carrying out a supported prompted task without fitting a new task-specific model on the target dataset. The answer remains conditional on the pretrained vocabulary and metadata.

Is a generated transcriptome a real cell?

No. It is a sampled or decoded profile under the model and prompt. Experimental measurements are required before biological or clinical conclusions.

Primary source and fact-check note

Haiyang Bian, Yixin Chen, Xiaomin Dong et al., “scMulan: A Multitask Generative Pre-Trained Language Model for Single-Cell Analysis,” Research in Computational Molecular Biology, LNCS, pp. 479–482 (2024), DOI 10.1007/978-1-0716-3989-4_57. 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

Grammar audit

Store field order, delimiters, entity/value roles, vocabulary and every task token.

Metadata provenance

Report missingness, label source, donor attributes and fields excluded for ethics or leakage.

Causal-mask test

Confirm no target or future tuple is visible while a token is predicted.

Prompt sensitivity

Use accurate synonymous task prompts and report variation, invalid outputs and rejection.

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.

Generation audit

Compare marginal counts, correlations, rare programmes and impossible combinations with measured cells.

Omitted-task challenge

Hold out labels, batches and conditions before prompt and threshold design.

Baseline comparison

Compare expression-only classifiers, batch methods and conditional generators under matched splits.

Final claim

Name c-sentence, metadata, prompt, mask and decoding. Generated cells are simulations, not observations.

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 serialize a cell

Start with this article's mechanism: A decoder predicts sequences, so a matrix row must become a declared sequence of typed fields. Work through the concrete case: One cell becomes a list of gene and metadata tuples. Make the boundary visible: Serialization imposes an order. Complete the evidence step: Record the exact grammar. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 2: Gene–expression tuple

Start with this article's mechanism: Each gene entity is paired with its encoded expression value so identity and abundance travel together. Work through the concrete case: The tuple for gene A includes value 4. Make the boundary visible: Discretization loses some numeric detail. Complete the evidence step: Publish bins or value encoding. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 3: Metadata–value tuple

Start with this article's mechanism: Organ, donor attributes, batch and labels can be represented with named fields and values. Work through the concrete case: An organ tuple says lung. Make the boundary visible: Metadata can be missing, wrong or confounded. Complete the evidence step: Audit completeness and provenance. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 4: Task placeholder tuple

Start with this article's mechanism: A special field tells the model which supported continuation it should generate. Work through the concrete case: The prompt requests cell-type annotation. Make the boundary visible: A token name does not guarantee task competence. Complete the evidence step: Evaluate every prompt separately. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

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: Vocabulary and token IDs

Start with this article's mechanism: Entities and values map to integer tokens and learned vectors before entering the decoder. Work through the concrete case: A gene symbol and an organ value get distinct IDs. Make the boundary visible: Unknown terms need a fallback rule. Complete the evidence step: Freeze vocabulary and aliases. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 6: Position and field structure

Start with this article's mechanism: Position and tuple roles help the model distinguish entity from value and context from target. Work through the concrete case: Gene ID precedes its expression token. Make the boundary visible: Changing order can change likelihood. Complete the evidence step: Run order and shuffle controls. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 7: Causal attention mask

Start with this article's mechanism: At position i, attention can use earlier tokens but cannot see the future target token. Work through the concrete case: A cell-type value is predicted from preceding genes and metadata. Make the boundary visible: Target leakage makes a task trivial. Complete the evidence step: Unit-test every allowed edge. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 8: Next-token probability

Start with this article's mechanism: A softmax over vocabulary estimates P(token_i given the prefix). Work through the concrete case: One label token receives probability 0.72. Make the boundary visible: Probability is relative to candidate vocabulary. Complete the evidence step: Inspect top alternatives and entropy. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

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: Autoregressive cross-entropy

Start with this article's mechanism: Negative log probability of each true next token is summed or averaged across the c-sentence. Work through the concrete case: Probability 0.8 gives loss minus log 0.8. Make the boundary visible: Long fields can dominate total loss. Complete the evidence step: Report loss by field type. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 10: Microscopic reconstruction task

Start with this article's mechanism: Gene and expression continuations force the model to learn local and global expression structure. Work through the concrete case: Given a prefix, the model predicts later gene tuples. Make the boundary visible: Generated genes need not be regulatory consequences. Complete the evidence step: Compare with held-out measured profiles. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 11: Macroscopic prediction task

Start with this article's mechanism: The model predicts cell-level metadata values from gene context and other declared fields. Work through the concrete case: A cell-type token follows the transcriptome prefix. Make the boundary visible: Dataset labels can encode curator bias. Complete the evidence step: Use independent relabelling and rejection. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 12: Conditional cell generation

Start with this article's mechanism: Metadata and a generation prompt condition a sequence of gene-expression tuples. Work through the concrete case: Request a profile for a declared cell type. Make the boundary visible: A plausible profile may be biologically impossible. Complete the evidence step: Check distributions and pathway constraints. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

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: Prompted batch integration

Start with this article's mechanism: Cell representations or outputs conditioned on task tokens can support alignment across batches. Work through the concrete case: Two technologies map into a shared representation. Make the boundary visible: Integration may erase real condition effects. Complete the evidence step: Measure batch removal and biology preservation. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 14: Worked tiny c-sentence

Start with this article's mechanism: Serialize three genes, one organ field and one task prompt; calculate a two-step softmax and cross-entropy. Work through the concrete case: The correct label follows a high-probability gene programme. Make the boundary visible: A tiny vocabulary exaggerates certainty. Complete the evidence step: Swap metadata and recompute. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 15: Zero-shot evaluation

Start with this article's mechanism: Hold out labels, studies and batches from any task-specific fitting and measure accuracy, calibration and rejection. Work through the concrete case: A new study uses the pretrained prompt directly. Make the boundary visible: Corpus overlap can mimic zero-shot transfer. Complete the evidence step: Audit dataset lineage. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.

Workshop 16: Governance and learning

Start with this article's mechanism: Version grammar, tuples, prompts, masks, checkpoint and decoding. This links probability, data modelling and language AI. Work through the concrete case: Students can start with conditional probability. Make the boundary visible: A fluent continuation is still a model output. Complete the evidence step: Write a scMulan prompt card. Write the input table or token list, transformation, output, dimensions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare masks, ranks, value vectors, retention outputs, logits, losses, embeddings, generated profiles, attention networks or calibration as relevant. Use complete donors, studies, tissues or technologies outside training when testing transfer, because random cells from one biological source are not independent evidence. Keep measurement, model estimate, interpretation and decision on separate notebook lines so a student, parent or reviewer can see what the mathematics establishes.