Chapter map

1. 1. Cell-by-gene matrix
2. 2. Gene-expression embedder
3. 3. Tissue as a token set
4. 4. Flowformer efficiency
5. 5. Two-dimensional sinusoidal position
6. 6. Non-spatial shared position
7. 7. Mask indicator matrix
8. 8. Cell and gene masking
9. 9. Gaussian-mixture component
10. 10. Continuous latent z
11. 11. Reconstruction term
12. 12. Conditional KL term
13. 13. Mixture-assignment KL
14. 14. Batch-aware decoder
15. 15. Worked three-cell ELBO
16. 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.

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1. Cell-by-gene matrix

This step deserves a careful pause. Rows are cells, columns are measured genes and entries form the data X whose missing subset will be predicted.

A concrete situation

A tissue has 500 cells by 2,000 genes.

What the mathematics does not license

Different platforms measure different gene sets. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Store a measured-gene mask. 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.

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2. Gene-expression embedder

The useful question is not only how to calculate, but what the calculation assumes. A multilayer map converts each cell’s full expression vector into one d-dimensional token.

A concrete situation

Two thousand values become a 1,024-dimensional cell vector.

What the mathematics does not license

Compression can discard rare programmes. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Measure reconstruction by cell 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.

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3. Tissue as a token set

A small example makes the mechanism visible. N cell embeddings are stacked into H with shape N by d and processed jointly.

A concrete situation

Neighbouring immune and stromal cells share one tissue context.

What the mathematics does not license

Sample composition becomes part of the prediction. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Hold out complete tissues. 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.

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4. Flowformer efficiency

This is where modelling choices begin to affect evidence. Linear-complexity attention approximates information flow among up to thousands of cell tokens.

A concrete situation

Ten thousand cells avoid a full 100-million-pair matrix.

What the mathematics does not license

Approximation changes the exact attention computation. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Compare accuracy and runtime on small tissues. 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.

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5. Two-dimensional sinusoidal position

The central mathematical idea is concrete. Sine and cosine functions of x and y coordinates create repeatable position features across several frequencies.

A concrete situation

Cells close in space have related positional vectors.

What the mathematics does not license

Coordinate scale and rotation affect encoding. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Normalize and test transformed coordinates. 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.

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6. Non-spatial shared position

Here the geometry becomes operational. Ordinary scRNA-seq cells receive a shared learned position vector instead of invented coordinates.

A concrete situation

All dissociated cells start with the same position term.

What the mathematics does not license

Sample membership still carries context. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

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

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7. Mask indicator matrix

This step deserves a careful pause. M equals one for observed entries and zero for deliberately masked entries, so X-tilde equals M elementwise multiplied by X.

A concrete situation

Mask 25 percent of measured genes in selected cells.

What the mathematics does not license

Zero can mean masked, unmeasured or observed zero. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Keep separate indicators for each meaning. 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.

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8. Cell and gene masking

The useful question is not only how to calculate, but what the calculation assumes. The reported pretraining settings select many cell tokens and hide a fraction of measured genes within them.

A concrete situation

Context cells help recover masked values.

What the mathematics does not license

Mask design can favour common cell states. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Report rates and stratified loss. 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.

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9. Gaussian-mixture component

A small example makes the mechanism visible. A categorical latent y chooses one of L Gaussian components with its own mean and diagonal variance.

A concrete situation

A progenitor cell has posterior mixture weights across components.

What the mathematics does not license

Mixture components are not guaranteed cell types. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Test stability and avoid automatic names. 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.

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10. Continuous latent z

This is where modelling choices begin to affect evidence. The encoder predicts a mean and variance for each cell, and reparameterization samples z while preserving gradient estimation.

A concrete situation

z equals mu plus sigma times standard-normal noise.

What the mathematics does not license

Posterior variance can collapse or inflate. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Plot KL and variance distributions. 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.

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11. Reconstruction term

The central mathematical idea is concrete. The decoder predicts expression from z, and mean-squared error estimates the Gaussian reconstruction contribution on measured genes.

A concrete situation

Prediction 1.8 versus truth 2 gives squared error 0.04.

What the mathematics does not license

MSE can overemphasize high-expression genes. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Report error by abundance. 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.

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12. Conditional KL term

Here the geometry becomes operational. KL divergence pulls q(z given masked X) toward the selected mixture-component prior p(z given y).

A concrete situation

A cell latent stays near a plausible component.

What the mathematics does not license

Strong regularization can oversmooth transitions. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Sweep the KL weight. 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.

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13. Mixture-assignment KL

This step deserves a careful pause. A second KL term regularizes posterior component probabilities toward the categorical prior.

A concrete situation

Posterior 0.7,0.2,0.1 is compared with pi.

What the mathematics does not license

An imbalanced prior can absorb sampling bias. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Audit component use by tissue. 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.

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14. Batch-aware decoder

The useful question is not only how to calculate, but what the calculation assumes. A learned sample or field-of-view embedding joins z only in the decoder, encouraging the latent space to omit reconstructable batch effects.

A concrete situation

Decoder uses z plus batch vector b.

What the mathematics does not license

Batch labels may coincide with biology. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Use confounded and balanced 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.

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15. Worked three-cell ELBO

A small example makes the mechanism visible. Mask two entries in a three-cell matrix, compute reconstruction errors, mixture probabilities and simple KL terms, then compare with shuffled tissue context.

A concrete situation

Joint context reduces one error.

What the mathematics does not license

Toy Gaussians hide optimization difficulty. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Repeat across held-out tissues. 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.

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16. Governance and careers

This is where modelling choices begin to affect evidence. Version tissue groups, coordinates, masks, mixtures, batch vectors, ELBO terms and downstream tuning. This connects probability, geometry and efficient AI.

A concrete situation

Students can begin with Gaussians and MSE.

What the mathematics does not license

Cell context is evidence of dependence, not communication. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Write a CellPLM 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.

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A seven-day practice lab

1. Day 1: define the decision, observation unit, X variables and Y or reference condition.
2. Day 2: reproduce the smallest worked example and check every dimension, unit and sign.
3. Day 3: build a transparent baseline and write what it assumes.
4. Day 4: fit the main method inside a training-only pipeline; record every parameter.
5. Day 5: challenge one assumption with a deliberately difficult dataset or operating regime.
6. Day 6: compare validation metrics with the practical workload created by errors.
7. 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 CellPLM audit treats cells as tokens and a tissue sample as the surrounding context. A gene-expression embedder creates one vector per cell, a Flowformer-style encoder mixes information among many cells, spatial coordinates can provide two-dimensional sinusoidal encodings, and a Gaussian-mixture latent prior represents several functional cell groups.

Record the tissue grouping, expression embedder, spatial coordinates, positional encoding, mask matrix, cell and gene mask rates, latent mixture components, posterior means and variances, batch embeddings, decoder and all terms in the denoising evidence lower bound. Cell-to-cell context can improve representations while also spreading batch, sampling and neighbourhood bias.

Validate with tissue-level holdouts, shuffled-cell and shuffled-coordinate controls, mixture-component sensitivity, masked-expression recovery, spatially separated tests and downstream baselines. A learned intercellular relation is statistical dependence inside the model; it does not by itself establish communication or molecular causation.

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Frequently asked questions

What is CellPLM?

CellPLM is a pretrained encoder–decoder for single-cell and spatial transcriptomic data. It treats cells as tokens within a tissue sample so masked gene expression can depend on information from other cells as well as the same cell.

Why treat cells as tokens?

Cells within one tissue share lineage, microenvironment and technical context. Modelling them jointly can supply useful denoising and state information that a one-cell-at-a-time model cannot access.

How are many cells processed efficiently?

The paper uses a Flowformer-style Transformer with linear complexity because a tissue can contain thousands of cell tokens, making ordinary quadratic self-attention costly.

How does spatial information enter?

For spatial transcriptomic data, two-dimensional coordinates generate sinusoidal positional vectors that are added to expression embeddings. Non-spatial data use a shared learned position vector for compatibility.

Why a Gaussian-mixture prior?

Several Gaussian components can represent distinct functional cell groups more flexibly than one isotropic Gaussian. A latent categorical variable selects the component for each cell.

What is the denoising ELBO?

It is a variational objective combining reconstruction of masked expression with KL-divergence terms that regularize the continuous latent posterior and mixture assignments toward their priors.

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Primary source and fact-check note

Hongzhi Wen, Wenzhuo Tang, Xinnan Dai et al., “CellPLM: Pre-training of Cell Language Model Beyond Single Cells,” International Conference on Learning Representations (ICLR 2024). 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

• scFoundation sparse asymmetric modelling
• scGPT gene-token pretraining
• totalVI latent-variable modelling
• How Mathematics Works

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

Tissue-boundary audit

Define which cells share a token set and keep entire tissues out of training and tuning during external evaluation.

Context-shuffle test

Shuffle cells across tissues while holding marginals fixed to measure how much performance comes from true intercellular context.

Coordinate-control test

Translate, rotate, scale and shuffle spatial coordinates; report which conclusions depend on positional encoding.

Mask-semantics audit

Distinguish deliberately masked, technically unmeasured and observed-zero entries in data and loss calculations.

Mixture-stability test

Vary component count, initialization and KL weights; do not label components as cell types without evidence.

Batch-decoder audit

Check whether batch embeddings remove technical variation while retaining condition and rare-state information.

ELBO ledger

Report reconstruction, conditional-prior and categorical-prior terms separately across datasets and cell types.

Final claim

Name tissue groups, coordinates, masks, mixture and ELBO. Learned context is association, not proof of cell communication.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Cell-by-gene matrix

Start with the mechanism: Rows are cells, columns are measured genes and entries form the data X whose missing subset will be predicted. The worked case is concrete: A tissue has 500 cells by 2,000 genes. Expose the boundary: Different platforms measure different gene sets. Complete this evidence step: Store a measured-gene mask. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 2: Gene-expression embedder

Start with the mechanism: A multilayer map converts each cell’s full expression vector into one d-dimensional token. The worked case is concrete: Two thousand values become a 1,024-dimensional cell vector. Expose the boundary: Compression can discard rare programmes. Complete this evidence step: Measure reconstruction by cell type. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 3: Tissue as a token set

Start with the mechanism: N cell embeddings are stacked into H with shape N by d and processed jointly. The worked case is concrete: Neighbouring immune and stromal cells share one tissue context. Expose the boundary: Sample composition becomes part of the prediction. Complete this evidence step: Hold out complete tissues. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 4: Flowformer efficiency

Start with the mechanism: Linear-complexity attention approximates information flow among up to thousands of cell tokens. The worked case is concrete: Ten thousand cells avoid a full 100-million-pair matrix. Expose the boundary: Approximation changes the exact attention computation. Complete this evidence step: Compare accuracy and runtime on small tissues. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 5: Two-dimensional sinusoidal position

Start with the mechanism: Sine and cosine functions of x and y coordinates create repeatable position features across several frequencies. The worked case is concrete: Cells close in space have related positional vectors. Expose the boundary: Coordinate scale and rotation affect encoding. Complete this evidence step: Normalize and test transformed coordinates. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 6: Non-spatial shared position

Start with the mechanism: Ordinary scRNA-seq cells receive a shared learned position vector instead of invented coordinates. The worked case is concrete: All dissociated cells start with the same position term. Expose the boundary: Sample membership still carries context. Complete this evidence step: Do not infer physical neighbourhoods. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 7: Mask indicator matrix

Start with the mechanism: M equals one for observed entries and zero for deliberately masked entries, so X-tilde equals M elementwise multiplied by X. The worked case is concrete: Mask 25 percent of measured genes in selected cells. Expose the boundary: Zero can mean masked, unmeasured or observed zero. Complete this evidence step: Keep separate indicators for each meaning. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 8: Cell and gene masking

Start with the mechanism: The reported pretraining settings select many cell tokens and hide a fraction of measured genes within them. The worked case is concrete: Context cells help recover masked values. Expose the boundary: Mask design can favour common cell states. Complete this evidence step: Report rates and stratified loss. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 9: Gaussian-mixture component

Start with the mechanism: A categorical latent y chooses one of L Gaussian components with its own mean and diagonal variance. The worked case is concrete: A progenitor cell has posterior mixture weights across components. Expose the boundary: Mixture components are not guaranteed cell types. Complete this evidence step: Test stability and avoid automatic names. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 10: Continuous latent z

Start with the mechanism: The encoder predicts a mean and variance for each cell, and reparameterization samples z while preserving gradient estimation. The worked case is concrete: z equals mu plus sigma times standard-normal noise. Expose the boundary: Posterior variance can collapse or inflate. Complete this evidence step: Plot KL and variance distributions. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 11: Reconstruction term

Start with the mechanism: The decoder predicts expression from z, and mean-squared error estimates the Gaussian reconstruction contribution on measured genes. The worked case is concrete: Prediction 1.8 versus truth 2 gives squared error 0.04. Expose the boundary: MSE can overemphasize high-expression genes. Complete this evidence step: Report error by abundance. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 12: Conditional KL term

Start with the mechanism: KL divergence pulls q(z given masked X) toward the selected mixture-component prior p(z given y). The worked case is concrete: A cell latent stays near a plausible component. Expose the boundary: Strong regularization can oversmooth transitions. Complete this evidence step: Sweep the KL weight. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 13: Mixture-assignment KL

Start with the mechanism: A second KL term regularizes posterior component probabilities toward the categorical prior. The worked case is concrete: Posterior 0.7,0.2,0.1 is compared with pi. Expose the boundary: An imbalanced prior can absorb sampling bias. Complete this evidence step: Audit component use by tissue. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 14: Batch-aware decoder

Start with the mechanism: A learned sample or field-of-view embedding joins z only in the decoder, encouraging the latent space to omit reconstructable batch effects. The worked case is concrete: Decoder uses z plus batch vector b. Expose the boundary: Batch labels may coincide with biology. Complete this evidence step: Use confounded and balanced tests. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 15: Worked three-cell ELBO

Start with the mechanism: Mask two entries in a three-cell matrix, compute reconstruction errors, mixture probabilities and simple KL terms, then compare with shuffled tissue context. The worked case is concrete: Joint context reduces one error. Expose the boundary: Toy Gaussians hide optimization difficulty. Complete this evidence step: Repeat across held-out tissues. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.

Workshop 16: Governance and careers

Start with the mechanism: Version tissue groups, coordinates, masks, mixtures, batch vectors, ELBO terms and downstream tuning. This connects probability, geometry and efficient AI. The worked case is concrete: Students can begin with Gaussians and MSE. Expose the boundary: Cell context is evidence of dependence, not communication. Complete this evidence step: Write a CellPLM model card. Write the input matrix or token list, every transformation, the output, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare ranks, masks, value projections, attention approximations, mixture probabilities, KL terms, reconstruction errors, embeddings, probabilities or calibration. Use untouched donors, studies, tissues or controlled downsampling because random cells can share hidden technical and biological structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so students and reviewers can see what the mathematics establishes.