Chapter map

1. 1. Reference atlas as a function
2. 2. Query matrix compatibility
3. 3. Condition as a covariate
4. 4. Conditional variational encoder
5. 5. Decoder likelihood choice
6. 6. Evidence lower bound
7. 7. Architecture surgery
8. 8. Frozen gradient
9. 9. Maximum mean discrepancy
10. 10. Query-to-reference mapping
11. 11. Four-orders parameter saving
12. 12. Iterative reference updates
13. 13. Missing-modality transfer
14. 14. Worked two-batch surgery
15. 15. Disease-state preservation
16. 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.

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1. Reference atlas as a function

The useful question is not only how to calculate, but what the calculation assumes. A trained encoder and decoder define a map from measured counts and condition labels into a latent distribution and back.

A concrete situation

A pancreas reference maps cells into a shared latent space.

What the mathematics does not license

A reference is shaped by its tissues, donors and technologies. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Publish the reference scope and exclusions. 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. Query matrix compatibility

A small example makes the mechanism visible. The query must use compatible genes or measured features, declared ordering and the same preprocessing contract.

A concrete situation

A query gene matrix is intersected with the reference vocabulary.

What the mathematics does not license

Silent column mismatch invalidates the map. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Checksum features and transformations. 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. Condition as a covariate

This is where modelling choices begin to affect evidence. A one-hot or learned condition code identifies batch or study so technical variation can enter designated network weights.

A concrete situation

Reference batch A and query batch Q have separate condition entries.

What the mathematics does not license

A condition code can absorb real biology. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Test known biological contrasts. 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. Conditional variational encoder

The central mathematical idea is concrete. The encoder approximates q(z given x and condition) with a mean and variance for each cell.

A concrete situation

A query cell yields a ten-dimensional Gaussian posterior.

What the mathematics does not license

A compact posterior can hide multimodality. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Inspect uncertainty and neighbours. 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. Decoder likelihood choice

Here the geometry becomes operational. The decoder reconstructs measurements under the base model, such as MSE for trVAE or a count distribution for scVI.

A concrete situation

RNA counts use a ZINB-style likelihood in the demonstrated scVI base.

What the mathematics does not license

The wrong likelihood distorts residuals. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Match assumptions to data. 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. Evidence lower bound

This step deserves a careful pause. A reconstruction expectation and KL regularization form the variational objective optimized by stochastic gradients.

A concrete situation

Good reconstruction competes with a controlled latent posterior.

What the mathematics does not license

A higher ELBO is not automatically better biology. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Report task and posterior checks. 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. Architecture surgery

The useful question is not only how to calculate, but what the calculation assumes. New condition-specific connections are introduced for the query while shared reference weights remain fixed.

A concrete situation

A new study adds adaptor columns to first-layer weights.

What the mathematics does not license

The surgery boundary must be explicit. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

List every trainable tensor. 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. Frozen gradient

A small example makes the mechanism visible. For frozen parameter theta, the update is zero even though the forward pass uses theta; gradients are applied only to query adaptors.

A concrete situation

A 1,000,000-weight reference trains only 500 new values.

What the mathematics does not license

Optimizer state can accidentally update protected weights. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Compare checksums before and after. 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. Maximum mean discrepancy

This is where modelling choices begin to affect evidence. In trVAE variants, MMD compares latent distributions across conditions through kernel averages.

A concrete situation

Reference and query latent samples receive a smaller discrepancy.

What the mathematics does not license

Forcing similarity can erase disease signal. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Stratify by biology. 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. Query-to-reference mapping

The central mathematical idea is concrete. Each query posterior is placed into the coordinate system defined by the frozen reference model.

A concrete situation

New immune cells can be compared with atlas neighbours.

What the mathematics does not license

Nearest reference does not guarantee a known type. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Add rejection and novelty 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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11. Four-orders parameter saving

Here the geometry becomes operational. The study reports query mapping with four orders of magnitude fewer optimized parameters than de novo integration in evaluated cases.

A concrete situation

Ten thousand adaptable values replace a much larger retraining job.

What the mathematics does not license

This is empirical, model- and setting-dependent. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Report actual parameter counts. 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. Iterative reference updates

This step deserves a careful pause. A mapped query can extend a reference model for later users without redistributing original raw cells.

A concrete situation

A new cohort becomes part of an updated atlas checkpoint.

What the mathematics does not license

Sequential order can matter. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Test update permutations. 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. Missing-modality transfer

The useful question is not only how to calculate, but what the calculation assumes. With a multimodal base model, shared latent structure can support estimates for a modality absent in the query.

A concrete situation

RNA in a query supports a protein estimate.

What the mathematics does not license

The estimate is not a measured protein count. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Carry posterior uncertainty. 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. Worked two-batch surgery

A small example makes the mechanism visible. Write a tiny encoder with one shared weight and two condition weights; freeze the shared value and update only the query term from one residual.

A concrete situation

The query loss falls while the reference output stays fixed.

What the mathematics does not license

A toy linear map hides nonlinear uncertainty. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Recalculate with a novel query state. 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. Disease-state preservation

This is where modelling choices begin to affect evidence. Mapping quality needs two axes: technical mixing and retention of query biology absent from a healthy reference.

A concrete situation

A COVID-19 state remains distinct after alignment.

What the mathematics does not license

Separation may reflect an unmodeled confounder. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Use orthogonal markers and cohorts. 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 learning

The central mathematical idea is concrete. Version reference, query, features, conditions, frozen set, adaptors and objective. This joins optimization, probability and privacy-aware collaboration.

A concrete situation

Students can begin with frozen linear regression.

What the mathematics does not license

A mapped coordinate is a model result. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Write a scArches transfer 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 scArches audit begins with a trained reference model, a query dataset and a list of parameters that may change. Architecture surgery adds query-specific condition weights while freezing the shared biological representation. The mathematics is selective optimization: gradients update the new adaptors, while protected weights retain the reference geometry. The method can be built on conditional variational autoencoders such as trVAE, scVI and totalVI.

Record the reference corpus, genes or modalities, preprocessing, base-model checkpoint, latent dimension, batch covariates, frozen parameter set, query adaptors, learning rate, loss terms and early-stopping rule. The peer-reviewed study reports preservation of query-specific biology while removing batch effects with four orders of magnitude fewer optimized parameters than de novo integration in its evaluated settings.

Validate with whole studies and biological conditions held outside reference training; compare surgery with full retraining and simple projection; inspect whether disease or rare-state variation survives alignment; and report out-of-reference detection. Privacy benefits from not redistributing raw reference cells do not remove governance duties for model weights, labels, consent or query data.

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Frequently asked questions

What is scArches?

scArches means single-cell architectural surgery. It maps query data into a pretrained reference by adding and optimizing query-specific parameters while keeping most shared reference parameters frozen.

What does architectural surgery change?

The precise trainable set depends on the base model. The central rule is to add condition-specific weights for the query and update only those selected weights instead of retraining the full reference.

Why freeze weights?

Freezing protects the shared representation learned from the reference and reduces trainable parameters. It also creates a clear transfer contract: the query may adapt through designated pathways without rewriting every learned relationship.

Which probability model can sit underneath scArches?

The paper demonstrates surgery with conditional variational models including trVAE, scVI and totalVI. Their reconstruction terms differ, so the base-model likelihood must be named.

Does mapping remove every batch effect?

No. It optimizes a declared objective and may under-correct or over-correct. Evaluation must test both batch mixing and preservation of real biology, especially disease and rare states.

Does scArches make data sharing risk-free?

No. Sharing a trained model can reduce the need to move raw reference data, while privacy, consent, membership leakage, labels and local query handling still need governance.

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Primary source and fact-check note

Mohammad Lotfollahi, Mohsen Naghipourfar, Malte D. Luecken et al., “Mapping single-cell data to reference atlases by transfer learning,” Nature Biotechnology 40, 121–130 (2022), DOI 10.1038/s41587-021-01001-7. Definitions and core claims in this article were checked against this primary publication. Calculations shown here were independently recomputed. Examples are educational illustrations; they are not reported industrial performance results.

Useful next reading

• scFoundation continuous-value transfer
• CellFM low-rank adaptation
• scGPT foundation-model transfer
• 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

Reference scope audit

Publish donors, tissues, technologies, diseases, labels and exclusions used to train the reference.

Frozen-set checksum

List every protected tensor and prove it is byte-identical before and after query mapping.

Adaptor ledger

Report new condition weights, trainable parameter count, optimizer, learning rate and early stopping.

Novelty challenge

Include query states absent from the atlas and measure rejection rather than forcing a familiar label.

Biology-preservation test

Measure known condition and rare-state separation alongside batch mixing.

Order sensitivity

Add multiple queries in different sequences and compare embeddings and labels.

Privacy review

Assess model sharing, membership leakage, consent and local query handling.

Final claim

Name reference, base model, frozen parameters and query adaptors. Atlas proximity is evidence, not identity proof.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Reference atlas as a function

Start with this article's mechanism: A trained encoder and decoder define a map from measured counts and condition labels into a latent distribution and back. Work through the concrete case: A pancreas reference maps cells into a shared latent space. Make the boundary visible: A reference is shaped by its tissues, donors and technologies. Complete the evidence step: Publish the reference scope and exclusions. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Query matrix compatibility

Start with this article's mechanism: The query must use compatible genes or measured features, declared ordering and the same preprocessing contract. Work through the concrete case: A query gene matrix is intersected with the reference vocabulary. Make the boundary visible: Silent column mismatch invalidates the map. Complete the evidence step: Checksum features and transformations. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Condition as a covariate

Start with this article's mechanism: A one-hot or learned condition code identifies batch or study so technical variation can enter designated network weights. Work through the concrete case: Reference batch A and query batch Q have separate condition entries. Make the boundary visible: A condition code can absorb real biology. Complete the evidence step: Test known biological contrasts. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Conditional variational encoder

Start with this article's mechanism: The encoder approximates q(z given x and condition) with a mean and variance for each cell. Work through the concrete case: A query cell yields a ten-dimensional Gaussian posterior. Make the boundary visible: A compact posterior can hide multimodality. Complete the evidence step: Inspect uncertainty and neighbours. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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 5: Decoder likelihood choice

Start with this article's mechanism: The decoder reconstructs measurements under the base model, such as MSE for trVAE or a count distribution for scVI. Work through the concrete case: RNA counts use a ZINB-style likelihood in the demonstrated scVI base. Make the boundary visible: The wrong likelihood distorts residuals. Complete the evidence step: Match assumptions to data. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Evidence lower bound

Start with this article's mechanism: A reconstruction expectation and KL regularization form the variational objective optimized by stochastic gradients. Work through the concrete case: Good reconstruction competes with a controlled latent posterior. Make the boundary visible: A higher ELBO is not automatically better biology. Complete the evidence step: Report task and posterior checks. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Architecture surgery

Start with this article's mechanism: New condition-specific connections are introduced for the query while shared reference weights remain fixed. Work through the concrete case: A new study adds adaptor columns to first-layer weights. Make the boundary visible: The surgery boundary must be explicit. Complete the evidence step: List every trainable tensor. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Frozen gradient

Start with this article's mechanism: For frozen parameter theta, the update is zero even though the forward pass uses theta; gradients are applied only to query adaptors. Work through the concrete case: A 1,000,000-weight reference trains only 500 new values. Make the boundary visible: Optimizer state can accidentally update protected weights. Complete the evidence step: Compare checksums before and after. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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 9: Maximum mean discrepancy

Start with this article's mechanism: In trVAE variants, MMD compares latent distributions across conditions through kernel averages. Work through the concrete case: Reference and query latent samples receive a smaller discrepancy. Make the boundary visible: Forcing similarity can erase disease signal. Complete the evidence step: Stratify by biology. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Query-to-reference mapping

Start with this article's mechanism: Each query posterior is placed into the coordinate system defined by the frozen reference model. Work through the concrete case: New immune cells can be compared with atlas neighbours. Make the boundary visible: Nearest reference does not guarantee a known type. Complete the evidence step: Add rejection and novelty tests. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Four-orders parameter saving

Start with this article's mechanism: The study reports query mapping with four orders of magnitude fewer optimized parameters than de novo integration in evaluated cases. Work through the concrete case: Ten thousand adaptable values replace a much larger retraining job. Make the boundary visible: This is empirical, model- and setting-dependent. Complete the evidence step: Report actual parameter counts. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Iterative reference updates

Start with this article's mechanism: A mapped query can extend a reference model for later users without redistributing original raw cells. Work through the concrete case: A new cohort becomes part of an updated atlas checkpoint. Make the boundary visible: Sequential order can matter. Complete the evidence step: Test update permutations. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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 13: Missing-modality transfer

Start with this article's mechanism: With a multimodal base model, shared latent structure can support estimates for a modality absent in the query. Work through the concrete case: RNA in a query supports a protein estimate. Make the boundary visible: The estimate is not a measured protein count. Complete the evidence step: Carry posterior uncertainty. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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 two-batch surgery

Start with this article's mechanism: Write a tiny encoder with one shared weight and two condition weights; freeze the shared value and update only the query term from one residual. Work through the concrete case: The query loss falls while the reference output stays fixed. Make the boundary visible: A toy linear map hides nonlinear uncertainty. Complete the evidence step: Recalculate with a novel query state. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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: Disease-state preservation

Start with this article's mechanism: Mapping quality needs two axes: technical mixing and retention of query biology absent from a healthy reference. Work through the concrete case: A COVID-19 state remains distinct after alignment. Make the boundary visible: Separation may reflect an unmodeled confounder. Complete the evidence step: Use orthogonal markers and cohorts. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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 reference, query, features, conditions, frozen set, adaptors and objective. This joins optimization, probability and privacy-aware collaboration. Work through the concrete case: Students can begin with frozen linear regression. Make the boundary visible: A mapped coordinate is a model result. Complete the evidence step: Write a scArches transfer card. Write the input table, graph or count vector, the transformation, output dimensions, probability assumptions, uncertainty and one observation that would contradict the conclusion. Repeat under a nearby defensible setting and compare latent distributions, frozen gradients, mixture probabilities, symmetric divergences, graph edges, discriminator scores or posterior decisions as relevant. Use complete donors, studies, batches 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.