WHY MATHEMATICS?

Why Mathematics? | OnClass for Ontology-Aware Cell Typing: Graph Diffusion, SVD Embeddings, Bilinear Networks and Unseen Labels

How OnClass turns a biological vocabulary into a learnable geometric map: graph diffusion spreads relationships across the Cell Ontology, SVD compresses them into label vectors, and a bilinear network compares each cell with both seen and unseen ontology terms.

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 cell-type graph from the Cell Ontology
Diffuse and compress graph relationships
Learn cell-to-label compatibility with a bilinear network
Evaluate unseen labels, hierarchy errors and ontology limits

Chapter map

1. Why label relationships matter
2. Mapping training labels to terms
3. Adjacency matrix
4. Random walk with restart
5. Four diffusion views
6. SVD compression
7. Seen and unseen label vectors
8. Cell expression matrix
9. Two ReLU transformations
10. Bilinear compatibility
11. Softmax probabilities
12. Cross-entropy training
13. Hierarchical error distance
14. Worked five-node ontology
15. Marker-gene inference
16. Governance and careers

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

1. Why label relationships matter

This step deserves a careful pause. Flat classifiers treat every wrong label equally, while an ontology records that some types are close siblings and others are distant.

A concrete situation

Confusing two T-cell subtypes is different from predicting an endothelial cell.

What the mathematics does not license

The ontology may lag current biology. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Version every term and 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.

2. Mapping training labels to terms

The useful question is not only how to calculate, but what the calculation assumes. Each dataset label must resolve to an unambiguous Cell Ontology identifier before learning.

A concrete situation

“B cell” maps to a stable CL term.

What the mathematics does not license

Free-text labels can merge or split concepts. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Keep a label-to-ID crosswalk. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

3. Adjacency matrix

A small example makes the mechanism visible. The graph becomes a matrix whose nonzero entries connect related cell-type nodes.

A concrete situation

Two is-a neighbours receive an edge.

What the mathematics does not license

Unweighted edges may hide evidence strength. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Inspect graph degree and components. 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. Random walk with restart

This is where modelling choices begin to affect evidence. A propagated vector combines direct neighbours with longer graph paths while a restart probability preserves locality.

A concrete situation

Restart 0.8 stays more local than 0.5.

What the mathematics does not license

Too much diffusion blurs fine labels. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Plot similarity across restart values. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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. Four diffusion views

The central mathematical idea is concrete. The paper trains models from restart probabilities 0.5, 0.6, 0.7 and 0.8, then averages predictions.

A concrete situation

Four graph scales vote on a label.

What the mathematics does not license

Ensembling does not remove shared ontology errors. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Report agreement among views. 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. SVD compression

Here the geometry becomes operational. Factorising the propagated graph yields orthogonal directions ordered by captured structure.

A concrete situation

Ten dimensions approximate many ontology terms.

What the mathematics does not license

Small dimensions can erase rare branches. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Plot singular values and reconstruction error. 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. Seen and unseen label vectors

This step deserves a careful pause. Every ontology term receives a representation, while only seen terms contribute labelled cells during training.

A concrete situation

An unseen sibling still has a graph coordinate.

What the mathematics does not license

Coordinates are prior knowledge, not expression evidence. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Mark which terms were never observed. 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. Cell expression matrix

The useful question is not only how to calculate, but what the calculation assumes. Rows are cells, columns are genes and each row supplies the measured input to the network.

A concrete situation

One cell has expression over shared genes.

What the mathematics does not license

Batch and species effects can dominate. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Audit preprocessing and gene overlap. 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. Two ReLU transformations

A small example makes the mechanism visible. Matrices W1 and W2 map expression through nonlinear hidden coordinates into the label-embedding dimension.

A concrete situation

Negative pre-activations become zero.

What the mathematics does not license

Small training sets can overfit flexible weights. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Use grouped validation and regularisation. 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. Bilinear compatibility

This is where modelling choices begin to affect evidence. The transformed cell vector is dotted with each fixed cell-type vector, producing one logit per ontology term.

A concrete situation

A cell aligns strongly with a nearby label vector.

What the mathematics does not license

A large dot product can reflect vector norm. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Inspect normalisation and contributions. 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. Softmax probabilities

The central mathematical idea is concrete. Exponentiated logits are divided by their sum so all label probabilities total one.

A concrete situation

Scores 2 and 1 become unequal probabilities.

What the mathematics does not license

A closed softmax can be confident out of domain. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Calibrate and consider 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. Cross-entropy training

Here the geometry becomes operational. For seen labels, the negative log probability of the correct term trains W1 and W2 while ontology vectors remain fixed.

A concrete situation

A correct probability of 0.9 gives small loss.

What the mathematics does not license

No direct loss supervises unseen labels. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Separate seen and unseen metrics. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

13. Hierarchical error distance

This step deserves a careful pause. Predictions can be evaluated by exact match and graph distance to the true term.

A concrete situation

A sibling error lies two edges away.

What the mathematics does not license

Edge count is not universal biological distance. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Publish several hierarchy-aware metrics. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

14. Worked five-node ontology

The useful question is not only how to calculate, but what the calculation assumes. Build a parent with two child branches, diffuse proximities, retain two SVD dimensions and score one withheld child.

A concrete situation

The withheld child inherits information from its branch.

What the mathematics does not license

Toy graphs are cleaner than curated ontologies. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Perturb one edge 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. Marker-gene inference

A small example makes the mechanism visible. Model parameters can rank genes associated with ontology terms, including terms without direct training cells.

A concrete situation

A predicted marker set follows a label embedding.

What the mathematics does not license

Association is not experimental specificity. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Validate markers in independent 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.

16. Governance and careers

This is where modelling choices begin to affect evidence. Version ontology, mappings, diffusion, SVD, weights, probabilities and validation. This links graph theory, linear algebra and AI.

A concrete situation

Students can begin with random walks and dot products.

What the mathematics does not license

An unseen label remains a hypothesis. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Write an ontology-aware model card. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

A seven-day practice lab

Day 1: define the decision, observation unit, X variables and Y or reference condition.
Day 2: reproduce the smallest worked example and check every dimension, unit and sign.
Day 3: build a transparent baseline and write what it assumes.
Day 4: fit the main method inside a training-only pipeline; record every parameter.
Day 5: challenge one assumption with a deliberately difficult dataset or operating regime.
Day 6: compare validation metrics with the practical workload created by errors.
Day 7: present one supported conclusion, one unresolved uncertainty and one safe next experiment.

Questions for a student, parent or mentor

Which part of the model is a mathematical definition, and which part is a choice?
What small calculation would catch a sign, scale or dimension error?
What evidence comes from training, validation and the untouched test?
What benign condition could look like a fault or prediction failure?
How would the answer change for another response, asset, school project or time period?
What should a human review before acting on the score?

A method-specific audit before deployment

An OnClass audit begins by mapping every training label to a current Cell Ontology term and constructing the ontology graph. Random walks with restart diffuse relationships through that graph, singular value decomposition compresses the resulting proximity matrices, and a bilinear neural model connects gene-expression embeddings with fixed cell-type embeddings.

Record ontology version, term identifiers, graph edges, restart probabilities, diffusion matrices, singular values, embedding dimensions, training genes, network weights, logits and probability vectors. Seen and unseen labels share the same ontology space, but an unseen prediction is still extrapolation through graph structure rather than direct evidence from labelled examples.

Validate with whole datasets and ontology terms withheld, compare sibling and distant labels, perturb graph edges, test species and technology shifts and report hierarchical error as well as exact-label accuracy. Ontology-aware mathematics can keep options open while making its assumptions inspectable.

Frequently asked questions

What is OnClass?

OnClass is an ontology-aware single-cell annotation method that learns from gene expression and a graph of Cell Ontology terms, allowing it to score both cell types present in training and ontology terms without labelled training cells.

What is the Cell Ontology graph?

Its nodes are controlled cell-type terms and its edges encode curated relationships such as is-a connections. OnClass uses this graph to represent relationships among labels.

What does random walk with restart do?

It repeatedly moves probability mass through neighbouring ontology terms while returning some mass to the starting term, producing a diffusion-based proximity profile.

Why use singular value decomposition?

SVD approximates the large propagated graph with a smaller set of orthogonal latent dimensions, giving every cell type a compact numeric embedding.

How does the bilinear model score a cell type?

A neural transformation maps expression into the same coordinate dimension as a fixed cell-type representation, and their dot product becomes a compatibility logit before softmax normalisation.

Can OnClass truly identify unseen types?

It can assign probability to ontology terms without labelled training examples by using their graph positions. Such predictions are extrapolations and require strong withheld-type validation and biological confirmation.

Primary source and fact-check note

Marinka Zitnik, Robert Sosič, Marcus W. Feldman and Jure Leskovec, “Leveraging the Cell Ontology to classify unseen cell types,” Nature Communications 12, 5556 (2021), DOI 10.1038/s41467-021-25725-x. 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

Ontology-version audit

Store release date, term IDs, obsolete mappings and every graph edge used. Predictions must be reproducible against the same vocabulary.

Diffusion-sensitivity test

Compare restart probabilities, path lengths and neighbour similarities. Report when fine distinctions disappear under propagation.

SVD-rank audit

Plot singular values, reconstruction error and unseen-label accuracy across embedding dimensions.

Seen–unseen firewall

Select withheld terms before model training and keep all their cells out of fitting and tuning.

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.

Hierarchy-error report

Publish exact accuracy, ancestor/descendant mistakes, sibling errors and graph distances rather than one flat score.

Graph-perturbation challenge

Remove or redirect selected ontology edges and measure prediction and marker-ranking stability.

Domain holdout

Keep complete datasets, species, tissues and technologies outside gene selection and network training.

Final claim

Name ontology, diffusion, SVD rank, network and withheld terms. Unseen classification remains structured extrapolation.

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 label relationships matter

Start with the mechanism: Flat classifiers treat every wrong label equally, while an ontology records that some types are close siblings and others are distant. The worked case is concrete: Confusing two T-cell subtypes is different from predicting an endothelial cell. Expose the boundary: The ontology may lag current biology. Complete this evidence step: Version every term and edge. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 2: Mapping training labels to terms

Start with the mechanism: Each dataset label must resolve to an unambiguous Cell Ontology identifier before learning. The worked case is concrete: “B cell” maps to a stable CL term. Expose the boundary: Free-text labels can merge or split concepts. Complete this evidence step: Keep a label-to-ID crosswalk. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 3: Adjacency matrix

Start with the mechanism: The graph becomes a matrix whose nonzero entries connect related cell-type nodes. The worked case is concrete: Two is-a neighbours receive an edge. Expose the boundary: Unweighted edges may hide evidence strength. Complete this evidence step: Inspect graph degree and components. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 4: Random walk with restart

Start with the mechanism: A propagated vector combines direct neighbours with longer graph paths while a restart probability preserves locality. The worked case is concrete: Restart 0.8 stays more local than 0.5. Expose the boundary: Too much diffusion blurs fine labels. Complete this evidence step: Plot similarity across restart values. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

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: Four diffusion views

Start with the mechanism: The paper trains models from restart probabilities 0.5, 0.6, 0.7 and 0.8, then averages predictions. The worked case is concrete: Four graph scales vote on a label. Expose the boundary: Ensembling does not remove shared ontology errors. Complete this evidence step: Report agreement among views. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 6: SVD compression

Start with the mechanism: Factorising the propagated graph yields orthogonal directions ordered by captured structure. The worked case is concrete: Ten dimensions approximate many ontology terms. Expose the boundary: Small dimensions can erase rare branches. Complete this evidence step: Plot singular values and reconstruction error. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 7: Seen and unseen label vectors

Start with the mechanism: Every ontology term receives a representation, while only seen terms contribute labelled cells during training. The worked case is concrete: An unseen sibling still has a graph coordinate. Expose the boundary: Coordinates are prior knowledge, not expression evidence. Complete this evidence step: Mark which terms were never observed. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 8: Cell expression matrix

Start with the mechanism: Rows are cells, columns are genes and each row supplies the measured input to the network. The worked case is concrete: One cell has expression over shared genes. Expose the boundary: Batch and species effects can dominate. Complete this evidence step: Audit preprocessing and gene overlap. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Did You Know? A sophisticated adjustment can be algebraically correct and still answer the wrong scientific question when samples, labels, batches or validation boundaries are wrong.

Workshop 9: Two ReLU transformations

Start with the mechanism: Matrices W1 and W2 map expression through nonlinear hidden coordinates into the label-embedding dimension. The worked case is concrete: Negative pre-activations become zero. Expose the boundary: Small training sets can overfit flexible weights. Complete this evidence step: Use grouped validation and regularisation. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 10: Bilinear compatibility

Start with the mechanism: The transformed cell vector is dotted with each fixed cell-type vector, producing one logit per ontology term. The worked case is concrete: A cell aligns strongly with a nearby label vector. Expose the boundary: A large dot product can reflect vector norm. Complete this evidence step: Inspect normalisation and contributions. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 11: Softmax probabilities

Start with the mechanism: Exponentiated logits are divided by their sum so all label probabilities total one. The worked case is concrete: Scores 2 and 1 become unequal probabilities. Expose the boundary: A closed softmax can be confident out of domain. Complete this evidence step: Calibrate and consider rejection. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 12: Cross-entropy training

Start with the mechanism: For seen labels, the negative log probability of the correct term trains W1 and W2 while ontology vectors remain fixed. The worked case is concrete: A correct probability of 0.9 gives small loss. Expose the boundary: No direct loss supervises unseen labels. Complete this evidence step: Separate seen and unseen metrics. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

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: Hierarchical error distance

Start with the mechanism: Predictions can be evaluated by exact match and graph distance to the true term. The worked case is concrete: A sibling error lies two edges away. Expose the boundary: Edge count is not universal biological distance. Complete this evidence step: Publish several hierarchy-aware metrics. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 14: Worked five-node ontology

Start with the mechanism: Build a parent with two child branches, diffuse proximities, retain two SVD dimensions and score one withheld child. The worked case is concrete: The withheld child inherits information from its branch. Expose the boundary: Toy graphs are cleaner than curated ontologies. Complete this evidence step: Perturb one edge and recompute. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 15: Marker-gene inference

Start with the mechanism: Model parameters can rank genes associated with ontology terms, including terms without direct training cells. The worked case is concrete: A predicted marker set follows a label embedding. Expose the boundary: Association is not experimental specificity. Complete this evidence step: Validate markers in independent data. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.

Workshop 16: Governance and careers

Start with the mechanism: Version ontology, mappings, diffusion, SVD, weights, probabilities and validation. This links graph theory, linear algebra and AI. The worked case is concrete: Students can begin with random walks and dot products. Expose the boundary: An unseen label remains a hypothesis. Complete this evidence step: Write an ontology-aware model card. Write inputs, the mathematical operation, expected output, uncertainty and one observation that would contradict the claim. Repeat under a nearby defensible setting and compare graph proximities, singular values, anchor weights, token masks, attention matrices, probabilities, embeddings, losses or calibration. Use untouched donors, studies or simulated truth because random cells can share hidden structure with training data. Keep measurement, model estimate, interpretation and decision on separate notebook lines so the conclusion remains auditable.