Chapter map

1. 1. Spatial expression matrix
2. 2. Cell-type distribution
3. 3. Ligand-receptor view
4. 4. Sender ligand intensity
5. 5. Receiver receptor intensity
6. 6. Distance-decay kernel
7. 7. Communication adjacency
8. 8. Multi-view collection
9. 9. Graph convolution
10. 10. Gated attention
11. 11. View fusion
12. 12. Target-gene prediction
13. 13. Reconstruction loss
14. 14. Regularization
15. 15. Contribution interpretation
16. 16. Transfer and governance

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1. Spatial expression matrix

This step deserves a careful pause. Genes are measured across cells or spots with coordinates.

A concrete situation

A matrix has 5,000 genes and 2,000 locations.

What the mathematics does not license

Normalization shapes every later score. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Freeze and document preprocessing. 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. Cell-type distribution

The useful question is not only how to calculate, but what the calculation assumes. Each location carries observed labels or estimated type proportions.

A concrete situation

A spot is 60% epithelial and 40% stromal.

What the mathematics does not license

Deconvolution uncertainty propagates. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Retain proportion intervals. 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. Ligand-receptor view

A small example makes the mechanism visible. One candidate mechanism defines one graph layer.

A concrete situation

L1-R1 forms view v.

What the mathematics does not license

Catalogue choice limits discovery. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Version every pair and complex. 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. Sender ligand intensity

This is where modelling choices begin to affect evidence. Sender expression supplies outgoing signal magnitude.

A concrete situation

Cell i has L1 expression four.

What the mathematics does not license

RNA is not secreted protein. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Label the quantity as expression evidence. 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. Receiver receptor intensity

The central mathematical idea is concrete. Receiver expression controls eligible incoming signal.

A concrete situation

Cell j has R1 expression three.

What the mathematics does not license

Detection noise creates zeros. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Audit detection and thresholds. 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. Distance-decay kernel

Here the geometry becomes operational. A function maps separation to a nonnegative weight.

A concrete situation

exp(-d/s) gives 0.37 when d=s.

What the mathematics does not license

Scale s changes effective range. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Sweep plausible scales. 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. Communication adjacency

This step deserves a careful pause. Edge i to j combines direction, expression and distance.

A concrete situation

Four times three times 0.5 gives six.

What the mathematics does not license

Products depend on normalization. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Publish every factor separately. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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8. Multi-view collection

The useful question is not only how to calculate, but what the calculation assumes. All event graphs share nodes but differ in edges.

A concrete situation

Twenty L-R events produce twenty views.

What the mathematics does not license

Views can be redundant. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Measure view correlation. 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. Graph convolution

A small example makes the mechanism visible. Neighbour messages are transformed and aggregated.

A concrete situation

Receiver j sums weighted sender vectors.

What the mathematics does not license

High-degree nodes may dominate. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Compare normalized aggregation. 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. Gated attention

This is where modelling choices begin to affect evidence. Learned gates weight view representations.

A concrete situation

Weights 0.6, 0.3 and 0.1 sum to one.

What the mathematics does not license

Weights are conditional on other views. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Inspect stability across seeds. 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. View fusion

The central mathematical idea is concrete. Weighted view messages form one receiver representation.

A concrete situation

Three graph vectors combine into h-j.

What the mathematics does not license

Fusion can hide opposing signals. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Keep signed or view-level outputs. 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. Target-gene prediction

Here the geometry becomes operational. The fused vector predicts expression of specified genes.

A concrete situation

Predicted target T is 7.8.

What the mathematics does not license

Targets may be co-expressed for other reasons. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Use held-out targets and locations. 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. Reconstruction loss

This step deserves a careful pause. Observed and predicted targets are compared.

A concrete situation

Squared error is (8-7.8)^2.

What the mathematics does not license

A low training loss can overfit. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Report validation 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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14. Regularization

The useful question is not only how to calculate, but what the calculation assumes. Penalties constrain weights and complexity.

A concrete situation

L2 shrinks a gate coefficient.

What the mathematics does not license

Too much shrinkage removes real structure. Evidence becomes stronger when the limitation is tested instead of hidden.

Try it, check it, transfer it

Plot a tuning path. 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. Contribution interpretation

A small example makes the mechanism visible. Ablations and weights identify influential views.

A concrete situation

Removing L1-R1 raises error by 12%.

What the mathematics does not license

Importance does not prove mechanism. Keeping this boundary clear makes the result easier to audit and transfer.

Try it, check it, transfer it

Triangulate weight and ablation. 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. Transfer and governance

This is where modelling choices begin to affect evidence. Models are tested across tissues, donors and kernels.

A concrete situation

A held-out donor preserves the ranking.

What the mathematics does not license

Spatial batches can masquerade as transfer. A trustworthy workflow records the choice before seeing the final test result.

Try it, check it, transfer it

Reserve whole biological units. 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

HoloNet represents spatial communication as a collection of graph views rather than one undifferentiated network. Each view corresponds to a candidate ligand-receptor event, with nodes describing spatial locations or cells and edges encoding how a sender can contribute signal to a receiver. Expression, cell-type composition and spatial separation enter as distinct mathematical ingredients. Keeping them separate makes the final prediction easier to audit than a score whose origin is hidden.

Distance is handled through a decay function. A nearby sender usually contributes more than a distant sender, but the exact rate depends on the kernel and its scale. The graph message arriving at a receiver combines sender ligand intensity, receiver receptor availability, cell-type information and the distance weight. A kernel is a modelling assumption about opportunity, not a measurement of molecular travel or binding.

A graph neural network propagates information within every view, while gated attention learns how much each ligand-receptor and cell-type view contributes to reconstruction of target-gene expression. Attention weights can guide interpretation because they show which views the fitted model relied on. They are conditional model weights, however, and should not be read as causal effect sizes without perturbation evidence.

The training objective compares reconstructed target-gene expression with observed expression and adds regularization to control complexity. Predictive accuracy on held-out locations is important because a flexible model can fit spatial autocorrelation without discovering transferable biology. HoloNet therefore teaches a useful sequence: define views, declare the distance kernel, propagate graph messages, fuse them with attention, test reconstruction and only then interpret communication hypotheses.

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Frequently asked questions

What is HoloNet?

HoloNet is a multi-view graph-learning framework that links spatial ligand-receptor events to target-gene expression.

Why does HoloNet use multiple graph views?

Each view preserves one candidate signalling mechanism and cell-type context so their contributions can be learned and compared.

What does distance decay mean?

It is a kernel that reduces the modelled contribution of more distant senders according to a declared scale and shape.

What does gated attention do?

It assigns data-dependent weights to view-specific representations before they are fused for prediction.

Does an attention weight equal a causal effect?

No. It records reliance within a fitted predictive model and may reflect correlation, spatial structure or shared inputs.

How should HoloNet be validated?

Use held-out locations or samples, ablations, kernel sensitivity, target reconstruction metrics and independent perturbation evidence.

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Primary source and fact-check note

Haochen Li, Tianxing Ma, Minsheng Hao, Wenbo Guo, Jin Gu, Xuegong Zhang and Lei Wei, “Decoding functional cell-cell communication events by multi-view graph learning on spatial transcriptomics,” Briefings in Bioinformatics 24(6), bbad359 (2023), DOI 10.1093/bib/bbad359. 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

• SpaTalk spatial signalling
• MISTy multiview spatial context
• CellChat communication networks
• 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

View audit

Version every ligand-receptor and cell-type graph view.

Kernel audit

Publish distance function, scale and sensitivity.

Message audit

Keep expression, adjacency and normalization components.

Attention audit

Check view weights across seeds and ablations.

Target audit

Separate train, validation and held-out targets.

Loss audit

Report reconstruction and regularization terms.

Transfer audit

Reserve whole donors, tissues or sections.

Final claim

Predictive contribution and attention are not causal effects.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Spatial expression matrix

Begin with this mechanism: Genes are measured across cells or spots with coordinates. Recreate the concrete case: A matrix has 5,000 genes and 2,000 locations. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Normalization shapes every later score. Complete the transfer step: Freeze and document preprocessing. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 2: Cell-type distribution

Begin with this mechanism: Each location carries observed labels or estimated type proportions. Recreate the concrete case: A spot is 60% epithelial and 40% stromal. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Deconvolution uncertainty propagates. Complete the transfer step: Retain proportion intervals. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 3: Ligand-receptor view

Begin with this mechanism: One candidate mechanism defines one graph layer. Recreate the concrete case: L1-R1 forms view v. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Catalogue choice limits discovery. Complete the transfer step: Version every pair and complex. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 4: Sender ligand intensity

Begin with this mechanism: Sender expression supplies outgoing signal magnitude. Recreate the concrete case: Cell i has L1 expression four. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: RNA is not secreted protein. Complete the transfer step: Label the quantity as expression evidence. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 5: Receiver receptor intensity

Begin with this mechanism: Receiver expression controls eligible incoming signal. Recreate the concrete case: Cell j has R1 expression three. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Detection noise creates zeros. Complete the transfer step: Audit detection and thresholds. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 6: Distance-decay kernel

Begin with this mechanism: A function maps separation to a nonnegative weight. Recreate the concrete case: exp(-d/s) gives 0.37 when d=s. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Scale s changes effective range. Complete the transfer step: Sweep plausible scales. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 7: Communication adjacency

Begin with this mechanism: Edge i to j combines direction, expression and distance. Recreate the concrete case: Four times three times 0.5 gives six. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Products depend on normalization. Complete the transfer step: Publish every factor separately. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 8: Multi-view collection

Begin with this mechanism: All event graphs share nodes but differ in edges. Recreate the concrete case: Twenty L-R events produce twenty views. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Views can be redundant. Complete the transfer step: Measure view correlation. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 9: Graph convolution

Begin with this mechanism: Neighbour messages are transformed and aggregated. Recreate the concrete case: Receiver j sums weighted sender vectors. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: High-degree nodes may dominate. Complete the transfer step: Compare normalized aggregation. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 10: Gated attention

Begin with this mechanism: Learned gates weight view representations. Recreate the concrete case: Weights 0.6, 0.3 and 0.1 sum to one. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Weights are conditional on other views. Complete the transfer step: Inspect stability across seeds. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 11: View fusion

Begin with this mechanism: Weighted view messages form one receiver representation. Recreate the concrete case: Three graph vectors combine into h-j. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Fusion can hide opposing signals. Complete the transfer step: Keep signed or view-level outputs. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 12: Target-gene prediction

Begin with this mechanism: The fused vector predicts expression of specified genes. Recreate the concrete case: Predicted target T is 7.8. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Targets may be co-expressed for other reasons. Complete the transfer step: Use held-out targets and locations. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 13: Reconstruction loss

Begin with this mechanism: Observed and predicted targets are compared. Recreate the concrete case: Squared error is (8-7.8)^2. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: A low training loss can overfit. Complete the transfer step: Report validation loss. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 14: Regularization

Begin with this mechanism: Penalties constrain weights and complexity. Recreate the concrete case: L2 shrinks a gate coefficient. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Too much shrinkage removes real structure. Complete the transfer step: Plot a tuning path. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 15: Contribution interpretation

Begin with this mechanism: Ablations and weights identify influential views. Recreate the concrete case: Removing L1-R1 raises error by 12%. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Importance does not prove mechanism. Complete the transfer step: Triangulate weight and ablation. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.

Workshop 16: Transfer and governance

Begin with this mechanism: Models are tested across tissues, donors and kernels. Recreate the concrete case: A held-out donor preserves the ranking. Write view labels, expression values, cell-type proportions, distances, kernel weights, adjacency entries, messages, gates, target predictions and losses with direction, units, denominators and assumptions. Calculate the smallest non-trivial example by hand, then reproduce it in a spreadsheet or short program. Challenge this limitation: Spatial batches can masquerade as transfer. Complete the transfer step: Reserve whole biological units. Change exactly one catalogue, normalization, threshold, neighbourhood radius, distance kernel, graph layer, hidden dimension, attention seed, corruption rule, latent prior, decoder mask, KL weight, sender bag, spatial metric, shrinkage prior or validation split. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep measurement, graph construction, probabilistic assumption, optimization, prediction, interpretation and validation on separate notebook lines. Reserve whole donors, tissues or conditions outside tuning when testing transfer.