Representation → perturbation

Does a good representation make a good perturbation model?

The two components share sources, and will share encoders. That makes the question testable at two levels: do the cell types that are hard to represent give perturbation conditions that are hard to predict, and do encoders that score high on one scale score high on the other.

Item level: Parse PBMC in both components

The Parse 10M PBMC atlas is an annotation panel (cell type is the label, donors held out) and a cytokine screen (context is donor and cell type). Every perturbation condition therefore has a context whose representation difficulty is already estimated. Five donors overlap.

Cell type level

Mean difficulty over the type's cells (x) and over the cytokine conditions in that type (y), with standard errors of the means.

Donor × cell type level

One point per context shared by both components.

The confound

Raw correlation is near zero at both levels, and the table shows why. The abundant T-cell types are the hardest to represent, because the probe confuses sibling states, and the easiest to predict perturbations for, because a condition with a thousand cells has a precise pseudobulk. Cells per condition pulls the two difficulties apart.

Controlling for cells per condition, the partial correlation turns positive but small. Sixteen types and sixty-nine contexts are too few to settle it; the screen-level test with shared encoders below is the one with power.

Every scale and split combination

Model level: shared encoders

Hold the perturbation model fixed and vary only the encoder underneath it. Every encoder then has one ability on each scale, and the random projections at each dimension say how much is dimension alone.

cells expression profiles of one screen encoder PCA, ICA, Nyström, random projection, … the only part that varies latent z one vector per cell frozen probe names the cell type from z representation ability pass = type named right all 14 panels A latent shift mean z of perturbed cells minus control, per condition perturbation ability fixed linear decoder to genes; pass = beats the mean shift B one point same encoder, two abilities Hold everything fixed except the encoder; the random projections at each dimension are the null.

Reading

Across the 27 classical encoders the two abilities move together: Spearman +0.94 and +0.95 on the two perturbation scales, and still +0.95 without the random projections. It is not only dimension: at equal dimension a random projection sits far below PCA on both sides.

encoderrepresentation abilityperturbation ability (unseen combination)
PCA-128D+0.69+0.63
random projection 128D (null)−0.07−1.27
Nyström-256D+0.72−0.57
PCA-256D+0.67+0.87
models that learn their basis from responses (PCA regression, MLP, low-rank)—+4.5 to +5.8

The mapping breaks at the top. Nyström features are the best annotation encoder and a poor response basis, and the whole family sits two to five logits below models that learn their basis from responses. Representation quality orders encoders within a family; it does not close that gap.

Foundation-model encoders enter through the same recipe once their embeddings are on the representation scale; see the contribute page.

Type level: does it transfer within a cell type?

If an encoder annotates cell type X well, does it predict perturbations in X well? Every encoder gets one representation ability per type and one perturbation ability per type, anchored to the panel and screen difficulties. Subtracting the encoder's overall ability leaves the type-specific part, which is what would have to transfer.