PIVOT / docs /method.md
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Equations and implementation

The original PIVOT formulation is preserved: mean-pooled gene-operation embeddings, a residual endpoint map, map/tangent/composition losses, and projected endpoint-reward gradients. The optional population loss compares response distributions.

Paper quantity Implementation
Cell-state representation and reconstruction data/preprocess.py, PerturbData.decode_to_genes
Mean-pooled intervention embedding models/encoders.py, PerturbationEncoder
Residual map and diagonal identity models/flow_map.py, FlowMap
Map, tangent, and composition objectives training/losses.py, compute_losses
Population MMD term training/train.py, evaluation/rewards.py
Exhaustive catalog score evaluation/inference.py, endpoint_ranking
Endpoint vector-Jacobian product evaluation/inference.py, reward_guidance
Nearest embedding projection and reranking project_and_rerank
Greedy gene-set construction greedy_combinatorial
Independent measured candidate outcomes evaluation/runner.py, evaluate

The cosine reward compares each predicted cell's control-relative effect with the target centroid effect. The centroid reward averages squared cell-to-centroid distances, so it includes predicted population spread. MMD and sliced-Wasserstein rewards operate on whole populations.

Guidance uses normalized ascent with a fixed step size. Discrete projection can lower the continuous reward. Exhaustive ranking maximizes the same predictor score over a finite fixed catalog. Guidance therefore requires evaluation of computation, measured outcome quality, and the reward change after projection. The implementation records candidate-cell evaluations and query timings. Projection over embeddings also scans the catalog; its cost should be included in full runtime comparisons.

The default full model uses a 64-dimensional intervention embedding, four 512-unit SiLU layers, Fourier time features, 60 epochs, batch size 1,024, and AdamW. small.json is a two-epoch workflow check with a 16-dimensional intervention embedding and two 64-unit layers. Configurations containing distribution activate population matching. The map_* configurations isolate the two auxiliary losses.

Historical source files also contain expression-derived cluster features. They remain in the preserved original archive. The corrected training interface accepts metadata-only gene/operation representations and does not offer those outcome-derived clusters as independent pathway features.