AdaPert: Perturbation-Conditioned Transcriptional Predictor

• AdaPert is a framework that predicts post-perturbation transcriptional profiles by conditioning on control signals and candidate perturbations.
• It leverages biological knowledge graphs with Gumbel-Softmax subgraph selection to focus on differentially expressed genes and suppress noise.
• The model integrates DEG-aware loss functions and interpretable graph representations to achieve accurate, robust predictions across diverse effect sizes.

AdaPert is a perturbation-conditioned, knowledge-guided framework for predicting high-dimensional transcriptional responses to genetic interventions while avoiding a pervasive failure mode known as mean collapse. In the formulation used by the method, a control gene-expression profile for a single cell, $X^c \in \mathbb{R}^N$, and a candidate perturbation gene $p \in K$ are mapped to a predicted post-perturbation profile $\hat X^p \in \mathbb{R}^N$ via $F:(X^c,p)\rightarrow \hat X^p$. AdaPert addresses the observation that single-cell perturbation effects are sparse, noisy, and often poorly captured by objectives that emphasize global reconstruction. Its central design couples perturbation-specific subgraph learning on a biological knowledge graph with DEG-aware objectives that explicitly separate responsive signal from non-responsive background (Piao et al., 21 Feb 2026).

1. Problem formulation and the mean-collapse failure mode

AdaPert is defined for the task of predicting the transcriptional response of a single cell after a genetic perturbation. The standard template described in the paper is a conditional autoencoder:

$$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$

trained with an MSE reconstruction objective $L(X^p,\hat X^p)$. In this setting, $z_c$ encodes the control state, while $z_p$ represents the perturbation.

The motivation for AdaPert is the mismatch between this training objective and the statistical structure of perturbation responses. Let $D(p)$ denote the set of differentially expressed genes (DEGs) under perturbation $p$ and $p \in K$0 its complement, with $p \in K$1. The reconstruction loss decomposes into contributions from responsive genes and non-responsive genes:

$p \in K$2

Because the non-DEG term dominates, pure MSE training prioritizes minimizing errors where the ground-truth effect is near zero. The paper characterizes the resulting behavior as mean collapse: predictions shrink toward global averages, yielding high global correlations while systematically underestimating large, perturbation-specific effects. In the reported interpretation, this produces many false positives and poor interpretability rather than faithful recovery of sparse transcriptional changes (Piao et al., 21 Feb 2026).

This framing places AdaPert in direct opposition to models that optimize only aggregate similarity. A plausible implication is that conventional global metrics can obscure failure precisely where perturbation biology is most informative: in the signed, sparse, high-effect tail of the response distribution.

2. Perturbation-conditioned subgraph learning on biological knowledge graphs

AdaPert uses a biological knowledge graph $p \in K$3 in which nodes are genes or proteins and edges represent interactions or functional relationships. The experiments use STRING PPI networks aligned to highly variable genes (HVGs). The raw STRING v11.5 graph has 18,382 nodes and 11,257,696 edges, with average degree approximately 1,225. An HVG-filtered example has 4,509 nodes and 1,090,554 edges, with average degree approximately 484. Top-$p \in K$4 filtering further reduces density: Top-20 yields 89,793 edges with average degree approximately 40, and Top-10 yields 45,013 edges with average degree approximately 20. These statistics motivate localized modeling rather than dense, static propagation.

Instead of embedding the perturbation by message passing over the full graph, AdaPert extracts a sparse perturbation-specific node-induced subgraph $p \in K$5 centered on the perturbed gene. The method combines structural and semantic information. Structural embeddings are obtained from mean-aggregation message passing:

$p \in K$6

with $p \in K$7 after $p \in K$8 layers. The perturbation gene also receives a semantic embedding from text,

$p \in K$9

which is concatenated with node structure:

$\hat X^p \in \mathbb{R}^N$0

Node relevance is scored by

$\hat X^p \in \mathbb{R}^N$1

AdaPert then applies differentiable sparse sampling through Gumbel-Softmax:

$\hat X^p \in \mathbb{R}^N$2

and selects nodes with $\hat X^p \in \mathbb{R}^N$3 to form $\hat X^p \in \mathbb{R}^N$4. The perturbation context representation is the sum of selected node embeddings:

$\hat X^p \in \mathbb{R}^N$5

The paper emphasizes two properties of this construction. Sparsity is enforced by thresholding Gumbel-Softmax scores, yielding small condition-dependent subgraphs and reducing noise propagation. Adaptivity arises because node selection depends on the perturbation through $\hat X^p \in \mathbb{R}^N$6, and because the learned subgraph representation is aligned during training with perturbation-specific DEG signals. In this sense, the graph is not treated as a fixed propagation substrate; it is filtered into a perturbation-conditioned context representation (Piao et al., 21 Feb 2026).

3. Architecture, forward pass, and anti-collapse objectives

AdaPert retains the conditional autoencoder template, but replaces a dense global graph embedding with the perturbation-conditioned subgraph context. The control state is encoded as $\hat X^p \in \mathbb{R}^N$7 using an MLP/transformer-like encoder, and the predicted perturbed profile is generated as $\hat X^p \in \mathbb{R}^N$8. The forward pass is described as five steps: compute $\hat X^p \in \mathbb{R}^N$9; compute graph structural embeddings $F:(X^c,p)\rightarrow \hat X^p$0 and semantic perturbation embeddings $F:(X^c,p)\rightarrow \hat X^p$1; score and sparsely sample nodes to build $F:(X^c,p)\rightarrow \hat X^p$2; aggregate selected nodes into $F:(X^c,p)\rightarrow \hat X^p$3; and decode the perturbed profile.

The anti-mean-collapse strategy is implemented through DEG-aware training. For each perturbation $F:(X^c,p)\rightarrow \hat X^p$4, the response is defined as $F:(X^c,p)\rightarrow \hat X^p$5. Statistical tests yield $F:(X^c,p)\rightarrow \hat X^p$6, and the DEG partition is

$F:(X^c,p)\rightarrow \hat X^p$7

The global reconstruction term is

$F:(X^c,p)\rightarrow \hat X^p$8

To suppress spurious changes on background genes, AdaPert adds a non-DEG robust loss on predicted response $F:(X^c,p)\rightarrow \hat X^p$9:

$$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$0

where $$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$1 is the Huber loss and $$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$2 is set proportional to the empirical standard deviation of non-DEG effects. The stated role of this term is to suppress small spurious deviations strongly while preventing large noisy residuals from dominating.

A second term aligns the learned subgraph representation with a response-driven target. The target masks non-DEGs and preserves signed effects:

$$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$3

A learnable head $$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$4 projects this target to $$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$5, and the alignment loss is

$$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$6

The total objective is

$$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$7

The paper reports that subgraph selection is trained end-to-end using Gumbel-Softmax continuous relaxation, with $$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$8 controlling exploration-exploitation and threshold $$z_c = ENC_\theta(X^c), \qquad z_p = GNN(G,p), \qquad \hat X^p = DEC_\phi(z_c, z_p),$$9 enforcing sparsity. It further analyzes $L(X^p,\hat X^p)$0: small/medium-effect perturbations benefit from larger $L(X^p,\hat X^p)$1, up to approximately $L(X^p,\hat X^p)$2, whereas large-effect settings need smaller $L(X^p,\hat X^p)$3. Excessively large $L(X^p,\hat X^p)$4, for example $L(X^p,\hat X^p)$5, over-suppresses signal. This establishes AdaPert as a model that does not merely regularize predictions; it regularizes specifically against background hallucination while constraining the perturbation context to encode DEG-relevant structure (Piao et al., 21 Feb 2026).

4. Evaluation protocol, benchmarks, and metrics

AdaPert is evaluated on single-cell CRISPR Perturb-seq datasets from Replogle et al.: K562.Replogle and RPE1.Replogle. Both use unseen perturbation splits, with train/validation/test defined by perturbation identity. The reported statistics are: K562 with Train 111,770 cells / 734 perturbations / 5,000 HVGs, Val 10,918 / 82, and Test 38,475 / 272; RPE1 with Train 74,474 / 771 / 3,352, Val 26,073 / 308, and Test 50,593 / 464. Perturbations are stratified by DEG proportion into small $L(X^p,\hat X^p)$6, medium $L(X^p,\hat X^p)$7–$L(X^p,\hat X^p)$8, and large $L(X^p,\hat X^p)$9 effect-size regimes.

The baselines are divided into graph-free methods—scVI, CPA, STATE—and graph-based methods—GEARS, TxPert, MORPH. All are trained under identical splits and protocols, and metrics are computed with cell-eval.

The evaluation protocol is explicitly DEG-aware. Global response is defined by $z_c$0 and predicted response by $z_c$1. The global metrics are Pearson-$z_c$2,

$z_c$3

and Perturbation Discrimination Score (PDS), defined from $z_c$4 distances to held-out perturbation effects. DEG-aware metrics are DES, DE-Spearman on significant genes, LFC-weighted DE-Spearman, and DE Direction Match. The paper’s stated reason for emphasizing these metrics is that mean collapse can inflate global correlation by matching the center of the effect distribution while missing strong perturbation-specific responses. In that interpretation, improvements on DES and DEG-restricted correlations are more probative of biologically meaningful recovery than improvements in aggregate reconstruction alone (Piao et al., 21 Feb 2026).

5. Empirical performance and biological interpretability

On K562, AdaPert achieves the best reported global results among all compared methods: Pearson-$z_c$5 $z_c$6 and PDS $z_c$7. The strongest baseline on Pearson-$z_c$8 is TxPert at $z_c$9, and the strongest baseline on PDS is also TxPert at $z_p$0. On RPE1, AdaPert attains the best reported Pearson-$z_p$1, $z_p$2, with PDS $z_p$3; MORPH has the best baseline PDS at $z_p$4, while TxPert has Pearson-$z_p$5 $z_p$6.

The DEG-aware results are more pronounced. On K562, AdaPert reports DES@50 $z_p$7, DES@100 $z_p$8, DE-Spearman(sig) $z_p$9, DE-Spearman(lfc-sig) $D(p)$0, and Direction-match $D(p)$1, which the paper identifies as best across all compared methods. On RPE1, AdaPert reports DES@50 $D(p)$2, DES@100 $D(p)$3, DE-Spearman(sig) $D(p)$4, DE-Spearman(lfc) $D(p)$5, and Direction-match $D(p)$6, again described as best overall.

The effect-size analysis on K562 compares AdaPert against TxPert and is explicitly framed as a mean-collapse sensitivity study. For small perturbations $D(p)$7, AdaPert yields Pearson-$D(p)$8 $D(p)$9 versus $p$0 and DES $p$1 versus $p$2, with PDS approximately similar. For medium perturbations $p$3–$p$4, it yields Pearson-$p$5 $p$6 versus $p$7, DES $p$8 versus $p$9, and PDS $p \in K$00 versus $p \in K$01. For large perturbations $p \in K$02, it yields Pearson-$p \in K$03 $p \in K$04 versus $p \in K$05, DES $p \in K$06 versus $p \in K$07, and PDS $p \in K$08 versus $p \in K$09. The paper concludes that AdaPert particularly strengthens DEG separation under small and medium effects, where mean collapse is most severe.

Ablation results support the architecture-level interpretation. Removing $p \in K$10 degrades global and DEG metrics across all effect sizes. Removing $p \in K$11 particularly harms small and medium perturbations, which are described as weak signals in high noise. Excessive $p \in K$12 over-smooths and degrades performance.

The model is also presented as interpretable. By selecting nodes conditioned on perturbation semantics and local graph topology, AdaPert forms compact subgraphs around biologically related genes. This is reported to reduce noise propagation from dense, static graphs and to focus on causal neighborhoods, consistent with observations that many DEGs lie within 1–3 hops of the perturbed gene in STRING. In the case of UQCRB, with $p \in K$13 DEGs, standard models exhibit shrinkage toward zero, whereas AdaPert better tracks large gene-level changes. In HIRA knockdown, Gene Set Enrichment Analysis shows predicted versus ground-truth pathway enrichment correlation $p \in K$14 with $p \in K$15, and the model correctly recovers downregulation of cell-cycle pathways including Myc Targets V1 and E2F Targets. The paper also notes preservation of coordinated pathway-level responses such as Myc Targets and Heme Metabolism, which supports biological fidelity beyond gene-level metrics (Piao et al., 21 Feb 2026).

6. Robustness, limitations, practical use, and nomenclature

AdaPert is evaluated under unseen-perturbation splits and is therefore framed as an out-of-distribution generalization method. The reported DEG-aware gains across effect sizes are used as evidence of robustness to noise and mean collapse, especially for weak signals. Scalability is managed through graph sparsification, including HVG restriction and top-$p \in K$16 edge filtering, and through Gumbel-Softmax subgraph extraction that selects only a small set of nodes per perturbation. The practical guidance in the paper recommends AdaPert for tasks involving single-gene perturbations with sparse, noisy effects, particularly when a biological knowledge graph such as STRING and textual gene descriptions are available and when DEG-aware accuracy and interpretability are more important than global correlation alone.

The stated limitations are specific. Performance depends on graph quality: STRING coverage and confidence can affect subgraph relevance, and missing or incorrect edges may limit performance. Node scoring depends on semantic embeddings from $p \in K$17 and LM embeddings, so text-based bias can mis-rank nodes weakly connected in structure. The sparsity threshold $p \in K$18 and Gumbel-Softmax temperature $p \in K$19 must be tuned jointly: overly aggressive sparsity may exclude relevant nodes, while insufficient sparsity may reintroduce noise. The message-passing operator is mean aggregation; the paper notes that richer GNNs such as attention could improve context modeling, but may also increase noise sensitivity if not well regularized. Future directions named in the paper include adaptive edge masking, multi-hop path scoring, causal constraints, and integration of multi-omics priors or context-specific graphs (Piao et al., 21 Feb 2026).

The name “AdaPert” in this context should be distinguished from several unrelated acronyms in the literature. “AdaPT: An interactive procedure for multiple testing with side information” denotes Adaptive p-value Thresholding for FDR control (Lei et al., 2016). “Adaptive Precision Training (AdaPT)” is a dynamic fixed-point quantized training method for DNNs (Kummer et al., 2021). “ADePT” refers to Adaptive Decomposed Prompt Tuning for parameter-efficient fine-tuning (Tang et al., 6 Jan 2025). “Adaptative Perturbation Pattern Method” is abbreviated A2PM rather than AdaPert (Vitorino et al., 2022). These homonymous or near-homonymous usages are methodologically unrelated to the perturbation-conditioned transcriptional response predictor defined in (Piao et al., 21 Feb 2026).