Adaptive Data-Knowledge Alignment in Genetic Perturbation Prediction

Conference: ICLR2026
OpenReview: https://openreview.net/forum?id=CxLaZWbUjc
Code: TBD
Area: Computational Biology / Neuro-symbolic Learning / Interpretable Machine Learning
Keywords: Genetic Perturbation Prediction, Abductive Learning, Neuro-symbolic Alignment, Gene Regulatory Networks, Knowledge Refinement

TL;DR

ALIGNED integrates data-driven neural networks with expert-curated gene regulatory knowledge within an Abductive Learning (ABL) framework. It utilizes a gradient-free adapter to decide whether to trust data or knowledge on a per-gene basis and subsequently refines the regulatory knowledge base using predictions. It achieves the highest "Balanced Consistency" across several large-scale perturbation datasets and re-discovers biologically meaningful regulatory relationships.

Background & Motivation

Background: Predicting "how the genome-wide transcriptome changes after knocking out or overexpressing a specific gene" is a core task in understanding cellular systems and drug discovery. Current mainstream approaches take two paths: one is purely data-driven, training large-scale models (e.g., scGPT, scFoundation) on massive single-cell data to learn latent representations; the other is a hybrid approach, incorporating prior gene regulatory knowledge (e.g., GEARS using GO graphs) as an inductive bias.

Limitations of Prior Work: Pure data-driven models are black boxes, offering no explanation for "why a gene is predicted to be up-regulated" or which regulatory relationship is at play. While hybrid methods utilize knowledge, they treat it as a static constraint, meaning knowledge only assists prediction unidirectionally without being corrected or updated by the data. Neither path provides an interpretable and evolving understanding of biological mechanisms.

Key Challenge: To achieve end-to-end bidirectional "Data ↔ Knowledge" integration, the primary obstacle is the inherent inconsistency between the two. The paper observes that in common knowledge bases (OmniPath, GO, EcoCyc) and datasets (Norman, Precise1k), 42%–71% of regulatory relationships in the data are absent from knowledge bases, and at least 14% directly conflict with knowledge base annotations. Furthermore, knowledge bases may be outdated or biased toward well-studied pathways. Naively merging these two noisy sources causes errors to propagate bidirectionally, compromising both neural learning and knowledge refinement.

Goal: Given systematic inconsistencies, the objective is to achieve high prediction accuracy while grounding predictions in interpretable biological priors and enabling reverse refinement of the knowledge base. This requires an adaptive mechanism to "judge per-gene whether to trust data or knowledge" and a metric to evaluate the balance between both.

Key Insight: The authors adopt the Abductive Learning (ABL) paradigm proposed by Zhi-Hua Zhou, which was designed to align neural predictions with symbolic knowledge bases through consistency optimization when they disagree. By encoding Gene Regulatory Networks (GRNs) into Boolean matrices for symbolic reasoning, the neural network and symbolic components each produce a prediction, which an adapter then reconciles.

Core Idea: A gradient-free trained adapter performs a binary selection between neural and symbolic predictions per output dimension (per gene) to form a neuro-symbolic fusion prediction. This fusion prediction is then used for reverse, sparse refinement of the knowledge base, allowing data and knowledge to mutually correct each other through iterations.

Method

Overall Architecture

ALIGNED formalizes the problem as a ternary classification: learning a function \(f:\{-1,0,1\}^n \to \{-1,0,1\}^n\), where the input represents the perturbation state of each gene (\(-1\) knockout / \(0\) no perturbation / \(1\) overexpression) and the output is the direction of change in gene expression (down-regulated / unchanged / up-regulated).

The framework consists of three components: the Neural Component \(f_y\) is a neural network (MLP or GNN with KB embedding) that directly predicts responses from input; the Symbolic Component KB compiles GRN activation (\(+\)) and inhibition (\(-\)) relationships into \(n\times n\) Boolean adjacency matrices \(\langle R^{(k)}_+, R^{(k)}_-\rangle\), performing efficient deductive queries via matrix operations \(\delta_{KB}(x)=(R^{(k)}_+-R^{(k)}_-)^\top x\) (where \(k\) controls the path length of indirect regulation); the Adapter \(f_a\) learns to fuse the two based on reliability.

The workflow is as follows: Jointly initialize \(f_y\) and \(f_a\) on labeled data. For every input (including unlabeled ones), both neural and symbolic components generate predictions. In the Adaptive Alignment phase, the adapter outputs a binary indicator vector \(a\) to select the source per dimension, resulting in the fusion prediction \(\bar y\). This is followed by Bidirectional Updates: retraining the neural component using \(\bar y\) and refining the symbolic GRN. This alignment and refinement cycle can be iterated (denoted as A, R, A-R, A-R-A...). Three elements persist throughout: an evaluation metric, an alignment mechanism, and a refinement mechanism.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Perturbation Input x<br/>(Including Unlabeled)"] --> B["Neural Component fy<br/>Neural Prediction ŷ"]
    A --> C["Symbolic Component KB<br/>Boolean Matrix Query δKB(x)"]
    B --> D["Adaptive Neuro-Symbolic Alignment<br/>Adapter fa per-dim selection → ȳ"]
    C --> D
    D --> E["Balanced Consistency Metric<br/>F1_balance evaluates alignment quality"]
    D -->|"Retrain with ȳ"| B
    D -->|"Gradient + Sparse Refinement"| F["Knowledge Refinement<br/>Update GRN Matrix"]
    F -->|"Next Iteration"| C

Key Designs

1. Balanced Consistency Metric: Accounting for both Data and Knowledge

Traditional metrics only consider prediction accuracy (data consistency), ignoring whether predictions violate biological priors. Thus, black-box models may fit noise to achieve high scores without explaining mechanisms. ALIGNED defines Balanced Consistency \(F1_{balance}\), which combines the "macro-F1 against test data" and the "macro-F1 against symbolic deduction \(\delta_{KB}(x)\)" using a generalized mean with \(\gamma>1\):

\[F1_{balance}(f(x),x,y,KB)=\left(\tfrac{1}{2}F1(y,f(x))^{-\gamma}+\tfrac{1}{2}F1(\delta_{KB}(x),f(x))^{-\gamma}\right)^{-1/\gamma}\]

The \(\gamma>1\) setting causes the mean to penalize the weakest score—if either F1 is too low, the overall score is significantly reduced. This forces the model to neither fit data at the expense of knowledge nor stick to knowledge at the expense of accuracy. This serves as the primary metric for all experiments. The data-knowledge inconsistency \(Inc(D_l,KB)=\sum_{x,y}\|\delta_{KB}(x)-y\|_0\) quantifies the conflicts shown in Figure 1, distinguishing itself from local Known Relationships Retrieval by respecting the entire GRN structure and transitivity.

2. Adaptive Neuro-Symbolic Alignment: Gradient-Free Selection per Gene

This addresses the core "who to trust" question per gene. The adapter outputs a binary vector \(a=f_a(x)\), where the fusion prediction is \(\bar y_i=\hat y_i\) (if \(a_i=0\), trust neural) or \(\bar y_i=\delta_{KB}(x)_i\) (if \(a_i=1\), trust symbolic). The adapter's objective \(L_a\) consists of three terms: ① Inconsistency term \(Inc(a,x,\hat y,KB)=\|\delta_{KB}(x)-\bar y\|_0\), encouraging fusion results not to conflict with the knowledge base; ② Knowledge usage limit \(L_{len}(a)=\max\{\|a\|_0-\theta,0\}\), which prevents over-reliance on the symbolic side; ③ Weighted representation \(L_{weight}(a)=w^\top(1-a)+(1-w)^\top a\), where \(w\) combines the "count of samples where the gene conflicts with KB" and "GO annotation volume"—genes better characterized in the KB (higher \(w_i\)) tend toward symbolic prediction, while others (knowledge-sparse or high-conflict) lean toward neural. The total loss is \(L_a=Inc+C_l L_{len}+C_w L_{weight}\) (Eq. 4).

The difficulty lies in minimizing \(L_a\) while querying discrete symbolic structures, which is a combinatorial optimization problem. The authors use REINFORCE to train \(f_a\) and initialize the sampling distribution with \(w\) to reduce complexity; \(f_a\) shares input and embedding layers with \(f_y\). The overall objective \(\min_{f_y,f_a} L\) (Eq. 5) = cross-entropy on labeled data + \(L_a(a,x,\hat y)\log f_a(x)\) on all data (policy-gradient form, \(L_a\) does not backpropagate gradients).

3. Gradient-based Sparse Knowledge Refinement: Minimal Changes via Prediction

Steps 1 and 2 ground prediction in knowledge; this step reverses the direction—using reliable neuro-symbolic predictions to update the GRN, filling gaps and correcting errors. The hurdle is that Boolean logic (Eq. 1) is non-differentiable. The authors introduce an approximation function \(\varepsilon_t(X)_{i,j}=1-\exp(-tX_{i,j})\) (where \(X_{i,j}\ge0\)) to relax Boolean elements into reals, enabling gradient-based optimization. The refinement goal (Eq. 6) fits the relaxed GRN to the neuro-symbolic prediction \(\langle X_u,\bar Y\rangle\) with an \(l_1\) sparse regularization:

\[\min_{\bar R^{(0)}_+,\bar R^{(0)}_-}\sum_{x,y}\big\|\varepsilon_{t_k}(\bar R^{(k)}_+-\bar R^{(k)}_-)^\top x-y\big\|_2^2+\lambda\big(\|\varepsilon_{t_0}(\bar R^{(0)}_+)-R^{(0)}_+\|_1+\|\varepsilon_{t_0}(\bar R^{(0)}_-)-R^{(0)}_-\|_1\big)\]

Solved via proximal gradient descent, the \(l_1\) term applies a "minimal modification" inductive bias: regulatory relationships are altered only with sufficient evidence, preventing noise or shortcut patterns in the data from corrupting the meaningful biological structure of the GRN. This proves superior to non-sparse baselines using Frobenius norms.

Loss & Training

Training utilizes both labeled data \(D_l\) and unlabeled data \(D_u\): Jointly initialize \(f_y,f_a\) on \(D_l\). In the alignment phase, jointly optimize \(f_y,f_a\) using REINFORCE per Eq. 5 (\(L_a\) doesn't pass gradients). In the refinement phase, update the GRN matrix using proximal gradient descent per Eq. 6. Alignment (A) and Refinement (R) alternate until convergence or a limit \(T\). Progressive configurations (A, A-R, A-R-A-R) were evaluated.

Key Experimental Results

Main Results

On three large-scale perturbation datasets (Norman Human K562, Dixit Mouse BDMC, Adamson Human K562), ALIGNED was compared with SOTA models like GEARS, scGPT, scFoundation, State, and Linear. For fairness, knowledge refinement was disabled in this set to focus on alignment.

Dataset	Metric	ALIGNED	Prev. SOTA	Conclusion
Norman / Dixit / Adamson	Knowledge Consistency	Significantly Highest	Low	Large Gain
Same as above	Data Consistency	Slightly Higher	Comparable	No loss in accuracy
Same as above	Balanced Consistency	Highest	Low	Optimal overall

Progressive iteration results on the E. coli genome (EcoCyc KB, 315 regulators / 3004 targets) (Table 1, GNN version):

Configuration	Data Consistency	Knowledge Consistency	Balanced Consistency
GNN only	0.3773	0.3605	0.3689
A (Alignment only)	0.3876	0.3714	0.3800
A-R	0.3876	0.4520	0.4130
A-R-A-R	0.3878	0.5348	0.4288

Each round of "Alignment + Refinement" continuously boosted knowledge consistency (0.36→0.45→0.53) without degrading data consistency, leading to steady gains in balanced consistency.

Ablation Study

Config	Impact	Mechanism
GNN only → A	Knowledge Consistency ↑	Adapter effectively assimilates symbolic info
A → A-R	Large Knowledge Consistency ↑	Symbolic refinement provides extra boost; accuracy remains stable
Random GRN as KB	Degenerates to pure neural	The adapter defaults to the neural side absent meaningful priors
Remove \(Inc\) term	Weaker knowledge alignment	This term is the primary driver for aligning with knowledge
Remove \(L_{len}\) limit	Over-reliance on symbolic	Usage limit prevents knowledge misuse
Random weight \(w\)	Worse balance	\(w\) helps balance accuracy vs. knowledge usage volume

Regarding robustness of refinement (synthetic data with noise-injected GRN): F1 for rebuilding interactions remains \(>0.7\) even at 40% noise. Within 20% noise, the reconstructed GRN topology (modularity, assortativity) remains close to the original. Enrichment scores on most KEGG pathways showed no significant change after refinement, indicating re-discovery of biologically meaningful relationships across databases.

Key Findings

• The combination of "Alignment + Refinement" provides the greatest contribution: alignment alone raises knowledge consistency, while refinement adds a significant layer, always without sacrificing data consistency—exactly as intended by the \(F1_{balance}\) design.
• The weighting vector \(w\) is the critical signal for the adapter's per-gene decision: trust symbolic for well-characterized genes and neural for sparse/conflicting ones.
• Sparse refinement recovers GRNs under high noise thanks to the "minimal change" bias of \(l_1\); non-sparse baselines are significantly more fragile.

Highlights & Insights

• Metric as Method: \(F1_{balance}\) uses the generalized mean (\(\gamma>1\)) to explicitly penalize weaknesses, baking the "accuracy + grounding" requirement into optimization and evaluation. This "penalize the weakest" approach is transferable to any multi-objective scenario where no goal can be sacrificed.
• Bidirectional Knowledge Utilization: Unlike previous hybrid methods that treat knowledge as static, Ours allows data to refine knowledge with a "minimal change" \(l_1\) constraint. This preserves structure while allowing biological understanding to "evolve."
• REINFORCE + Differentiable Relaxation: A dual-strategy for non-differentiability—using REINFORCE for discrete symbolic queries and \(\varepsilon_t(\cdot)\) for Boolean matrix relaxation. Selecting optimizers based on the nature of the obstacle is a valuable design pattern.

Limitations & Future Work

• The framework relies on ternary (-1/0/1) GRN representations, losing continuous information like regulatory strength and dose effects, which is needed for quantitative dynamics.
• Knowledge refinement validation uses synthetic data (injecting noise into OmniPath), which is a semi-artificial setting; real-world knowledge errors may not follow uniform noise distributions.
• The symbolic side relies on compiling GRNs into Boolean matrices with a fixed \(k\) to approximate indirect regulation. There are many hyperparameters (\(k\), \(\gamma\), \(\theta\), \(\lambda\)), and their tuning/robustness for new species/KBs requires further investigation.
• The convergence and sampling variance of REINFORCE on very large genomes are potential risks; while initial sampling helps, scalability remains a factor.

Related Work & Insights

• vs GEARS (GNN hybrid): GEARS treats knowledge as a static inductive bias for unidirectional prediction; ALIGNED is bidirectional—using knowledge to correct predictions and predictions to refine knowledge, with adaptive selection.
• vs scGPT / scFoundation (Data-driven foundation models): These learn latent representations from massive data but are black boxes; ALIGNED’s symbolic component makes predictions traceable to specific regulatory links, yielding significantly higher Knowledge Consistency.
• vs Classic Abductive Learning (ABL): Standard ABL assumes a relatively reliable KB to correct neural predictions; Ours addresses the reality where both are unreliable and conflicting, extending ABL for noisy knowledge scenarios via balanced consistency and weighted adapters.

Rating

• Novelty: ⭐⭐⭐⭐⭐ Adapting ABL to genetic perturbation with bidirectional refinement is highly novel.
• Experimental Thoroughness: ⭐⭐⭐⭐ Coverage of Human/Mouse/Bacteria + synthetic robustness + ablation, though refinement validation is synthetic-heavy.
• Writing Quality: ⭐⭐⭐⭐ Logical clarity, complete equations, but high density of symbols/figures requires careful reading.
• Value: ⭐⭐⭐⭐⭐ Provides a framework for "interpretable and evolvable biological mechanism understanding," significant for drug discovery.

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