Adaptive Data-Knowledge Alignment in Genetic Perturbation Prediction
Authors: Yuanfang Xiang
Lun Ai
Venue: ICLR 2026 Poster (2026)
Keywords: Genetic Perturbation
Gene Expression Prediction
AI for Biology
Neuro-Symbolic AI
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: We introduce an end-to-end framework aligns neural and symbolic components and performs systematic knowledge refinement for genetic perturbation prediction.

Abstract: The transcriptional response to genetic perturbation reveals fundamental insights into complex cellular systems. While current approaches have made progress in predicting genetic perturbation responses, they provide limited biological understanding and cannot systematically refine existing knowledge. Overcoming these limitations requires an end-to-end integration of data-driven learning and existing knowledge. However, this integration is challenging due to inconsistencies between data and knowledge bases, such as noise, misannotation, and incompleteness. To address this challenge, we propose ALIGNED (Adaptive aLignment for Inconsistent Genetic kNowledgE and Data), a neuro-symbolic framework based on the Abductive Learning (ABL) paradigm. This end-to-end framework aligns neural and symbolic components and performs systematic knowledge refinement. We introduce a balanced consistency metric to evaluate the predictions' consistency against both data and knowledge. Our results show that ALIGNED outperforms state-of-the-art methods by achieving the highest balanced consistency, while also re-discovering biologically meaningful knowledge. Our work advances beyond existing methods to enable both the transparency and the evolution of mechanistic biological understanding.

Published as a conference paper at ICLR 2026
ADAPTIVE DATA-KNOWLEDGE ALIGNMENT IN GENETIC PERTURBATION PREDICTION
Yuanfang Xiang
Lun Ai EMBL-EBB ail@ebi ac..
Nanjing University
yf. .xxxangdsamil.n. wtt.::ammil.n.........m .nju. edu..d.cco
ABSTRACT
The transcriptional response to genetic perturbation reveals fundamental insights into complex cellular systems. While current approaches have made progress in predicting genetic perturbation responses, they provide limited biological understanding and cannot systematically refine existing knowl- edge. Overcoming these limitations requires an end-to-end integration of data-driven learning and existing knowledge. However, this integration is challenging due to inconsistencies between data and knowledge bases, such as noise, misannotation, and incompleteness. To address this chal- lenge, we propose ALIGNED (Adaptive aLigmment for Inconsistent Genetic kNowledgE. and Data), a neuro-symbolic framework based on the Abductive Learning (ABL) paradigm. This end-to-end framework aligns neural and symbolic components and performs systematic knowledge refinement. We introduce a balanced consistency metric to evaluate the predictions' consis- tency against both data and knowledge. Our results show that ALIGNED outperforms statc-of-the-art methods by achieving the highest balanced consistency, while also re-discovering biologically meaningful knowledge. Our work advances beyond existing methods to enable both the trans- parency and the evolution of mechanistic biological understanding.
INTRODUCTION
Understanding how genetic perturbation affects transcriptional regulation is essential for deciphering complex biological
conplex_hiologiieal systems, with profound implications, for drug discovery and mediiiie (Badia-i Mompel et al., 2023; Gavriilidis et al, 2024; Ahlmann-Fltas et al., 2025). While advances in experimental technology now a allow systematio iestemaaiciinn interrooottoooooioo
of gfne regulatory landscapes at an unprecedented scale (Norman al., 2019: Replogle et al, 2022), existing datasets remain insufficient. for buildinggpredictiing predictive models that can elucidate the full complexity of cellular system (Peidli al, 2024).. This raises a critical question of how to design predictive frameworks that not only achieve high accuracy but also yield deeper biological understanding from these experimental capabilities.
Two complementary approaches have emerged either by leveraging latent representation
trained on extensive cell data (Lotfollahi et al., 2023; Thcodoris et al, 2023 Cui all 2024
Hao et 2024) or incorporating prior biological knowledge for inductive biases (Roohani
et al. 2024 Wang et al., 2024 Littman et al., 2025; Wenkel et al,, 2025). Yet, both ap- proaches provide limited insights into the biological mechanisms underlying their predic- it difficult to understand which regulatory relationships drive specific predictions (Bendidi et al,, 2024). While hybrid meth- ods incorporate prior biological knowledge, they treat this knowledge as static const rather than interpretable and updatable representations of biological understanding. Impor- tantly, current approaches provide no end-to-end solution to identify and resolve divergences between data-driven learning and existing knowledge, which limits limits opportanities for contin- ual refinemept of hiological understanding (Gavriilidis et al., 2024 Zuidberg Dos Martires ct al., 2024: Kodzierska al., 2025).
tions. Data-driven models operate as black boxes__makle

---

Published as a conference paper at ICLR 2026
(a) OmaiFPah Norman
(b) GO KB Norman
(c) EcoCyc Precise
15.7%
14,0%
164%
15,95 13.%%
9.0%
9.4%
13.4%
$4.7%
91.4%
67.7%
10.7%
Conission: (inser)
Mising in KBB (Oute))
Canflict
Figure 1: Inconsistency between gene regulatory knowledge bases [KBs)_and data-derived pertuurbation-rreppnnes hww.:oooo--eeooooososoorrriiiaaa We examined OmniPath (Türei et al, 2016), Gene Ontology (GO) (Ashburner et al, 2000) and EcoCyc (Moore et al 2024 knowledge bases, human NNrman et al. 2019) and bacterial (Preciselk, Lamoureux et al. 2023) datasets.
Overcoming these limitations requires explicitly integrating data-driven learning with tablished knowledge. However, a key challenge is the the pervasiee inconsistencies between experimental data and curated knowledge (Lu et al. 2024) due to imperfections in both in- formation sources Perturbation datasets exhibit multiple sources of noise (Lin ot al
2025
Rohatgi et al., 2024), experimental measurement. biascs (Kim ct al 2015 Peidli ct al. 2024
and weak post-perturbation signals (Nadig et al, 2025; Aguirre et al. 2025). Meanwhil leanscriptionalleegllaae
knowledge bases curated by experts often suller from outdated information (Khatri et al. 2012). limited coverage (Saint-André, 2021) and biases towards better-studied pathways (Chevalley al, 2025).
To illustrate this challenge, we analyzed popular knowledge bases and benchmark datasets (Figure D), finding that 42-71% of data-derivod regulatory rclationships are missing across curated knowledge bases, while a minimum of 14% directly conflict with existing annota- tions, Naive integration of inconsistent sources risks bidircctional error propagation (Lu et al. 2024) that can corrupt both data-driven learning and knowledge refinement. This inconsislency prevents models, from fromm- effectively leveraging prior biological knowledge pre- dictions (Ahlmann- Balmannn-Eltze Eltze et al., 2025) and compromises their ability to produce biologically meaningful regulatory relationships from learned representations.
To address, this challenge, the Abductive Learning (ABL) paradigm (Kho,, 2019 Huang ct al. 2023) offers a foundation for integrating data-driven lcarning with symbolic knowl- edge refinement through consistency optimization. Based on this approach, propose ALIGNED (Adaptive aLigunent for Inconsistent Genetic kNowledgE and Data), an end- lo-end framework that enables neuro-symbolic alignment and knowledge refinement in ge- netic perturbation prediction. ALIGNED advances beyond existing predictive methods to enhance transparency about the underlying biological mechanisms and enable continual evolution of understanding from large-scale perturbation datasets.
Our main contributions are:
Balanced Consistency Metric. We design balanced evaluation metric that assesses predictions against both experimental data and curaled knowledge. This addresses the limitation that standard metrics evaluate only predictive accuracy without considering consistency with biological knowledge (Bendidi et al. 2024).
Adaptive Neuro-Symbolic Alignment. We adaptively combine neural and symbolic predictions from inconsistent information sources by weighting neural and symbolic components with a gradient-free optimization mechanism.
Knowledge Refinement. We enable systematic update of regulatory interactions by introducing gradient-based optimization approach over a symbolic representa- tion of the GRNs.
Results. ALIGNED matches or exceeds state-of-the-art methods in predictive accuracy while substantially outperforms existing methods in balanced consistency. In addition, we show that ALIGNED's knowledge refinement can re-discover cross- referenced regulatory relationships.
2

---

Published as a conference paper at ICLR 2026
2 PRELIMINARIES
2.1 PROBLEM SETTING
We formalize the prediction of genome-scale response genetic perturbation ternary classification problem. The goal is to learn function f 1,-1,0,13 + {-1,00,1", where the total number of genes. The imput values -1, 0, and represent negative perturbation (deletion or knockout), no perturbation, and positive perturbation (overexpression). respec- tively. The output values indicate decreased expression, no significant change, or increased expression for each gene. Ternary representation of gene expression profiles is commonly used in downstream biological research Lasks, such as gene watpfereennaleepeesseseeee analysis and pathway annotations (Love et. al. 2014; Badia-i Mompel et al. 2023).
We denote the labelled dataset by Dj = (X,, Yi), where X, contains the perturbed gene puts and Y contains the corresponding perturbation responses obtained from transcriptome sequencing experiments. An unlabelled dataset X, also used for training in abductive learning, which contains only the perturbation input.
2.2 SYMBOLIC REASONING OVER GENE REGULATORY NETWORKS
We focus on gene regulatory networks (GRNs) as our knowledge bases, which contain activa- tion (+) and inhibition (-) interaction relations between genes It is widcly used qualitative
approach to capture directed regulatory effects (Chevalley et a 2025). We utilize symbolic
reasoning via Boolean matrices (loannidis & Wong. 1991; Ai 2025). Direct activation and
inhibition interactions are compiled as X adjacency matrices (R R )
R
R R R R(-1)
((-11)
+ R RR (1-1)
R R
We approximate the fixpoint of (R( R ( by interleaving the computations with respect
to partial ordering on the matrices R(A)) R for finite k (Tarski 1955). The obtained knowledge base KB (Re(A R! represents indirect regulations via pathways up to maximum length of & interactions.
Given an input perturbation æ, we infer its effect on genome scale by performing a de- R
ductive query in the knowledge base KB. The matrix operations 6xg(z)= = (R - ) Tx
allow us to perform this query with high computational efficiency. Based on this approach, we define a measurement for the kntalkno inconsistency illustrated Figure 1
Inc(Di,XBB)
Σ a.DED
[(<c((x) yylo
(2)
where Di= (X,, Yi) is a labelled dataset Our approach differs from the Known Relation- ships Retrieval metric (Celik et. al, 2024; Bendidi et al., 2024) in that the deductive queries respect the global GRN structure and preserve the transitivity of genetic interactions.
2.3 ABDUCTIVE LEARNING
Our framework explicitly integrates the neural and symbolic components and handles data- knowledge inconsistencies based on the Abductive learning (ABL) paradigm (Zhou, 2019).
ABL is a neuro-symbolic approach that aims to learn a function and align its predictions with the knowledge base KB via consistency optimization.
A general ABL training pipeline takes a neural model f pretrained on labelled data (X,, Y) as initialization. From the unlabelled dataset X., f makes neural predictions ÿ - f(x.), which may be inconsistent with K.B. Consistency optimization is then performed, with revising ý to and updating / on the revised dalaset (X.,, Y). This process can be executed iteratively until convergence or reaching an iteration limit Formally, the objective of ABL
3

---

Published as a conference paper at ICLR 2026
Data-Knewlrdge Inconsistency
Component
Adaptor
Updane
Potturbation Data
Nexsa
Preductioo
Naroo Systolic Prdiition
Train
Adaptive Aligament
Symbolic Component
Symbhii
Refired Knowledge Rase
Upshoi
Knowledge Refinement
Gene Regulatory
Knowledge Base
Figure 2:
The ALIGNED (Adaptive aLignment of Inconsistent Genetic kNowledgE and Data) framework. ALIGNED contains neural component (blue), symbolic component (green) and an adaptor (purple).
is to make predictions that are most consistent with K.B:: max pvy x;; f, KB) = I(KBU= f(x)) ply x)
where on the right hand side "| denotes logical entailment, the first term is an indicator of consistency and the second term denotes the posterior distribution of neural predictions.
3 THE ALIGNED METHOD
We first introduce a consistency metric for evaluating how well predictions align with both the test data and the knowledge base, We then present ALIGNED (Adaptive aLignment for Inconsistent Genetic kNowledgE and Data), a framework which adaptively integrates reliable information from both sources to predict genetic perturbation responses.
3.1 THE BALANCED CONSISTENCY METRIC
To evaluate the consistency of prediction against both the test data and the knowledge base, we define balanced consistency metric F1 balance, which considers the macro F1 scores from both the test dataset and the knowledge basc. Fi balance includes a coefficient. y > to balance the two macro Fi scores and penalize when either score being too low:
Fi balance (f(z), x. y. KB) = -(5 f(x))
+ f(x)) -1/7 2
1
This metric evaluates the model's performance on making generalizable predictions while remaining grounded in curated biological prior. Unless specified, all Fi scores in evaluations are computed as macro Fi.
3.2 ALIGNED FRAMEWORK OVERVIEW
The ALIGNED framework (Figure integrates three components to leverage reliable infor- mation from data and knowledge for predicting perturbation response and refining regula- tory knowledge. The neural component fy is a neural network which predicts perturbation responses from input data, while the symbolic component KBB performs symbolic reasoning over gene regulatory networks encoded as matrices (computed via Equation []. The adap- tor fa learns to combine neural and symbolic predictions based on their relative reliability for each prediction. ALIGNED assumes that (i) when perturbation data is relatively more reliable than prior knowledge, the adaptor would increase reliance the neural component,

---

Published as a conference paper at ICLR 2026
(ii) when the prior knowledge provides more reliable information, the symbolic component would contribute more to overall predictions.
Training proceeds using both labelled and unlabelled data. We initialize components fy and fa by training them jointly on the labelled dataset. For each unlabelled input, the framework produces neural and symbolic prediction. In adaptive alignment, since these predictions may be inconsistent, the adaptor is trained to produce a binary indicator vector that selects which predictive source to trust for each output dimension. This creates an integrated neuro-symbolic prediction that combines results from both predictive sources. The framework then performs multiple iterations of alignment and bidirectional updates to neural and symbolic components. Using the neural- nymbol-yymbolic predictions, we re-train the neural component and perform knowledge refinement to the symbolic component.
3.3 ADAPTIVE NEURO-SYMBOLIC ALIGNMENT WITH GRADIENT-FRES OPTIMIZATION
In this section, we will introduce the alignment mechanism used by ALIGNED to adaptively integrate neural and symbolic predictions. We denote a binary alignment indicator vector = fa(x) and the neuro-symbolic prediction y. After the initialization and each round of bidirectional update, y is produced from both neural prediction ý and symbolic prediction
(x (>) according the indicator a, such that y:
U/
a, a, =
(xx(());
Our definition of the training objectives for the adaptor can be divided into three parts. First, since information derived from experimental data and curated knowledge may be inconsistent, the adaptor considers how neuro-symbolic predictions differ from the curated knowledge. We describe this using the inconsistency between and KB based on Equation 2
Inc(a, x, D. KB)) = [1ōx=(z) - ølla
Second, we design a loss term leverage much information from labelled training data as possible to reduce the predictions inconsistency with data. Therefore, we restrict the frame- work to only use knowledge-derivel derived information when nccessary. We defined the knowlodge usage restriction with threshold 6: (a) = max[|lallo - 0,03 0,00
Third, take into account how well each gene is represented in knowledge. To measure this, we use a weight vector w as hyperparameter, which contains the number of training data samples that are inconsistent with (computed by Equation 2), and the number of annotations from Gene Ontology (Ashburner et al, 2000). This allows us to reward a by maximizing the usage of symbolic prediction when gene is represented well in KB, otherwise use neural prediction. We define a loss with regard to w:
(weighe(a) = w (1 - a) + (1-
where higher values w; indicate that gene i is well-represented in the knowledge base and more consistent with data, suggesting the symbolic prediction should be preferred. Lower values indicate sparser knowledge or more kntw-lno conflicts, and so the noural prediction should be favored. We combine the above three parts in the adaptor's objective:
La(a, x, 9) = Inc(a, æ, KBB) + CiLten (a) + La
(4)
where hyperparameter Cw: C are trado-off cocfficients. Minimizing La includes qucrying the symbolic XCB, which has discrete structure. This creates combinatorial optimization problem, so a gradient-free optimization meihad necessary. We train fo with the REIN- FORCE algorithm (Williams, 1992; Hu et all. 2025) and initialize its sampling distribution based on w to reduce sampling complexity. To exploit representations captured by the neural component fy from the experimental data, fa shares imput and embedding layers with fy- Adaptive alignment optimizes fy and fa jointly with the following objective:
min -= Diil fy.ta
Σ CE(f((z),)) (2.v)ED:
1
+0
La x. 9) log fx
(5)
D.
DE DEDDDD.
5

---

Published as a conference paper at ICLR 2026
where (a x. does not involve gradient passing. CE(:,-) denotes the cross-entropy loss function, C' is a trade-off coefficient, Dj and Du are labelled and unlabelled datasets.
3.4 GRADIENT-BASED KNOWLEDGE REFINEMENT WITH SPARSE REGULARIZATION
To address missing and inaccurate interactions in XCB, incorporate knowledge refine- ment mechanism into the ALIGNED framework that leverages reliable information from neural and symbolic predictions. For computational elficiency on large-scale GRNs, we con- sider gradient-basee
polinizatiinnaaae introduce an approximation function e(.) for Boolean elements (Ravanbakhsh et al. 2016). This approximation enables madient-basse optimiza- tion compatibility of the non cin-dfffeeetiablle Boolean matrix operations in Equation
E/ (XX j. = - (xp() X 2 0
We introduce an inductive bias for minimal modifications the GRN during refinement. This ensures the biological relationships and structure in the GRN are not distorted by spuri- ous signals from data, such as overfitting noise or learning shorteut patterns. We perform an l sparse regularized optimization to_achieve this, fitting KR to neurn-symbolic predic- tions using proximal gradient descent (Tibshirani, 1996; Candes & Recht, 2012). Knowl- edge refinement optimizes the following objective:
min _7 2R Lrefine (R (0)
Σ (XV.(X...))
11sr, (R - R(()) x x-y12
A(1EEt R 11 1 (R
R (11)
R
(6)
where KB substituted with (ex, (R.
) Eth (T after the knowledge refinement step.
( and R represent the initial GRN before refinement, real-valued non-negative matrices
O and R (0) are the refined GRN with direct regulatory interactions. To facilitate gradient
passing, we use real-number matrix computation instead of Boolean matrix in Equation
and use R( and (0) to compute indirect regulatory interactions R(h) and R A denotes
regularization parameter, 4 tg denote coefficients of approximation, ||2 denotes the clement-wise matrix I norm.
4 EXPERIMENTS
We evaluate ALIGNED on multiple large-scale perturbation datasets for prodicting genome- wide responses and assess the knowledge refinement mechanism in isolation! The experi- ments address the following research questions:
Q1 Can ALIGNED achieve a higher balanced consistency than existing methods with- out damaging eit data or knowledge consistency?
Q2 Is the knowledge refinement mechanism capable of re-discovering biologically mean- ingful and well-structured regulatory knowledge?
Q3 Does the framework leverage knowledge to improve prediction unseen data, par- ticularly under limited data availability?
4.1 PERTURBATION PREDICTION ON BENCHMARK DATASETS (Q1)
We focused multiple large-scale perturbation datasets that are widely adopted for this prediction task: (i) Norman et al. (2019) for human K562 cells, including gene expression
profiles under single and double perturbations across 102 genes (128 double and 102 single
perturbations) with 89,357 samples; (ii) Dixit et al (2016) for mouse RDMCLcells contain-
ing 19 single gene perturbations with 43,401 samples; and (iii) Adamson et al. (2016) for
human K562 cells, containing 82 single gene perturbations with 65,899 samples. ALIGNED
Details of experiment hardware and runtime in Section
222

---

Published as a conference paper at ICLR 2026
(a) Norman al. Dataset
(b) Dixit et al. Dataset
(c)
Adamson et al. Dataset
Balanod Cou..
Data Cress
Knowiedge Cous.
Data Can
Know Cous.
Dats Cans.
Kuow Cous.
ALINED (ONN)
ALIGNED (MI.P)
Linerr
FRARS
Stade
WGP
xd Rirnookko
Figure 3: Balanced, data and knowledge consistency across methods.
predicts perturbation response profiles for all genes in the datasets. Our knowledge base KB integrates the Omnipath GRR (Türei et al, 2016) and the GQ=based gene interac- tion graph from Roohani et al. (2024). covering, 3,949 genes for the Norman et al. (2019) dataset and 2,958 genes for the Dixit et al ( (2016) dataset. To evaluate methods on unseen perturbations, split the test set of Norman single-gene perturbationnssss. and 18 unseen double-gens perturbations. The Dixit et al. (2016) and Adamson et al. (2016) datasets were split randomly.
al (2019) dataset to inchude 19 unseen
We evaluated ALIGNED variants built with an MLP or a KBB-embodded GNN as the neural component. Performance of ALIGNED was compared in Figure g with stato-of-the-att methods including: (i) GEARS, a GNN-based da fa-knowledge hybrid model (Roohani et
2024); (ii) foundation models scGPT (Cui al 2024) and seFoundation (Hao et all 2024 (ifi) a transformer-
model State (Adduri at (ix)) lincaradditivee pertur bation model incorporating regulatory knowledge (Ahlmann- Matann-Eltzee al, 2025). To ensure that all methods are measured on the same knowledge base, ALIGNED does not perform knowledge refinement during this comparison.
The ALIGNED framework with GNN and MLP results in Figure 3 performed adaptive ncuro-symbolic alignment, but not knowledge refinement. For each method, we evaluated (i) data consistency Fj (Y, Ylest) which measures predictive performance; (ii) knowledge con- sislency FY (xx(()) which quantifies the exlent to which the model remains grounded in curated biological prior; and (fii) the balanced consistency metric Fi balance defined as Equation g evaluating the trade-off between inconsistent sources.
Observation 1. In Figure 3 ALIGNED achieved significantly higher knowledge consistency than other mothods, with slightly higher data consistency. consequently outperformed existing methods in balanced consistency. This shows ALIGNED's ability make bet- ter trade-off between inconsistent data and knowledge, enabling the framework to provide mechanistic understandings for black-box neural predictions.
Observation 2. In Figure E after one round of alignment and refinement, ALIGNED improved knowledge consistency significantly while keeping comparable data consistency. This further demonstrates that ALIGNED had learned an effective adaptor function to trade off data- and knowledge-derived information.
4.2 KNOWLEDGE REFINEMENT OF GENE REGULATORY NETWORKS (Q2)
In this section, we aim to answer whether ALIGNED can re-discover biologically meaningful and well-structured knowledge. We tested ALIGNED's knowledge refinement, in isolation and evaluated the refined GRN interactions in three aspects: accuracy (Figure 4a), topology (Figure gbb and pathway enrichment (Figure ge).
We used the accuracy of interactions to test if ALIGNED's knowledge refinement can bekcover_underble regulations from synthetic data generated from OmniPath GRN (Türei et al., 2016). For topology, evaluated the method's ability to produce well-structured
7

---

Published as a conference paper at ICLR 2026
(a) Interaction Accuracy
(b) Network Topelogy
(c) Pathway Enrichment Scores
1.0
Calne Gosts Dtggied XB
1.000
03
Popologtral Stom
0.4
Aserialond Nas-pane Oriiia GRR
-185
Kesepane
Oridial
103
GHN
(Connd)
Spare
Interactions (36)
Incrrcctions
Nekon Intercttoon (96)
Figure 4: GRN knowledge refinement performance with ALIGNED.
GRNs, in terms of: (i) network modularity, for clustering quality of functional mondles Alonn 2007) and (ii) degree assortativity, for regulatory hub structures (Segal et al., 2003). In addition, we examined the method's ability re-discover biologically meaningful interac- tions by cross-referencing external pathway datahases We compareed overlaps with refined pathways using a gene set recovery algorithm (Huang al. 2018) to obtaín pathway en- richment scores.
The original OmniPath GRN (Türei et al. 2016) contains 2,958 genes and 113,056 regulatory interactions. We corrupted the original GRN by randomly adding and removing equal mumbers of interactions at different noise levels, ranging from 5% to 90%, to simulate varying degrees of knowledge base errors. The experiment aimed to recover the original GRN from its synthetic data, using our knowledge refinement method initialized with the noisy GRN.
The non-sparse regularized baseline ablated the refinement mechanism in Equation placing the 1 sparsc regularization term with Frobenius regularization. Existing approaches, such as GRN inference, treat the knowledge base static instcad of performing incremental refinement, and therefore are not suitable for the comparison.
The accuracy was measured in F1 score both direct and indirect interactions (defined as Equation [) of refined GRNs, assuming the original GRN as ground-truth. Network modularity and assortativity were measured on direct interactions of the GRN, with higher modularity scores for better clustering quality, and assortativity is usually negative in GRNs with well-structured regulatory hubs. To show the method's 's ability in re-discovering bio- logically mcaningful interactions, we took 302 pathways from the KEGG pathway databasc KKanehisa et al., 2025) as a cross-reference for gene set recovery, and measured the difference of recovery scores between reconstructed and original GRN for each pathway.
Observation In Figure [a, the accuracy of refined interactions by ALIGNED remained high (Fi > 0.7) even with up to 40% noise. This shows that underlying regulatory knowledge in synthetic data can be captured by ALIGNED.
Observation 2. In Figure o. up to 20% noise, the topological measurements of the refined interactions are similar to those from the original GRN. This demonstrates the ability of ALIGNED in producing well- rell-structured refined GRNs.
Observation 3. In Figure pc. there are no significant differences of enrichment scores between the original and refined GRNs in most pathways. This indicates that ALIGNED can ro-discover biologically meaningful knowledge annotated in cross-reference databases.
4.3 PERTURBATION PREDICTION ON BACTERIAL GENOME (Q3)
We evaluate our method the Escherichia coli (F.. coli) K-12 MG1655 strain using combined dataset. that includes 70 knockout perturbations by Lamoureux et al. (2023) (comprising 4 triple, 7 double, and 59 single perturbations, totaling 433 samples); and data series with 16 overeleeeovrrressssiooo perturbations (73 samples) from the NCBI sequence read archive (Sayers al. 2025). The knowledge basc constructed from the EcoCye GRN
8

---

Published as a conference paper at ICLR 2026
Table 1: Performance of ALIGNED
E.coli genome. The symbol "A" indicates align-
ment stage, and "R" represents a refinement stage. ALIGNED with "A-R" exccutes align-
ment and then refinement, whereas " "A-R-A" performs an additional alignment step.
Model
ALIGNED Stages
Data Cons. Knowledge Cons. Balanced Cons.
MLP GNN
MLP ouly
0.33 0.331220.0004
0.3371 1.000009
0.3341
GNN only
0.3773
0.360544.000 +0.0021
0.3689+0.0012
A
0.387210.0009
0.3708
0.378410..0002
ALIGNED
A-R
0.3872+0.000 0009
0.3836400000
0.3851 +0.0033
(MLP)
A-R-A
0.3812+0 0029
0.4025 000000
0.394404=0.0015
A-R-A-R
0.3812+0.000 0009
0.4045 0038
0.3912+40.013
A
0.387640.. 0000
0.37 1 4 0269
0.3800
ALIGNED
A-R
0.3876+00.0000
7.452041..0mm
0.4130410.0059
(GNN)
A-R-A
0.3878
0.4668 0235
0.4124
A-R-A-R
0.3878:4000061
0.5348 +0.4888+00099 0069
0.4288 +000003
MMoree et al., 2024). covering 315 regulator genes and 3,004 regulated genes. To evaluate generalization unseen instances, split the test set of unseen perturbations including 4 single overexpressions, double knockouts, and 2 triple knockouts.
We tracked performance through a progressively richer procedure of ALIGNED iterations, including the neural-only models trained solely on labelled data and two complete iterations of neuro-symbolic alignment and knowledge refinement.
Table ] performance of prediction, i.e. data consistency, was signifi- cantly improved on unseen perturbations, simultancously improving knowledge and balanced consistency. This indicates ALIGNED's ability of effectively leveraging knowlodge-derived information under limited data availability.
Observation 1.
4.4 ABLATIONS
In Figure E. we compare three progressively richer variants: (i) neural-only model with no symbolic refinement (GNN only) (ii) adaptive neuro-symbolic alignment without refinement (*A") and (iii) the complete ALIGNED framework (*A-R"). Setting (i) GNN trained solely labelled data, with symbolic aligmment or refinement. Setting (ii) adds the aligmment procedure on top of the neural-only baseline, but without updating the knowledge base. Setting (iii) includes both adaptive alignment and knowledge refinement steps. These ablations isolate the contribution of cach component. We observe that adaptive alignmont alone improves knowledge consistency, showing that the adaptor effectively incorporates information ion from the symbolic component. In addition, symbolic refinement provides substantial additional improvement in knowledge consistency, while maintaining accuracy comparable to the neural-only model.
Table 2 reports ablations on KB and the adaptor loss (Equation ! using the Norman al. dataset and GNN as the neural component. We compare ALIGNED with: (i) randomly structured GRN KB; (ii) removal of the inconsistency term inc(a, x, ÿ, KB);; (iii) removal of the knowledge-usage restriction term (a);; and (iv) random weight vector w. The results show: (i) without meaningful prior knowledge, the adaptor defaults to neural predictions; (ii) the inconsistency term encourages stronger alignment with knowledge, at small cost in predictive accuracy; (iii) the usagerresttiction term prevents over-reliance on symbolic predictions; and (iv) the weight vector helps balance predictive performance with appropriate knowledge usage.
5 RELATED WORK
Perturbation Response Prediction. Recent approaches fall into two categories: meth- ods that utilize the compositional nature of genetic perturhations in learning latent repre-
sentations (Lotfollahi et al. 2023: Cui et al. 2024: Hao et al., 2024), hybrid methods that

---

Published as a conference paper at ICLR 2026
(a) Norman et al. Dataset
(b) Dixit al. Dataset
[c] Adamson et al. Dataset
06-
055
0.0
0.90
50om
0.02
0.55
0.55
0.00
11.31
0.43
646
Only
Ouly
Comebtoncy
Anowdolg: Coriierryy
Cknekieery
Figure 5: Performance of the complete ALIGNED framework built with GNN. The symbol " "A" indicates an aligmment stage, and "R" represents a refinement stage. ALIGNED with "A-R" executes alignment and then refinement, whereas "A-R-A" performs an additional alignment slep.
Table 2:
Ablation of KB and La "A" indicates ALIGNED performs one alignment step.
Ablation Settings
ALIGNED
Data
Balanced Knowledge Cons.
Stages
Cons.
Cons.
Default
A
0.5101
0.4172
0.4567
Random KB
A
0.5611
0.3190
0.3921
Remove Inc
A
0.5399
0.3469
0.4127
Remove Lien
A
0.5047
0.4442
0.4715
Random u
A
0.4074
0.6194
0.4813
leverage.prin prior knowleddge from biological networks (Roohanj at.
Corroorrsssooooann Littman et al, 2025) or textual embeddings (Wang et al.. 2024). In contrast, ALIGNED does not assume GR.Ns be static and can systematically refine GRNs by adaptive learning from datasets and knowledge bases to leverage reliable information.
2024 Wenkel al, 2025
Neuro-Symbolic Learning. The Abductive Learning (ABL) framework (Zhou, 2019 integrates deep learning with symboolc const vaints through consistency optimization. Ex- tensions include Metaatd (Dai Mugeletor 2021) for visual-symbolic reatoniesnnnng ABLyc for knowledge refinement (Huang et al, 2023), and AB (Hu al., 2025) for for_efficient neuro-gymbolii integration using reinforcement learning mechanisms. Additionally, (Conello et al (2023) proposed learnable trade-off mechanism between data and knowledge sources. In comparison, ALIGNED does not assume the knowledge base to be fixed or absolutely correct. Since both biological data and curated knowledge exhibit domain-specific noise and incompleteness, ALIGNED jointly aligns neural and symbolic predictions to leverage the most reliable signals and actively refines knowledge bases during training.
CONCLUSION AND FUTURE WORK
In this work, we introduced ALIGNED, novel end-to-end framework that achieves balanced neuro-symbolic alignment and knowledge refinement for predicting genetic perturbation. Importantly, our work not only enhances transparency about the biological relationships behind predictions but also enables the evolution of biological knowledge from large-scale datascts, advancing beyond current black-box approaches.
While we acknowlodge the limitations in our regulatory network modelling, alternative meth- ods (Covert et al. 2004; Stoll al., 2017: Abou-Jaoudé et. al. 2016) face significant scala- bility issues. Future work could explore differentiable models (Faure et al. 2023) and refine them with experimental data. Furthermore, the ALIGNED framework only assumes the availability of a neural predictor and symbolic component with consistency measurement. Therefore, ALIGNED can be extended to different biological tasks by leveraging other prior knowledge, such as protein-pratein interaction networks (Rodriguez-Micr et al. 2025) and motabolic networks (Faure al. 2023).
10

---

Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
We thank our colleagues the European Bioinformatics Institute (EMBL-EBI), Julio Saez- Rodriguez, Aurelien Dugourd, Ricardo O. Ramirez-Plores, Pablo Rodriguez Mier, Philipp Schaefer, and Daniele Bottazzi, for their valuable feedback and discussions throughout the development of this work; our colleagues at Nanjing University, Yu-Feng Li, Xin-Hao Zhu, Jun-Tong Wang, and Jing He, for their discussions and suggestions throughout the initializa- tion and implementation of this work; our collaborators at Imperial College London, Geoff S. Baldwin, Shi-Shun Liang, and Alfie Brown on discussions and directions on biological applications.
REPRODUCIBILITY
Details of experiments and reproducibility are included in Section The code repository is available at https://gituub.comm wttp://wwb.oooo/ylannn11200 (1xiann0112/Aligneee
REFERENCES
Wassim Abou-Jaoudé, Pauline Traynard, Pedro T. Montciro, Julio Sacz-Rodrigues Tomáš Helikar, Denis Thieffry, and Claudinc Chaouiya. Logical Modeling and Dynamical Anal- ysis of Cellular Networks. Frontiers in Genetics. 7, May 2016. ISSN 1664-8021. doi: 10.3389 10.3389/fgene.22 2016 6.00944. URL https::////// http:://wwwfffotieeeeeeee articles/10 3389/fgene 2016 00094/ful1.
pogg/jouraals. /ggeeticc/ggeesss/////cc
Britt Adamson, Thomas M Norman, Marco Jost, Min Cho, James K Nuñcz, Yuwen Chen, Jacqueline E Villalta, Luke A Gilbert, Max A Horlbeck, Marco Y Hein, et al. A multiplexed single-cell crispr screening platform enables systematic dissection of the unfolded protein response. Cell, 167 1882, 2016.
Abhinav K. Adduri, Dhruv Gautam, Beatrice Bevilacqua, Alishba Imran, Rohan Shah, Mohsen Naghipourfar, Noam Teyssier, Rajesh Ilango, Sanjay Nagaraj, Mingze Dong, Chiara Ricci-Tam, Christopher Carpenter, Vishvak Subramanyam, Aidan Winters, Sravya Tirukkovular, Jeremy Sullivan, Brian S. Plosky, Basak Eraslan, Nicholas D. Youngblut, Jure Leskovec, Luke A. Gilbert, Silvana Konermann, Patrick D. Hsu, Alexander Dobin, Dave P. Burke, Hani Goodarzi, and Yusuf H. Roohani. Predicting cellular responses to perturbation across diverse contexts with state. bioRriv, 2025. doi: 10.1101/2025 06.26.661 66115.. URL https: pttps://www/ //www. biorxiv org/ 26. 66.16.1
Matthew Aguirre, Jeffrey P. Spence, Guy Sella, and Jonathan K. Pritchard. Gene regulatory network structure informs the distribution of perturbation effects. PLOS Computational Biologu. 21(9)11331, 09 2025. doi: 10.1371 1..11//journal cetrrnal..cbb.lu.e pcbi.1013387 org/10. 1371/ wwb.pccbio.... 1013387
URL Attps://dol
Constantin Ahlmann-Eltz Wolfgang Huber, and Simon Anders. Deep-learning- based gene perturbation effect prediction does not yet outperform simple linear baselines. Nature Methods, pp. 1-5, 2025.
Lun Ai. Boolean matrix logic programming on the gpu, 2025. URL https://arxiv.org abs/2408.
Uri Alon. Network motifs: theory and experimental approaches. Nature Reviews Genetics, 86)):450-661, 2007.
Michael Ashburner, Catherine A. Ball, Judith A. Blake, David Botstein, Heather Butler, J. Michael Cherry, Allan P. Davis, Kara Dolinski, Selina S. Dwight, Janan T. Eppig, Midori A. Harris, David P. Hill, Laurie Issel- Tarver, Andrew Kasarskis, Suzanna Lewis, John C. Matese, Joel F. Richardson, Martin Ringwald, Gerald M. Rubin, and Gavin Sherlock. Gene ontology: tool for the unification of biology. Nature Genetics, 25(1):25-22 29. doi: 0..1038/75551 URL https://tdai http:://do..org/1..1 1038/75566
May 2000. ISSN 1546-1711
11

---

Published as a conference paper at ICLR 2026
Pau Badia-i Mompel, Lorna Wessels, Sophia fiiler-Dottt Rémi Trimbour, Ricardo O. Ramirez Flores, Ricard Argelaguet, and Julio Maez-Rodriguez. Gene regulatory net- work inference in the era of single-cell multi-omics. Neture Reviews Genetics, 24(11): 739 754. November 2023. ISSN 1471-0064. doi: 10.1038 - https://www
94415776-023-00611-55 URL
https://www.nature.com www.anaattt.earrreee wwtpc///arr..cceee///11000033330
Ihab Bendidi, Shawn Whitfield, Kian Kenyon-Dean, Hanene Ben Yedder, Yassir El Mesbahi, Emmanuel Noutahi, and Alisandra K. Denton. Benchmarking Transcriptomies Founda- tion Models for Perturbation Analysis : one PCA still rules them all, November 2024.
URL http:://t/tatt /tarxiv//xxvvvv/// org aat///////////// 13956. ar arXiv:2410. 13:556 [cs].
Emmanuel Candes and Benjamin Recht. Exact matrix completion via convex optimization. Communications of the ACM, 55(6):111-119, 2012.
Safiye Celik, Jan-Christian Hütter, Sandra Melo Carlos, Nathan H. Lazar, Rahul Mo- han, Conor Tillinghast, Tommaso Biancalani, Marta M. Fay, Berton A. Earnshaw, and Imran S. Haque Building, benchmarking, and exploring perturbative maps of tran- scriptional and morphological data. PLOS Computational Biology, :0110264 October 2024. ISSN 1553-7358 doi: 10.1371 pcb. //journals plos. wwwps.oro/pp..pppp.p...p..p www.scommmoollartiillleeee. 1tt.://:.....11//ooo/ooo.ooo pcb.i 1012463.
URL https:
Mathieu Chevalley, Yusuf H. Roohani, Arash Mehrjou, Jure Leskovec, and Patrick Schwab. A large-scale benchmark for network inference from single-cell perturbation data. Communications Biology, 8(1):412, March 2025. ISSN 2399-3642. doi: 10.1 -22003-05-077644-y URL https://www http:///wwwwnnuuu.eeeeee nature. wwt.a//arttcccle///2000055553351
Cristina Cornelio, Jan Stuehmer, Shell Xu Hu, and Timothy Hospedales. Learning where and when to reason in neuro-symbolic inference. 2023. URL https://openrevie..u
forum?id=en3V5FPPR
Markus W Covert, Eric M Kuight, Jennifer Reed, Markus Herrgard, and Bernhard O Palsson. Integrating high-throughpu and computational data elucidates bacterial net- works. Nature, (298879))9922-99 96, 2004.
Haotian Cui, Chloc Wang. Hassaan Maan, Kuan Pang, Fengning Luo, Nan Duan, and Bo Wang. segpt: toward building foundation model for single-cell multi-omics using generative ai. Nature methods, 21 (8):114770- 1480, 2024.
Wang- Zhou Dai and Stephen Muggleton. Abductive knowledge induction from raw data. In Zui-Hua Zhou (ed.), Proceedings of the Thirtieth International Joint Conference Artificial Intelligence, IJCAI-21, pp. 1845 1851. International Joint Conferences doi: 1244996//jaai20222 stttps://oii. www.:/..../././..... 24963/1jcai.200 2021/254
on Artificial Intelligence Organization, 2021.
URL
Atray Dixit, Oren Parnas, Biyu Li, Jenny Chen, Charles P Fulco, Livnat Jerby-Arnon, Nemanja D Marjanovic, Danielle Dionne, Tyler Burks, Raktima Raychowdhury, et al. Perturb-seq: dissecting molecular circuits with scalable single-cell rna profiling of pooled genetic screens. cell, (6)111)8533-188)) 2016.
Léon Faure, Bastien Mollet, Wolfram Liebermeister, and Jean-Loup Faulon. A neural- mechanistic hybrid approach improving the predictive power of genome-scale metabolic models. Nature Communicattins., 14(1):4669, 2023.
George I. Gavriilidis, Vasilcios Vasileion, Aspasia Orfanou, Naveed Ishaque, and Fo- tis Psomopoulos. A mini-reviow on perturbation modelling across single-cell omic modalities. Compulational and Struclural Biolechnology Journal, 23:1886 1896, 2024. ISSN 2001-0370. doi: http::://cbi..oog..0000///L.eiid wttp:ttt..ccccccccccceeececcece oet.epawe..a.c.c.c..cccccccaaaae
05.0 URL https://wwwt
Minsheng Hao, Jing Gong, Xin Zeng, Chiming Liu, Yucheng Guo, Xingyi Cheng, Taifeng Wang, Jianzhu Ma, Xuegong Zhang, and Le Song. Large-scale foundation model on single-cell transcriptomics. Nature methods, 28 2024.
12

---

Published as a conference paper at ICLR 2026
Wen-Chao Hu, Wang-Zhou Dai, Yuan Jiang, and Zhi-Hua Zhou. Efficient rectification of neuro-symbolic reasoning inconsistencies by abductive reflection. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 17333 113311 2025.
Justin K Huang, Daniel E Carlin, Michael Ku Yu, Wei Zhang, Jason F Kreisberg, Pablo Tamayo, and Trey Ideker. Systematic evaluation of molecular networks for discovery of disease genes. Cell Systems, 6(4)::84-4955 -94.8,,595.., April 2018.
Yu-Xuan Huang, Wang-Zhor Zhou Dai, Yuan Jiang, and Zhi-Hua Zhou. Enabling knowlodge ro- finement upon new concepts in abductive learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 7928 7935, 2023.
Yannis E. Toannidis and Eugene Wong. Towards an algebraic thoory of recursion. Journal of the ACM. 389 381. 1991. ISSN 0004-5411. doi: 041115/113511.1000 URL https://di acm. www.oogg/..oo/ooooooooooo /ot///.1..////
Minoru Kanehisa, Miho Furumichi, Yoko Sato, Yuriko Matsuura, and Mari Ishiguro- Watanabe. KEGG: biological systems database as a model of the real world. Nucleic Acids Res., (3(D1):D6722D677 Jamuary 2025.
Kasia Z. Kedzierska, Lorin Crawford, Ava P. Amini, and Alex X. Lu. Zero-shot evaluation reveals limitations single-cell foundation models. Genome Biology, 26(1):101, April 2025. ISSN 1474-760X. doi: 10.1186 (01/86/111399-000 025-037447 URL hthps://ddo.org//// 1186/s13059- 03574-x
Purvesh Khatri, Marina Sirota, and Atul J Butte, Ten years of pathway analysis: current approaches and outstanding challenges. PLo8 computational biology, 8(2), 2012.
Jong Kyoung Kim, Aleksandra Kolodziejezyk, Tomislav Tlicic, Sarah Teichmann, and John C Marioni. Characterizing noise structure in single-cell RNA-seq distinguishes gen- uine from technical stochastic allelic expression. Nature Communications, 6(1):8687, Oc- tober 2015.
Cameron R Lamoureux, Katherine T Decker, Anand V Sastry, Kevin Rychel, Ye Gao, John Luke McConn, Daniel C Zielinski, and Bernhard O Palsson. A multi-scale ex- pression and regulation knowledge base for Escherichia coli. Nucleic Acids Reseorch, 51(19):10176 10193, October 2023. ISSN 0305-1048. doi: 10.1093 10.1093/nar/gkaddte gkk///7750. URL https://doi. htt.://..rrrg...../////a/aa///// 10t.0/0000/////gaaa//// gkad750.
Russell Littman, Jacob Levine, Sepideh Maleki, Yongju Lee, Vladimir Ermakov, Lin Qiu, Alexander Wu, Kexin Huang. Romain Lopez, Gabriele Scalia, Tommaso Biancalani, David Richmond, Aviv Regev, and Jan- Christian Hütter. Gene-embeddingg based prediction and functional evaluation of perturbation expression responses with PRESAGE, June 2025.
URL https: //ww:/ biorxiv.....iv..... org///oot//ooo httpa/ttetnnt...1100222......0. www.11100022000000 06. 03. 657653v1
Siyan Lin, Marisa C Hamilton, Thomas Cowart, Alejandro Barrera, Lexi R Bounds, Alexan- der C Nelson, Sophie Dornbaum, Julia W Riley, Richard W Doty, Andrew S Allen, Gregory E Crawford, William H Majoros, and Charles A Gersbach. Characteriza- tion and bioinformatic filtering of ambicnt gRNAs in single-cell CRISPR screens using CLEANSER. Cell Genomics, 5(2), February 2025.
Mohammad Lotfollahi, Anna Klimovskaia Susmelj, Carlo De Donno, Leon Hetzel, Yuge Ji, Ignacio L Ibarra, Sanjay R Srivatsan, Mohsen Naghipourfar, Riza M Daza, Beth Martin, ct al. Predicting cellular responses to complex perturbations in high-throughput screens. Molecular systems biology, 19(6) 2023.
Michael 1 Love, Wolfgang Huber, and Simon Anders. Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol., 15(12):550, 2014.
Zhen Lu, Imran Afridi, Hong Jin Kang, Ivan Ruchkin, and Xi Zheng. Surveying neuro- symbolic approaches for reliable artificial intelligence of things. Journal of Reliable Intel- ligent Environments, 10(3):257 279, September 2024.
13

---

Published as a conference paper at ICLR 2026
Jack Minker. Foundations of Deductive Databases and Logic Programming. 1988.
Lisa R Moore, Ron Caspi, Dana Boyd, Mchmet Berkmen, Amanda Mackic, Suzanne Paley, and Peter D Karp. Revisiting the y-ome of escherichia coli. Nucleic Acids Research. 52
(20):12201 12207, 10 2024. ISSN 0305-1048. doi: 10.1093/nat garr/k URL https:
//doi.org//i 1ww.11009//////ae ggka8877
Ajay Nadig, Joseph M Replogle, Angela N Pogson, Mukundh Murthy, Steven A McCarroll, Jonathan S Weissman, Elisc B Robinson, and Luke J O'Connor. Transcriptome- wide analysis of differential expression in perturbation atlases. Nature Genetics, 57(55)1228 1237, May 2025.
Thomas M Norman, Max A Horlbock, Joseph M Replogle, Alex Y Ge, Albert Xu, Marco Jost, Luke A Gilbert, and Jonathan Weissman. Exploring genetic interaction manifolds constructed from rich single-cell phenotypes. Science, 365(6455) 786 793, 2019.
Stefan Peidli, Tessa D Green, Ciyue Shen, Torsten Gross, Joseph Min, Samuele Garda, Bo Yuan, Linus J Schumacher, Jake P Taylor-King, Debora Marks, et al. seperturb: harmonized single-cell perturbation data. Nature Methods, 21(3):531-540, 2024.
Siamak Ravanbakhsh, Barnabas Poczos, and Russell Greiner. Boolean matrix factoriza- tion and noisy completion via message passing. In Maria Florina Balcan and Kilian Q. Weinberger (eds.), Proceedings of The 33rd International Conference Machine Learn- ing, volume 48 of Proceedings of Machine Learning Research, pp. 945-954. New York, New York, USA, 20 22 Jun 2016. PMLR. URL https://proceeednng.. mlr. press/v48/ ravanbakhsha16 1htmm
Joseph M. Replogle, Reuben A. Saunders, Angela N. Pogson, Jeffrey A. Hussmann, Alexan- der Lenail, Alina Guna, Lauren Mascibroda, Eric J. Wagner, Karen Adelman, Gila Lithwick-Yane Yanai, Nika Iremadze, Florian Oberstrass, Doron Lipson, Jessica L. Bonnar, Marco Jost, Thomas M. Norman, and Jonathan Weissman. Mapping information- rich genotype-phenooopee landscapes with genome-scale Perturb-seq. Cell, 185(14):2555) 2575.e28, July 2022. ISSN 0092-8674. doi: 10.101//11.e112222000... htt.a//cww..a.tto..c......./eeea
URL https:
Pablo Rodriguez-Mier, Martin Garrido-Rodriguez, Attila Gabor, and Julio Saez- Rodriguz. Unifying multi-sample network inference from prior knowledge and omics data with CORNETO. Nature Machine Intelligence, 7(7): 1186, July 2025. ISSN 2522- 5839. doi: 10.1038/s422566 011225660225-0069-3 s42256 025-01069-9
URL https://ww/ www.we.ture...m cow.ereiccm/rtrrsess....
Neha Rohatgi, Jean-Philippe Fortin, Ted Lau, Yi Ying, Yue Zhang, Bettina I Lee, Michael R Costa, and Rohit Reja. Seed sequences mediate off off-target activity in the CRISPR- interference system. Cell Genomics, 4(11), November 2024.
Yusuf Roohani, Kexin Huang, and Jure Leskovec. Predicting transcriptional outcomes of novel multigene perturbations with gears. Nature Biolechnologu. 42(6):927 935, Jun 2024. ISSN 1546-16999 doi: 0010088/411887-02--010953 URL http:://ddi.orr////
1038/8415877003-010055
Violaine Saint-André. regulatory networks. Compulalional and Structural Biotechnology Journal, 19:4884- 4895. 2021. ISSN 2001-0370. doi: http::://doi..og110100010011
Computational biology approaches for mapping transcriptional
.08.028. URL
Eric W Sayers, Jeffrey Beck, Evan E Bolton, J Rodney Brister, Jessica Chan, Ryan Con- nor, Michael Feldgarden, Anna M Fine, Kathryn Funk, Jinna Hoffman, Sivakumar Kan- nan, Christopher Kelly, William Klimke, Sunghwan Kim, Stacy Lathrop, Aron Marchler- Bauer, Terence D Murphy, Chris O'Sullivan, Erin Schmieder, Yuriy Skripchenko, Adam Stine, Francoise Thibaud-Nissen Jiyao Wang, Jian Ye, Erin Zellers, Valerie A Schneider, and Kim D Pruitt Database resources of the national center for biotechnology informa- tion 2025. Nucleic Acids Res., 53(D1))D20-D29) Jamuary 2025.
14

---

Published as a conference paper at ICLR 2026
Eran Segal, Michael Shapira, Aviv Regev, Dana Pe'er, David Botstein, Daphne Koller, and Nir Friedman. Module networks: identifying regulatory modules and their condition- specific regulators from gene expression data. Nature genetics, 34(():166-177 2003.
Gautier Stoll, Barthélémy Caron, Eric Viara, Aurélien Dugourd, Andrei Zinovyev, Aurélien Naldi, Guido Kroemer, Emmanuel Barillot, and Laurence Calzone. MaBoSS 2.0: an environment for stochastic Boolean modeling. Bioinformatics, 33(14):2226 2228 July 2017. ISSN 1367-4803. doi: 10.1093/ http///iooooomatie/bbaaeaee btxl112. URL https: / oraaiiissttomaattitttt//xxx2
Alfred Tarski. A lattice- fixpoint theorem and its applications. Pacific Journal of Mathematics, 5(2):85 309, 1955. doi: doi:10.2140/pp http:/ppmm1995...... 1955.5.285.
Christina V. Thcodoris, Ling Xiao, Anant Chopra, Mark D. Chaffin, Zcina R. Al Sayed, Matthew C. Hill, Helene Mantineo, Elizabeth M. Brydon, Zexian Zeng, X. Shirley Liu, and Patrick T. Ellinor. Transfer learning enables predictions in network biology. Nature, 618(7965):616-622 June 2023. ISSN 1476-4687, doi: 10. 0188////1186-02---110 httpp://ww, nature. cwm/ wwom//rticles/eeeeeeeeeeeee s4158 023 06139--
URL
Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Sociely Series B: Stalistical Melhodologu, 58(1):267 288, 1996.
Dénes Türci, Tamás Korcsmáros, and Julio Sacz-Rodriguez. OmniPath: guidelines and gateway for literature-curated signaling pathway resources. Not. Methods, 13(12):966- 967, nov 2016.
Gefei Wang, Tianyu Liu, Jia Zhao, Youshu Cheng, and Hongyu Zhao. Modeling and pre- dicting single-cell multi-gene perturbation responses with sclambda. bioRrie, 2024.
Frederik Wenkel, Wilson Tu, Cassandra Masschelein, Hamed Shirzad, Cian Fastwood, Shawn T. Whitfield, Ihab Bendidi, Craig Russell, Liam Hodgson, Yassir El Mesbahi, Jiarui Ding, Marta M. Fay, Berton Earnshaw, Emmanuel Noutahi, and Alisandra K. Denton. TxPert: Leveraging Biochemical Relationships for Distribbtitt Transcrip- tomic Porturbation Prediction, May 2025. URL http://arxiv org/ atwgg/////////.../////// 14919 sxXiv:2505.14911 [cs].
http:///arr....oog/b///5555..
Ronald J. Williams. Simple statistical fralient-following algorithms for connectionist rein- forcement learning. Machine Learning, 8(3):229 256. May 1992. ISSN 1573-0565. doi:
10.1007/BF0099220 URL https://doi.org/ org/ 100000000//00/ 1007///000000////09922556
Zhi-Hua Zhou. Abductive learning: towards bridging machine learning and logical reasoning. Science China Information Sciences, 62(7):76101, 2019.
Pedro Zuidberg Dos Martires, Vincent Derkinderen, Luc De Raedt, and Marcus Krantz. Automated reasoning in systems biology: necessity for precision medicine. In Proceedings of the International Conference on Knowledge Representation and Reasoning, 2024.
A USAGE OF LARGE LANGUAGE MODELS
We used Claude and ChatGPT mainly to polish the language after all intellectual content has boen drafted, along with Grammarly as a language oditing tool.
B DETAILS OF THE KNOWLEDGE BASE
B.1 FORMAL DEFINITION
With regard to positivity of edges, the GRN be represented datalog program (Minker, 1988) with two predicates, regulates, /2 and regulates_ where genes are constant names. We use the transitive closure of regulates, and regulates_ as the knowledge base
15

---

Published as a conference paper at ICLR 2026
Figure 6: A 5-node GRN example.
k
k=1
k
k=
Figure 7: A demonstration of approximative lixpoint.
in the reasoning component of our framework, denoted as as and r /2_ The transitive closure can be evaluated as a bilinear recursive program (loannidis & Wong
1991):
r+ (regulates+ (a, c) (c, b)) V (aguulates-aa, Ar r- + (regulates+ (a, c) A r- (c. b)) v (regulates (a, (c)
r4 (a, regulates (a, b)
r (a b) + regulates_
(7)
The transitive closure represents all regulatory pathways, accounting for the indirect effects of positive and negative regulation. The recursive program states that all direct positive (negative) regulations are included in the positive (negative) transitive closure, while an in- direct pathway containing an even number of negative regulations contributes to the positive closure, and an odd number negative regulations contributes the negative closure. The datalog program can then be compiled as recursive Boolcan matrix multiplication (Equa-
tion 1), where matrices of positive (negative) direct regulations R. compiled from regulates,, regulates_:
R (0, 10xn are
[1,
regulates (i,j)
= {t.
regulates- (i.
(R
(R
(, otherwisc
otherwisc
and indirect regulation matrices (
R(N) are computed from Equation
B.2 DEMONSTRATION
For nodes example GRN in Figure simple demonstration of the approximative is shown as Figure
fixpoint of regulatory interactions (Equation
In this example, RDO R (0)
compiled as:
0
1
0
0
0
0
0
0
0
0
R
0
1
1
0
R
(
0
0
0
1
0
0
1
16

---

Published as a conference paper at ICLR 2026
and the symbolic prediction when & = 2 is:
1
0
1
1
1
0
0
0 I
0
0
0
0
? R (
0
1
1
1
0
0
1
0
0
1
i
0
0
0
0
1
0 0
0
0
0
And (n m 0 for k x 4 in this example, due to the negative feedback loop.
B.3 DISCUSSION
Our modelling of regulatory ellect given by Equation | does not assume that activating and inhibitory effects combine through simple additive rules. The formulation patl-dependent and encodes how positive and negative regulations compose across multi-step pathways. However, such modelling still not enough to describe the biological reality, and future work could further explore the other differentiable modelling approaches of genome-scale GRN under the ALIGNED framework.
In actual experiments in Section 4.1. we introduced an assumption that up/down regulation of a node can be decided by its in-degree of positive and negalive interactions, order to capture more detailed regulatory behaviours. This is achieved by using an integer variant. of Equation In this setting, the value node in Figure [ will be -1 when & = 2, i.e. 6 (i(") ") (x) [0, 1, - and the network behaviour will be more complicated in complex networks.
C DISCUSSIONS OF CONVERGENCE
The convergence of the ALIGNED iterations is guaranteed under certain theoretical as- sumptions. The inconsistency measurement defined in Equation non-negative, lower- bounded by O. Since both the neural and the symbolic component are updated with the neuro-symbolic prediction (Xu, Ya) in each iteration, the inconsistency measurement re- duces the following assumptions hold: (a) the neural prediction Y, aligns better with Y, after update, and (b) the symbolic prediction 5xz(X, aligns better with Y, after the knowledge refinement. Therefore, the inconsistency decreases monotonically until it reaches fixed point, where further updates to either module no longer reduce disagreement and the ALIGNED reaches convergence.
In practice, ALIGNED also converges when the assumptions (a), (b) do not strictly hold in theory. Empirically, the iterations are observed to stabilize within a small number of iterations (lypically 2-3), as shown in Figure
D FRAMEWORK OVERVIEW
Additional demonstrations for the ALIGNED framework, including an overview figure Fig- ure and pseudo-code Algorithm are included here.
17

---

Published as a conference paper at ICLR 2026
KB
trimerippiioal regolatory
0
8(x) = (x'
A
(x
deduce
spary consistency
ML
-
0
fa
0
prodict
pretrain
Y
y
(xx
X
Fevise
retrain
Figure 8: The ALIGNED framework. The mueral component is marked in blue, and the symbolic component ingreen.
Algorithm 1: ALIGNED Framework
input Labelled dataset D; = (X1, Yi); Unlabelled dataset Da, X.;;
Gene interactions ( R. R!))) Iteration limit T
output: Trained neural model fa);
Updated knowledge base KBB
KB + (R(), R!))
(Sy, fa) + train (1,, KB,;
for 1 5
do
Ý + (X,);
A - (a(),);
8KB + X. (R
R (0)
Y (Y Yij.
Aij 0
Fig ōKB( Xx.)is,
Aij 1
(av + uupuatttX..... Xu, Y.);
KBB -- refine(X, Yu,KB) KB)
10 end
E EXPERIMENT DETAILS AND REPRODUCIBILITY
E.1 REPRODUCIBILITY AND CODE AVAILABILITY
Unless specified, our experiments on ALIGNED and other methods used random seeds to split for training, validation and test set.
E.2 HARDWARE AND RUNTIME
All experiments were conducted using single Intel Xeon Gold 6342 CPU (2.80 GHz, 32 GB memory) and single NVIDIA A100 GPU (80 GB). Training ALIGNED took an average of 10-12 hours per run. Under our experimental sctup, the training time of ALIGNED manageable given the size of the GRN and the complexity of the refinement procedure.
18

---

Published as a conference paper at ICLR 2026
E.3 HYPERPARAMETERS
In Section
4.1. koy hyperparameters of our ALIGNED method as follows:
A in Equation 1
w 0.5(
Σ y (z) ( ( +0.2(
E (R +..
+ R {.2)//n)) +0.3coo in Equation g
E.EE(X.
13t5
tuned on Norman et al. (2019) dataset and Türei et al. (2016) knowledge base, where (X, Y)
the training dataset, KB = (R _R!h)) is the knowledge base, n is the total number of genes. Cao is the number of GO annotations for each gene, normalized to [0,
The weight vector w computed separately for each dataset, but always using the same fixed procedure above. In particular, the component of w that reflects dntw-knoweedge inconsistency derived only from the training split, while the other components encode priors from the structured knowledge bases. This makes dataset-specifie but non-hand- tuned quantity.
y 5 in Equation
C 10, G 0 0.3/a] in Equation f
C
10 in Equation
1, to = 100 and ig = 1 in Equation
E.4 EXPERIMENTS ON HYPERPARAMETERS OF THE ADAPTOR
To study the effect ALIGNED's overall performance of each hyperparameter, con- ducted a comparison of different parameter selection of k in Equation 4 0 in Equation 4
t in Equation L. as well as different computing for in Equation 4. The comparison in
Table [ was ran for 2 ALIGNED loops, and we report the performance at neuro-symbolic alignment of the first loop (Align 1) since the hyperparameters put most effect on the behavior of the adaplor, as well as the performance at the end of the loops (Refine 2).
All comparisons were performed on the Norman al. (201g) dataset with GNN as the neural component, including the default seiting in Section 4.1 (denoted as "default", with k = 4, in
= 0.3 and w computed as Section E.3), different values of k, 0, and seffferett.coeffccieee computing ("term i +" means that the i-th term's coefficient in Section E.3 w's formula increased by 0.1, following by clipping the w 's elements to keep in [0, 1])
The results in Table / indicate that, maximum allowed pathway length (k) in the modelling of KB is positively correlated with data consistency (predictive performance on test data), but negatively correlated with the knowledge consistency. The threshold of KB usage (0) has a minor effect on encouraging KB usage with higher 0. Term coefficients in w''s formula has a positive effect balanced consistency, in comparison with setting all elements of w to 0.5. Every term in w's formula is positively correlated with knowledge consistency but slightly compromises data consistency.
E.5 EXPERIMENTS HYPERPARAMETERS KNOWLEDGE REFINEMENT
We conducted experiment in Section 4.2 to examine the effect, of the approximation coeffi- cient &ę and to Equation & The default sctting in Section 4.2 (to 100,4, = 1) denoted as "Default" and the performance was compared in F1 score of direct interactions, same knowledge refinement is posi-
with Figure A.. As shown Table 4. the performance lively correlaled with to and lg- Larger values of to and 4 than default have diminishing improvement returns performance. Generally, larger values of ly and 4 require higher computational resource. Therefore, we decided on the current default values based on both performance and computational cost.
E.6 DATASET SPLIT
The detail of train-test data split in Experiment of Section 4.1 is shown in Table
19

---

Published as a conference paper at ICLR 2026
Table 3: Performance of ALIGNED on different hyperparameter selections. The symbol "A" indicates an alignment stage, and "R" represents a refinement stage. ALIGNED with "A" exccutes one alignment step, whereas "A-R-A-R" performs two rounds of alignment and refinement steps.
ALIGNED
Data
Knowledge Cons.
Balanced Cons.
Operation
Stages
Cons.
GNN only delault
0.5344
0.3823
0.4397
default
0.5101
0.4172
0.4567
=
0.4426
0.3270
0.3719
0.4960
0.4545
0.4738
k
0.5129
0.4159
0.4568
0.1
0.5148
0.4051
0.4502
A
0 = 0.5
0.5047
0.4442
0.4715
w 0.5
0.3944
0.6381
0.4744
term 1
0.4993
0.6577
0.5624
w: term 2 +
0.5120
0.4335
0.4678
term 3
0.4999
0.4294
0.4606
default
0.5233
0.6570
0.5788
k
0.4377
0.3388
0.3788
0.5115
0.6416
0.5656
0.5028
0.6606
0.5658
= 0.1
0.5254
0.6549
0.5795
A-R-A-R
0 0.5
0.5175
0.6607
0.5761
W = 0.5
0.4047
0.6476
0.4853
W: term 1 +
0.5003
0.6509
0.5609
w: term 2 +
0.5226
0.6614
0.5798
w: term 3
0.5099
0.6582
0.5700
Table Performance of knowledge refinement on different hyperparameter selections
Noisy
to 1000,
to 10,
Default
Interactions
ty = 10
fę = 0.1
0%
0.8896
0.9052
0.6726
5%
0.8554
0.8895
0.6262
10%
0.8339
0.8753
0.5921
30%
0.7894
0.8181
0.5347
50%
0.7233
0.7604
0.5357
F ADDITIONAL RESULTS
F.1 CURATION EFFORT AND KB PREDICTION CONTRIBUTION
We conducted experiment to stratify edges in OmniPath by their curation effort (a proxy for knowledge reliability) and measured how oflen the adaptor selects the symbolic versus neural predictions in each regime. ALIGNED did pot have access to this curation ellort information during training. Our results in Table show that the adaptor automatically down- weights the symbolic predictions when the GRN is less reliable (low curation effort) and relies more heavily on the noural predictor in those cases. Conversely, when the edges in KB are better curated, the adaptor increases its symbolic usage.
20

---

Published as a conference paper at ICLR 2026
Table 5: Test dataset split in Experiment of Section 4.1
Dataset
Replicates
Test sct perturbations
FEV, TBX3, AHR, SIPR2, TBX2,
MAP7D1, ZBTB1, OSR2, ISL2, BPGM,
SGK1, MAP7D1, PRDM1, UBASH3B + OSR2,
PRDMI CBFA2T3, SGK1 TBX3, TBX3 TBX2, PTPN12 + OSR2, BPGM + SAMD1,
Norman
AHR + KLFF1, FEV MAP7D1, SAMD1 + ZBTBI,
CEBPB + OSR2, SGKI S1PR2, FEV + ISL2,
SGKI TBX2, ETS2 MAP7D1, AHR FEV,
FEV + CBFA2T3, FOSB + OSR2, BPGM + ZBTBI
ELFI, E2F4, CIT, CEP55, AURKA
2
ELKI, NR2C2, ECT2, CENPE
Dixit
ELKI, E2F4
CENPE TORTAIPI, RACGAPI GABPA, F2F4, CENPE
DDIT3, OST4, SEC61A1, HARS, TARS2, SOCS1, MRGBP, MTHFD1, TMEM167A, TTI2, SLC39A7, MRPL39, SEC63, MARS, ARHGAP22, E1F2S1, TIMM44, PTDSSI, CHERP, SRPRB, DHDDS, COPZI, CARS, РАHB
Adamson
BHLHE40, DDIT3, SAMM50, MTHFD1, EIF2B2, PSMD4 EIF2S1, CCND3, PPWD1, COPZ1, EIF2B3, XRNI, TMED2, SPCS2
DASAMM50, MRGBP, TMEM167A, NEDD8, HSPA9, MRPL39, FARSB, HSDI7B12, SEC6IB, ASCC3, ARHGAP22, HSPA5, CHERP
ZNF326, DDIT3, OST4, QARS, MRGBP, MRPL39, SEC63, MANF, HSD17B12, SARS,
4
TIMM44, DDOST, SLC35B1, CCND3, EIF2B3, XRNI, TMED2, SPCS3
ZNF326, BHLHE40, SEC61A1, TER3IPT, YIPF5,
LARS2, ATP5B, MTHFD1, GNPNATI, TARS,
PSMD4, CHERP, DHDDS, DNAJC19
Table 6: Knowledge vs. data usage across curation effort levels
Curation Effort Knowledge Usage
Data Usage
0
13.3%
86.7% 7%%
1,5)
24.7%
75.3%
5,10)
31.9%
08.1%
2 10
31.7%
68.3%
F.2 GRN FAILURE MODES
We experimented using multiple external knowledge sources built by Chevalley el al. (2025) include STRINGdb (PPI), CORUM (PPI) and ChipSeq network derived from Chip Atlas and ENCODE, as independent cross-references,
We stratified gene pairs into three categories: (i) not regulated in both (sparse), (ii) regulated in both (high confidence), (iii) regulated only in our XB or in reference (low confidence). The rationale is that interactions supported by both KB (OmniPath) and an external reference are more likely to be reliable, whereas interactions found in only one source may systematic errors. The results in Table demonstrate that.
imply biases, incompleteness, when coverage is sparse or inconsistent, ALIGNED relies heavily on the neural component
21

---

Published as a conference paper at ICLR 2026
( 90%).. This prevents the model from propagating uncertain symbolic signals. In addition, when prior knowledge is less reliable, the symbolic component contributes less to the overall predictions compared to high-confidence edges.
Table 7: Knowledge vs, data usage comparing with external databases
Database
Edges
Knowledge Usage
Data Usage
sparse STRINGdb high confidence
10.5%
89.5%
74.6%
25.4%
low confidence sparse CORUM high confidence
54.8%
45.2%
89.4%
10.6%
16.9%
83.1%
low confidence sparse high confidence
28.2%
71.8%
89.4%
10.6%
ChipSeq
25.4%
74.6%
low confidence
29.4%
70.6%
F.3 INTERACTION RECOVERY
We randomly sampled interactions (3 replicates) from our KB that simullaneously exists in PPI database (STRING or Corum) and the ChipSeq network by Chevalley et al. (2025), which we believe that they tend to be true interactions with a high confidence. We removed them selected interactions from our KBB, ran ALIGNED using the KCB with removed edges and examined whether the removed interactions can be recovered after 2 alignment refinement iterations.
The selected interactions and the performance of recovery are listed in Table The results show that the ALIGNED iterations are able to correct potential noise and incompleteness in KB using neural predictions.
Table Recovery rate of confident interaction removal
Replicate Recovered/ Total
Interactions
JUN CTNNBI, SPII FCGRT, CEBPA SPI1,
CEBPB TGFB1, CEBPB GDF15, CEBPB TRIB3,
11/12
CEBPB HSP90AA1, CEBPB RUN X2, CEBPA CEBPE,
JUN BEX2, JUN GSTP1, JUN KRT18
JUN CTNNBL, JUN GSTPI, CEBPB TGFBI,
CEBPB CEBPA, CEBPB TRIB3, CEBPB HSP90AA1,
2
10/10
CEBPB DDIT3, CEBPB GST P1, CEBPB CSF3R,
CEBPA CEBPE
JUN STMNI, JUN MYC, JUN GSTP1, JUN VIM,
JUN KRT18, SPN FCGRT, CEBPB CSF3R, CEBPB RUNX2, CEBPB -
3
10/11
CEBPB GDF15, CEBPA CSF3R
F.4 CROSS-REFERENCE FOR SECTION 4.2
We extended the GRN refinement experiment in Section with additional cross-reference comparisons using external databases built by Chevalley et al. (2025). Performance of the knowledge refinement is measured via comparing the accuracy of GRN after refinement contrasting with the reference database, terms of Fj score. The performance is compared with the non-sparse baseline (using Frobenius regularization), noted in Section 4.2 Our results are shown in Table g. The results demonstrate that our method able to learn interactions that are verified by external reference sources.
22

---

Published as a conference paper at ICLR 2026
Table 9: GRN after refinement contrasting with reference databases in terms of Fi
Method Noisy Interactions
STRINGdb
CORUM
ChipSeq
0%
0.4561
0.0310
0.2015
5%
0.4406
0.0293
0.1814
ALIGNED
10%
0.4271
0.0270
0.1764
30%
0.4093
0.0258
0.1714
50%
0.3706
0.0207
0.1363
0%
0.2644
0.0058
0.0372
5%
0.2600
0.0054
0.0350
Non-sparse
10%
0,2685
0.0074
0.0530
30%
0,2351
0.0041
0.0315
50%
0.0472
0.0002
0.0018
F.5 SHORTCUT REGULATIONS SECTION 4.2
To examine whether the knowledge refinement learns undesirable shortcut signals from the data, we extended the GRN-refinmmnnl experiment in Section 4.2 by comparing the proportion of direct versus indirect interactions after knowledge refinement on the noisy GRN. We evaluated how many direct and indirect interactions in the original GRN were learned, where direct interactions desired and indirect interactions represents shortcut regulatory effects in the data.
The results in Table 10 show that ALIGNED's refinement prodominantly recovers direct interactions, while indirect ones remain limited. In contrast, the non-sparse baseline (using Frobenius regularization) overfits to indirect interactions. These findings suggest that our sparse refinement strategy effectively guards against overfitting to shortcut signals.
Table 10: Direct vs. indirect interactions in Section 4.2
Noisy
ALIGNED
Non-sparse
Interactions
Direct
Indirect
Direct
Indirect
0%
81.4%
17.0%
16.6%
68.0%
5%
73.3%
21.3%
15.0%
68.6%
10%
71.8%
23.2%
24.1%
53.6%
30%
71.2%
18.8%
11.9%
70.5%
50%
58.6%
24.7%
0.6%
36.8%
F.6 FULL RESULTS OP CONSISTENCY BENCHMARK ON NORMAN ET AL. (2166) DATASETS
(019
DIXII
AL. (2016) ADAMSON ET
Evaluations of Section 1.1 on train and test data in precision and recall are shown in Table
Full benchmark results of Section 4.1 are shown in Table 12
23

---

Published as a conference paper at ICLR 2026
"A" is an alignment stage, and "R" is a refinement stage. ALIGNED with "A-R" exccutes alignment and then refinement.
Table 11: Precision and recall Figure
ALIGNED
Train Data
Test Data
Knowledge Base
Dataset
Model
Stage
Precision
Recall
Precision
Recall
Precision
Recall
MLP only
0.556
0.544
0.543
0.541
0.568
0.427
MLP
A
0.510
0.539
0.503
0.537
0.593
0.465
A-R
0,553
0.535
0.537
0.534
0.644
0.652
Norman
GNN only
0.552
0.556
0.552
0.553
0.576
0.433
GNN
A
0.524
0.544
0.523
0.543
0.597
0.458
A-R
0.553
0.538
0.545
0.540
0.653
0.655
MLP only
0.498
0.449
0.494
0.448
0.708
0.476
MLP
A
0.474
0.445
0.454
0.445
0.599
0.483
A-R
0.503
0.446
0.462
0.441
0.590
0.645
Dixit
GNN only
0,493
0.489
0.514
0.505
0.604
0.502
GNN
0.480
0.499
0.480
0.504
0.563
0.525
A-R 0.485
0.498
0.484
0.499
0.616
0.638
MLP only
0.559
0.463
0.524
0.467
0.587
0.448
MLP
A
0.537
0.464
0.486
0.467
0.533
0.460
A-R 0.571
0.461
0.496
0.457
0.562
0.643
Adamson
GNN only
0.561
0.555
0.578
0.579
0.577
0.502
GNN
A
0.511
0.528
0.531
0.366
0.676
0.634
A-R
0.557
0.543
0.553
0.560
0.633
0.645
24

---

Published as a conference paper at ICLR 2026
Table 12: Consistency benchmark in Figure "A" is an alignment stage, and "R" is
refinement stage. ALIGNED with " "A-R" executes alignment and then refinement.
Dataset
Model
ALIGNED
Data
Knowledge Balanced
Stages
Cons.
Cons.
Cons.
linear
0,487540.0m 0000
0.3009 000000
0.3621
GEARS
0.4755 7.475510.0063
0.3175
0.3731
State
0.1440 10.0001
0.381 1.3811110.000 1..0003
0.2473
Morph
0.3378:10.om
0.2580
0.2900
scGPT
0.484640.00m
0.3016440.00 00000
0.3622.40.00
sc scFoundation
0.4505+0.0000
0.3110+0.000
0.3692
MLP only
0.5360=00.000 0019
0.3767 +00 40.063
0063
0.4192+00.0083 200002
Norman
A
0.5040+0.00
0.4307 +:0 0191
0.4575+0.0125
ALIGNED
A-R
0.525210.0mm 10.0042
0.654911.00444
0.569710.0024
(MLP)
A-R-A
0.524611.o0m
0.6528 10128....000 0.00064
0.5687
A-R-A-R
0.5248 =0 0046
0.6573+0.000
0.5698+0.002
GNN only
0.5386
0.3820+0.0100
0.4242+0.0100
0.515440.0163
0.4133340.080
0.4447+0.0260
ALIGNED
A-R
0.5270+0.mm 20.0023
0.6555
0.5714
(GNN)
A-R-A
0.5261 10.011000003
0.6559
0.5711
A-R-A-R
0.5261 +0.0033
0.65964n.0019
0.571 +.00009
lincar GEARS
0.2827 10.0000
0.1432
0. 0.1807
0.4330
0.2704
0.3243-20.000
State
0.1889+00 +0.0008
0.35304..0010
0. 0.1745
scGPT
0.4361 10.000
0.2804
0.3335
scFoundation
0.4335 000-1
0.2722+
0.3260
MLP only
0.4207 -0.8
0.39304+0.0184
0.4052
A
0.4126.1..om
0.4245 10.0168
0.417310.0006
ALIGNED
Dixit
A-R
0.4188 0.418810.00339
0.6591 10.0036
0.471 0.4718 1:0.004
(MLP)
A-R-A
0.4181 10.0036
0.6579
0.4711
A-R-A-R
0.4180+000036
0.6630+0.0014
0.471140.0037
GNN only
0.4509
0.3808
0.4069
0.4534+0.01z
00.4147+0.055/
0.428940.0126
ALIGNED
A-R
0.4585+0 0048
0.6367 0..022222222
0.5082+0.000
(GNN)
A-R-A
0.4588 1.458880.0005
0.637610.0130
0.5082
A-R-A-R
0.4589 0.458911..0047 10.0047
0.6555
0.51 ..5110.0..047
linear
0.2806
0.186640.000
0.2198
GEARS
0.4687 10.0018
0.3737 10.0045
0.4132.
State
0.2868
0.3539 10.0009
0.23399..000
scGPT
0.4703 0000
0.3563 0.0001
0.4016 6+0.0001
scFoundation
0.4704+0.om
0.3678
0.4097+0.0000
MLP only
0.2588 10.000
0.3554
0.0993 0.0029
0.3128+..000
A
0.4767 0.4767+0.0108
0.3725
0.40634400064
ALIGNED
Adamson
A-R
0.4682+0.01c0
0.411140.0266
0.4325
(MLP)
A-R-A
0.467240.0082
0.6:667 40.066
0.517844..077
A-R-A-R
0.467440.0078
0.6418
0.517840.0077
GNN only
0.5436440.0 .0039
0.4319 0.0017
0.4692+40.020
ALIGNED
0.492544.000 0.0050
0.5589+0.100
1079
0.5023+0.0220
(GNN)
A-R
0.5225 10.0177
0.6321
10.0097
0.5641 0.5641 10.0142
A-R-A
0.5205 10000510..0166
0.6328
10.010
0.561 10.0122
A-R-A-R
0.5235
0.6504
00.004000000066
0.5665-10.0143
25


Reviews:
[{"review_id": "qA7nZ4NK5i", "reviewer": "Reviewer_Zesh", "summary": "This paper proposes ALIGNED, a neuro-symbolic framework that jointly optimizes a neural predictor and a symbolic reasoning module over GRNs via abductive learning. The method introduces (i) a balanced consistency metric that merges agreement with data and with knowledge bases, (ii) an adaptive alignment mechanism (learned with REINFORCE) to select per-gene whether to trust neural or symbolic predictions, and (iii) gradient-based knowledge refinement with sparse regularization to update GRNs. Experiments on Norman, Dixit, Adamson (human/mouse) and an E. coli setting show higher “balanced consistency” than recent baselines and indicate that refinement can re-discover biologically meaningful relations.", "questions": "1. How are threshold θ and weights w tuned—per dataset or globally? Any risk of overfitting via these hyperparameters?\n2. For double-vs-single perturbations, does k need to scale, and does refinement overfit to short-cycle artifacts?  \n\nMinor comments / nits\n1. Typos/formatting: “Algin 2” → Align 2; “ALIGEND” → ALIGNED; ensure consistent “knowledge base (KB)” capitalization.\n2. In Fig. 3–5 captions, explicitly state metric definitions (macro vs micro F1).", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Overall, I think this paper has a potentially significant contribution to perturbation-response prediction and neuro-symbolic learning, with a thoughtful framing of data-vs-knowledge trade-offs. With clarifications on theoretical assumptions, ablation coverage, and computational costs, I’d be inclined to raise my score.", "weaknesses": "1. The paper’s core ideas: balanced consistency, per-output adaptive selection, and sparse refinement—are compelling, but please delineate what is novel vs. adapted from prior ABL/REINFORCE literature (e.g., ABL variants, learnable trade-offs). A table that maps each ALIGNED component to closest prior art and states the delta would help.\n\n2. Results implicitly require that either the neural model can approximate the true response mapping or the KB’s transitive closure (up to path length k) can approximate symbolic ground truth. Please state these assumptions explicitly and discuss failure modes when (a) GRN coverage is sparse/bias-prone or (b) δ_{KB} is systematically wrong for some modules. What guarantees (if any) are possible for convergence of the alternating align/refine loop under misspecification?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wsxkirXBhQ", "reviewer": "Reviewer_6cxn", "summary": "This paper introduces ALIGNED, a neuro-symbolic learning framework that integrates gene regulatory knowledge bases (KBs) with data-driven learning to improve consistency between biological prior knowledge and empirical data. The core contribution is a bi-directional alignment mechanism:\nAlignment stage — adapts the model to existing biological knowledge.\nRefinement stage — updates and corrects the knowledge base itself using learned patterns.\nIt defines a novel Balanced Consistency metric to jointly evaluate data-knowledge coherence, addressing a gap in current hybrid bioinformatics methods that often treat biological priors as static and non-adaptive. The work is motivated by the high inconsistency (14–71%) between curated knowledge bases (OmniPath, GO, EcoCyc) and observed perturbation data, and proposes a continuous refinement cycle to resolve such mismatches.", "questions": "1. The paper introduces “bi-directional alignment” between the neural model and symbolic knowledge base. However, the exact mathematical formalization of the alignment operator and refinement update is somewhat ambiguous.\nHow is the “knowledge correction” signal computed and propagated?\nDoes the refinement step have convergence guarantees, or can it drift over repeated iterations?\n\n2. The model includes multiple interacting components: gradient-based learning, abductive reasoning (gradient-free correction), and symbolic consistency scoring.\nWhat is the contribution of each?\nWould ALIGNED still outperform baselines without symbolic refinement?\n\n3. The paper’s datasets are mostly transcriptomic (gene-expression–based). Could the same approach generalize to cross-modal or spatial data (e.g., imaging, proteomics)?\nDoes ALIGNED require structural priors specific to GRNs, or can it adapt to other biological or symbolic domains?\n\n4. Baseline comparisons (GEARS, scGPT, etc.) are strong, but all are data-driven. What about existing neuro-symbolic or knowledge graph–augmented models (e.g., DeepProbLog, NeuroLogic, or KG-BERT)?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Timely problem framing: Tackles a critical limitation in hybrid biological modeling—static priors that cannot evolve alongside new data.\nMethodological novelty: The dual-stage alignment/refinement loop and Balanced Consistency metric provide a principled way to unify knowledge and data learning.\nStrong empirical evidence: Across datasets (Norman et al. 2019, Adamson et al. 2016, Precise1K, E. coli), ALIGNED consistently outperforms baselines like GEARS, scGPT, and scFoundation in both prediction accuracy and knowledge consistency metrics.\nBiological interpretability: Unlike pure neural models, the system supports symbolic reasoning and interpretable GRN (Gene Regulatory Network) updates.", "weaknesses": "Limited ablation of symbolic components: While gradient-free and gradient-based updates are both introduced, their relative contributions are only superficially analyzed.\nDataset diversity: Most evaluations center on transcriptional perturbation data; extension to morphological or cross-modal biological data is not shown.\nTheoretical grounding: The abductive reasoning formulation (based on ABL) could benefit from clearer formal definitions and proofs of convergence or stability.\nPotential overfitting to KB biases: Since refinement still depends on noisy or incomplete KBs, it’s unclear how ALIGNED avoids reinforcing existing errors.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PhWwZQ2AfJ", "reviewer": "Reviewer_nsYx", "summary": "This paper proposes to tackle a ternarized version of gene perturbation prediction through incorporating prior domain knowledge given by a knowledgebase in the learning process. They suggest to alternatingly refine the predicted outcomes and the knowledge base during the learning process and propose a gradient-free algorithm for this.", "questions": "-\tWhat is the justification on the assumption made for how activating and inhibitory effects propagate and interact?\n-\tGiven that the KB is given as binary matrices, why can’t you do gradient-based optimization on this? You can follow a similar scheme as in 3.4 as far as the explanations go – what is prohibiting this?\n-\tWhat is the (exact!) architecture you are using in the experiments?\n-\tHow many and which genes do you consider in the experiments? What happens if you consider more/less?\n-\tWhat are the precision and recall, given that the KB is so sparse, which is hidden in the F1?\n-\tWhat is the performance on training data?\n-\tWhat is the performance on unseen (hold-out) data?\n-\tWhat is the performance of KB reconstruction on an unseen KB (e.g. PPI-derived)?\n-\tWhat is the comparison to SOTA methods using common benchmarking protocols, both regarding metrics as well as separate data (see Weaknesses)?", "limitations": "", "rating": 2, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The presented paper is original in that it presents a novel way of introducing prior knowledge into gene perturbation prediction models.", "weaknesses": "-\tThis paper considers a simplified ternarized version of the underlying problem of gene perturbation prediction, **which is not useful in practice**. The extent of change introduced by a prediction is essential to know. The de facto gold-standard challenge in the field right now is the virtual cell challenge held by the Arc institute (https://virtualcellchallenge.org/, [1]), for which the evaluation metrics already disclose that continuous predictions are necessary. I have seen academic works using this binary or ternary prediction framework to be able to use language models before, but that does not make the task in anyway useful.\n-\tThere are **strong assumptions on how inhibitory and activating effects are interacting** that are not discussed in the main paper. I.e., to perform a query on the KB (the $\\delta_{KB}$), it is assumed that activating and inhibitory effects are additive, which needs clear justification.\n-\tIt is **unclear how scalable this approach is** in practice, the adjacency matrices are #genes x # genes, which can go up to n>60k (all annotated genes) or n>24k (protein-coding genes), in both cases resulting in restrictively large matrices. It is unclear from the writing what subset of genes is used in the experiments, but it appears to be a small selection which needs justification.\n-\tThe writing is incomplete and in its current form the paper **can not be reproduced**.\n1. How is the threshold $\\theta$ defined and picked in practice? Why?\n2. How is weight vector $w$ constructed exactly? A vector that “contains the number of training data samples[…] and the number of annotations from gene Ontology[…]” leaves a lot of questions – these are two numbers (counts) which clearly can not make up $w$. Do you sum per gene? Then add up the two numbers (KB and GO)? What is the rationale?\n3. What are the number of genes (and which ones) considered for the experiments?\n4. **What are the model architectures you use exactly**?\n5. **Do you evaluate on hold-out data and KBs unseen during training**? What would the performance then be, e.g. evaluating on a PPI-derived KB or other datasets on the same (or even different) cell line, which is fairly common in the literature?\n-\tWhat is the comparison to SOTA methods, including the currently not discussed Morph [2], and STATE [3] models? Fig. 4,5 and Table 1 simply **miss a comparison of the actual prediction to any SOTA**.\n\n[1] Rohaani, Y H et al. * Virtual Cell Challenge: Toward a Turing test for the virtual cell.* Cell 188(13), pages 3370-3374, 2025.\n\n[2] He, C et al. * MORPH Predicts the Single-Cell Outcome of Genetic Perturbations Across Conditions and Data Modalities.* bioRxiv, DOI: https://doi.org/10.1101/2025.06.27.661992, 2025.\n\n[3] Adduri, A K et al. * Predicting cellular responses to perturbation across diverse contexts with State.* bioRxiv, DOI:https://doi.org/10.1101/2025.06.26.661135, 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "h4hjPMtJO6", "reviewer": "Reviewer_YBGA", "summary": "The paper presents ALIGNED, a method for predicting the effects of gene perturbations in single-cell transcriptomic data using prior gene regulatory networks (GRNs). Unlike earlier models that also leverage GRNs—such as GEARS—the proposed approach does not treat the regulatory information as static but instead refines it dynamically throughout training. The training process itself is complex, involving a multistage optimization scheme that combines gradient descent with a Monte Carlo, ultimately aiming to align predictions based on data with the ones based on GRN.", "questions": "**I am willing to improve the score of the paper if:**\n\n1. The authors explain why the knowledge consistency metric is important and prove that their way of computing it is not circular.  \n2. The authors conclusively show that their approach provides substantial benefits in terms of perturbation prediction as compared to other methods in the field, including the current state-of-the-art STATE.  \n3. The authors describe the optimization procedure from a practical point of view, explaining how different parameters at each stage influence the accuracy of predictions.  \n4. *(Minor)* The authors mention that two of the datasets were split randomly — please clarify what is meant by that.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "The authors employ a genuinely new strategy that leverages GRN for perturbation prediction that does not treat the GRN as static during training. They also devise a complex strategy of optimizing the neuro-symbolic alignment.", "weaknesses": "In terms of the accuracy of perturbation respnse predictions, the algorithm provides only marginal gains, while being notably resource-intensive—requiring up to 12 hours of training on an 80 GB GPU. The authors, nevertheless, argue that the true advantage of their method lies not in predictive accuracy but in its improved alignment with the prior GRN and in the refinement of the GRN during optimization. However, the first claim is problematic: the reported GRN-alignment metric seems circular, as the GRN serves both as an input to the model and as a reference for evaluation. The second claim—that the optimization refines the GRN—is also inconclusive, since the authors do not quantify the number or directionality of corrected regulatory links but instead report pathway enrichment scores, which appear only tangentially related.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)