Towards Universal Gene Regulatory Network Inference: Unlocking Generalizable Regulatory Knowledge in Single-cell Foundation Models

# Towards Universal Gene Regulatory Network Inference: Unlocking Generalizable Regulatory Knowledge in Single-cell Foundation Models
Source: [https://arxiv.org/html/2605.08128](https://arxiv.org/html/2605.08128)
###### Abstract

Gene Regulatory Network \(GRN\) inference is essential for understanding complex cellular mechanisms, rendered tractable through single\-cell transcriptomic data\. With the emergence of single\-cell Foundation Models \(scFMs\), enhanced transcriptomic encoding is widely expected to revolutionize GRN inference\. However, we observe that their performance remains far from satisfactory\. The primary reason is that the standard reconstruction\-based pre\-training objectives often fail to explicitly capture latent regulatory signals\. To bridge this gap, we first introduce a GRN generalization benchmark designed to evaluate regulatory predictions on unseen genes and datasets, which relies on the zero\-shot capabilities of scFMs and is inherently challenging for traditional methods\. Furthermore, to unlock the regulatory knowledge within the foundation models, we propose two novel methods, Virtual Value Perturbation and Gradient Trajectory, to distill implicit regulatory information from scFMs into highly generalizable inter\-gene features\. Extensive experiments demonstrate that our approach significantly outperforms existing methods, establishing a new paradigm for leveraging the potential of scFMs in universal GRN inference\.

Machine Learning, ICML

## 1Introduction

![Refer to caption](https://arxiv.org/html/2605.08128v1/x1.png)Figure 1:\(a\) Traditional GRN inference operates in a closed\-world setting, where optimizedfθf\_\{\\theta\}struggles with dimension mismatches on unseen genes from heterogeneous datasets\. \(b\) Our UGRN setting utilizes frozen scFMs for universal feature extraction, enabling the generalization of regulatory predictions by “translator”fϕf\_\{\\phi\}to open\-world scenarios involving unseen genes and datasets\.Gene Regulatory Networks \(GRN\) constitute the core mechanisms that govern complex biological processes by encoding the intricate causal dependencies among genes\(Davidsonet al\.,[2002](https://arxiv.org/html/2605.08128#bib.bib1)\)\. Recent advancements in single\-cell RNA sequencing \(scRNA\-seq\) have provided high\-resolution, cell\-level gene expression profiles, enabling the estimation of GRNs directly from observational data\(Aibaret al\.,[2017](https://arxiv.org/html/2605.08128#bib.bib4); Pratapaet al\.,[2020](https://arxiv.org/html/2605.08128#bib.bib5)\)\. For example, if the expression of genegig\_\{i\}is consistently correlated with that ofgjg\_\{j\}, a potential regulatory link is hypothesized\(Eisenet al\.,[1998](https://arxiv.org/html/2605.08128#bib.bib6)\)\. Traditionally, as shown in Figure[1](https://arxiv.org/html/2605.08128#S1.F1)\(a\), GRN inference has relied on identifying co\-expression dependencies between genes within specific datasets\(Songet al\.,[2012](https://arxiv.org/html/2605.08128#bib.bib20)\)\. However, these methods are often constrained to a “closed\-world” setting, where they remain effective only for genes observed during training and struggle to generalize to unseen genes from heterogeneous datasets\. This limitation primarily stems from the lack of unified expression manifolds and generalizable regulatory representations between genes\.

Recently, Single\-Cell Foundation Models \(scFMs\)\(Haoet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib10); Yanget al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib9)\)have emerged as a promising paradigm for addressing various downstream biological tasks, including GRN inference\. By pre\-training on large\-scale gene expression data via self\-supervised objectives, e\.g\., masked value reconstruction, scFMs are expected to capture profound biological priors for inter\-gene relationships\. Consequently, an increasing number of studies attempt to leverage scFMs for zero\-shot GRN inference through two primary strategies: \(1\) In\-silico Perturbation, which simulates biological knockouts by zeroing out the input expression of a source genegig\_\{i\}to observe the response of a target genegjg\_\{j\}\(Theodoriset al\.,[2023](https://arxiv.org/html/2605.08128#bib.bib12); Cuiet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib11)\); and \(2\) Attention\-based analysis, which interprets the model’s attention weights as proxies for regulatory strength to predict inter\-gene relations\(Yanget al\.,[2022](https://arxiv.org/html/2605.08128#bib.bib13); Cuiet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib11)\)\. Despite their theoretical appeal, recent works point out that these methods often exhibit suboptimal performance, sometimes even failing to surpass random prediction\(Jinet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib14); Ahlmann\-Eltzeet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib16)\)\. This phenomenon may stem from the misalignment between the reconstruction\-based pre\-training and the downstream requirements of inter\-gene inference, leading to growing skepticism regarding the empirical efficacy of scFMs within the biological community\(Wuet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib15)\)\.

In this paper, we argue that scFMs possess rich and transferable regulatory knowledge, but current methods are too simplistic to bridge the gap between correlation\-based reconstruction output and gene regulation\. For example, the influence of genegig\_\{i\}ongjg\_\{j\}estimated via simple “zero\-out” perturbations merely reflects the model’s reliance ongig\_\{i\}to reconstructgjg\_\{j\}, which represents neither true causality nor the full correlation between them\. However, we posit that such conditioned inter\-gene influences reflect a consistent internal understanding of gene relationships within the scFMs\. As shown in Figure[1](https://arxiv.org/html/2605.08128#S1.F1), the challenge lies in “translating” this latent knowledge into gene regulatory insights\. To this end, we introduce a novel setting termed Universal Gene Regulatory Network inference\. This paradigm requires the model to learn a mapping \(a “translator”\) from scFM\-derived inter\-gene knowledge to ground\-truth GRNs using source genes and then generalize to unseen genes from heterogeneous datasets\. This setting serves as a rigorous benchmark for evaluating whether foundation models can capture generalizable regulatory principles, a capability unattainable by traditional statistical methods constrained to dataset\-specific expression understanding\.

We first establish two baselines by utilizing gene embeddings and traditional “zero\-out” perturbation influences between genes as features to map onto gene regulatory relationships, thereby constructing a benchmark for our universal GRN setting\. To derive more profound and generalizable inter\-gene features from scFMs, we propose two novel methods, Virtual Value Perturbation \(VVP\) and Gradient Trajectory \(GDT\)\. For VVP, observing that distinct genes possess different baseline expressions, we point out that the “zero\-out” operation introduces inconsistent perturbation magnitudes\. Consequently, we standardize this process by employing a unified virtual value as the base expression, ensuring that gene interactions are queried under a consistent reference value\. Furthermore, since scFMs can encode and reconstruct arbitrary expression values beyond the observed cellular range, we define a series of perturbation target values, rather than a single zero, to extract richer inter\-gene influences\. For GDT, as discrete perturbations only represent the influence over a change interval, we argue that the influence at specific expression levels should be characterized by gradients\. Leveraging the gradient backpropagation of scFMs, we propose the Gradient Trajectory method, which extracts gradients along a series of virtual values, to reflect the gene relationship across varying expression levels\.

Extensive experiments across multiple datasets and different settings demonstrate that our proposed methods significantly outperform traditional scFM\-based methods and our baselines\. The results show that when properly queried, scFMs exhibit a stable and profound understanding of GRNs that far exceeds random expectation, thereby validating the utility of large\-scale pre\-training for single\-cell transcriptomics\. Notably, because our method utilizes virtual values to extract inter\-gene features for GRN inference, it can predict regulatory links even in the absence of real\-world expression measurements, providing a powerful tool for constructing Universal Gene Regulatory Networks\.

Our main contributions are summarized as follows:

- •We analyze scFM\-based GRN inference, identifying the critical misalignment between reconstruction objectives and gene regulation that limits current methods\.
- •We introduce the UGRN framework, a benchmark evaluating the generalizability of scFM regulatory knowledge across unseen genes and heterogeneous datasets\.
- •We propose VVP and GDT, achieving SOTA performance in extensive experiments and ablations by extracting generalizable regulatory features from scFMs\.

## 2Related Works

Gene Regulatory Network Inference\. Inferring GRNs from single\-cell transcriptomics has evolved from statistical approaches to deep learning frameworks\. Traditional methods utilize tree\-based regression\(Huynh\-Thuet al\.,[2010](https://arxiv.org/html/2605.08128#bib.bib7); Moermanet al\.,[2019](https://arxiv.org/html/2605.08128#bib.bib28)\)or information\-theoretic metrics\(Margolinet al\.,[2006](https://arxiv.org/html/2605.08128#bib.bib29); Faithet al\.,[2007](https://arxiv.org/html/2605.08128#bib.bib30)\)to capture non\-linear co\-expression patterns\. More recent deep learning approaches, such as GNNs and VAEs, explicitly model network topology to learn latent representations of gene dependencies\(Chen and Liu,[2022](https://arxiv.org/html/2605.08128#bib.bib31); Shuet al\.,[2021](https://arxiv.org/html/2605.08128#bib.bib33)\)\. However, these methods predominantly operate under a “closed\-world” assumption, where they capture the manifold of specific datasets and cannot generalize to unseen genes without retraining\(Kedzierskaet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib17)\)\. In contrast, we introduce a Universal GRN setting\. Instead of fitting dataset\-specific distributions, we leverage pre\-trained foundation models to extract generalizable regulatory features, enabling generalization to unseen genes and heterogeneous datasets\.

Single\-cell Foundation Models\. Inspired by Large Language Models, Single\-cell Foundation Models \(scFMs\) such as scGPT\(Cuiet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib11)\), Geneformer\(Theodoriset al\.,[2023](https://arxiv.org/html/2605.08128#bib.bib12)\), and scBERT\(Yanget al\.,[2022](https://arxiv.org/html/2605.08128#bib.bib13)\)learn transcriptomic representations via masked value modeling on massive cell atlases\. Current strategies for GRN inference with scFMs rely on simple heuristics, either by interpreting raw attention weights as regulatory strength\(Kalfonet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib34); Yanget al\.,[2022](https://arxiv.org/html/2605.08128#bib.bib13)\)or by performing in\-silico perturbation by zeroing out input genes\(Theodoriset al\.,[2023](https://arxiv.org/html/2605.08128#bib.bib12); Cuiet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib11)\)\. However, recent benchmarks reveal that these methods often yield suboptimal performance\(Kedzierskaet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib17); Jinet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib14); Ahlmann\-Eltzeet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib16); Wuet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib15)\)\. We argue that this failure stems from the simplistic implementation of scFMs rather than its lack of regulatory knowledge\. Unlike direct heuristic mapping, we propose Virtual Value Perturbation and Gradient Trajectory to actively distill implicit regulatory signals from frozen scFMs, bridging the gap between correlation\-based features and gene regulations\.

## 3Method

### 3\.1Preliminaries

Current GRN inference research mainly characterizes regulatory dependencies between individual gene pairs\. Following\(Wanget al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib25)\), we treat GRN inference as a pair\-wise prediction task\. Note that, although the global GRN topology constitutes essential background knowledge\(Barabási and Oltvai,[2004](https://arxiv.org/html/2605.08128#bib.bib19)\), such information is practically incorporated into the latent gene embeddings to facilitate pair\-wise learning objectives\. Thus, for simplicity, we omit the explicit global network formulation and focus on pair\-wise learning\.

GRN Inference\. Given a set of genes𝒢=\{g1,…,gK\}\\mathcal\{G\}\\\!=\\\!\\\{g\_\{1\},\\dots,g\_\{K\}\\\}and a single\-cell gene expression matrix𝐗∈ℝN×K\\mathbf\{X\}\\\!\\in\\\!\\mathbb\{R\}^\{N\\times K\}, let𝐱i∈ℝN\\mathbf\{x\}\_\{i\}\\\!\\in\\\!\\mathbb\{R\}^\{N\}denote the expression vector of genegig\_\{i\}acrossNNobserved cells \(corresponding to theii\-th column of𝐗\\mathbf\{X\}\)\. We have access to ground\-truth regulatory annotations, formalized as a training set𝒟t​r=\{\(𝐱i,𝐱j,yi​j\)\}\(i,j\)∈Ωt​r\\mathcal\{D\}\_\{tr\}\\\!=\\\!\\\{\(\\mathbf\{x\}\_\{i\},\\mathbf\{x\}\_\{j\},y\_\{ij\}\)\\\}\_\{\(i,j\)\\in\\Omega\_\{tr\}\}, whereyi​j∈\{0,1\}y\_\{ij\}\\\!\\in\\\!\\\{0,1\\\}indicates whethergig\_\{i\}regulatesgjg\_\{j\}, andΩt​r\\Omega\_\{tr\}denotes the set of observed pair indices\.

The fundamental objective of GRN inference is to learn a parameterized mapping functionfθf\_\{\\theta\}from expression to regulatory probabilities based on𝒟t​r\\mathcal\{D\}\_\{tr\}, to generalize to unseen pairs in a held\-out test set𝒟t​e\\mathcal\{D\}\_\{te\}under the same expression matrix𝐗\\mathbf\{X\}\. Formally, for any pair\(gi,gj\)\(g\_\{i\},g\_\{j\}\)in𝒟t​e\\mathcal\{D\}\_\{te\}, the model predicts a regulatory score

si​j=fθ​\(𝐱i,𝐱j\),\(i,j\)∈Ωt​e\.s\_\{ij\}\\\!=\\\!f\_\{\\theta\}\(\\mathbf\{x\}\_\{i\},\\mathbf\{x\}\_\{j\}\),\\;\(i,j\)\\in\\Omega\_\{te\}\.\(1\)
Traditional Methods\. Existing methods typically employ linear regression or deep neural networks to learn the mappingfθf\_\{\\theta\}by minimizing the empirical risk over𝒟t​r\\mathcal\{D\}\_\{tr\}\(Hauryet al\.,[2012](https://arxiv.org/html/2605.08128#bib.bib27); Yuan and Bar\-Joseph,[2019](https://arxiv.org/html/2605.08128#bib.bib18)\)\. The training objective is formulated as the binary cross\-entropy loss:

ℒθ=−∑\(i,j\)∈Ωt​r\[yi​j​log⁡si​j\+\(1−yi​j\)​log⁡\(1−si​j\)\],\\mathcal\{L\}\_\{\\theta\}\\\!=\\\!\-\\\!\\sum\_\{\(i,j\)\\in\\Omega\_\{tr\}\}\\left\[y\_\{ij\}\\log s\_\{ij\}\+\(1\-y\_\{ij\}\)\\log\(1\-s\_\{ij\}\)\\right\],\(2\)wheresi​js\_\{ij\}denotes the predicted regulatory probability between geneiiand genejjdefined in Eq\. \([1](https://arxiv.org/html/2605.08128#S3.E1)\)\.

However, this paradigm relies on the assumption that the training and testing data share the same expression distribution and graph structure\. Since the dimension of features𝐱i\\mathbf\{x\}\_\{i\}is tied to the number of cells in𝒟t​r\\mathcal\{D\}\_\{tr\}, the learned functionfθf\_\{\\theta\}is bound to this fixed size\. Consequently, when applied to a new dataset with a distinct cell countN′N^\{\\prime\}, the misaligned expression dimension renders the model ineffective\. Furthermore, if the method explicitly encodes the global topology of𝒢\\mathcal\{G\}\(Chen and Liu,[2022](https://arxiv.org/html/2605.08128#bib.bib31)\), it becomes unable to generalize to novel gene sets𝒢′\\mathcal\{G\}^\{\\prime\}with unseen network topologies\.

scFM\-based Methods\.Single\-Cell Foundation Models \(scFMs\)\(Cuiet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib11)\)leverage large\-scale pre\-training on massive single\-cell corpora to encode gene representations and the inter\-gene interaction mechanism\. These models encode a unified gene vocabulary𝒱\\mathcal\{V\}\(where\|𝒱\|≫K\|\\mathcal\{V\}\|\\gg K\), capturing complex regulatory semantics that facilitatezero\-shotGRN inference without explicit supervision from𝒟t​r\\mathcal\{D\}\_\{tr\}\.

Formally, letℳ\\mathcal\{M\}denote a Transformer\-based scFM\. The model takes a cell’s expression vector𝐱c∈ℝK\\mathbf\{x\}\_\{c\}\\\!\\in\\\!\\mathbb\{R\}^\{K\}\(corresponding to a row in𝐗\\mathbf\{X\}\) as input and outputs a reconstructed vector𝐱^c=ℳ​\(𝐱c\)\\hat\{\\mathbf\{x\}\}\_\{c\}=\\mathcal\{M\}\(\\mathbf\{x\}\_\{c\}\)in the same feature space\. Leveraging this input\-output architecture, existing approaches primarily employ two strategies to estimate the regulatory scoresi​js\_\{ij\}\.

\(1\) In\-Silico Perturbation\. This approach simulates biological knockout experiments\. It measures the regulatory effect of genegig\_\{i\}ongjg\_\{j\}by computing the shift in the predicted expression ofgjg\_\{j\}when the input value forgig\_\{i\}is set to zero\. For a given cell expression𝐱c\\mathbf\{x\}\_\{c\}, the regulatory score is defined as

si​j=ℳ​\(𝐱c\)j−ℳ​\(𝐱c¬i\)j,s\_\{ij\}=\\mathcal\{M\}\(\{\\mathbf\{x\}\_\{c\}\}\)\_\{j\}\-\\mathcal\{M\}\(\{\\mathbf\{x\}\_\{c\}\}\_\{\\neg i\}\)\_\{j\},\(3\)whereℳ​\(⋅\)j\\mathcal\{M\}\(\\cdot\)\_\{j\}represents the reconstructed expression for genejj,𝐱¯c​¬i\\bar\{\\mathbf\{x\}\}\_\{c\\neg i\}denotes the cell expression forccwith geneiiset to zero\. In practice,si​js\_\{ij\}is computed either by using the dataset\-level mean expression as𝐱c\\mathbf\{x\}\_\{c\}, or by averaging the perturbation scores across all individual cells in𝒟t​r\\mathcal\{D\}\_\{tr\}\.

![Refer to caption](https://arxiv.org/html/2605.08128v1/x2.png)Figure 2:Illustration of methods for extracting𝐞i​j\\mathbf\{e\}\_\{ij\}from scFMℳ\\mathcal\{M\}\. The figure compares baselines \(a\) Perturbation and \(b\) Embedding against our proposed \(c\) Virtual Value Perturbation and \(d\) Gradient Trajectory\. Green and blue blocks highlight the entries corresponding to source genegig\_\{i\}and target genegjg\_\{j\}, respectively, while grey blocks represent background genes\. Note that \(a\) utilizes real mean expressionx¯\\bar\{x\}, whereas \(c\) and \(d\) employ virtual expression vectors\. Mathematical notations are simplified for visual clarity\.\(2\) Attention Extraction\. This approach hypothesizes that the internal attention weights of Transformers implicitly encode regulatory dependencies\. By forwarding a cell expression𝐱c\\mathbf\{x\}\_\{c\}throughℳ\\mathcal\{M\}, the regulatory score forgig\_\{i\}togjg\_\{j\}is defined as

si​j=∑lAtt\(l\)​\(ℳ,𝐱c\)i​j,s\_\{ij\}=\\sum\\nolimits\_\{l\}\\text\{Att\}^\{\(l\)\}\(\\mathcal\{M\},\\mathbf\{x\}\_\{c\}\)\_\{ij\},\(4\)whereAtt\(l\)​\(ℳ,𝐱c\)i​j\\text\{Att\}^\{\(l\)\}\(\\mathcal\{M\},\\mathbf\{x\}\_\{c\}\)\_\{ij\}denotes the attention weight between geneiiand genejjin thell\-th layer, extracted from the forward pass of𝐱c\\mathbf\{x\}\_\{c\}throughℳ\\mathcal\{M\}, and the summation aggregates these weights across all layers\.

Despite their theoretical appeal for zero\-shot GRN inference, these methods significantly underperform supervised baselines\(Wanget al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib25); Kommuet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib26)\)\. We argue that such straightforward heuristics, Eqs\. \([3](https://arxiv.org/html/2605.08128#S3.E3)\) and \([4](https://arxiv.org/html/2605.08128#S3.E4)\), fail to explicitly represent regulatory effects, as they merely reflect the model’s gene reconstruction capability\. Furthermore, the standard GRN evaluation setting is hard to assess the generalization power of scFMs\. To address these gaps, we propose a novel framework designed to unlock the true potential of scFMs for gene regulatory inference\.

### 3\.2Universal Gene Regulatory Network Inference

To fully unlock the potential of scFMs and bridge the gap between model predictions and regulatory relationships, we propose a novel framework termed Universal Gene Regulatory Network \(UGRN\) Inference\. This framework learns a “translator” mapping scFM\-derived inter\-gene features to regulatory probabilities\. By exploiting the unified vocabulary and transferable knowledge of scFMs, UGRN facilitates regulatory prediction for any arbitrary gene pairs\.

Problem Definition\.Letℳ\\mathcal\{M\}denote an scFM, and we assume access to a base GRN dataset𝒟b=\{𝐗b,Ωb\}\\mathcal\{D\}\_\{b\}\\\!=\\\!\\\{\\mathbf\{X\}\_\{b\},\\Omega\_\{b\}\\\}defined over a gene set𝒢b\\mathcal\{G\}\_\{b\}\. The goal of UGRN is to learn a projectorfϕf\_\{\\phi\}, which takes pair\-wise features𝐞i​j\\mathbf\{e\}\_\{ij\}extracted byℳ\\mathcal\{M\}forgig\_\{i\}andgjg\_\{j\}and predicts their regulatory link

si​j=fϕ​\(𝐞i​j\),gi,gj∉𝒢b,s\_\{ij\}=f\_\{\\phi\}\(\\mathbf\{e\}\_\{ij\}\),\\;g\_\{i\},g\_\{j\}\\notin\\mathcal\{G\}\_\{b\},\(5\)wherefϕf\_\{\\phi\}can be trained by Eq\. \([2](https://arxiv.org/html/2605.08128#S3.E2)\)\. During inference, both the expression𝐗\\mathbf\{X\}and the gene set𝒢\\mathcal\{G\}differ from those in the training\. Therefore, the core challenge of UGRN is how to extract a more generalizable𝐞i​j\\mathbf\{e\}\_\{ij\}from scFMs\.

Baseline Methods\. To establish benchmarks for our setting, we propose two straightforward strategies to deriveei​j\{e\}\_\{ij\}\.

\(1\) Perturbation\-based Features\.Instead of using the raw value change from In\-Silico Perturbation directly as the regulatory prediction, we treat the perturbation response as an inter\-gene feature\. Based on the formulation in Eq\. \([3](https://arxiv.org/html/2605.08128#S3.E3)\), we derive the featureei​j\{e\}\_\{ij\}as

ei​j=ℳ​\(𝐱¯\)j−ℳ​\(𝐱¯¬i\)j,\{e\}\_\{ij\}=\\mathcal\{M\}\(\\bar\{\\mathbf\{x\}\}\)\_\{j\}\-\\mathcal\{M\}\(\\bar\{\\mathbf\{x\}\}\_\{\\neg i\}\)\_\{j\},\(6\)where𝐱¯\\bar\{\\mathbf\{x\}\}denotes the mean expression averaged across all cells in the given dataset, with other notations remaining consistent with Eq\. \([3](https://arxiv.org/html/2605.08128#S3.E3)\)\. This strategy effectively standardizes the input dimension, thereby mitigating discrepancies caused by varying cell counts across different GRN datasets\.

\(2\) Embedding\-based Features\.Since scFMs are pre\-trained to reconstruct expressions across massive gene corpora, the learned gene vocabulary embedding𝐄ℳ∈ℝ\|𝒱\|×d\\mathbf\{E\}\_\{\\mathcal\{M\}\}\\in\\mathbb\{R\}^\{\|\\mathcal\{V\}\|\\times d\}naturally serves as an intrinsic encoding for genes, where\|𝒱\|\|\\mathcal\{V\}\|denotes the vocabulary size andddis the hidden dimension\. For a gene pair \(gig\_\{i\},gjg\_\{j\}\), the pair\-wise feature can be directly constructed by summing their embeddings

𝐞i​j=𝐄ℳ,i\+𝐄ℳ,j,\\mathbf\{e\}\_\{ij\}=\\mathbf\{E\}\_\{\\mathcal\{M\},i\}\+\\mathbf\{E\}\_\{\\mathcal\{M\},j\},\(7\)where𝐄ℳ,i∈ℝd\\mathbf\{E\}\_\{\\mathcal\{M\},i\}\\in\\mathbb\{R\}^\{d\}denotes the gene embedding ofgig\_\{i\}\.

While these baselines validate the feasibility of the UGRN setting, they still represent a simplistic exploitation of the foundation models\. To fully unlock the potential of scFMs, we require methods that can deeply probe the model for comprehensive inter\-gene representations\.

### 3\.3Our Methods

We propose Virtual Value Perturbation \(VVP\) and Gradient Trajectory \(GDT\) to serve as the advanced extractors for𝐞i​j\\mathbf\{e\}\_\{ij\}\. Both are motivated by the need to derive the comprehensive influence ofgig\_\{i\}ongjg\_\{j\}via counterfactual reasoning\.

Virtual Value Perturbation \(VVP\)\. Conventional perturbation estimates the response of a target genegjg\_\{j\}by zeroing outgig\_\{i\}from its observed value𝐱c,i\\mathbf\{x\}\_\{c,i\}under cellcc\. This approach inherently suffers from scale inconsistency, where the perturbation magnitude is coupled with the original value ofgig\_\{i\}, rendering predicted influences incomparable across different genes from heterogeneous datasets\.

To decouple perturbation features from dataset statistics, we utilize the capability of scFMs, which can process arbitrary expression values beyond the observations\. Thus, we introduce a unified virtual base valuevbv\_\{b\}to serve as a consistent reference for all genes\. Instead of querying the model with a simple “on/off” state, we perturb the source genegig\_\{i\}fromvbv\_\{b\}to another virtual target valuevpv\_\{p\}, and the corresponding inter\-gene feature is formulated as:

ei​jvp=ℳ​\(𝐯gi←vp\)j−ℳ​\(𝐯gi←vb\)j,\{e\}\_\{ij\}^\{v\_\{p\}\}=\\mathcal\{M\}\(\\mathbf\{v\}\_\{g\_\{i\}\\leftarrow v\_\{p\}\}\)\_\{j\}\-\\mathcal\{M\}\(\\mathbf\{v\}\_\{g\_\{i\}\\leftarrow v\_\{b\}\}\)\_\{j\},\(8\)where𝐯gi←v\\mathbf\{v\}\_\{g\_\{i\}\\leftarrow v\}denotes virtual cell expression with the entry forgig\_\{i\}set tovvand other genes are fixed atvbv\_\{b\}\. To capture comprehensive dynamics, we define a set of target values\{vp,1,…,vp,M\}\\\{v\_\{p,1\},\\dots,v\_\{p,M\}\\\}and construct𝐞i​j\\mathbf\{e\}\_\{ij\}by concatenating the corresponding responses,𝐞i​j=\[ei​jvp,1;…;ei​jvp,M\]\\mathbf\{e\}\_\{ij\}=\[e\_\{ij\}^\{v\_\{p,1\}\};\\dots;e\_\{ij\}^\{v\_\{p,M\}\}\], which serve as a comparable representation for all gene pairs regardless of their observational data\.

Gradient Trajectory \(GDT\)\. Since VVP essentially represents the regulatory influence induced by expression variations over an interval, we argue that instantaneous regulatory mechanics are characterized by local sensitivity\.

Leveraging the differentiability of scFMs, we propose to extract the instantaneous rate of change via gradient backpropagation\. We define an ordered set of virtual base values\{vb,1,…,vb,T\}\\\{v\_\{b,1\},\\dots,v\_\{b,T\}\\\}covering the dynamic range\. For each statevb,tv\_\{b,t\}, we compute the partial derivative of the reconstruction of target genejjwith respect to the input of source geneii, and concatenate them into a trajectory vector

𝐞i​j=\[∇i​j\(1\);…;∇i​j\(T\)\];∇i​j\(t\)=∂ℳ​\(𝐯gi←vb,t\)j∂vi,\\mathbf\{e\}\_\{ij\}=\[\\nabla\_\{ij\}^\{\(1\)\};\\dots;\\nabla\_\{ij\}^\{\(T\)\}\];\\;\\nabla\_\{ij\}^\{\(t\)\}=\\frac\{\\partial\\mathcal\{M\}\(\\mathbf\{v\}\_\{g\_\{i\}\\leftarrow v\_\{b,t\}\}\)\_\{j\}\}\{\\partial v\_\{i\}\},\(9\)where𝐯gi←vb,t\\mathbf\{v\}\_\{g\_\{i\}\\leftarrow v\_\{b,t\}\}denotes the virtual input vector with the entry forgig\_\{i\}set tovb,tv\_\{b,t\},viv\_\{i\}denotes the scalar input corresponding to genegig\_\{i\}in𝐯\\mathbf\{v\}, and\[;\]\[;\]represents the concatenation operation\. By organizing these local sensitivities into an ordered trajectory, GDT effectively describes the evolution of regulatory relationships, thereby providing generalizable inter\-genic features for universal GRN inference\.

Note that VVP and GDT characterize the regulatory dependency from complementary perspectives, where VVP measures the response over value intervals, and GDT reflects instantaneous local sensitivities\. To leverage their combined strengths, we implement a straightforward Ensemble \(Ens\) strategy by averaging their predicted logits, thereby producing a comprehensive and more generalizable description for regulatory relationships\.

## 4Experiments

### 4\.1Datasets

GRN datasets\.We evaluate our method on seven scRNA\-seq datasets from the BEELINE framework\(Pratapaet al\.,[2020](https://arxiv.org/html/2605.08128#bib.bib5)\)spanning human \(hESC, hHEP\) and mouse \(mDC, mESC, mHSC lineages\) cell types, benchmarked against ground\-truth GRNs derived from four distinct categories of biological evidence\. Following the standard preprocessing pipeline, we focus on interactions outgoing from transcription factors \(TFs\)\. For each dataset, we select the top 500 and 1,000 highly variable genes \(Bonferroni\-corrected varianceP<0\.01P<0\.01\)\(Stuartet al\.,[2019](https://arxiv.org/html/2605.08128#bib.bib21)\)alongside all identified TFs to construct the target networks\. These two dataset configurations are hereafter referred to as TFs\+500 and TFs\+1000, respectively\. All datasets are available via GEO\.

UGRN settings\.The core objective of UGRN inference is to assess the cross\-dataset generalizability of the learned projector\. Unlike conventional supervised methods that train and test on held\-out pairs within the same dataset \(sharing identical gene sets and expression matrix\), we adopt aLeave\-One/Some\-Dataset\-Outprotocol\. Formally, given the collection of GRN datasets𝔻=\{𝒟1,…,𝒟N\}\\mathbb\{D\}\\\!=\\\!\\\{\\mathcal\{D\}\_\{1\},\\dots,\\mathcal\{D\}\_\{N\}\\\}, we iterate through each dataset𝒟k∈𝔻\\mathcal\{D\}\_\{k\}\\in\\mathbb\{D\}\(or a group of datasets for ablation studies\) serving as the training source𝒟t​r\\mathcal\{D\}\_\{tr\}\. The trained projectorfϕf\_\{\\phi\}is then evaluated on the remaining datasets\.

Table 1:AUPRC performance comparison on the UGRN benchmark employing scGPT and scBenchmark as frozen scFMs\. The trainable parametersfϕf\_\{\\phi\}are optimized on the hESC dataset \(from the STRING network\), while evaluation is performed on all other heterogeneous datasets except hESC\. Bold indicates the best performance, andunderlineddenotes the runner\-up\.Table 2:Extended AUPRC comparison using scBenchmark across different UGRN settings\. Each row represents the performance of a model trained on the specified dataset, reported as the average AUPRC calculated across all other datasets \(excluding the training source and its network variants\), e\.g\., the Str hESC row corresponds to the average performance reported in Table[1](https://arxiv.org/html/2605.08128#S4.T1)\. “Need Exp” indicates whether input expression data is required for inference\. The full AUROC performance could be found in the Appendix\.Table 3:Ablation study on cross\-dataset generalization performance using scBenchmark\.fϕf\_\{\\phi\}is trained on the specific source dataset \(indicated in each row\) and evaluated on all other heterogeneous datasets\. The reported results represent the average AUPRC on the test sets\. Bold indicates the best performance\.Table 4:Ablation study on cross\-species generalization performance\.fϕf\_\{\\phi\}is trained on the species indicated in each row and evaluated on the dataset of the other species\. The reported results represent the average AUPRC on the test sets\.
### 4\.2Implementation Details

For scFMs, we utilized the official implementations of scGPT\(Cuiet al\.,[2024](https://arxiv.org/html/2605.08128#bib.bib11)\)and scBenchmark\(Qiet al\.,[2025](https://arxiv.org/html/2605.08128#bib.bib2)\)\. These serve as base pre\-trained models with binned and continuous inputs, respectively\. We implement the UGRN projectorfϕf\_\{\\phi\}as an MLP to map the scFM\-derived features to regulatory probabilities\. The MLP consists of two hidden layers with dimensions 128 and 64, respectively, with ReLU activation functions, where the input size is defined by the specific feature extraction method\. The final layer projects the latent representation to a scalar score bounded by a Sigmoid function\. The model is trained using the Adam\(Kingma and Ba,[2015](https://arxiv.org/html/2605.08128#bib.bib24)\)optimizer with a learning rate of1×10−31\\times 10^\{\-3\}and a batch size of 128 for 50 epochs, minimizing the binary cross\-entropy loss\. These hyperparameters are consistent across all methods to ensure fairness\.

To capture comprehensive gene relationships, for all methods, we explicitly incorporate information from both directions when constructing the pair\-wise feature𝐞i​j\\mathbf\{e\}\_\{ij\}\. Specifically, for a given pair, we concatenate the extracted vectors for both the forward and reverse directions\. When implementing scGPT, by assigning virtual values to input gene expressions, we bypass the binning operation, which otherwise blocks gradient backpropagation, thereby enabling the calculation of gradients for genes\. All hyperparameters are applied uniformly to all settings and datasets for UGRN, without specific tuning for individual settings\. More details about the hyperparameters and additional ablation studies can be found in the Appendix\.

### 4\.3Result Analysis

To provide deeper insights into the effectiveness of the UGRN setting and proposed methods, we organize our experiments to address the following core questions\.

Q1: Is the proposed Universal GRN setting rational?

As shown in Table[1](https://arxiv.org/html/2605.08128#S4.T1), the baseline Emb method, which maps pre\-trained gene embeddings to regulatory links, consistently outperforms the original scFM methods \(Origin\-Pert and Origin\-Attn\) across most datasets\. For example, on the scBenchmark, Baseline\-Emb achieves an average AUPRC of 0\.663, significantly surpassing the 0\.630 average of Origin\-Attn and the 0\.584 average of Origin\-Pert\. This performance gap confirms our hypothesis that scFMs possess rich and generalizable latent biological priors\. By adopting the UGRN setting, we can effectively bridge the gap between pre\-trained representations of scFMs and explicit gene regulatory network inference, enabling better generalization to unseen genes and heterogeneous datasets than traditional implementations\.

Q2: Are the proposed methods effective?

As shown in Table[1](https://arxiv.org/html/2605.08128#S4.T1), our proposed methods demonstrate superior effectiveness across various datasets\. On scBenchmark, our Ensemble \(Ens\) method achieves a state\-of\-the\-art average AUPRC of 0\.768, establishing a new benchmark for the task\. This dominance is consistent across all categories; for instance, on the Str mH\-L dataset, our method reaches a remarkable AUPRC of 0\.934, significantly outperforming the strong Baseline\-Emb’s 0\.784\. Notably, the GDT method alone reaches an average AUPRC of 0\.738, outperforming the strong Baseline\-Emb \(0\.663\) by a substantial margin\. The advantage is even more pronounced when compared to naive perturbation methods, where our Ens method outperforms Origin\-Pert \(0\.584\) by approximately 31\.5% and surpasses Baseline\-Pert \(0\.596\) by 28\.8%\. This superiority is also observed in results based on scGPT\. These findings validate that our VVP and GDT methods successfully extract significantly richer and more generalizable inter\-gene features from scFMs, far exceeding the capabilities of traditional simplistic strategies like zero\-out\.

Regarding more “Leave\-one\-out” experiments, as shown in Table[2](https://arxiv.org/html/2605.08128#S4.T2), our method maintains a dominant position across different UGRN settings where varying datasets are used for training\. We achieve an average AUPRC of 0\.699, significantly surpassing the averages of baselines\. We observe that our method exhibits remarkable stability even in extreme cases where baselines collapse\. For example, in the L/G mESC setting, Baseline\-Emb fails to generalize, yielding an AUPRC of 0\.515 \(near random guessing\), whereas our method recovers a high performance of 0\.668, an improvement of over 34%\. Even in the most challenging Spc network settings, our method consistently matches or exceeds the baselines\. This indicates that our methods effectively extract intrinsic regulatory mechanisms that are invariant across datasets\.

Q3: Are the proposed methods robust?

To assess the robustness of our methods, we evaluate generalization capabilities across distinct data sources \(Table[3](https://arxiv.org/html/2605.08128#S4.T3)\), species \(Table[4](https://arxiv.org/html/2605.08128#S4.T4)\), and networks \(Table[5](https://arxiv.org/html/2605.08128#S4.T5)\)\. As shown in Table[3](https://arxiv.org/html/2605.08128#S4.T3), our Ens demonstrates exceptional transferability in cross\-dataset settings, achieving an average AUPRC of 0\.741 compared to 0\.644 for the strong Baseline\-Emb\. In cross\-species settings, Ens achieves up to 0\.936 AUPRC, substantially outperforming all baselines\. Furthermore, Table[5](https://arxiv.org/html/2605.08128#S4.T5)highlights the stability of our methods against network variations\. In challenging settings such as the Spc network, where Baseline\-Emb performance collapses to 0\.540, our GDT method maintains 0\.702\. These results confirm that our methods effectively probe intrinsic and generalizable inter\-gene mechanisms, ensuring robust prediction even under various settings with significant distribution shifts\.

Q4: How do our methods perform under imbalanced regulatory scenarios?

While our primary experiments apply a balanced 1:1 ratio, we conduct additional experiments to investigate robustness by varying the Negative\-to\-Positive \(N/P\) ratio from 1 to 10 in Table[6](https://arxiv.org/html/2605.08128#S4.T6)\. As the prevalence of positive samples becomes increasingly sparse, AUPRC naturally decreases\. However, the AUROC scores remain remarkably stable, indicating that the intrinsic ranking capability is preserved\. Crucially, our methods exhibit significantly higher resilience to sparsity compared to baselines\. Under the extreme N/P ratio of 10, our Ens method outperforms Baseline\-Emb by 56\.4% \(0\.413 compared to 0\.264\)\. This relative margin is substantially larger than the 15\.8% improvement observed in the balanced setting \(0\.768 compared to 0\.663\), demonstrating superior robustness in sparse scenarios\.

Table 5:Ablation study on cross\-network generalization performance\.fϕf\_\{\\phi\}is trained on the specific source network and evaluated on datasets from the other networks\. The reported results represent the average AUPRC on the test sets\.
### 4\.4Further Discussion

We established the UGRN setting to provide a rigorous benchmark for evaluating the extent to which features extracted by scFMs retain generalizable regulatory semantics\. Our results validate UGRN settings and confirm that scFMs possess profound latent knowledge regarding gene regulation\. We remain cognizant of the fact that real\-world gene regulation is strictly context\-dependent, heavily influenced by diverse biological covariates such as tissue ontology and the cellular microenvironment\(Sonawaneet al\.,[2017](https://arxiv.org/html/2605.08128#bib.bib22); Browaeyset al\.,[2020](https://arxiv.org/html/2605.08128#bib.bib23)\)\. While our current work isolates the underlying invariant mechanism of regulation, future applications should integrate these context variables into the UGRN framework to model complex, environment\-specific GRN inference\.

Unlike traditional scFM applications that rely on direct outputs \(e\.g\., attention weights\), our approach utilizes a labeled dataset to train a “translator”\. While this may appear to relax the zero\-shot constraint on the genes from the training set, it remains strictly zero\-shot regarding the inference on unseen genes\. By leveraging a limited set of known interactions as a biological prior, we successfully align the scFM’s latent representation space with the gene regulation\. This implies that realizing UGRN inference relies on a combination of pre\-trained scFMs and generalizable priors, a challenge that warrants significant attention in future investigations\.

Table 6:Ablation study on the impact of class imbalance\. We report both AUROC and AUPRC performance under varying Negative\-to\-Positive \(N/P\) ratios in the training/test set\. The AUPRC N/P=1 row corresponds to the average performance reported in Table[1](https://arxiv.org/html/2605.08128#S4.T1)\. Bold indicates the best performance\.

## 5Conclusion

In this paper, we identified and addressed the critical misalignment between the reconstruction\-based pre\-training of Single\-cell Foundation Models \(scFMs\) and the implicit inter\-gene relationship requirements of GRN inference\. To bridge this gap, we established the Universal Gene Regulatory Network \(UGRN\) framework, shifting the paradigm from dataset\-specific fitting to the learning of generalizable regulatory features, thereby validating the rich regulatory knowledge latent within these pre\-trained models\. Furthermore, we proposed Virtual Value Perturbation \(VVP\) and Gradient Trajectory \(GDT\)\. These methods decouple feature extraction from observational expressions, allowing us to distill intrinsic regulatory logic from frozen scFMs through virtual queries, successfully extracting deep, generalizable features inherent in scFMs\. Extensive experiments validate the rationality of the UGRN setting, demonstrating that our methods significantly outperform both original scFM applications and strong baselines\. Notably, our approach exhibits exceptional resilience, where it maintains high performance in challenging cross\-species and cross\-network scenarios where baseline methods collapse, and demonstrates more stability under class imbalance\. These findings confirm that scFMs encode profound, generalizable biological priors and that our methods effectively unlock this potential to establish a solid foundation for Universal GRN Inference\.

## 6Acknowledgments

This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No\. XDA0460205\.

## Impact Statement

This paper presents work aimed at advancing the field of single\-cell foundation models\. By enabling Universal Gene Regulatory Network inference, our framework has the potential to accelerate the identification of disease mechanisms and therapeutic targets, particularly in scenarios lacking extensive observational data\. While this work facilitates biological discovery, regulatory links predicted by our models are computational hypotheses that require experimental validation before clinical application\. We do not foresee immediate negative ethical or societal consequences specifically arising from this work\.

## References

- C\. Ahlmann\-Eltze, W\. Huber, and S\. Anders \(2025\)Deep\-learning\-based gene perturbation effect prediction does not yet outperform simple linear baselines\.Nature Methods22\(10\),pp\. 1657–1661\.External Links:[Document](https://dx.doi.org/10.1038/s41592-025-02772-6),[Link](https://doi.org/10.1038/s41592-025-02772-6)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2),[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- S\. Aibar, C\. B\. González\-Blas, T\. Moerman, V\. A\. Huynh\-Thu, H\. Imrichová, G\. Hulselmans, J\. Rambow, J\. Marine, P\. Geurts, J\. Aerts,et al\.\(2017\)SCENIC: single\-cell regulatory network inference and clustering\.Nature Methods14\(11\),pp\. 1083–1086\.External Links:[Document](https://dx.doi.org/10.1038/nmeth.4463)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p1.2)\.
- A\. Barabási and Z\. N\. Oltvai \(2004\)Network biology: understanding the cell’s functional organization\.Nature Reviews Genetics5\(2\),pp\. 101–113\.External Links:[Document](https://dx.doi.org/10.1038/nrg1272),[Link](https://doi.org/10.1038/nrg1272)Cited by:[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p1.1)\.
- R\. Browaeys, W\. Saelens, and Y\. Saeys \(2020\)NicheNet: modeling intercellular communication by linking ligands to target genes\.Nature Methods17\(2\),pp\. 159–162\.External Links:[Document](https://dx.doi.org/10.1038/s41592-019-0667-5),[Link](https://doi.org/10.1038/s41592-019-0667-5)Cited by:[§4\.4](https://arxiv.org/html/2605.08128#S4.SS4.p1.1)\.
- G\. Chen and Z\. Liu \(2022\)Graph attention network for link prediction of gene regulations from single\-cell rna\-sequencing data\.Bioinformatics38\(19\),pp\. 4522–4529\.Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1),[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p5.6)\.
- H\. Cui, C\. Wang, H\. Maan,et al\.\(2024\)ScGPT: toward building a foundation model for single\-cell multi\-omics using generative ai\.Nature Methods21\(8\),pp\. 1470–1480\.External Links:[Document](https://dx.doi.org/10.1038/s41592-024-02201-0),[Link](https://doi.org/10.1038/s41592-024-02201-0)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2),[§2](https://arxiv.org/html/2605.08128#S2.p2.1),[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p6.3),[§4\.2](https://arxiv.org/html/2605.08128#S4.SS2.p1.2)\.
- E\. H\. Davidson, J\. P\. Rast, P\. Oliveri, A\. Ransick, C\. Calestani, C\. Yuh, T\. Minokawa, G\. Amore, V\. Hinman, C\. Arenas\-Mena, O\. Otim, C\. T\. Brown, C\. B\. Livi, P\. Y\. Lee, R\. Revilla, A\. G\. Rust, Z\. J\. Pan, M\. J\. Schilstra, P\. J\. Clarke, M\. I\. Arnone, and H\. Bolouri \(2002\)A genomic regulatory network for development\.Science295\(5560\),pp\. 1669–1678\.External Links:[Document](https://dx.doi.org/10.1126/science.1069883),[Link](https://doi.org/10.1126/science.1069883)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p1.2)\.
- M\. B\. Eisen, P\. T\. Spellman, P\. O\. Brown, and D\. Botstein \(1998\)Cluster analysis and display of genome\-wide expression patterns\.Proceedings of the National Academy of Sciences95\(25\),pp\. 14863–14868\.External Links:[Document](https://dx.doi.org/10.1073/pnas.95.25.14863)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p1.2)\.
- J\. J\. Faith, B\. Hayete, J\. T\. Thaden, I\. Mogno, J\. Wierzbowski, G\. Cottarel, S\. Kasif, J\. J\. Collins, and T\. S\. Gardner \(2007\)Large\-scale mapping and validation of E\. coli transcriptional regulation from a compendium of expression profiles\.PLoS Biology5\(1\),pp\. e8\.External Links:[Document](https://dx.doi.org/10.1371/journal.pbio.0050008)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1)\.
- M\. Hao, J\. Gong, X\. Zeng,et al\.\(2024\)Large\-scale foundation model on single\-cell transcriptomics\.Nature Methods21\(8\),pp\. 1481–1491\.External Links:[Document](https://dx.doi.org/10.1038/s41592-024-02305-7)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2)\.
- A\. Haury, F\. Mordelet, P\. Vera\-Licona, and J\. Vert \(2012\)TIGRESS: trustful inference of gene regulation using stability selection\.BMC Systems Biology6\(1\),pp\. 145\.External Links:[Document](https://dx.doi.org/10.1186/1752-0509-6-145),[Link](https://doi.org/10.1186/1752-0509-6-145)Cited by:[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p4.2)\.
- V\. A\. Huynh\-Thu, A\. Irrthum, L\. Wehenkel, and P\. Geurts \(2010\)Inferring regulatory networks from expression data using tree\-based methods\.PLoS ONE5\(9\),pp\. e12776\.External Links:[Document](https://dx.doi.org/10.1371/journal.pone.0012776)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1)\.
- Z\. Jin, Y\. Dong, A\. M\. Rafi, M\. M\. Patwary, C\. Xu, M\. H\. Raadam, C\. G\. de Boer, and C\. Ignea \(2025\)Unraveling the regulatory dynamics of bidirectional promoters for modulating gene co\-expression and metabolic flux in Saccharomyces cerevisiae\.Nucleic Acids Research53\(11\),pp\. gkaf511\.External Links:[Document](https://dx.doi.org/10.1093/nar/gkaf511),[Link](https://doi.org/10.1093/nar/gkaf511)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2),[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- J\. Kalfon, J\. Samaran, G\. Peyré,et al\.\(2025\)ScPRINT: pre\-training on 50 million cells allows robust gene network predictions\.Nature Communications16\(1\),pp\. 3607\.External Links:[Document](https://dx.doi.org/10.1038/s41467-025-58699-1),[Link](https://doi.org/10.1038/s41467-025-58699-1)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- K\. Z\. Kedzierska, L\. Crawford, A\. P\. Amini,et al\.\(2025\)Zero\-shot evaluation reveals limitations of single\-cell foundation models\.Genome Biology26\(1\),pp\. 101\.External Links:[Document](https://dx.doi.org/10.1186/s13059-025-03574-x),[Link](https://doi.org/10.1186/s13059-025-03574-x)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1),[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- D\. P\. Kingma and J\. Ba \(2015\)Adam: a method for stochastic optimization\.InInternational Conference on Learning Representations \(ICLR\),External Links:[Link](https://arxiv.org/abs/1412.6980)Cited by:[§4\.2](https://arxiv.org/html/2605.08128#S4.SS2.p1.2)\.
- S\. Kommu, Y\. Wang, Y\. Wang, and X\. Wang \(2025\)Prediction of gene regulatory connections with joint single\-cell foundation models and graph\-based learning\.Bioinformatics41\(Supplement1\),pp\. i619–i627\.External Links:[Document](https://dx.doi.org/10.1093/bioinformatics/btaf217),[Link](https://doi.org/10.1093/bioinformatics/btaf217)Cited by:[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p10.1)\.
- A\. A\. Margolin, I\. Nemenman, K\. Basso, C\. Wiggins, G\. Stolovitzky, R\. Dalla Favera, and A\. Califano \(2006\)ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context\.BMC Bioinformatics7\(S1\),pp\. S7\.External Links:[Document](https://dx.doi.org/10.1186/1471-2105-7-S1-S7)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1)\.
- T\. Moerman, S\. Aibar, C\. Bravo González\-Blas, J\. Gleerup, M\. Fiers, S\. Aerts, and K\. Van Steen \(2019\)GRNBoost2 and arboreto: efficient and scalable inference of gene regulatory networks\.Bioinformatics35\(12\),pp\. 2159–2161\.External Links:[Document](https://dx.doi.org/10.1093/bioinformatics/bty916)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1)\.
- A\. Pratapa, A\. P\. Jalhal, J\. N\. Law, A\. Bharadwaj, and T\. M\. Murali \(2020\)Benchmarking algorithms for gene regulatory network inference from single\-cell transcriptomic data\.Nature Methods17\(2\),pp\. 147–154\.External Links:[Document](https://dx.doi.org/10.1038/s41592-019-0690-6)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p1.2),[§4\.1](https://arxiv.org/html/2605.08128#S4.SS1.p1.1)\.
- J\. Qi, Y\. Cui, K\. Guo, X\. Zhang, J\. Huang, and G\. Xie \(2025\)A simple and comprehensive benchmark for single\-cell transcriptomics\.InProceedings of the AAAI Conference on Artificial Intelligence,Vol\.39,pp\. 676–684\.Cited by:[§4\.2](https://arxiv.org/html/2605.08128#S4.SS2.p1.2)\.
- H\. Shu, J\. Zhou, X\. Lian, H\. Li, Z\. Zhao, J\. Zeng, and J\. Ma \(2021\)Modeling gene regulatory networks using neural network architectures\.Bioinformatics37\(19\),pp\. 3139–3150\.External Links:[Document](https://dx.doi.org/10.1093/bioinformatics/btab226)Cited by:[§2](https://arxiv.org/html/2605.08128#S2.p1.1)\.
- A\. R\. Sonawane, S\. T\. Weiss, K\. Glass, and M\. L\. Kuijjer \(2017\)Understanding tissue\-specific gene regulation\.Cell Reports21\(4\),pp\. 1077–1088\.External Links:[Document](https://dx.doi.org/10.1016/j.celrep.2017.10.032),[Link](https://doi.org/10.1016/j.celrep.2017.10.032)Cited by:[§4\.4](https://arxiv.org/html/2605.08128#S4.SS4.p1.1)\.
- L\. Song, P\. Langfelder, and S\. Horvath \(2012\)Comparison of co\-expression measures: mutual information, correlation, and model based indices\.BMC Bioinformatics13\(1\),pp\. 328\.External Links:[Document](https://dx.doi.org/10.1186/1471-2105-13-328),[Link](https://doi.org/10.1186/1471-2105-13-328)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p1.2)\.
- T\. Stuart, A\. Butler, P\. Hoffman, C\. Hafemeister, E\. Papalexi, W\. M\. Mauck, Y\. Hao, M\. Stoeckius, P\. Smibert, and R\. Satija \(2019\)Comprehensive integration of single\-cell data\.Cell177\(7\),pp\. 1888–1902\.e21\.External Links:[Document](https://dx.doi.org/10.1016/j.cell.2019.05.031),[Link](https://doi.org/10.1016/j.cell.2019.05.031)Cited by:[§4\.1](https://arxiv.org/html/2605.08128#S4.SS1.p1.1)\.
- C\. V\. Theodoris, L\. Xiao, A\. Chopra,et al\.\(2023\)Transfer learning enables predictions in network biology\.Nature618\(7965\),pp\. 616–624\.External Links:[Document](https://dx.doi.org/10.1038/s41586-023-06139-9),[Link](https://doi.org/10.1038/s41586-023-06139-9)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2),[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- Y\. Wang, X\. Chen, Z\. Zheng, L\. Huang, W\. Ye, F\. Wang, Z\. Zhang, and K\. Wong \(2024\)ScGREAT: transformer\-based deep\-language model for gene regulatory network inference from single\-cell transcriptomics\.iScience27\(4\),pp\. 109532\.Cited by:[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p1.1),[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p10.1)\.
- J\. Wu, Q\. Ye, Y\. Wang,et al\.\(2025\)Biology\-driven insights into the power of single\-cell foundation models\.Genome Biology26\(1\),pp\. 334\.External Links:[Document](https://dx.doi.org/10.1186/s13059-025-03781-6),[Link](https://doi.org/10.1186/s13059-025-03781-6)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2),[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- F\. Yang, W\. Wang, F\. Wang, Y\. Fang, D\. Tang, J\. Huang, H\. Lu, and J\. Yao \(2022\)ScBERT as a large\-scale pretrained deep language model for cell type annotation of single\-cell rna\-seq data\.Nature Machine Intelligence4\(10\),pp\. 852–866\.External Links:[Document](https://dx.doi.org/10.1038/s42256-022-00534-z)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2),[§2](https://arxiv.org/html/2605.08128#S2.p2.1)\.
- X\. Yang, G\. Liu, G\. Feng,et al\.\(2024\)GeneCompass: deciphering universal gene regulatory mechanisms with a knowledge\-informed cross\-species foundation model\.Cell Research34\(12\),pp\. 830–845\.External Links:[Document](https://dx.doi.org/10.1038/s41422-024-01034-y)Cited by:[§1](https://arxiv.org/html/2605.08128#S1.p2.2)\.
- Y\. Yuan and Z\. Bar\-Joseph \(2019\)Deep learning for inferring gene relationships from single\-cell expression data\.Proceedings of the National Academy of Sciences116\(52\),pp\. 27151–27158\.External Links:[Document](https://dx.doi.org/10.1073/pnas.1911536116),[Link](https://doi.org/10.1073/pnas.1911536116)Cited by:[§3\.1](https://arxiv.org/html/2605.08128#S3.SS1.p4.2)\.