Local Causal Structures

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Latest papers 17

Aug 5, 2026cs.LG

Adversarial Causal Intervention Falsification

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

Mojtaba Eslami

University of Calgary

Local Causal Structures Causal Adversarial Robustness

Aug 4, 2026cs.AI

Computing Actual Causes for Neural Network Predictions under Structured Causal Inputs

Explaining the predictions of neural networks is a central challenge in trustworthy AI. Existing explanation methods, such as those based on feature attribution or minimal sufficient sets, typically treat input features as independent, which can yield misleading explanations when inputs exhibit structured dependencies. We address this by formalizing explanations as Halpern-Pearl (HP) actual causes, modeling input dependencies using Boolean Structural Causal Models (SCMs). We compute HP causes by applying bound propagation and branch-and-bound techniques, while providing formal guarantees of completeness and minimality. Our experiments show that we substantially outperform brute-force and ILP baselines in scalability, and outperform heuristic search as graph size grows, computing all minimal actual causes on instances with search spaces of up to

2.3\times10^{13}

candidate (cause, contingency) pairs, on SCMs with up to 28 nodes, within a 180s per-instance budget. In a case study, we further show that ignoring input dependencies inflates the number of reported causes, 14.9% of which are spurious under our SCM.

Jannick Strobel, Muqsit Azeem, Stefan Leue

University of Konstanz

Local Causal Structures Explainable AI Methods Trustworthy Artificial Intelligence Limited Data

Jul 30, 2026cs.CL

Causal Discovery with Inverted Self-attention for Multivariate Time Series

Causal discovery in multivariate time series data is challenging due to complex interactions, high dimensionality, and nonlinear dependencies among variables. Existing methods often struggle to capture these complexities, resulting in inaccurate causal structures. To address this issue, we propose a novel framework that leverages self-attention mechanisms within the transformer architecture for causal discovery. Our approach introduces a novel inverted causal self-attention mechanism (CSAM) that emphasizes latent and indirect causal relationships by inverting tokens and inducing sparsity in attention scores, focusing on significant causal interactions and reducing spurious correlations. Additionally, we develop a global causal algorithm to identify global causal links, providing a holistic metric for causal influence, along with a causal verification module to ensure robustness in the identified causal relationships, enhancing the reliability of our framework. Experiments on both linear and nonlinear datasets, along with ablation studies and sensitivity analyses, show that our framework outperforms existing methods, demonstrating its potential for causal discovery in complex multivariate time series.

Yusen Liu, Yong Wang, Yifan Yin +3

School of Computer Science, University of Technology Sydney, Sydney, Australia · TianFu YongXing Laboratory, Chengdu, China · Faculty of Data Science, City University of Macau, Macau, China +1

Causal Discovery Methods Multivariate Time-Series Local Causal Structures Causal Attention

Jul 24, 2026cs.LG

Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equations

Pearl's structural causal model (SCM) framework, built on directed acyclic graphs (DAGs) and the do-calculus, is the dominant formal language for causal reasoning. Yet it carries two structural restrictions: every relationship must be pre-specified as a directed causal edge, and feedback cycles are forbidden. This paper examines two classes of phenomena that strain these restrictions. First, symmetric physical and economic constraints, the ideal gas law being the canonical case, carry no intrinsic causal direction. Direction emerges only under intervention, and which variable is solved for must be specified as part of the intervention. We formalize such constraints as causal zeros within an Extended Causal Model by adding an activation operator, subject to local solvability and graph-admissibility conditions. Second, for the class of finite-propagation state-space systems considered here, we treat apparent instantaneous cycles as artifacts of suppressed time and ground both causal zeros and feedback in Causal Differential Equations (CDEs). In these, the transient regime is a time-unrolled acyclic causal process, and causal zeros arise as the defining functions of attracting equilibrium manifolds; periodic and chaotic attractors define further regimes of the same dynamics, treated through attractor-relative intervention. We give the extended do-calculus, identifiability conditions, counterfactual semantics, and open problems.

Sergei V. Kalinin

Department of Materials Science and Engineering, University of Tennessee, Knoxville

Local Causal Structures Directed Acyclic Graph Acyclic Graphs Ordinary Differential Equations Attractors

Jul 24, 2026cs.LG

Indexing: the Beginning and the End

We study information bottlenecks in modern deep-learning architectures -- RNNs, softmax transformers, linear-attention transformers and state-space models -- through the lens of the indexing primitive. In this primitive, the input consists of

n

bits and one integer

i

from

1

to

n

called the index, and the output equals the value of the

i

-th bit. We introduce causal complexity for masked architectures. We show that architectures with low causal complexity cannot solve the indexing primitive in any constant number of layers when the index appears at the end of the input. In particular, this limitation applies to low-parameter RNNs, SSMs and masked linear-attention transformers. In contrast, small softmax transformers can solve it in one layer, while non-masked linear-attention transformers can solve it in 2, which separates them from their masked counterparts. In turn, when the index appears at the beginning, we show that small RNNs are capable of solving this task in 1 layer, while all the other architectures require 2. All our impossibility results are unconditional and apply even to models that employ infinite-precision real arithmetic. Moreover, experiments for up to

n=64

qualitatively align with our theory: configurations with low-parameter theoretical solutions learn the indexing task easily, while configurations that do not admit such theoretical solutions struggle to learn as the sequence length grows.

Alexander Kozachinskiy, Vicente Opazo, Felipe Urrutia

CENIA · Pontifical Catholic University of Chile

Deep Learning Architectures Information Bottleneck Local Causal Structures

Jul 23, 2026cs.AI

How Rules Represent Causal Knowledge: Causal Modeling with Probabilistic Logic Programming

Pearl famously argues that causal knowledge enables the prediction of intervention effects. By contrast, purely descriptive knowledge supports only conclusions drawn from observations. His theory of causality, however, is developed exclusively within Bayesian networks and causal models. Consequently, it is largely restricted to acyclic causal relationships, and transferring its ideas to other formalisms risks misinterpretation or inconsistency. This paper brings Pearl's approach to causality into probabilistic logic programming (PLP). To this end, such programs are aligned with philosophical foundations established in prior work that do not rely on temporal notions; that is, all relevant events are assumed to occur simultaneously. A formal causal semantics for these programs, together with a notion of intervention and an implementation, is proposed. It is shown that this semantics coincides with the P-log semantics for stratified ProbLog programs, while the two may differ in the non-stratified case and for other PLP formalisms.

Kilian Rueckschloss, Felix Weitkaemper

Eberhard Karls Universitaet Tuebingen · University of Tübingen Tübingen, Germany · German University of Digital Science +1

Causal Modeling Local Causal Structures Logic Bayesian Networks

Jul 22, 2026cs.LG

Local Causal Structure Learning in the Presence of Latent Variables and Selection Bias

Discovering the direct causes and effects of a target variable from observational data is a fundamental problem in causal discovery, with broad applications in domains such as gene regulatory analysis and biomedical research. Existing causal discovery methods either learn a global causal structure, which incurs substantial computational cost, or assume the absence of latent variables and selection bias, assumptions that are often violated in real-world settings. Motivated by these challenges, we study local causal structure learning in the presence of latent variables and selection bias. Specifically, we first characterize a local region that enables target-specific causal discovery without recovering the entire global structure. We then establish a theoretical bridge between causal information learned from the observed distribution induced on this local region and the corresponding information in the global causal structure. Building on these foundations, we propose LoCaLS, a local causal structure learning algorithm that is sound and complete under standard assumptions and identifies the same direct causes and effects of a target variable as those identifiable by global causal discovery methods, while allowing for latent variables and selection bias. Extensive experiments on random and real-world structures demonstrate that the proposed method consistently achieves higher structural accuracy than existing local methods while requiring substantially less computational effort than state-of-the-art global methods. Furthermore, applications to two real-world gene expression datasets reveal biologically plausible target-specific causal structures, demonstrating its practical applicability in large-scale biological data analysis.

Zheng Li, Hao Zhang, Ruxin Wang +3

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China. · School of Computer Science, Guangdong University of Technology, Guangzhou, China. · Peng Cheng Laboratory, Shenzhen, China. +3

Causal Discovery Methods Local Causal Structures Selection Bias Latent Variable

Jul 13, 2026cs.AI

StructAgent: Harness Long-horizon Digital Agents with Unified Causal Structure

Recent advances in large language models (LLMs) and vision-language models (VLMs) have enabled increasingly capable digital agents for computer use. However, real-world tasks are often long-horizon and involve evolving contexts containing accumulated observations, intermediate edits, failed attempts, and partially completed executions. Existing agents typically operate over raw interaction history, making task progress difficult to interpret, verify, and recover, which ultimately limits reliable long-horizon execution. In this paper, we argue that addressing this challenge requires explicitly structuring both the agent's state and workflow around a unified causal representation of task progress. We present \textbf{StructAgent}, a state-centered framework that introduces a unified state for maintaining compact, verifiable task progress and a structured workflow that regulates progress through verifier-backed state transitions. Building on this design, StructAgent further enables explicit progress checkpointing, evidence-driven task completion, targeted failure recovery, and tool-supported execution, while ensuring that all progress updates remain grounded in verification. Extensive experiments demonstrate that StructAgent consistently improves a wide range of LLM and VLM backbones on long-horizon computer-use tasks. On OSWorld-Verified, it improves Qwen3.5-9B from 27.0% to 46.9% success rate and Qwen3.5-27B from 31.6% to 62.2%, while achieving a new open-source state of the art of 78.9% with MiniMax-M3. Moreover, the same framework generalizes beyond desktop environments to Minecraft, demonstrating the generality of our design.

Wenyi Wu, Sibo Zhu, Kun Zhou +3

University of California, San Diego · 2Aether AI Lab · §Work done during an internship at Aether AI.

Long-Horizon Agents Agent Loop State-Tracking Agentic Workflow Design Local Causal Structures Intermediate Checkpoints+1

Jun 21, 2026cs.CL

Words as Difference Makers: How Large Language Models Determine Causal Structure in Text

Because large language models (LLMs) are impressively successful in predicting text, it appears that they must have access to a 'world model' representing causal and definitional structure. However, the dominant formalisms of modern causal inference -- Judea Pearl's interventionist approach and the Neyman-Rubin potential outcomes framework -- struggle to illuminate how LLMs learn causal structure. I resolve this puzzle by arguing that LLMs employ a specific inductive approach based on a difference-making logic -- sometimes called variational induction. I demonstrate how central aspects of this logic are realized during training, where LLMs require enormous amounts of text data from a wide range of contexts to identify difference- and indifference-makers within word sequences. Furthermore, I analyze specific architectural features of LLMs -- such as token embeddings and self-attention -- to determine their roles in variational induction. The difference-making logic of LLMs fundamentally parallels the experimental method, where causal relations are derived by systematically varying individual circumstances to determine their influence on a phenomenon.

Wolfgang Pietsch

tum

Local Causal Structures Causal Text Analysis and Detection Variational

Jun 20, 2026cs.LG

FedCausal-Dyn: A Causal-Dynamic Paradigm for Federated Learning under Dynamic Feature Drift

This paper addresses the challenging problem of dynamic feature drift in federated learning, where data distributions evolve across clients and over time -- a common scenario in real-world applications like financial technology. Existing approaches often assume static drift, limiting their effectiveness in non-stationary environments. To overcome this, we propose \textbf{FedCausal-Dyn}, a novel federated learning framework built on a causal-dynamic paradigm. Its key innovation is \textit{causal-domain feature separation}, which disentangles domain-invariant causal features from spurious, domain-specific variations via specialized projection heads and adversarial training. This enables \textit{reliable and dynamic prototype aggregation}, weighting local class prototypes by estimated reliability before global aggregation. We further introduce \textit{causal-feature guided collaborative regularization}, unifying prototype contrastive alignment and domain invariance into a cohesive objective. Extensive experiments on three federated domain generalization benchmarks demonstrate that FedCausal-Dyn consistently achieves state-of-the-art performance, with the highest average accuracy and the most stable results. Ablation studies confirm each component's critical contribution. Our work provides a robust and principled solution for federated learning under dynamic feature drift.

Kaijie Chen, Alex Johnson, Maria Garcia +2

Mindlab

Federated Learning Regularization Local Causal Structures

Jun 3, 2026cs.LG

Pattern Selectivity is Not Task-Causal Structure: A Cross-Architecture Mechanistic Study of Composed-Task Circuits in 1B-Class Language Models

We test whether a single screen-and-ablate recipe -- identify attention-head circuits by task-pattern selectivity, then verify by causal ablation against a matched-random null -- produces consistent mechanistic claims across model families. The recipe ports across pipelines; the specific circuit it identifies does not. Across four composed tasks (indirect-object identification, greater-than, successor sequences, variable binding) and three 1B-class language models from distinct training pipelines (Pythia 1B / Pile / dense; OLMo 1B / DCLM / dense; OLMoE 1B-7B / DCLM / mixture-of-experts), we run a unified protocol with the matched-random null sampled across ten seeds per cell. The resulting 12 (task, model) cells contain no two that share the same primary causal screen at comparable effect size: the same task, with the same behavioral capability, is implemented through different attention-pattern types across models. We introduce a five-category screen-outcome taxonomy -- primary cause, secondary cause, correlate, interferer, null -- with quantitative thresholds, and show that all five outcomes appear in the panel. We propose a falsifiable hypothesis: the MoE model in our panel builds composed-task circuits on top of a foundational previous-token positional substrate (the prev-token-circuit ablation is the strongest causal screen on 3 of 4 tasks for OLMoE 1B-7B), with the IOI exception consistent with IOI being a final-position name-copying task whose structure directly probes a different pattern. The hypothesis comes with explicit predictions for other MoE language models. We frame the methodology honestly: the spectral participation-ratio signal from the companion methodology paper is a general indicator of specialized computation; what makes a finding task-specific is the task-pattern screen plus a per-model causal verification.

Yongzhong Xu

Ablation Language Modeling Selectivity Cross-Architecture Generalization Local Causal Structures Circuits+1

May 30, 2026cs.LG

The Paradox of Outcome Optimization: A Causal Information-Theoretic Bound on Reasoning Shortcuts in LLMs

Large Language Models (LLMs) aligned via outcome-based Reinforcement Learning (RL) frequently exhibit a critical failure mode: they achieve high performance on in-distribution benchmarks while demonstrating brittle reasoning capabilities on out-of-distribution (OOD) tasks. We term this phenomenon Reward-Induced Manifold Collapse. We establish a theoretical framework bridging Structural Causal Models (SCM) and the Information Bottleneck (IB) principle to explain this paradox. We define reasoning as a high-complexity causal process and shortcut learning as the exploitation of low-complexity spurious correlations. Under the implicit inductive bias of Stochastic Gradient Descent (SGD), models optimized for outcome rewards are biased toward shortcut solutions whenever the training distribution allows for a ``Markovian Screening'' of the true causal mechanism. We derive a new generalization bound based on Semantic Coverage Measure (

η

) rather than sample size, showing why data scaling on homogeneous distributions may fail to correct reasoning flaws. We also show that Process Reward Models (PRMs) function as Topological Filters, enforcing step-wise mutual information constraints that render the low-complexity shortcut manifold inadmissible. These results provide a mathematical grounding for the role of process supervision beyond simple credit assignment.

Zihan Chen, Yiming Zhang, Wenxiang Geng +2

1HFIPS, Chinese Academy of Sciences · University of Science and Technology of China

LLM Reasoning Strategies Process Reward Model Reasoning Skills Local Causal Structures Information-Theoretic Limits Causal

May 20, 2026cs.LO

Causal Past Logic for Runtime Verification of Distributed LLM Agent Workflows

Distributed LLM agent workflows should not be monitored as if they produced a single sequential log. In an asynchronous execution, a decision can only depend on events that are causally visible to the lifeline that makes it: an event that appears earlier in some log may still be unknown locally. We extend the ZipperGen agent-workflow framework with Causal Past Logic (CPL), a small past-time temporal logic for guards in conditionals and while loops. In addition to standard past-time modalities such as previous and since, a guard can inspect the latest causally visible event of another lifeline and selected variables stored there. The formula is a source-level guard: it is evaluated online by the owner lifeline and can influence control flow at runtime. We give a vector-clock monitor with latest-value views and prove that the locally computed monitor value coincides with the denotational semantics of the guard at the current event. Thus runtime verification becomes part of the coordination language itself, rather than a post-hoc check over an execution log.

Benedikt Bollig

Universit´e Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France

Runtime Enforcement Local Causal Structures Large Language Model Workflows Agent Loop

May 17, 2026cs.LG

CasualSynth: Generating Structurally Sound Synthetic Data

Large Language Models (LLMs) generate realistic synthetic data but offer no guarantee that their outputs respect the causal mechanisms governing the target domain. We introduce CausalSynth, a framework that decouples causal structure generation from semantic realization, yielding synthetic data that is both causally valid and linguistically rich. The framework operates in three phases. First, a Structural Causal Model (SCM) - a tuple of structural equations defined over a directed acyclic graph (DAG) generates causal skeletons, i.e., variable assignments that satisfy the Global Markov Property of the governing DAG, via ancestral sampling. Second, an LLM acts as a constrained \emph{realizer}, a conditional translator that maps each skeleton to a high-dimensional observation such as a clinical note or a transaction log. Third, an Iterative Consistency Verification module detects structural violations through deterministic extraction and feeds targeted corrections back to the LLM, forming a closed-loop refinement process. We identify the Semantic Backdoor problem the systematic tendency of LLMs to override imposed causal facts with pre-training priors -- and prove that our iterative mechanism reduces the resulting selection bias relative to standard rejection sampling. On three causal benchmarks (ASIA, ALARM, and MIMIC-Struct), CausalSynth preserved conditional independencies with false-positive rates near the nominal

α=0.05

level and achieved realizability rates above 96% with 70B-parameter LLM backbones. The framework additionally supports principled interventional and counterfactual generation through noise retention and graph mutilation.

Zehua Cheng, Wei Dai, Jiahao Sun +1

Department of Computer Science, University of Oxford · FLock.io United Kingdom · Institute of Logic and Computation, TU Wien

Synthetic Data Local Causal Structures Synthesizer Data Generation Large Language Model Backbones

May 7, 2026cs.AI

Event-Causal RAG: A Retrieval-Augmented Generation Framework for Long Video Reasoning in Complex Scenarios

Recent large vision-language models have achieved strong performance on short- and medium-length video understanding, yet they remain inadequate for ultra-long or even infinite video reasoning, where models must preserve coherent memory over extended durations and infer causal dependencies across temporally distant events. Existing end-to-end video understanding methods are fundamentally limited by the

O(n^2)

complexity of self-attention, while recent retrieval-augmented generation (RAG) approaches still suffer from fragmented clip-level memory, weak modeling of temporal and causal structure, and high storage and online inference costs. We present Event-Causal RAG, a lightweight retrieval-augmented framework for infinite long-video reasoning. Instead of indexing fixed-length clips, our method segments streaming videos into semantically coherent events and represents each event as a structured State-Event-State (SES) graph, capturing the event together with its surrounding state transitions. These graphs are merged into a global Event Knowledge Graph and stored in a dual-store memory that supports both semantic matching and causal-topological retrieval. On top of this memory, we design a bidirectional retrieval strategy to efficiently identify the most relevant event causal chains and provide them, together with the associated video evidence, to a backbone video foundation model for answer generation. Experiments on long-video understanding benchmarks demonstrate that Event-Causal RAG consistently outperforms strong clip-based retrieval baselines and long-context video models, particularly on questions requiring multi-event integration and causal inference across long temporal gaps, while also achieving improved memory efficiency and robust streaming performance.

Peizheng Yan, Yu Zhao, Liang Xie +3

Tianjin Key Lab of Intelligent Unmanned Swarm Tech & System Tianjin University Tianjin, China · Institute of Computing and Intelligence Harbin Institute of Technology (Shenzhen) Shenzhen, China · Tianjin Artificial Intelligence Innovation Center Tianjin, China +2

Video Understanding Fine-Grained Video Understanding Local Causal Structures Knowledge Graphs

May 1, 2026cs.LG

M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data

Causal graph discovery for space-time systems is challenging in high-dimensional gridded data, which often has many more grid cells than temporal observations per cell. The Causal Space-Time Stencil Learning (CaStLe) meta-algorithm was developed to address that niche under space-time locality and stationarity assumptions, but it is currently limited to univariate analyses. In this work, we present M-CaStLe. M-CaStLe generalizes the local embedding and parent-identification phases of CaStLe to jointly model local within-variable and cross-variable space-time causal structures in gridded data. Like CaStLe, by constraining candidate parents to a constant-size space-time neighborhood and pooling spatial replicates, M-CaStLe increases effective sample size to make discovery tractable in high-dimensional settings. We further decompose the resulting multivariate stencil graph into reaction and spatial graphs to aid interpretation in complex settings. We study M-CaStLe in four settings: a multivariate space-time vector autoregression benchmark with known ground truth, an advective-diffusive-reaction partial differential equation verification problem with derived physical reference structure, an atmospheric chemistry case study in a low-temporal-sample regime, and an El Niño Southern Oscillation study on reanalysis data, identifying phase-dependent ocean--atmosphere coupling. Across these settings, M-CaStLe more accurately recovers multivariate causal structure in controlled settings and identifies important physical dynamics in real-world case studies. Overall, M-CaStLe advances causal discovery for multivariate space-time systems while retaining interpretability at the grid level.

J. Jake Nichol, Michael Weylandt, G. Matthew Fricke +2

Scientific Machine Learning, Center for Computing Research Sandia National Laboratories · Zicklin School of Business Baruch College, CUNY · Department of Computer Science University of New Mexico +2

Causal Discovery Methods Local Causal Structures Spatiotemporal Atmospheric Dynamics

Apr 18, 2026cs.AI

A phenotype-driven and evidence-governed framework for knowledge graph enrichment and hypotheses discovery in population data

Current knowledge graph (KG) construction methods are confirmatory, focusing on recovering known relationships rather than identifying novel or context-dependent nodes. This paper proposes a phenotype-driven and evidence-governed framework that shifts the paradigm toward structured hypothesis discovery and controlled KG expansion. The approach integrates graph neural networks (GNNs) for phenotype discovery, causal inference, probabilistic reasoning and large language models (LLMs) for hypothesis generation and claim extraction within a unified pipeline. The framework prioritizes relationships that are both structurally supported by data and underexplored in the literature. KG expansion is formulated as a multi-objective optimization problem, where candidate claims are jointly evaluated in terms of relevance, structural validation and novelty. Pareto-optimal selection enables the identification of non-dominated claims that balance confirmation and discovery, avoiding trivial or redundant knowledge inclusion. Experiments on heterogeneous population datasets demonstrate that the proposed framework produces more interpretable phenotypes, reveals context-dependent causal structures and generates high-quality claims that align with both data and scientific evidence. Compared to rule-based and LLM-only baselines, the method achieves the best trade-off across plausibility, novelty, validation and relevance. In retrieval-augmented settings, it significantly improves performance (Recall@5=0.98) while reducing hallucination rates (0.05), highlighting its effectiveness in grounding LLM outputs.

Adela Bâra, Simona-Vasilica Oprea

Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, Bucharest, Romania

Knowledge Graphs Local Causal Structures Phenotypes Evidence-Grounded Questions Hypothesis Graph Neural Networks+2