NeurIPS 2026 Papers

Expert background knowledge is often available in practical applications of causal discovery. Such constraints on the true causal graph can help causal discovery in terms of identifiability of causal effects and accuracy of the learned structure, but also in reducing the space of candidate causal graphs. As causal discovery can become computationally expensive for large number of variables, it is crucial to utilize background knowledge effectively \emph{during} the causal discovery process. However, most current methods only use background knowledge in a postprocessing step after causal discovery to refine the learned graph. In this work, we develop a framework for utilizing background knowledge during the causal discovery process, focusing especially on scalable causal discovery methods that recover only a subset of the whole graph. We implement our framework for multiple algorithms and empirically show that utilizing background knowledge can both reduce computational requirements and increase the quality of the learned structures.

Large language models (LLMs) are increasingly deployed in teams, yet existing coordination approaches often occupy two extremes. Highly structured methods rely on fixed roles, pipelines, or task decompositions assigned a priori. In contrast, fully unstructured teams enable adaptability and exploration but suffer from inefficiencies such as error propagation, inter-agent conflicts, and wasted resources (measured in time, tokens, or file operations). We introduce Language Agent Teams for Task Evolution (LATTE), a framework for coordinating LLM teams inspired by distributed systems, where processors must operate under partial observability and communication constraints. In LATTE, a team of agents collaboratively construct and maintain a shared, evolving coordination graph which encodes sub-task dependencies, individual agent assignment, and the current state of sub-task progress. This protocol maintains consistency while empowering agents to dynamically allocate work, adapt coordination, and discover new tasks. Across multiple collaborative tasks and a variety of base models, we demonstrate how LATTE reduces token usage, wall-clock time, communication, and coordination failures (e.g. file conflicts and redundant outputs) while matching or exceeding the accuracy of standard designs including MetaGPT, decentralized teams, top-down leader-worker hierarchies, and static decompositions.

Real-world evolving networks are naturally modeled as temporal graphs (TGs), where capturing temporal dynamics is essential for predicting future graph properties that support downstream decision-making. Existing temporal graph methods have been developed primarily for single-task prediction, and little is known about their generalization across tasks or transfer to unseen networks. This leaves the challenge of multi-task graph property prediction in TGs largely open. We address this challenge by introducing Hydra, a novel architecture that integrates local connectivity features from temporal GNNs with a spectral learning module that captures global connectivity patterns. This design enables joint learning of local and global information under a multi-task objective. In multi-task classification, Hydra achieves an 8.9% relative gain in AUC over the strongest competitor. In multi-task regression, Hydra achieves competitive results in all three tasks, while obtaining the best results in two tasks with a 8.2% relative gain in MAE compared to the strongest baseline. Moreover, Hydra delivers these gains with a 22× reduction in training time compared to temporal transfer models. These results provide the first systematic evidence that multi-task transferable learning on temporal graphs is effective. By delivering consistent top-ranked performance, Hydra highlights multi-task training on temporal graphs as a promising direction toward adaptable foundation models for temporal graphs.

Diffusion Maps (DM) is a well studied and popular non-linear dimension reduction algorithm. Surprisingly, while the convergence properties of DM are well understood, the {\em geometric} properties of the embedding, such as reach and smoothness have not yet been studied. Under a set of standard assumptions on a family of submanifolds $\subset \mathbb{R}^D$, we derive a series of geometric properties that are preserved by DM, including almost uniform density, finite polynomial approximation and reach. Leveraging these properties, we establish rigorous bounds on the embedding errors introduced by the DM algorithm, of the order $(\frac{\log n}{n})^{\frac{1}{8d+16}}$. These results offer a solid theoretical foundation for understanding the performance and reliability of DM in practical applications.

Forecasting the behavior of spatio-temporal systems often requires more than accurate predictions: models should uncover the dynamical modes governing future evolution. Existing temporal graph and latent dynamical models achieve strong forecasting performance, but their latent representations often entangle multiple dynamical patterns, limiting interpretability. Conversely, regime-inference methods explicitly model such modes but typically do not support generative forecasting over graph-structured systems. We introduce HERON, a self-supervised regime-aware generative framework that unifies graph-structured trajectory generation with regime identification. HERON factorizes the latent state into discrete system-level regimes, capturing global dynamical modes, and continuous entity-level dynamics, yielding a modular regime interface compatible with existing spatio-temporal backbones. Crucially, the inferred regime actively conditions system dynamics, enabling regime tracking and controlled simulations under alternative dynamical modes. Without regime annotations, HERON jointly learns forecasts and regime dynamics in a self-supervised manner, recovering meaningful modes across controlled synthetic and real-world datasets while maintaining competitive forecasting performance. These results open a path toward interpretable, controllable generative modeling of spatio-temporal dynamics.

Knowledge graph question answering (KGQA) systems are typically evaluated on questions whose surface tokens lexically expose the gold KG path. Real users, however, ask questions without knowing the underlying schema: "Which condition could Andrew have due to family history?" compresses a 4-hop chain (Andrew - father → father → medical condition → subclass of - hereditary disorder) into a single phrase (family history) whose tokens name none of those relations. We show that this collapse of path-question alignment is a blind spot of existing KGQA evaluation. The three dominant Large Language Model (LLM)-KG paradigms — hop-by-hop KG exploration, plan-then-retrieve, and similarity-based retrieval — all implicitly rely on the question's surface leaking the gold path, an assumption rarely tested in practice. We make three contributions. (i) HiddenPathQA, a human-validated KGQA benchmark of 1,055 multi-hop questions (2-6 hops, multiple domains) constructed so that the question surface does not leak the gold KG path's relations. (ii) Holistic Path Selection, a reasoning paradigm that exposes all candidate relation chains around the topic entity to the LLM at once, replacing per-hop relation scoring with question-against-full-chain alignment. Two implementations, TieredHolistic and FlatHolistic, outperform six strong baselines (ToG, PoG, FiDeLiS, R2-KG, KAPING, KARPA) on HiddenPathQA by +8.8 to +17.9 points over the strongest baseline across all four (backbone × split) settings. (iii) A pseudoword stress test that replaces entity surfaces with placeholder tokens. It both confirms HiddenPathQA items are solvable from KG structure alone — not from entity-level priors — and reveals that several baselines rely on entity memorization rather than KG-grounded reasoning.

How novel ideas are discovered and spread through a population is a well-studied phenomenon in the fields of computer science, computational social science, marketing/business research and higher education studies. In this paper, we study a particular version of this phenomenon, namely the spread of ideas among a network of researcher agents. We use a computational model in which each agent has a finite computational budget, that it can spend on a mixture of conducting its own research, and learning from the research of others in the network. By framing the problem as a continuous optimisation on the edge weights, we can applying gradient-based optimisation, similar to that from graph neural networks, to search for the graph configuration that maximises the amount of knowledge uncovered by the network. This contrasts with existing works that simply compare a fixed set of configurations. We find that (i) the optimisation succeeds in producing graphs that lead to a high total knowledge score, (ii) the optimum configuration has somewhat short shortest path lengths and a low clustering coefficient, (iii) the nodes end up broadly divided between researchers, who focus solely on their own research, and learners, who focus mostly on viewing research of others, and (iv) the learners consistently have higher knowledge scores, and this drives a rise in inequality across nodes over time.

We present GenZ, a hybrid model that turns a foundational model (FM) into a {\bf knowledge-discovery engine} explaining variation in real-valued multidimensional targets. The FM is treated as a noisy oracle that can answer yes/no questions about a semantic item $s$ (text, image, or both) and GenZ learns {\bf which questions to ask} so that the answers $\bz$ explain the statistical link to a possibly high-dimensional target $\by$. Discovery is driven by {\bf group reasoning}: at each step, the model partitions items by the posterior of the current latent features, and asks the FM to articulate the semantic commonality that explains the divide. The resulting feature descriptors $\theta_f$ are the primary product---human-readable hypotheses about why $s$ predicts $\by$---while predictive accuracy is a secondary, but consistently strong, by-product (e.g.~beating both the 0-shot FM baseline and TabPFN on LLM embeddings of the same items in hedonic price regression). Across four domains---hedonic house pricing, Netflix cold-start recommendations, Arizona species ecology, and human visual-cortex fMRI---GenZ recovers dataset-specific structure that the FM does not surface from priors alone. Holding the items $s$ fixed and varying only the target $\by$ (Arizona species under spatial/taxonomic/functional targets; the same natural images under FFA/EBA/PPA brain responses) yields {\bf qualitatively different} discovered feature sets, demonstrating that GenZ characterizes the $s\!\to\!\by$ link rather than the marginal distribution of $s$.

Learning neural stochastic differential equations (SDEs) from trajectory data is a central task in scientific machine learning, but standard neural SDEs trade flexibility for coefficient fidelity: flexible parameterizations recover coefficients poorly, while structured architectures impose strong coefficient priors. We introduce *Gaeta-Lie Neural SDEs*, a three-stage pipeline that improves coefficient recovery through discovered symmetries without priors on the drift or diffusion. Building on the Itô SDE symmetry framework of Gaeta and Quintero (1999), we first train a flexible neural SDE surrogate, then discover approximate projectable Lie symmetries of the learned surrogate in a finite basis of canonical symmetry generators, and finally regularize the surrogate by penalizing the residual of the Itô symmetry determining equations. The discovery stage is *lightweight*, scalable, and theory-guided: the SDE symmetry Lie algebra has known dimensional bounds that constrain the symmetry search space. The resulting regularization is *architecture-agnostic* and improves existing neural SDE methods when combined with them. Across non-trivial SDEs spanning low and high dimensions and a real-data setting, Gaeta-Lie regularization consistently improves fidelity over multiple baselines, with gains that persist in the data-scarce regime as guaranteed by the symmetry residual's freedom from data sparsity. To our knowledge, this is the first method to use SDE Lie symmetry to improve a learned stochastic surrogate.

Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification (UQ) with finite samples. However, applying CP to graph neural networks (GNNs) remains challenging. The combinatorial nature of graphs makes their encoding non-trivial, leading to insufficiently uncertain prediction logits and indiscriminative embeddings. Existing methods mostly rely on the embedding space for conformal prediction, which can be unreliable for graphs and often yields inefficient prediction sets. We propose GRAPHLCP, a structure-aware weighted conformal prediction framework that explicitly incorporates the graph topology and inter-node dependencies into localization and weighting. Based on experimental results that show a strong correlation between node homophily and sample coverage, we propose GRAPHLCP that utilizes a feature-aware densification followed by Personalized PageRank–based kernel computation to model structural proximity between nodes. Accounting for both structural and feature similarity allows GRAPHLCP to efficiently guarantee marginal coverage while attaining favorable test conditional coverage across extensive experiments on multiple datasets for both regression and classification.

Neural operators on irregular meshes face a fundamental tension. Spectral positional encodings, the natural choice for capturing geometry, require cubic-complexity eigendecomposition and inadvertently break gauge invariance through numerical solver artifacts; existing efficient approximations sacrifice gauge symmetry by design. Both failure modes break discretization invariance: models fail to transfer across mesh resolutions of the same domain, and similarly across different graphs of related structure in inductive settings. We propose GIST (Gauge-Invariant Spectral Transformer), a scalable neural operator that resolves this tension by restricting attention to pairwise inner products of efficient approximate spectral embeddings. We prove these inner products estimate an exactly gauge-invariant graph kernel at end-to-end $\mathcal{O}(N)$ complexity, and establish a formal connection between gauge invariance and discretization-invariant learning with bounded mismatch error. To our knowledge, GIST is the first scalable graph neural operator with a provable discretization-mismatch bound. Empirically, GIST sets state-of-the-art on the AirfRANS, ShapeNet-Car, DrivAerNet, and DrivAerNet++ mesh benchmarks (up to 750K nodes), and additionally matches strong baselines on standard graph benchmarks (e.g., 99.50\% micro-F1 on PPI).

Large language models encode rich representations in their hidden states, yet these representations remain largely opaque and disconnected from the model's vocabulary. We introduce Geometric Embedding Mixture (GEM), a pre-training regularization method that aligns transformer hidden states with the geometry of the vocabulary embedding space. GEM utilizes a self-supervised objective to encourage the final hidden state to approximate a probability-weighted mixture of token embeddings. This effectively minimizes the free energy of the models and pushes the representation into the convex hull of the vocabulary. We pre-train models at three scales (135M, 360M, and 760M) and demonstrate that GEM yields superior predictive uncertainty compared to standard training, reducing perplexity by up to 53\% on benchmarks. Furthermore, we show that this geometric structural constraint mitigates representation anisotropy and unlocks \emph{native interpretability}. Unlike baseline models, GEM enables direct layer-wise decoding of intermediate hidden states and better causal faithfulness using the untuned language head, revealing coherent semantic trajectories without the need for auxiliary probes. Our work demonstrates that imposing geometric structure during pre-training improves both performance and transparency, offering a path toward language models that are interpretable by construction.

Medical image segmentation requires the precise alignment of macroscopic semantics and microscopic geometry, yet existing representation paradigms struggle to balance massive low-frequency semantic context with ultra-sparse, high-frequency boundary details. To address this fundamental information asymmetry, we introduce Fractal-G, a plug-and-play multi-scale fusion module that presents a continuous Grid-Graph-Grid feature reconstruction paradigm. Within this framework, an Uncertainty-Aware Fission Router dynamically translates regular image grids into a non-uniform heterogeneous graph, adaptively allocating dense microscopic nodes to complex boundaries while retaining sparse macroscopic nodes in homogeneous background regions. To ensure unbiased feature aggregation across these varying physical scales, an Area-Aware Continuous Neighborhood Graph explicitly incorporates physical node sizes into the topological message passing. Finally, a Topology-Aware Implicit Renderer projects the unstructured graph back into dense, artifact-free continuous feature fields. Extensive experiments on diverse medical image segmentation tasks (including skin lesions and polyps) demonstrate that Fractal-G easily integrable with mainstream backbones, consistently achieving state-of-the-art geometric fidelity and cross-resolution robustness with only 12\% GFLOPs increase (U-Net based). Our code is publicly available at https://anonymous.4open.science/r/Fractal-G/.

The rapid deployment of generative AI has amplified the critical need for Training Data Attribution to ensure transparency and accountability. However, current parametric approaches require computationally prohibitive access to model weights, while similarity-based methods ignore deep structural context. We propose a novel probabilistic framework that operates entirely in a black-box setting. Our method fuses continuous feature similarities with discrete, domain-specific Knowledge Graphs (KGs). This approach ensures the attribution is grounded in structural reality, explicitly rewarding highly specific historical samples while preventing generic background data from dominating the results. We evaluate our framework across two distinct domains where linking outputs to data and domain context is inherently complex: abstract artistic image synthesis and high-dimensional physical weather forecasting. Extensive benchmarking demonstrates the robust efficacy of our approach. In the artistic domain, it achieves a strong Linear Datamodeling Score that exceeds standard black-box similarity baselines, while closing much of the gap to gradient-based estimators. We additionally present a cross domain feasibility case study in environmental forecasting, where we use domain KGs to retrieve physically consistent historical analogs for regional flood forecasts, improving geographic localisation over a latent-only baseline. Operating entirely without internal model access, our approach provides an efficient, interpretable mechanism for post-hoc influence analysis and domain-grounded retrieval.

Scientific knowledge bases accelerate discovery by curating findings from primary literature into structured, queryable formats for both human researchers and emerging AI systems. Maintaining these resources requires expert curators to search papers, reconcile evidence across documents, and produce ontology-grounded annotations. Existing benchmarks usually evaluate isolated subtasks, such as named entity recognition or relation extraction, and therefore do not capture this end-to-end workflow. We present FlyAOC to evaluate AI agents on end-to-end agentic ontology curation from scientific literature. Given a gene symbol, a concise FlyBase gene description, access to a 16,898-paper corpus, and ontology resources, agents must search for evidence and recover as many curator-relevant structured annotations as possible. Outputs span standardized function terms, expression patterns, and historical synonyms linking decades of nomenclature. The benchmark includes 7,397 expert-curated annotations across 100 genes drawn from FlyBase, the Drosophila knowledge base. Across four baseline agent harnesses--memorization, fixed pipeline, single-agent, and multi-agent--FlyAOC is sensitive to harness design, model family, and tool-use reliability. These results reveal system-level failure modes that model-only evaluations do not capture. FlyAOC provides a reproducible testbed for retrieval-augmented scientific curation. - Code: https://github.com/xingjian-zhang/flyaoc - Data: https://huggingface.co/datasets/anonymous-042/flyaoc

Federated Continual Learning (FCL) suffers from spatial-temporal catastrophic forgetting caused by sequential task learning on individual clients and the aggregation of heterogeneous client knowledge. However, most existing methods either overemphasize preserving old knowledge, which restricts model plasticity for new tasks, or rely on training complex generative models for replay, incurring substantial computational overhead. In the human immune system, immune memory is preserved implicitly and can be reactivated through vaccination even after long periods of dormancy. Motivated by this, we propose ***FedVaccine***, a novel framework that explicitly permits forgetting to preserve high plasticity for new tasks, while efficiently recovering past knowledge through re-learning a compact vaccine set. Specifically, the vaccine set for each task is synthesized by compress task gradient information under the guidance of the fine-tuned local model, capturing representative data characteristics and task-specific discriminative patterns. Two novel components are also introduced: ***Priming & Boosting***, which encodes task-specific knowledge in a compact spectral form, priming the model with essential information and enabling efficient memory boosting via vaccine set replay after forgetting; and ***Vaccination Aggregation***, which aggregates vaccine sets from all clients to train a globally generalized model without accessing any raw private data. Extensive experiments on three benchmarks demonstrate that FedVaccine achieves competitive performance, enables rapid knowledge recovery after forgetting, and incurs no additional overhead from training generative models.

Federated Graph Learning (FGL) on Text-Attributed Graphs often encounters the missing neighbor issue. This problem arises from structural fragmentation across dispersed clients, which restricts the effective message passing of Graph Neural Networks. Current completion methods frequently struggle in cross-domain, non-IID scenarios because they lack access to external knowledge. To address these limitations, we propose FedProG, an asymmetric framework that utilizes a frozen server-side LLM to reconstruct missing structural contexts. Furthermore, deploying Large Language Models locally to augment these graphs incurs prohibitive computational costs for edge devices. We introduce a split architecture where a lightweight client-side generator maps graph features into the LLM’s embedding space. This allows the server to produce virtual neighbors via uploaded soft prompts. To ensure system reliability and privacy, we implement a dual-guard mechanism: a server-side uncertainty filter rejects low-confidence generations through multi-path sampling, while a client-side semantic consistency projector maintains utility under differential privacy. Experiments show that FedProG improves robustness and generalization over baselines while drastically reducing client computational overhead.

We study clustering algorithm for dynamic evolving graphs $\{ G_t\}$, in which new edges (and potentially new vertices) are added into a graph, and the underlying cluster structure of the graph gradually changes over time. By designing a hierarchical data structure for dynamically maintaining the cluster structure of $\{ G_t\}$, we prove that the cluster structure of $G_T$ can be maintained with $O(d)$ amortised update time and $\widetilde{O}\left(n_T^{1/d}\right)$ amortised query time, for an arbitrary large constant $d$. This significantly improves the previous state-of-the-art (Laenen and Sun, ICML~'24), which requires $O(1)$ update time and $O(n_T/\log n_T)$ amortised query time. We further demonstrate this improvement with experiments on both synthetic and real-world datasets.

Diverse applications on signed networks, ranging from leader-follower opinion dynamics to graph semi-supervised learning, fundamentally reduce to solving the discrete Dirichlet boundary value problem. The computational bottleneck of this problem lies in evaluating the entries of the label propagation operator $Q = -L_{U,U}^{-1}L_{U,L}$. While existing approximation methods based on absorbing random walks attempt to address this complexity, they often suffer from high variance and limited precision. To overcome these limitations, we propose MultiTreeQ, a novel and efficient framework designed to approximate the operator's entries with high accuracy. Specifically, MultiTreeQ is constructed based on the Signed Multi-Rooted Spanning Tree and leverages Rao-Blackwellized variance reduction to significantly improve estimation precision. Extensive experiments on real-world networks confirm that MultiTreeQ substantially outperforms existing baselines, scaling to massive graphs with up to 10 million nodes while delivering remarkable improvements in computational efficiency and precision. Our code is available at https://anonymous.4open.science/r/label-propagation-operator-2059/.