NeurIPS 2026 Papers

Manipulation planners depend on accurate predicates about physical state---is an object occluded? is a container open? is a path blocked?---but such predicates are hard to read off an image. Contrastively-trained vision--language models capture semantic content but collapse to near-zero binary F1 on these predicates, and even GPT-4o few-shot falls below random on multiple-choice physical-state questions. We present \ours, which predicts physical-state scene graphs from a single image and a natural-language goal. A frozen CLIP ViT, adapted with LoRA, feeds a heterogeneous graph of object, relation, and learnable memory tokens into a Latent Graph Reasoning Transformer (\lgrt); training combines supervised, counterfactual-margin, contrastive, and calibration losses with offline counterfactual-pair augmentation. On \pacbench, \ours reaches $\mu$-F1$\,{=}\,0.651$ and $99.3\%$ MCQ accuracy, a $+0.170$ absolute $\mu$-F1 gain over the strongest no-graph supervised baseline, with $99.6\%$ counterfactual directional consistency. Component ablations attribute $+0.426$ $\mu$-F1 to the \lgrt and $+0.392$ to the counterfactual loss. A \manipbench-trained variant scores $74.4\%$ MCQ against $30.0\%$ for the best zero-shot VLM on that benchmark's 4-choice format.

Evaluating machine learning in scientific domains requires separating correct predictions from correct reasons under realistic distribution shifts. We introduce PerturbReason, a knowledge‑grounded benchmark for cell‑state--conditioned reasoning about perturbation effects. It tests the models to generate mechanistically faithful explanations and assesses their robustness against complex shifts, such as new cells, unseen perturbations, and cross-modal or combinatorial extrapolations. PerturbReason combines single‑cell genetic and chemical perturbation data across multiple cell lines with knowledge graphs, and dynamically conditions pathways on cell‑specific basal states to avoid generic memorization. Evaluations on state-of-the-art models reveal systematic gaps between predictive accuracy and mechanistic reasoning. Specifically, these models exhibit failure modes largely invisible to standard benchmarks, such as deriving correct answers through flawed logic, ignoring cellular context, and generating directionally inconsistent mechanisms. As a reference probe of the benchmark, we present PerturbRM, a large language model trained to align outcome predictions with context-specific regulatory reasoning. PerturbReason thus provides a rigorous diagnostic benchmark for studying and improving faithful, generalizable reasoning in data-rich scientific systems.

Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated by using permutation-equivariant learning architectures. Despite their computational efficiency, existing graph diffusion models struggle to distinguish certain graph families and their spectra, unless graph data are augmented with ad hoc features. This shortcoming stems from enforcing the inductive bias within the learning architecture. In this work, we leverage random matrix theory to analytically extract the spectral properties of the diffusion process, allowing us to push most of the inductive bias from the architecture into the dynamics. Building on this, we introduce the Dyson Diffusion Model, which employs Dyson's Brownian motion to capture the spectral dynamics of an Ornstein-Uhlenbeck process on the adjacency matrix. Furthermore, conditioned on the spectral dynamics, we formulate a Lie group diffusion, appropriately modeling the remaining degrees of freedom. Strikingly, the resulting learning problem becomes permutation invariant at the Lie algebra level. We demonstrate that the Dyson Diffusion Model learns graph spectra accurately and outperforms existing graph diffusion models.

Retrieval-augmented generation (RAG) is increasingly used to ground Large language Models (LLMs) with up-to-date or private information, and has become a key component for knowledge-intensive LLM systems (e.g., LLM agents). However, RAG with LLMs often hallucinate due to unreliable retrieved information or outdated internal knowledge, making hallucination detection crucial for reliable LLM workflows. Recently, reasoning-intensive LLMs that produce explicit reasoning trajectories before answering have shown promise in RAG by examining and synthesizing retrieved evidence. Yet, they often suffer from overthinking: generating redundant or unproductive reasoning with limited performance gains. While prior work mainly studies overthinking in closed-book reasoning tasks that mainly rely on internal knowledge, overthinking in RAG-based question answering (QA) that requires open-book reasoning over both internal knowledge and external context remains underexplored. Thereby, we conduct empirical studies to investigate the relationship between overthinking and hallucination in RAG-based QA and find: (1) Overthinking in reasoning LLMs produces lengthy reasoning trajectories that are correlated with hallucinations; (2) This overthinking is often associated with knowledge conflict, where LLMs struggle to reconcile retrieved context with internal knowledge. Based on our findings, we propose a knowledge conflict-aware hallucination detection framework. We train a classifier to identify the three knowledge conflict reasoning patterns, design a knowledge conflict score to measure knowledge conflict severity, and apply tailored detection strategies with different prompts for different conflict levels. Unlike existing methods, our approach requires neither LLM parameter access nor retrieval reliability, and only needs the LLM output in a single run. Experiments on three QA datasets and three LLMs confirm our framework's effectiveness.

One-shot Federated Graph Learning (OFGL) has emerged as a communication-efficient paradigm for Federated Graph Learning (FGL) under strict bandwidth constraints, compressing collaboration into a single transmission round. Nevertheless, this extreme setting suffers from a fundamental **Single-Transmission Bottleneck**, which limits both the quality and utility of exchanged knowledge. First, while existing methods attempt to distill private graphs into shareable proxies, their aggressive one-shot compression inherently triggers a fidelity crisis. This compression distorts local graph topology and semantics across clients, leading to **externalized knowledge underexpression**. Second, although the server aggregates these proxies to update global models, current integration schemes suffer from transferability agnosticism. The server cannot reliably identify cross-client collaboration potential, resulting in **integrated knowledge underutilization**. To tackle these dual challenges, we propose FedHFT, an effective One-shot Personalized Federated Graph Learning (OPFGL) framework that addresses this bottleneck from two perspectives, namely High-Fidelity Knowledge Externalization and Transferability-Ware Knowledge Integration. We use Fidelity-Driven Proxy Refinement to preserve client-side knowledge fidelity, and Transferability-Steered Personalized Collaboration to enable adaptive server-side collaboration. The superiority of FedHFT is validated through extensive experiments on both homophilic and heterophilic graphs. The code is available at https://anonymous.4open.science/r/FedHFT-DC7F/.

Large language model (LLM) unlearning has emerged as an essential post-training mechanism for erasing specific knowledge or undesirable behaviors. However, forgetting target data often causes an unintended degradation in overall model utility. Although various advanced methods have explored different learning objectives to mitigate the trade-off, it remains unclear how the highly entangled internal representations in LLMs contribute to unlearning. In this work, we introduce the notion of latent knowledge fragility to explore the vulnerability of retained knowledge to unlearning. We develop a unified analytical approach via component-wise parameter patching that isolates and quantifies fragility in terms of different transformer blocks. We observe that the LLM encodes different levels of abstraction, from surface syntax in shallow layers to complex semantics in deeper layers, which align with different degrees of representation disruption and utility degradation. Based on the insights, we propose a lightweight framework called Component-wise Replacement Unlearning (CRU) that restores fragile layers (also extendable to other components) from the original model based on post-hoc validation, which allows us to obtain a hybrid model without additional training. Extensive experiments on various aspects verify that CRU generally improves the trade-off between removal and retention with non-uniform unlearning influence.

The expressivity of graph neural networks is predominantly characterized in a noiseless setting via binary graph isomorphism tests. This perspective certifies whether two graphs can be distinguished, but does not quantify how robust such distinctions are under structural perturbations. In practice, however, real-world graphs are often corrupted by noise, where even small structural changes might lead to disproportionate distortions in learned representations. In this study, we generalize graph isomorphism to a noisy alignment criterion, requiring that graphs that remain identifiable under noise are embedded closer to their source than to any alternative. This yields a margin-based formulation of expressivity that bridges the gap between combinatorial isomorphism-based theory and the continuous learned representations. Notably, our framework is architecture-agnostic and strictly generalizes classical isomorphism-based expressivity. We further derive certified robustness guarantees for node-level tasks and an explicit robustness radius for graph-level representations. Experiments confirm that our criteria predict and improve robustness under structural perturbations.

Foundation Models for Electroencephalography (EEG) are trained with masked reconstruction, contrastive alignment, and language-model interfaces, yet their learned representations remain difficult to inspect: raw EEG lacks canonical token semantics, and models may preserve waveform detail while discarding physiologically meaningful structure. We introduce Neuro-KE (Neuro-Knowledge Engine), a knowledge interface that computes EEG descriptors without additional human annotation and renders them as paradigm-specific supervision for semantic grounding. Rather than using handcrafted features as standalone classifiers, Neuro-KE converts the same domain knowledge into numeric prediction targets, feature-state text anchors, and feature-grounded instruction answers. Across three interfaces, Neuro-KE improves aggregate grounding and transfer metrics, with task-dependent exceptions: it improves balanced accuracy (BAcc) by 2.60 points over reconstruction-only masked pretraining across 12 datasets and three backbones, improves six-dataset EEG--text validation BAcc by 2.23 points over label-only anchors, and improves EEG-MLLM feature-grounded generation to ROUGE-L F1 0.607 and BERTScore F1 0.929. These results suggest that established EEG descriptors can serve as reusable grounding signals for inspecting and supervising EEG foundation-model interfaces.

Local field potentials (LFPs) are population-level neural signals central to brain-computer interfaces and systems neuroscience, yet unlike spike-based population codes, their dynamics lack a principled geometric description that connects spectral structure to latent state-space geometry. Here we establish, analytically and empirically, that the lag-embedded dynamics of LFP signals lie on a low-dimensional K-torus, where K equals the number of sustained oscillatory modes present in the signal. Modeling LFPs as bounded autoregressive processes, we show that each oscillatory component contributes an independent circular degree of freedom, while aperiodic 1/f structure and noise contribute only geometric thickness around the manifold without altering its topology. To apply this theory to real nonstationary recordings, we introduce DeepLagField, a physics-informed network that jointly estimates time-varying AR structure and effective model order, with formal guarantees that local toroidal geometry is preserved despite drifting oscillatory dynamics.We validate the predicted toroidal geometry using persistent homology across primate visual cortex LFP, rodent hippocampal LFP, and mouse cortical EEG recordings, confirming the expected Betti number signatures across species and recording modalities. Critically, we demonstrate that this geometric structure is not merely descriptive but carries behaviorally relevant information inaccessible to standard spectral summaries — as evidenced by torus parameters derived purely from manifold geometry outperforming multi-band spectral features for sleep-state decoding without any hand-crafted frequency design. This proof of concept points toward broad downstream utility wherever oscillatory field signals are recorded, from neural decoding and brain-state monitoring to clinical biomarker development. These results reframe neural oscillations not as isolated spectral features but as coordinate directions of a low-dimensional delay manifold, opening a geometry-first approach to neural signal analysis that is simultaneously theoretically grounded, empirically validated across species, and predictive of behaviorally relevant brain states.

We present GenusSink, a new class of approximate generalized Sinkhorn algorithms with shortest-path-distance costs for bounded genus (e.g. planar) graphs, providing near-linear time: (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory. Graphs handled by GenusSink include in particular planar graphs and bounded-genus meshes approximating 3D objects. GenusSink addresses total quadratic time complexity of its brute-force counterpart by leveraging separator-based decomposition of graphs, computational geometry techniques, and new results on fast matrix-vector multiplications with generalized distance matrices, using in particular Fourier analysis and low displacement rank theory. It is inspired by recent breakthroughs in graph theory on approximating bounded genus metrics with small treewidth metrics minor. The graph-centric approach enables us to target optimal transport problem with the corresponding distributions defined on the manifolds approximated by weighted graphs and with cost functions given by geodesic distances. We conduct rigorous theoretical analysis of GenusSink, provide practical implementations, leveraging newly introduced in this paper separation graph field integrators (S-GFIs) data structures and present empirical verification. GenusSink provides orders of magnitude more accurate computations than other efficient Sinkhorn algorithms, while still guaranteeing significant computational improvements, as compared to the baseline. As a by-product of the developed methods, we show that GenusSink is $\textbf{numerically equivalent}$ to the brute-force geodesic Sinkhorn algorithm on n-vertex graphs with treewidth $O(\log \log (n))$ (e.g. on trees).

Lifelong learning requires embodied agents to continuously understand the environment and learn how to use that understanding to guide action, enabling future interactions to yield more informative experiences. Prior language model (LM)-based agents have primarily addressed these requirements in isolation, emphasizing either declarative knowledge acquisition or procedural knowledge reuse, leaving the continual interplay between the two during lifelong learning underexplored. We introduce Neurosymbolic Knowledge Compilation (NeSyKC), a lifelong learning framework that couples declarative knowledge formation with incremental compilation into procedural knowledge through a shared symbolic representation. In NeSyKC, accumulated experience is abstracted into symbolic rules that capture reusable environmental structure, and these rules provide the basis for deriving executable procedures that are incrementally compiled into neural adapters. This creates a feedback loop in which experience is abstracted into symbolic rules and compiled into procedures that guide the LM's reasoning on future tasks, yielding further experience for learning. Across four open-ended environments instantiated from established embodied benchmarks, NeSyKC expands and refines reusable knowledge across tasks, improving task performance and inference efficiency while supporting generalization to unseen tasks. Real-world experiments on two robots further show that the agent continues to learn from post-deployment experience, allowing acquired knowledge to be compiled for reuse in future tasks.

Neural Graph Databases (NGDBs) support complex logical reasoning over incomplete knowledge structures, yet their training efficiency and expressivity are constrained by rigid query-level batching and structure-only embeddings. We present NGDB-Zoo, a unified framework that resolves these bottlenecks by synergizing operator-level training with semantic augmentation. By decoupling logical operators from query topologies, NGDB-Zoo transforms training loops into dynamically scheduled data-flow executions, enabling multi-stream parallelism and achieving a $1.8\times$-$6.8\times$ average throughput compared to baselines. Furthermore, we formalize a decoupled architecture to integrate semantic priors from pre-trained text embeddings without triggering I/O stalls or memory overflows. Experiments on six benchmarks, including $\textit{ogbl-wikikg2}$ and $\textit{ATLAS-Wiki}$, show that NGDB-Zoo scales dense query-embedding training to million-entity graphs while maintaining competitive filtered MRR.

Long-horizon embodied intelligence requires agents to improve through interaction, not merely to execute plans generated from static goals. A central challenge is therefore to transform past executions into knowledge that can shape future decisions. Minecraft provides a representative testbed for this problem, where tasks such as crafting tools, building redstone components, and obtaining diamond equipment involve long prerequisite chains and are frequently disrupted by missing tools, blocked paths, GUI failures, or stagnant execution. To this end, we propose \textbf{MineEvolve}, a knowledge-driven self-evolution framework that converts execution feedback into actionable behavioral knowledge. MineEvolve first uses \underline{\emph{\textbf{\ding{182}Monitor}}} to convert each subgoal execution into typed feedback, including state changes, inventory changes, failure types, progress signals, and stagnation indicators. \underline{\emph{\textbf{\ding{183}Inducer}}} then derives reusable skills from successful executions and remedies from failed or stagnant executions. \underline{\emph{\textbf{\ding{184}Curator}}} validates, merges, filters, and retrieves these knowledge entries, while \underline{\emph{\textbf{\ding{185}Adaptor}}} uses them to repair the unfinished part of the plan under repeated failures or stagnation. Experiments on the Minecraft MCU long-horizon task suite show that MineEvolve consistently improves performance across multiple language-model planners, with larger gains on high-dependency task groups. Ablation and knowledge-accumulation studies further demonstrate that converting execution signals into structured behavioral knowledge is an effective path toward self-evolving embodied agents in long-horizon environments. Our code is available at \url{https://anonymous.4open.science/r/MineEvolve-1B5B}.

Multimodal large language models (MLLMs) show remarkable potential for scientific reasoning, yet their performance in specialized domains such as microscopy remains limited by the scarcity of domain-specific training data and the difficulty of encoding fine-grained expert knowledge into model parameters. To bridge the gap, we introduce MicroWorld, a framework that constructs a multimodal attributed property graph (MAPG) from large-scale scientific image-caption corpora and leverages it to augment MLLM reasoning at inference time without any domain-specific fine-tuning. MicroWorld extracts biomedical entities and relations via scispaCy or LLM-based triplet mining, aligns images and entities in a shared embedding space using Qwen3-VL-Embedding, and assembles a knowledge graph comprising approximately 111K nodes and 346K typed edges spanning eight relation categories. At inference time, a graph-augmented retrieval pipeline matches query entities to the MAPG and injects structured knowledge context into the MLLM prompt. On the MicroVQA benchmark, MicroWorld improves the reasoning performance of Qwen3-VL-8B-Instruct by 37.5%, outperforming GPT-5 by 13.0% to achieve a new state-of-the-art. Furthermore, it yields a 6.0% performance gain on the MicroBench benchmark. Extensive experiments demonstrate the enhanced generalization capability introduced by MicroWorld. A qualitative case study further reveals both the mechanisms through which structured knowledge improves reasoning and the failure modes that point to promising future directions. Code and data are available at anonymous GitHub.

Existing locate-then-edit Knowledge Editing (KE) methods typically decompose editing into two stages: upstream target representation optimization and downstream constrained parameter optimization. The optimization across the two stages is disconnected: upstream applies uniform regularization without observing downstream realization of the planned residual, hindering a refined accuracy–editability trade-off. Since this realization is request-specific and depends on downstream constraints, uniform regularization can over-shrink high-association requests, causing insufficient editing, while it can under-regularize low-association requests, producing over-large planned residuals that reduce downstream editability. To bridge this disconnect, we propose $\textbf{MetaKE}$ ($\textbf{Meta}$-learning for $\textbf{K}$nowledge $\textbf{E}$diting), a new framework that unifies upstream and downstream stages into a bi-level optimization problem. The inner level optimizes parameter updates for the target representation, while the outer level optimizes representation using feedback from downstream constraints, achieving a better semantic accuracy-editability trade-off. To avoid costly multi-layer backpropagation, we introduce a Structural Gradient Proxy to approximate and propagate this feedback. Extensive experiments show that MetaKE outperforms strong baselines, offering a new perspective on KE. Code at: https://anonymous.4open.science/r/MetaKE-C160.

Memory systems enable LLM agents to consolidate and retrieve relevant evidence from the factual knowledge accumulated through growing interaction histories for downstream reasoning. Existing approaches have explored diverse strategies for organizing and compressing these histories. However, balancing compression with retrieval effectiveness remains challenging: retaining too much content can cause relevant evidence to be obscured by redundant entries, while discarding too aggressively may remove content that later proves relevant. This amounts to a tradeoff between compressing redundancy and preserving enough structure to retrieve target evidence, as formalized by the information bottleneck. To this end, we propose **MemCoRe**, which organizes memory as a compression hierarchy where each level compresses redundancy further while retaining the structure needed for retrieval at that level. In this hierarchy, evidence is progressively compressed from detailed records through extracted keywords to topic groups. This enables retrieval to locate target evidence by searching across levels of the hierarchy. Comprehensive experiments demonstrate that MemCoRe outperforms existing state-of-the-art baselines.

Large language models (LLMs) have shown promise in medical question answering and clinical reasoning, yet their improvement remains constrained by static parametric knowledge and costly expert supervision. Self-evolving agents offer a promising alternative by enabling models to improve through iterative task generation and problem-solving. However, most existing self-evolving methods are designed for easily verifiable domains such as mathematics and coding, where solutions can be checked by exact answers or executable programs. Medical reasoning is fundamentally different: it is open-ended, knowledge-intensive, and often only partially verifiable. We present \textbf{MedZERO}, a self-evolving framework for open-ended medical reasoning. MedZERO couples an \textit{Examiner} that generates frontier medical question-option pairs with a \textit{Reasoner} that solves them through evidence-grounded multi-turn reasoning with external knowledge tools. To support reliable, continual improvement, MedZERO introduces controlled knowledge accumulation, which maintains temporary exploratory knowledge and curated persistent knowledge in reasoning. We evaluate MedZERO on five public medical reasoning benchmarks using 4B- and 8B-scale base models under open-ended evaluation. Across all settings, MedZERO consistently outperforms the underlying base models and prior self-evolving baselines, achieving up to 13.7 average accuracy-point gains over the next-best self-evolving baseline.

Constantly evolving real-world knowledge necessitates models to be updated continuously. Especially in medicine, as clinical evidence changes over time, outdated knowledge can pose safety risks. Existing evaluations of knowledge integration focus on factual recall, offering limited insight into whether newly integrated knowledge is actually usable. Our benchmark __MedKIT__ (Medical Knowledge Integration and Transfer) provides a granular evaluation of how models integrate and apply knowledge under realistic sequences of clinical updates. Each instance corresponds to a factual update derived from clinical evidence, paired with targeted probes that assess transfer across lexical variation, relational transformations, compositional reasoning, and open-ended operationalization, as well as locality tests for knowledge preservation. Using MedKIT, we conduct a large-scale empirical study of 12 knowledge integration strategies across 5 diverse models, including both general-purpose and medical LLMs. Our results reveal a consistent gap between recall and usable knowledge: while most methods achieve strong gains on the original update task and under lexical variation, relational generalization is limited, and no method yields meaningful improvements on compositional or operational tasks. These findings highlight a fundamental challenge in knowledge integration and position MedKIT as a testbed for developing methods that make newly integrated knowledge more consistently usable across tasks and contexts.

Mean-field control (MFC) offers a scalable solution to the curse of dimensionality in multi-agent systems but traditionally hinges on the restrictive assumption of exchangeability via dense, all-to-all interactions. In this work, we bridge the gap to real-world network structures by proposing a rigorous framework for MFC on large sparse graphs. We redefine the system state as a probability measure over decorated rooted neighborhoods, effectively capturing local heterogeneity. Our central contribution is a theoretical foundation for scalable reinforcement learning in this setting. We prove horizon-dependent locality: for finite-horizon problems, an agent's optimal policy at time t depends strictly on its (T-t)-hop neighborhood. This result renders the infinite-dimensional control problem tractable and underpins a novel Dynamic Programming Principle (DPP) on the lifted space of neighborhood distributions. Furthermore, we formally and experimentally justify the use of Graph Neural Networks (GNNs) for actor-critic algorithms in this context. Our framework naturally recovers classical MFC as a degenerate case while enabling efficient, theoretically grounded control on complex sparse topologies.