Daily Papers

Effective interaction modeling and behavior prediction of dynamic agents play a significant role in interactive motion planning for autonomous robots. Although existing methods have improved prediction accuracy, few research efforts have been devoted to enhancing prediction model interpretability and out-of-distribution (OOD) generalizability. This work addresses these two challenging aspects by designing a variational auto-encoder framework that integrates graph-based representations and time-sequence models to efficiently capture spatio-temporal relations between interactive agents and predict their dynamics. Our model infers dynamic interaction graphs in a latent space augmented with interpretable edge features that characterize the interactions. Moreover, we aim to enhance model interpretability and performance in OOD scenarios by disentangling the latent space of edge features, thereby strengthening model versatility and robustness. We validate our approach through extensive experiments on both simulated and real-world datasets. The results show superior performance compared to existing methods in modeling spatio-temporal relations, motion prediction, and identifying time-invariant latent features.

A key component of Visual Simultaneous Localization and Mapping (VSLAM) is estimating relative camera poses using matched keypoints. Accurate estimation is challenged by noisy correspondences. Classical methods rely on stochastic hypothesis sampling and iterative estimation, while learning-based methods often lack explicit geometric structure. In this work, we reformulate relative pose estimation as a relational inference problem over epipolar correspondence graphs, where matched keypoints are nodes and nearby ones are connected by edges. Graph operations such as pruning, message passing, and pooling estimate a quaternion rotation, translation vector, and the Essential Matrix (EM). Minimizing a loss comprising (i) L_2 differences with ground truth (GT), (ii) Frobenius norm between estimated and GT EMs, (iii) singular value differences, (iv) heading angle differences, and (v) scale differences, yields the relative pose between image pairs. The dense detector-free method LoFTR is used for matching. Experiments on indoor and outdoor benchmarks show improved robustness to dense noise and large baseline variation compared to classical and learning-guided approaches, highlighting the effectiveness of global relational consensus.

This paper is concerned with learning to solve tasks that require a chain of interdependent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational network, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]'s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty-CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.

Relational reasoning requires the process of perceptual understanding, comparing, and integrating the underlying relationships between concepts. This ability consists of multiple categories, such as analogical, structural, and cause-effect, each capturing a different aspect of higher-order understanding. To examine the performance of multimodal large language models (MLLM) on these relational inference tasks, we developed SciReC, a model-adaptive multimodal academic dialog benchmark. As the relational reasoning process involves multiple representations and various factors (visual understanding, exhibiting knowledge, and memory recall), we propose DMRA, a deficit-based diagnostic framework that quantifies the contribution of these components to identify the primary cause of unsuccessful cases. Claude 4.6 achieved the best performance on the overall relational score with 73\%, followed by GPT 5.4 with 68\%. Performance trends indicate that open-source models achieve their lowest scores on spatial relations, while proprietary models struggle more with hierarchical and sequential relations. Across domains, model performance is lowest on Astronomy and highest on Psychology. The results of DMRA reveal that relational reasoning is the primary source of error across all models, followed by memory limitations.

People readily generalize knowledge to novel domains and stimuli. We present a theory, instantiated in a computational model, based on the idea that cross-domain generalization in humans is a case of analogical inference over structured (i.e., symbolic) relational representations. The model is an extension of the LISA and DORA models of relational inference and learning. The resulting model learns both the content and format (i.e., structure) of relational representations from non-relational inputs without supervision, when augmented with the capacity for reinforcement learning, leverages these representations to learn individual domains, and then generalizes to new domains on the first exposure (i.e., zero-shot learning) via analogical inference. We demonstrate the capacity of the model to learn structured relational representations from a variety of simple visual stimuli, and to perform cross-domain generalization between video games (Breakout and Pong) and between several psychological tasks. We demonstrate that the model's trajectory closely mirrors the trajectory of children as they learn about relations, accounting for phenomena from the literature on the development of children's reasoning and analogy making. The model's ability to generalize between domains demonstrates the flexibility afforded by representing domains in terms of their underlying relational structure, rather than simply in terms of the statistical relations between their inputs and outputs.

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing a persistent gap between comprehension and competence. Through controlled experiments and architectural analysis, we demonstrate that LLMs often articulate correct principles without reliably applying them--a failure rooted not in knowledge access, but in computational execution. We term this phenomenon the computational split-brain syndrome, where instruction and action pathways are geometrically and functionally dissociated. This core limitation recurs across domains, from mathematical operations to relational inferences, and explains why model behavior remains brittle even under idealized prompting. We argue that LLMs function as powerful pattern completion engines, but lack the architectural scaffolding for principled, compositional reasoning. Our findings delineate the boundary of current LLM capabilities and motivate future models with metacognitive control, principle lifting, and structurally grounded execution. This diagnosis also clarifies why mechanistic interpretability findings may reflect training-specific pattern coordination rather than universal computational principles, and why the geometric separation between instruction and execution pathways suggests limitations in neural introspection and mechanistic analysis.

State-of-the-art Video Scene Graph Generation (VSGG) systems provide structured visual understanding but operate as closed, feed-forward pipelines with no ability to incorporate human guidance. In contrast, promptable segmentation models such as SAM2 enable precise user interaction but lack semantic or relational reasoning. We introduce Click2Graph, the first interactive framework for Panoptic Video Scene Graph Generation (PVSG) that unifies visual prompting with spatial, temporal, and semantic understanding. From a single user cue, such as a click or bounding box, Click2Graph segments and tracks the subject across time, autonomously discovers interacting objects, and predicts <subject, object, predicate> triplets to form a temporally consistent scene graph. Our framework introduces two key components: a Dynamic Interaction Discovery Module that generates subject-conditioned object prompts, and a Semantic Classification Head that performs joint entity and predicate reasoning. Experiments on the OpenPVSG benchmark demonstrate that Click2Graph establishes a strong foundation for user-guided PVSG, showing how human prompting can be combined with panoptic grounding and relational inference to enable controllable and interpretable video scene understanding.

The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation (IMLE, Niepert, Minervini, and Franceschi 2021), a class of gradient estimators for discrete exponential family distributions, was proposed by combining implicit differentiation through perturbation with the path-wise gradient estimator. However, due to the finite difference approximation of the gradients, it is especially sensitive to the choice of the finite difference step size, which needs to be specified by the user. In this work, we present Adaptive IMLE (AIMLE), the first adaptive gradient estimator for complex discrete distributions: it adaptively identifies the target distribution for IMLE by trading off the density of gradient information with the degree of bias in the gradient estimates. We empirically evaluate our estimator on synthetic examples, as well as on Learning to Explain, Discrete Variational Auto-Encoders, and Neural Relational Inference tasks. In our experiments, we show that our adaptive gradient estimator can produce faithful estimates while requiring orders of magnitude fewer samples than other gradient estimators.

Recent advances in large language models (LLMs) have intensified efforts to fuse heterogeneous open-source models into a unified system that inherits their complementary strengths. Existing logit-based fusion methods maintain inference efficiency but treat vocabulary dimensions independently, overlooking semantic dependencies encoded by cross-dimension interactions. These dependencies reflect how token types interact under a model's internal reasoning and are essential for aligning models with diverse generation behaviors. To explicitly model these dependencies, we propose InfiGFusion, the first structure-aware fusion framework with a novel Graph-on-Logits Distillation (GLD) loss. Specifically, we retain the top-k logits per output and aggregate their outer products across sequence positions to form a global co-activation graph, where nodes represent vocabulary channels and edges quantify their joint activations. To ensure scalability and efficiency, we design a sorting-based closed-form approximation that reduces the original O(n^4) cost of Gromov-Wasserstein distance to O(n log n), with provable approximation guarantees. Experiments across multiple fusion settings show that GLD consistently improves fusion quality and stability. InfiGFusion outperforms SOTA models and fusion baselines across 11 benchmarks spanning reasoning, coding, and mathematics. It shows particular strength in complex reasoning tasks, with +35.6 improvement on Multistep Arithmetic and +37.06 on Causal Judgement over SFT, demonstrating superior multi-step and relational inference.

Existing spatial reasoning benchmarks mainly test spatial perception: reading off relations already visible in the input. Yet real-world spatial intelligence demands predictive spatial reasoning: constructing a scene from observations, anticipating how an intervention changes it, and reasoning about the unseen outcome. We introduce SpaceCast-Bench, the first benchmark to directly and diagnostically evaluate this capability. Built around an observe-transform-infer framework, its 3,862 questions from 182 real-world scenes span 16 task types at three levels: static perception, local prediction, and global prediction, progressively requiring scene understanding, spatial state updating, and relational inference over unobserved outcomes. Evaluating 21 models exposes a stark gap: the strongest model reaches only 58.0% against 87.2% human performance, while spatially specialized models remain near random chance. Controlled analyses further reveal that bridge views are critical for integrating distributed observations, and that explicit 3D evidence benefits models more reliably than generated outcome images or videos. Fine-tuning on our programmatically generated data lifts Qwen3-VL-4B from 34.0% to 65.7% with macro-average gains across six out-of-domain benchmarks.

A number of datasets for Relation Extraction (RE) have been created to aide downstream tasks such as information retrieval, semantic search, question answering and textual entailment. However, these datasets fail to capture financial-domain specific challenges since most of these datasets are compiled using general knowledge sources such as Wikipedia, web-based text and news articles, hindering real-life progress and adoption within the financial world. To address this limitation, we propose REFinD, the first large-scale annotated dataset of relations, with sim29K instances and 22 relations amongst 8 types of entity pairs, generated entirely over financial documents. We also provide an empirical evaluation with various state-of-the-art models as benchmarks for the RE task and highlight the challenges posed by our dataset. We observed that various state-of-the-art deep learning models struggle with numeric inference, relational and directional ambiguity.

Relational foundation models (RFMs) are pretrained once on a collection of relational databases and prediction tasks, and then applied zero-shot to previously unseen databases and tasks. To make a prediction for a target row, an RFM samples a neighborhood of rows linked to that row through foreign keys and uses this neighborhood as its inference context. Lowering inference cost is an important goal for any foundation model, and for RFMs this cost grows with the size of the context. The simplest ways to shrink the context is to drop some of the sampled rows, but this ignores the semantics of the database schema, so it is as likely to discard informative rows as uninformative ones. We propose STEER, a sampling approach that shrinks the inference context by concentrating it on the tables most relevant to the prediction task at hand. STEER obtains relevance information by prompting a large language model to rank the foreign-key edges of the database schema into relevance tiers for the given task, and then maps each tier to a probability of following that edge during traversal. Because the ranking uses only the schema, it is computed once per task and reused across all subsequent predictions, amortizing its cost. We evaluate STEER on three state-of-the-art RFMs (RT, RT-J, and Griffin) and show that it reduces inference context size by about 40% on average while maintaining, and in some cases improving, prediction accuracy.

Relational graph neural networks (RGNNs) are graph neural networks (GNNs) with dedicated structures for modeling the different types of nodes and/or edges in heterogeneous graphs. While RGNNs have been increasingly adopted in many real-world applications due to their versatility and accuracy, they pose performance and system design challenges due to their inherent computation patterns, gap between the programming interface and kernel APIs, and heavy programming efforts in optimizing kernels caused by their coupling with data layout and heterogeneity. To systematically address these challenges, we propose Pigeon, a novel two-level intermediate representation (IR) and its code generator framework, that (a) represents the key properties of the RGNN models to bridge the gap between the programming interface and kernel APIs, (b) decouples model semantics, data layout, and operators-specific optimization from each other to reduce programming efforts, (c) expresses and leverages optimization opportunities in inter-operator transforms, data layout, and operator-specific schedules. By building on one general matrix multiply (GEMM) template and a node/edge traversal template, Pigeon achieves up to 7.8x speed-up in inference and 5.6x speed-up in training compared with the state-of-the-art public systems in select models, i.e., RGCN, RGAT, HGT, when running heterogeneous graphs provided by Deep Graph Library (DGL) and Open Graph Benchmark (OGB). Pigeon also triggers fewer out-of-memory (OOM) errors. In addition, we propose linear operator fusion and compact materialization to further accelerate the system by up to 2.2x.

Accurate road topology reasoning is critical for autonomous driving, as it requires both perceiving road elements and understanding how lanes connect to each other (L2L) and to traffic elements (L2T). Existing methods often focus on either perception or L2L reasoning, leaving L2T underexplored and fall short of jointly optimizing perception and reasoning. Moreover, although topology prediction inherently involves relations, relational modeling itself is seldom incorporated into feature extraction or supervision. As humans naturally leverage contextual relationships to recognize road element and infer their connectivity, we posit that relational modeling can likewise benefit both perception and reasoning, and that these two tasks should be mutually enhancing. To this end, we propose RelTopo, a multi-level relational modeling approach that systematically integrates relational cues across three levels: 1) perception-level: a relation-aware lane detector with geometry-biased self-attention and curve-guided cross-attention enriches lane representations; 2) reasoning-level: relation-enhanced topology heads, including a geometry-enhanced L2L head and a cross-view L2T head, enhance topology inference via relational cues; and 3) supervision-level: a contrastive InfoNCE strategy regularizes relational embeddings. This design enables perception and reasoning to be optimized jointly. Extensive experiments on OpenLane-V2 demonstrate that RelTopo significantly improves both detection and topology reasoning, with gains of +3.1 in DET_l, +5.3 in TOP_{ll}, +4.9 in TOP_{lt}, and +4.4 overall in OLS, setting a new state-of-the-art. Code will be released.

Few-shot learning research is predominantly evaluated on accuracy alone, with limited attention to the parameter and training-sample budgets required to reach that accuracy - a real constraint for practitioners without large-scale compute. We present an ultra-lightweight (22,249-34,917 parameter) spatial-relational architecture for few-shot image classification that combines fixed Gabor edge-energy guidance with a windowed, content-adaptive patch locator. Under a strictly matched, iso-episode-budget protocol (250 meta-training episodes, 5 canonical seeds, 600 evaluation episodes per seed), our architecture achieves 5-shot accuracy gains, consistent across all five seeds, over Prototypical Networks, Relation Networks, and MAML on both CIFAR-FS and MiniImageNet, while using 27-53% fewer parameters than any baseline. It also converges in fewer training episodes, generalizes better to an unseen fine-grained domain (CUB-200-2011 birds, zero retraining), and is more robust to 50% occlusion and 25% spatial translation than all three baselines. A series of falsification ablations - zeroing relational tokens at inference and retraining without them entirely - shows that the architecture's pairwise relational computation, while present, is not the primary driver of its performance; the content-adaptive patch locator is. We report this honestly, together with a capacity sweep showing a genuine accuracy plateau near 22-35k parameters, and release full seed-level results and checkpoint hashes for reproducibility.

Auxiliary signal pathways in VLMs are routinely fitted with learnable gates so the optimiser can decide how much of the signal to admit. We find that the optimiser almost always decides on zero: across five injection designs, every gated pathway becomes behaviourally closed, with accuracy invariant to ablating the pathway at inference even when the gate parameter would nominally pass 30-45% of the signal. We attribute this suppression phenomenon to two regimes, a dead-gradient regime formalised through the caption-invariance of image-derived signals, and a negative-utility regime in which the auxiliary signal actively hurts the loss. Rather than fight suppression, we exploit it: we regularise LoRA fine-tuning with geometric auxiliary losses from hyperbolic visual relational graphs (IoA-driven entailment cones and angular repulsion on the Lorentz manifold), coupled only through the forward pass at training time and dropped at inference. Disaggregating GQA by question type exposes a clean dissociation. Three configurations without geometric losses at inference lose 2.85-3.39pp on relational questions while gaining ~1pp on attribute questions; a fourth that trains with the losses but infers through a soft prompt loses 5.14pp on rel for only +0.23pp on attr, so training-time regularisation alone does not protect relational accuracy without a geometric inference pathway. Configurations that keep the geometric pathway at inference preserve vanilla-level relational accuracy and match the attribute gain. Out of distribution on VSR, the RMS-prefix recipe preserves the spatial signal; stripping the geometric losses (G2) collapses VSR by 4.6pp, isolating them as the OOD source. A secondary result: embedding-norm alignment is necessary for generation-safe prefix injection, and learnable gates should be replaced with fixed, non-optional injection at matched scales.

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models often focus on structured inputs such as tables, graphs, or synthetic tasks, and do not isolate the difficulty introduced by higher-arity relational binding. We study this problem through the lens of Relational Complexity (RC), which we define as the minimum number of independent entities or operands that must be simultaneously bound to apply a relation. RC provides a principled way to vary reasoning difficulty while controlling for confounders such as input size, vocabulary, and representational choices. Building on RC, we introduce REL, a generative benchmark framework spanning algebra, chemistry, and biology that varies RC within each domain. Across frontier LLMs, performance degrades consistently and monotonically as RC increases, even when the total number of entities is held fixed. This failure mode persists with increased test-time compute and in-context learning, suggesting a limitation tied to the arity of the required relational binding rather than to insufficient inference steps or lack of exposure to examples. Our results identify a regime of higher-arity reasoning in which current models struggle, and motivate re-examining benchmarks through the lens of relational complexity.

Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins, and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset.

Relational Databases (RDBs) are the backbone of modern business, yet they lack foundation models comparable to those in text or vision. A key obstacle is that high-quality RDBs are private, scarce and structurally heterogeneous, making internet-scale pre-training infeasible. To overcome this data scarcity, We introduce RDB-PFN, the first relational foundation model trained purely via synthetic data. Inspired by Prior-Data Fitted Networks (PFNs) where synthetic data generated from Structural Causal Models (SCMs) enables reasoning on single tables, we design a Relational Prior Generator to create an infinite stream of diverse RDBs from scratch. Pre-training on over 2 million synthetic single-table and relational tasks, RDB-PFN learns to adapt to any new database instantly via genuine in-context learning. Experiments verify RDB-PFN achieves strong few-shot performance on 19 real-world relational prediction tasks, outperforming graph-based and single-table foundation-model baselines (given the same DFS-linearized inputs), while using a lightweight architecture and fast inference. The code is available at https://github.com/MuLabPKU/RDBPFN

Knowledge graphs enable a wide variety of applications, including question answering and information retrieval. Despite the great effort invested in their creation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata) remain incomplete. We introduce Relational Graph Convolutional Networks (R-GCNs) and apply them to two standard knowledge base completion tasks: Link prediction (recovery of missing facts, i.e. subject-predicate-object triples) and entity classification (recovery of missing entity attributes). R-GCNs are related to a recent class of neural networks operating on graphs, and are developed specifically to deal with the highly multi-relational data characteristic of realistic knowledge bases. We demonstrate the effectiveness of R-GCNs as a stand-alone model for entity classification. We further show that factorization models for link prediction such as DistMult can be significantly improved by enriching them with an encoder model to accumulate evidence over multiple inference steps in the relational graph, demonstrating a large improvement of 29.8% on FB15k-237 over a decoder-only baseline.

We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and/or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2% vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning.

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatio-temporal modeling, Bayesian Optimization and continuous control, inherently contain equivariances -- for example to translation -- which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.

Investigating whether pre-trained language models (LMs) can function as knowledge bases (KBs) has raised wide research interests recently. However, existing works focus on simple, triple-based, relational KBs, but omit more sophisticated, logic-based, conceptualised KBs such as OWL ontologies. To investigate an LM's knowledge of ontologies, we propose OntoLAMA, a set of inference-based probing tasks and datasets from ontology subsumption axioms involving both atomic and complex concepts. We conduct extensive experiments on ontologies of different domains and scales, and our results demonstrate that LMs encode relatively less background knowledge of Subsumption Inference (SI) than traditional Natural Language Inference (NLI) but can improve on SI significantly when a small number of samples are given. We will open-source our code and datasets.

This work aims at advancing temporal action detection (TAD) using an encoder-decoder framework with action queries, similar to DETR, which has shown great success in object detection. However, the framework suffers from several problems if directly applied to TAD: the insufficient exploration of inter-query relation in the decoder, the inadequate classification training due to a limited number of training samples, and the unreliable classification scores at inference. To this end, we first propose a relational attention mechanism in the decoder, which guides the attention among queries based on their relations. Moreover, we propose two losses to facilitate and stabilize the training of action classification. Lastly, we propose to predict the localization quality of each action query at inference in order to distinguish high-quality queries. The proposed method, named ReAct, achieves the state-of-the-art performance on THUMOS14, with much lower computational costs than previous methods. Besides, extensive ablation studies are conducted to verify the effectiveness of each proposed component. The code is available at https://github.com/sssste/React.

Multi-robot systems (MRS) offer significant advantages over single-robot platforms by enabling information sharing and coordination for different tasks in complex environments. However, reliable cooperation critically depends on inferring trust over both information sources and their reported hypotheses, particularly under partial observability and potential adversarial interference. Existing approaches frequently depend on pre-established trust relationships or side-channel information, which may not be available or reliable in realistic MRS deployments. This work introduces NeST-Bayes, a neural-symbolic framework that jointly infers robot and hypothesis trust using only inter-robot observation consistency, without requiring preassigned robot trust, reputation information, or side-channel identity signals. NeST-Bayes infers instantaneous trust evidence scores for robots and object hypotheses by reasoning over ego-centric relational graphs constructed from cross-robot observation consistency. These evidence scores are accumulated over time through Bayesian updates of Beta-distributed trust beliefs to maintain temporally consistent trust estimates. Extensive evaluations show that NeST-Bayes achieves the highest mean object precision and robot recall across all benchmark settings, and the highest robot precision and object recall in most settings, compared to trust-based methods. Under aggressive optimized attacks, it achieves 98.8\% robot precision with 93.8\% recall and 98.3\% object precision with 95.4\% recall. In an occlusion-rich Webots warehouse, it maintains 92.5\% robot precision with 92.0\% recall and 97.3\% object precision with 85.0\% recall. These results demonstrate joint improvements in the reliability and coverage of retained information.

Understanding a painting is never a single act. Art historians may analyze the same work through concepts of style, iconography, or historical context, dimensions that are not interchangeable, and each carries distinct semantic relationships between the visual and the textual. Vision-Language Models (VLMs) like CLIP, which learn a single shared embedding space, collapse this richness into a single homogeneous alignment, thereby losing the multi-relational structure that defines art-historical reasoning. We introduce CANVAS (Contrastive Art-aware Network for Vision-Language Alignment with Sheaves), a framework for learning relation-aware multimodal representations inspired by sheaf theory. Each artwork is projected into multiple embeddings conditioned on the type of relation (i.e., the context), and a novel contrastive loss encodes contextual information during training, with no dependency on external data at inference. We evaluate on three newly introduced benchmarks of artworks for multi-relational art understanding: WikiArt+, derived from WikiArt and Wikipedia, HertzianaDP, from the Bibliotheca Hertziana collection, and SemArt+, refined from the SemArt dataset. In multimodal retrieval and art understanding, CANVAS outperforms the baselines, supporting the view that multi-relational alignment is not just theoretically motivated but also practically essential.

Answering complex real-world questions often requires accurate retrieval from textual knowledge graphs (TKGs). The scarcity of annotated data, along with intricate topological structures, makes this task particularly challenging. As the nature of relational path information could enhance the inference ability of Large Language Models (LLMs), efficiently retrieving more complex relational path information from TKGs presents another key challenge. To tackle these challenges, we first develop a Dataset for LLMs Complex Reasoning over Textual Knowledge Graphs (RiTeK) with a broad topological structure coverage.We synthesize realistic user queries that integrate diverse topological structures, relational information, and complex textual descriptions. We conduct rigorous expert evaluation to validate the quality of our synthesized queries. And then, we introduce an enhanced Monte Carlo Tree Search (MCTS) method, Relational MCTS, to automatically extract relational path information from textual graphs for specific queries. Our dataset mainly covers the medical domain as the relation types and entity are complex and publicly available. Experimental results indicate that RiTeK poses significant challenges for current retrieval and LLM systems, while the proposed Relational MCTS method enhances LLM inference ability and achieves state-of-the-art performance on RiTeK.

Graph-based retrieval-augmented generation (Graph RAG) is increasingly deployed to support LLM applications by augmenting user queries with structured knowledge retrieved from a knowledge graph. While Graph RAG improves relational reasoning, it introduces a largely understudied threat: adversaries can reconstruct subgraphs from a target RAG system's knowledge graph, enabling privacy inference and replication of curated knowledge assets. We show that existing attacks are largely ineffective against Graph RAG even with simple prompt-based safeguards, because these attacks expose explicit exfiltration intent and are therefore easily suppressed by lightweight safe prompts. We identify three technical challenges for practical Graph RAG extraction under realistic safeguards and introduce GRASP, a closed-box, multi-turn subgraph reconstruction attack. GRASP (i) reframes extraction as a context-processing task, (ii) enforces format-compliant, instance-grounded outputs via per-record identifiers to reduce hallucinations and preserve relational details, and (iii) diversifies goal-driven attack queries using a momentum-aware scheduler to operate within strict query budgets. Across two real-world knowledge graphs, four safety-aligned LLMs, and multiple Graph RAG frameworks, GRASP attains the strongest type-faithful reconstruction where prior methods fail, reaching up to 82.9 F1. We further evaluate defenses and propose two lightweight mitigations that substantially reduce reconstruction fidelity without utility loss.

The convolution layer has been the dominant feature extractor in computer vision for years. However, the spatial aggregation in convolution is basically a pattern matching process that applies fixed filters which are inefficient at modeling visual elements with varying spatial distributions. This paper presents a new image feature extractor, called the local relation layer, that adaptively determines aggregation weights based on the compositional relationship of local pixel pairs. With this relational approach, it can composite visual elements into higher-level entities in a more efficient manner that benefits semantic inference. A network built with local relation layers, called the Local Relation Network (LR-Net), is found to provide greater modeling capacity than its counterpart built with regular convolution on large-scale recognition tasks such as ImageNet classification.

Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and complex query answering tasks by learning representations of entities, relations, and queries. Still, most existing query answering methods rely on transductive entity embeddings and cannot generalize to KGs containing new entities without retraining the entity embeddings. In this work, we study the inductive query answering task where inference is performed on a graph containing new entities with queries over both seen and unseen entities. To this end, we devise two mechanisms leveraging inductive node and relational structure representations powered by graph neural networks (GNNs). Experimentally, we show that inductive models are able to perform logical reasoning at inference time over unseen nodes generalizing to graphs up to 500% larger than training ones. Exploring the efficiency--effectiveness trade-off, we find the inductive relational structure representation method generally achieves higher performance, while the inductive node representation method is able to answer complex queries in the inference-only regime without any training on queries and scales to graphs of millions of nodes. Code is available at https://github.com/DeepGraphLearning/InductiveQE.

Multimodal Large Language Models (MLLMs) capable of thinking with images often rely on external tools for fine-grained perception. However, this reliance introduces significant inference latency and fails to effectively resolve the spatial-structural gap-a fundamental challenge in text-dense and structurally relational visuals (e.g., charts and visual tables) where strict relative spatial arrangements bind textual elements. Without external tools, standard MLLMs struggle with such fine-grained visual reasoning tasks. To address these issues, we propose Think with Structured Grounding (TwSG), a novel fine-grained image perception framework designed to internalize complex images's tool-use capabilities within the model. TwSG distills the benefits of multi-step reasoning and micro-cropping into a single efficient forward pass during inference. Specifically, we use an MLLM to identify key regions guided by ground-truth answers, and then prompt a teacher model to generate high-quality visual question-answering (VQA) data. These fine-grained, region-based supervisory signals are subsequently distilled back into the full-image representation. Our training pipeline consists of two stages: (1) a cold-start supervised fine-tuning (SFT) phase using multi-turn data with focused area descriptions to foster complex reasoning and error recovery; and (2) a reinforcement fine-tuning (RFT) phase driven by a novel process reward mechanism, TL-GRPO, which encourages strategic reasoning. Extensive experiments across various MLLM architectures demonstrate that TwSG reduces inference latency while substantially improving accuracy and robustness, endowing models with native fine-grained region description and flexible reasoning capabilities.

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved), hyperbolic space (negatively curved) or hyperspherical space (positively curved) to maintain their specific geometric structures (e.g., chain, hierarchy and ring structures). However, the topological structure of KGs appears to be complicated, since it may contain multiple types of geometric structures simultaneously. Therefore, embedding KGs in a single space, no matter the Euclidean space, hyperbolic space or hyperspheric space, cannot capture the complex structures of KGs accurately. To overcome this challenge, we propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Theoretically, our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities. Experimental results on three well-established knowledge graph completion benchmarks show that our GIE achieves the state-of-the-art performance with fewer parameters.

Scene understanding is central to general physical intelligence, and video is a primary modality for capturing both state and temporal dynamics of a scene. Yet understanding physical processes remains difficult, as models must combine object localization, hand-object interactions, relational parsing, temporal reasoning, and step-level procedural inference. Existing benchmarks usually evaluate these capabilities separately, limiting diagnosis of why models fail on procedural tasks. We introduce BARISTA, a densely annotated egocentric dataset and benchmark of 185 real-world coffee-preparation videos covering fully automatic, portafilter-based, and capsule-based workflows. BARISTA provides verified per-frame scene graphs linking persistent object identities to masks, tracks, boxes, attributes, typed relations, hand-object interactions, activities, and process steps. From these graphs, we derive zero-shot language-based tasks spanning phrase grounding, hand-object interaction recognition, referring, activity recognition, relation extraction, and temporal visual question answering. Experiments reveal strong variation across task families and no consistently dominant model family, positioning BARISTA as a challenging diagnostic benchmark for procedural video understanding. Code and dataset available at https://huggingface.co/datasets/ramblr/BARISTA.

Answering navigation-relevant questions over long egocentric videos requires retrieving and organizing evidence distributed across distant temporal moments while maintaining spatial and contextual consistency. Although long-context vision--language models can achieve strong answer quality, they are computationally expensive for long trajectories and inefficient for repeated querying. Recent graph-based approaches such as VL-KnG address this challenge through persistent spatio-temporal knowledge graphs, but graph-centric retrieval alone may underrepresent broader temporal continuity and contextual cues. We present VL-MemKnG, a hybrid memory framework that extends VL-KnG by combining a spatio-temporal knowledge graph with persistent segment-level contextual memory. The knowledge graph captures structured relational information and long-range object associations, while segment-level memory preserves broader temporal context for long-horizon evidence retrieval. A hybrid retrieval-and-reasoning module jointly operates over both memory representations to produce evidence-grounded answers and temporally organized supporting evidence. We also introduce WalkieKnowledgeT+, an extension of WalkieKnowledge for long-horizon navigation-oriented video question answering. The benchmark includes temporally distributed reasoning tasks requiring evidence aggregation across multiple non-cooccurring moments. On WalkieKnowledgeT+, VL-MemKnG improves Top-1 retrieval accuracy from 58% to 67% and Recall@1 from 34.50% to 40.55%, outperforming all compared methods, including Gemini 2.5 Pro and Qwen 3.5+. The gains are particularly pronounced on temporal-global and temporally scattered aggregation questions, demonstrating the benefits of combining structured relational memory with segment-level contextual memory while maintaining efficient query-time inference.

In self-supervised learning, a system is tasked with achieving a surrogate objective by defining alternative targets on a set of unlabeled data. The aim is to build useful representations that can be used in downstream tasks, without costly manual annotation. In this work, we propose a novel self-supervised formulation of relational reasoning that allows a learner to bootstrap a signal from information implicit in unlabeled data. Training a relation head to discriminate how entities relate to themselves (intra-reasoning) and other entities (inter-reasoning), results in rich and descriptive representations in the underlying neural network backbone, which can be used in downstream tasks such as classification and image retrieval. We evaluate the proposed method following a rigorous experimental procedure, using standard datasets, protocols, and backbones. Self-supervised relational reasoning outperforms the best competitor in all conditions by an average 14% in accuracy, and the most recent state-of-the-art model by 3%. We link the effectiveness of the method to the maximization of a Bernoulli log-likelihood, which can be considered as a proxy for maximizing the mutual information, resulting in a more efficient objective with respect to the commonly used contrastive losses.

Relational reasoning is a central component of generally intelligent behavior, but has proven difficult for neural networks to learn. In this paper we describe how to use Relation Networks (RNs) as a simple plug-and-play module to solve problems that fundamentally hinge on relational reasoning. We tested RN-augmented networks on three tasks: visual question answering using a challenging dataset called CLEVR, on which we achieve state-of-the-art, super-human performance; text-based question answering using the bAbI suite of tasks; and complex reasoning about dynamic physical systems. Then, using a curated dataset called Sort-of-CLEVR we show that powerful convolutional networks do not have a general capacity to solve relational questions, but can gain this capacity when augmented with RNs. Our work shows how a deep learning architecture equipped with an RN module can implicitly discover and learn to reason about entities and their relations.

Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they remember. Here, we first confirm our intuitions that standard memory architectures may struggle at tasks that heavily involve an understanding of the ways in which entities are connected -- i.e., tasks involving relational reasoning. We then improve upon these deficits by using a new memory module -- a Relational Memory Core (RMC) -- which employs multi-head dot product attention to allow memories to interact. Finally, we test the RMC on a suite of tasks that may profit from more capable relational reasoning across sequential information, and show large gains in RL domains (e.g. Mini PacMan), program evaluation, and language modeling, achieving state-of-the-art results on the WikiText-103, Project Gutenberg, and GigaWord datasets.

Relational reasoning lies at the core of many NLP tasks, drawing on complementary signals from text and graphs. While prior research has investigated how to leverage this dual complementarity, a detailed and systematic understanding of text-graph interplay and its effect on hybrid models remains underexplored. We take an analysis-driven approach to investigate text-graph representation complementarity via a unified architecture that supports knowledge co-distillation (CoD). We explore five tasks involving relational reasoning that differ in how text and graph structures encode the information needed to solve that task. By tracking how these dual representations evolve during training, we uncover interpretable patterns of alignment and divergence, and provide insights into when and why their integration is beneficial.

Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions.

Lying at the core of human intelligence, relational thinking is characterized by initially relying on innumerable unconscious percepts pertaining to relations between new sensory signals and prior knowledge, consequently becoming a recognizable concept or object through coupling and transformation of these percepts. Such mental processes are difficult to model in real-world problems such as in conversational automatic speech recognition (ASR), as the percepts (if they are modelled as graphs indicating relationships among utterances) are supposed to be innumerable and not directly observable. In this paper, we present a Bayesian nonparametric deep learning method called deep graph random process (DGP) that can generate an infinite number of probabilistic graphs representing percepts. We further provide a closed-form solution for coupling and transformation of these percept graphs for acoustic modeling. Our approach is able to successfully infer relations among utterances without using any relational data during training. Experimental evaluations on ASR tasks including CHiME-2 and CHiME-5 demonstrate the effectiveness and benefits of our method.

Analogical reasoning is at the core of human cognition, serving as an important foundation for a variety of intellectual activities. While prior work has shown that LLMs can represent task patterns and surface-level concepts, it remains unclear whether these models can encode high-level relational concepts and apply them to novel situations through structured comparisons. In this work, we explore this fundamental aspect using proportional and story analogies, and identify three key findings. First, LLMs effectively encode the underlying relationships between analogous entities; both attributive and relational information propagate through mid-upper layers in correct cases, whereas reasoning failures reflect missing relational information within these layers. Second, unlike humans, LLMs often struggle not only when relational information is missing, but also when attempting to apply it to new entities. In such cases, strategically patching hidden representations at critical token positions can facilitate information transfer to a certain extent. Lastly, successful analogical reasoning in LLMs is marked by strong structural alignment between analogous situations, whereas failures often reflect degraded or misplaced alignment. Overall, our findings reveal that LLMs exhibit emerging but limited capabilities in encoding and applying high-level relational concepts, highlighting both parallels and gaps with human cognition.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.

Learning with relational and network-structured data is increasingly vital in sensitive domains where protecting the privacy of individual entities is paramount. Differential Privacy (DP) offers a principled approach for quantifying privacy risks, with DP-SGD emerging as a standard mechanism for private model training. However, directly applying DP-SGD to relational learning is challenging due to two key factors: (i) entities often participate in multiple relations, resulting in high and difficult-to-control sensitivity; and (ii) relational learning typically involves multi-stage, potentially coupled (interdependent) sampling procedures that make standard privacy amplification analyses inapplicable. This work presents a principled framework for relational learning with formal entity-level DP guarantees. We provide a rigorous sensitivity analysis and introduce an adaptive gradient clipping scheme that modulates clipping thresholds based on entity occurrence frequency. We also extend the privacy amplification results to a tractable subclass of coupled sampling, where the dependence arises only through sample sizes. These contributions lead to a tailored DP-SGD variant for relational data with provable privacy guarantees. Experiments on fine-tuning text encoders over text-attributed network-structured relational data demonstrate the strong utility-privacy trade-offs of our approach. Our code is available at https://github.com/Graph-COM/Node_DP.

Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms operate only on classical, triple-based graphs, whereas modern KGs often employ a hyper-relational modeling paradigm. In this paradigm, typed edges may have several key-value pairs known as qualifiers that provide fine-grained context for facts. In queries, this context modifies the meaning of relations, and usually reduces the answer set. Hyper-relational queries are often observed in real-world KG applications, and existing approaches for approximate query answering cannot make use of qualifier pairs. In this work, we bridge this gap and extend the multi-hop reasoning problem to hyper-relational KGs allowing to tackle this new type of complex queries. Building upon recent advancements in Graph Neural Networks and query embedding techniques, we study how to embed and answer hyper-relational conjunctive queries. Besides that, we propose a method to answer such queries and demonstrate in our experiments that qualifiers improve query answering on a diverse set of query patterns.

Knowledge graphs are incomplete by nature, with only a limited number of observed facts from the world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear map as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on the embedding dimensionality and factorization rank. Our model naturally generalizes Tucker decomposition based TuckER model, which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising the performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, reaching on par or state-of-the-art performance. At extreme low-ranks, model preserves the performance while staying parameter efficient.

Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.

How do transformer language models memorize factual associations? A common view casts internal weight matrices as associative memories over pairs of embeddings, requiring parameter counts that scale linearly with the number of facts. We develop a theoretical and empirical account of an alternative, geometric form of memorization in which learned embeddings encode relational structure directly, and the MLP plays a qualitatively different role. In a controlled setting where a single-layer transformer must memorize random bijections from subjects to a shared attribute set, we prove that a logarithmic embedding dimension suffices: subject embeddings encode linear superpositions of their associated attribute vectors, and a small MLP acts as a relation-conditioned selector that extracts the relevant attribute via ReLU gating, and not as an associative key-value mapping. We extend these results to the multi-hop setting -- chains of relational queries such as ``Who is the mother of the wife of x?'' -- providing constructions with and without chain-of-thought that exhibit a provable capacity-depth tradeoff, complemented by a matching information-theoretic lower bound. Empirically, gradient descent discovers solutions with precisely the predicted structure. Once trained, the MLP transfers zero-shot to entirely new bijections when subject embeddings are appropriately re-initialized, revealing that it has learned a generic selection mechanism rather than memorized any particular set of facts.

Large language models encapsulate knowledge and have demonstrated superior performance on various natural language processing tasks. Recent studies have localized this knowledge to specific model parameters, such as the MLP weights in intermediate layers. This study investigates the differences between entity and relational knowledge through knowledge editing. Our findings reveal that entity and relational knowledge cannot be directly transferred or mapped to each other. This result is unexpected, as logically, modifying the entity or the relation within the same knowledge triplet should yield equivalent outcomes. To further elucidate the differences between entity and relational knowledge, we employ causal analysis to investigate how relational knowledge is stored in pre-trained models. Contrary to prior research suggesting that knowledge is stored in MLP weights, our experiments demonstrate that relational knowledge is also significantly encoded in attention modules. This insight highlights the multifaceted nature of knowledge storage in language models, underscoring the complexity of manipulating specific types of knowledge within these models.

Inference, especially those derived from inductive processes, is a crucial component in our conversation to complement the information implicitly or explicitly conveyed by a speaker. While recent large language models show remarkable advances in inference tasks, their performance in inductive reasoning, where not all information is present in the context, is far behind deductive reasoning. In this paper, we analyze the behavior of the models based on the task difficulty defined by the semantic information gap -- which distinguishes inductive and deductive reasoning (Johnson-Laird, 1988, 1993). Our analysis reveals that the disparity in information between dialogue contexts and desired inferences poses a significant challenge to the inductive inference process. To mitigate this information gap, we investigate a contrastive learning approach by feeding negative samples. Our experiments suggest negative samples help models understand what is wrong and improve their inference generations.

Compositional relational reasoning (CRR) is a hallmark of human intelligence, but we lack a clear understanding of whether and how existing transformer large language models (LLMs) can solve CRR tasks. To enable systematic exploration of the CRR capability of LLMs, we first propose a new synthetic benchmark called Generalized Associative Recall (GAR) by integrating and generalizing the essence of several tasks in mechanistic interpretability (MI) study in a unified framework. Evaluation shows that GAR is challenging enough for existing LLMs, revealing their fundamental deficiency in CRR. Meanwhile, it is easy enough for systematic MI study. Then, to understand how LLMs solve GAR tasks, we use attribution patching to discover the core circuits reused by Vicuna-33B across different tasks and a set of vital attention heads. Intervention experiments show that the correct functioning of these heads significantly impacts task performance. Especially, we identify two classes of heads whose activations represent the abstract notion of true and false in GAR tasks respectively. They play a fundamental role in CRR across various models and tasks. The dataset and code are available at https://github.com/Caiyun-AI/GAR.

Graph neural networks (GNNs) have shown promising performance for knowledge graph reasoning. A recent variant of GNN called progressive relational graph neural network (PRGNN), utilizes relational rules to infer missing knowledge in relational digraphs and achieves notable results. However, during reasoning with PRGNN, two important properties are often overlooked: (1) the sequentiality of relation composition, where the order of combining different relations affects the semantics of the relational rules, and (2) the lagged entity information propagation, where the transmission speed of required information lags behind the appearance speed of new entities. Ignoring these properties leads to incorrect relational rule learning and decreased reasoning accuracy. To address these issues, we propose a novel knowledge graph reasoning approach, the Relational rUle eNhanced Graph Neural Network (RUN-GNN). Specifically, RUN-GNN employs a query related fusion gate unit to model the sequentiality of relation composition and utilizes a buffering update mechanism to alleviate the negative effect of lagged entity information propagation, resulting in higher-quality relational rule learning. Experimental results on multiple datasets demonstrate the superiority of RUN-GNN is superior on both transductive and inductive link prediction tasks.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

A prominent challenge for modern language understanding systems is the ability to answer implicit reasoning questions, where the required reasoning steps for answering the question are not mentioned in the text explicitly. In this work, we investigate why current models struggle with implicit reasoning question answering (QA) tasks, by decoupling inference of reasoning steps from their execution. We define a new task of implicit relation inference and construct a benchmark, IMPLICITRELATIONS, where given a question, a model should output a list of concept-relation pairs, where the relations describe the implicit reasoning steps required for answering the question. Using IMPLICITRELATIONS, we evaluate models from the GPT-3 family and find that, while these models struggle on the implicit reasoning QA task, they often succeed at inferring implicit relations. This suggests that the challenge in implicit reasoning questions does not stem from the need to plan a reasoning strategy alone, but to do it while also retrieving and reasoning over relevant information.

Although reinforcement learning has been successfully applied in many domains in recent years, we still lack agents that can systematically generalize. While relational inductive biases that fit a task can improve generalization of RL agents, these biases are commonly hard-coded directly in the agent's neural architecture. In this work, we show that we can incorporate relational inductive biases, encoded in the form of relational graphs, into agents. Based on this insight, we propose Grid-to-Graph (GTG), a mapping from grid structures to relational graphs that carry useful spatial relational inductive biases when processed through a Relational Graph Convolution Network (R-GCN). We show that, with GTG, R-GCNs generalize better both in terms of in-distribution and out-of-distribution compared to baselines based on Convolutional Neural Networks and Neural Logic Machines on challenging procedurally generated environments and MinAtar. Furthermore, we show that GTG produces agents that can jointly reason over observations and environment dynamics encoded in knowledge bases.

Relational databases (RDBs) are widely regarded as the gold standard for storing structured information. Consequently, predictive tasks leveraging this data format hold significant application promise. Recently, Relational Deep Learning (RDL) has emerged as a novel paradigm wherein RDBs are conceptualized as graph structures, enabling the application of various graph neural architectures to effectively address these tasks. However, given its novelty, there is a lack of analysis into the relationships between the performance of various RDL models and the characteristics of the underlying RDBs. In this study, we present REDELEX-a comprehensive exploration framework for evaluating RDL models of varying complexity on the most diverse collection of over 70 RDBs, which we make available to the community. Benchmarked alongside key representatives of classic methods, we confirm the generally superior performance of RDL while providing insights into the main factors shaping performance, including model complexity, database sizes and their structural properties.

Deductive reasoning is the process of deriving conclusions strictly from the given premises, without relying on external knowledge. We define honesty in this setting as a model's ability to respond only when the conclusion is logically entailed by the premises, and to abstain otherwise. However, current language models often fail to reason honestly, producing unwarranted answers when the input is insufficient. To study this challenge, we formulate honest deductive reasoning as multi-step tasks where models must either derive the correct conclusion or abstain. We curate two datasets from graph structures, one for linear algebra and one for logical inference, and introduce unanswerable cases by randomly perturbing an edge in half of the instances. We find that prompting and existing training methods, including GRPO with or without supervised fine-tuning initialization, struggle on these tasks. In particular, GRPO optimize only for final task outcomes, leaving models vulnerable to collapse when negative rewards dominate early training. To address this, we propose ACNCHOR, a reinforcement learning method that injects ground truth trajectories into rollouts, preventing early training collapse. Our results demonstrate that this method stabilizes learning and significantly improves the overall reasoning performance, underscoring the importance of training dynamics for enabling honest deductive reasoning in language models.

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data is both challenging and time consuming. The core problem is that no machine learning method is capable of learning on multiple tables interconnected by primary-foreign key relations. Current methods can only learn from a single table, so the data must first be manually joined and aggregated into a single training table, the process known as feature engineering. Feature engineering is slow, error prone and leads to suboptimal models. Here we introduce an end-to-end deep representation learning approach to directly learn on data laid out across multiple tables. We name our approach Relational Deep Learning (RDL). The core idea is to view relational databases as a temporal, heterogeneous graph, with a node for each row in each table, and edges specified by primary-foreign key links. Message Passing Graph Neural Networks can then automatically learn across the graph to extract representations that leverage all input data, without any manual feature engineering. Relational Deep Learning leads to more accurate models that can be built much faster. To facilitate research in this area, we develop RelBench, a set of benchmark datasets and an implementation of Relational Deep Learning. The data covers a wide spectrum, from discussions on Stack Exchange to book reviews on the Amazon Product Catalog. Overall, we define a new research area that generalizes graph machine learning and broadens its applicability to a wide set of AI use cases.

Large Language Models (LLMs) have demonstrated strong performance in handling complex tasks requiring both extensive knowledge and reasoning abilities. However, the existing LLM inference pipeline operates as an opaque process without explicit separation between knowledge retrieval and reasoning steps, making the model's decision-making process unclear and disorganized. This ambiguity can lead to issues such as hallucinations and knowledge forgetting, which significantly impact the reliability of LLMs in high-stakes domains. In this paper, we propose a new inference paradigm that decomposes the complex inference process into two distinct and clear actions: (1) memory recall: which retrieves relevant knowledge, and (2) reasoning: which performs logical steps based on the recalled knowledge. To facilitate this decomposition, we introduce two special tokens memory and reason, guiding the model to distinguish between steps that require knowledge retrieval and those that involve reasoning. Our experiment results show that this decomposition not only improves model performance but also enhances the interpretability of the inference process, enabling users to identify sources of error and refine model responses effectively. The code is available at https://github.com/MingyuJ666/Disentangling-Memory-and-Reasoning.

Knowledge probing assesses to which degree a language model (LM) has successfully learned relational knowledge during pre-training. Probing is an inexpensive way to compare LMs of different sizes and training configurations. However, previous approaches rely on the objective function used in pre-training LMs and are thus applicable only to masked or causal LMs. As a result, comparing different types of LMs becomes impossible. To address this, we propose an approach that uses an LM's inherent ability to estimate the log-likelihood of any given textual statement. We carefully design an evaluation dataset of 7,731 instances (40,916 in a larger variant) from which we produce alternative statements for each relational fact, one of which is correct. We then evaluate whether an LM correctly assigns the highest log-likelihood to the correct statement. Our experimental evaluation of 22 common LMs shows that our proposed framework, BEAR, can effectively probe for knowledge across different LM types. We release the BEAR datasets and an open-source framework that implements the probing approach to the research community to facilitate the evaluation and development of LMs.

Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real world datasets. We focus on the Neural Theorem Prover (NTP) model proposed by Rockt{ä}schel and Riedel (2017), a continuous relaxation of the Prolog backward chaining algorithm where unification between terms is replaced by the similarity between their embedding representations. For answering a given query, this model needs to consider all possible proof paths, and then aggregate results - this quickly becomes infeasible even for small Knowledge Bases (KBs). We observe that we can accurately approximate the inference process in this model by considering only proof paths associated with the highest proof scores. This enables inference and learning on previously impracticable KBs.

Pre-trained language models have been found to capture a surprisingly rich amount of lexical knowledge, ranging from commonsense properties of everyday concepts to detailed factual knowledge about named entities. Among others, this makes it possible to distill high-quality word vectors from pre-trained language models. However, it is currently unclear to what extent it is possible to distill relation embeddings, i.e. vectors that characterize the relationship between two words. Such relation embeddings are appealing because they can, in principle, encode relational knowledge in a more fine-grained way than is possible with knowledge graphs. To obtain relation embeddings from a pre-trained language model, we encode word pairs using a (manually or automatically generated) prompt, and we fine-tune the language model such that relationally similar word pairs yield similar output vectors. We find that the resulting relation embeddings are highly competitive on analogy (unsupervised) and relation classification (supervised) benchmarks, even without any task-specific fine-tuning. Source code to reproduce our experimental results and the model checkpoints are available in the following repository: https://github.com/asahi417/relbert

We present ATOMIC, an atlas of everyday commonsense reasoning, organized through 877k textual descriptions of inferential knowledge. Compared to existing resources that center around taxonomic knowledge, ATOMIC focuses on inferential knowledge organized as typed if-then relations with variables (e.g., "if X pays Y a compliment, then Y will likely return the compliment"). We propose nine if-then relation types to distinguish causes vs. effects, agents vs. themes, voluntary vs. involuntary events, and actions vs. mental states. By generatively training on the rich inferential knowledge described in ATOMIC, we show that neural models can acquire simple commonsense capabilities and reason about previously unseen events. Experimental results demonstrate that multitask models that incorporate the hierarchical structure of if-then relation types lead to more accurate inference compared to models trained in isolation, as measured by both automatic and human evaluation.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Neural link predictors learn distributed representations of entities and relations in a knowledge graph. They are remarkably powerful in the link prediction and knowledge base completion tasks, mainly due to the learned representations that capture important statistical dependencies in the data. Recent works in the area have focused on either designing new scoring functions or incorporating extra information into the learning process to improve the representations. Yet the representations are mostly learned from the observed links between entities, ignoring commonsense or schema knowledge associated with the relations in the graph. A fundamental aspect of the topology of relational data is the cardinality information, which bounds the number of predictions given for a relation between a minimum and maximum frequency. In this paper, we propose a new regularisation approach to incorporate relation cardinality constraints to any existing neural link predictor without affecting their efficiency or scalability. Our regularisation term aims to impose boundaries on the number of predictions with high probability, thus, structuring the embeddings space to respect commonsense cardinality assumptions resulting in better representations. Experimental results on Freebase, WordNet and YAGO show that, given suitable prior knowledge, the proposed method positively impacts the predictive accuracy of downstream link prediction tasks.

Large Language Models (LLMs) have demonstrated the ability to tackle increasingly complex tasks through advanced reasoning, long-form content generation, and tool use. Solving these tasks often involves long inference-time computations. In human problem solving, a common strategy to expedite work is collaboration: by dividing the problem into sub-tasks, exploring different strategies concurrently, etc. Recent research has shown that LLMs can also operate in parallel by implementing explicit cooperation frameworks, such as voting mechanisms or the explicit creation of independent sub-tasks that can be executed in parallel. However, each of these frameworks may not be suitable for all types of tasks, which can hinder their applicability. In this work, we propose a different design approach: we run LLM "workers" in parallel , allowing them to synchronize via a concurrently-updated attention cache and prompt these workers to decide how best to collaborate. Our approach allows the instances to come up with their own collaboration strategy for the problem at hand, all the while "seeing" each other's partial progress in the concurrent cache. We implement this approach via Hogwild! Inference: a parallel LLM inference engine where multiple instances of the same LLM run in parallel with the same attention cache, with "instant" access to each other's generated tokens. Hogwild! inference takes advantage of Rotary Position Embeddings (RoPE) to avoid recomputation while improving parallel hardware utilization. We find that modern reasoning-capable LLMs can perform inference with shared Key-Value cache out of the box, without additional fine-tuning.

Much of the knowledge encoded in transformer language models (LMs) may be expressed in terms of relations: relations between words and their synonyms, entities and their attributes, etc. We show that, for a subset of relations, this computation is well-approximated by a single linear transformation on the subject representation. Linear relation representations may be obtained by constructing a first-order approximation to the LM from a single prompt, and they exist for a variety of factual, commonsense, and linguistic relations. However, we also identify many cases in which LM predictions capture relational knowledge accurately, but this knowledge is not linearly encoded in their representations. Our results thus reveal a simple, interpretable, but heterogeneously deployed knowledge representation strategy in transformer LMs.

Knowledge Graph Embedding (KGE) models are used to learn continuous representations of entities and relations. A key task in the literature is predicting missing links between entities. However, Knowledge Graphs are not just sets of links but also have semantics underlying their structure. Semantics is crucial in several downstream tasks, such as query answering or reasoning. We introduce the subgraph inference task, where a model has to generate likely and semantically valid subgraphs. We propose IntelliGraphs, a set of five new Knowledge Graph datasets. The IntelliGraphs datasets contain subgraphs with semantics expressed in logical rules for evaluating subgraph inference. We also present the dataset generator that produced the synthetic datasets. We designed four novel baseline models, which include three models based on traditional KGEs. We evaluate their expressiveness and show that these models cannot capture the semantics. We believe this benchmark will encourage the development of machine learning models that emphasize semantic understanding.

The traditional i.i.d.-based learning paradigm faces inherent challenges in addressing causal relationships, which has become increasingly evident with the rise of applications in causal representation learning. Our understanding of causality naturally requires a perspective as the creator rather than observer, as the ``what...if'' questions only hold within the possible world we conceive. The traditional perspective limits capturing dynamic causal outcomes and leads to compensatory efforts such as the reliance on hidden confounders. This paper lays the groundwork for the new perspective, which enables the relation-first modeling paradigm for causality. Also, it introduces the Relation-Indexed Representation Learning (RIRL) as a practical implementation, supported by experiments that validate its efficacy.

Recently, the Natural Language Inference (NLI) task has been studied for semi-structured tables that do not have a strict format. Although neural approaches have achieved high performance in various types of NLI, including NLI between semi-structured tables and texts, they still have difficulty in performing a numerical type of inference, such as counting. To handle a numerical type of inference, we propose a logical inference system for reasoning between semi-structured tables and texts. We use logical representations as meaning representations for tables and texts and use model checking to handle a numerical type of inference between texts and tables. To evaluate the extent to which our system can perform inference with numerical comparatives, we make an evaluation protocol that focuses on numerical understanding between semi-structured tables and texts in English. We show that our system can more robustly perform inference between tables and texts that requires numerical understanding compared with current neural approaches.

Relational learning typically predicts from a database state, but decision making asks a different question: how will that state change under an action? In operational systems, the answer depends on system-specific dynamics that may not be visible in the database itself. We view each such system as a relational "world" and ask whether a model can infer how it behaves from observed executions. We introduce TabWM (Tabular World Model) and WorldRel, a generator of executable relational worlds for pretraining. Given executions from an unseen world, TabWM uses them as context to predict the sparse structured edits caused by a new action without parameter updates. Across 512 held-out worlds, complete-edit F1 rises from 0.016 with no observed executions to 0.685 with 64, where a correct edit must match its operation, relational location, and value. Because these predictions are explicit relational edits, they can be applied recursively to imagine candidate futures and compare actions before they are taken. Broader search over these predicted futures improves the realized return of selected action sequences. Together, these results suggest that relational dynamics can be learned in context, broadening relational learning from modeling system state to modeling how that state changes under action.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We find neural networks are able to learn (1) basic equality (mathematical identity), (2) sequential equality problems (learning ABA-patterned sequences) with only positive training instances, and (3) a complex, hierarchical equality problem with only basic equality training instances ("zero-shot'" generalization). In the two latter cases, our models perform tasks proposed in previous work to demarcate human-unique symbolic abilities. These results suggest that essential aspects of symbolic reasoning can emerge from data-driven, non-symbolic learning processes.

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of LLMs. To address this, our goals are to make model beliefs and their inferential relationships explicit, and to resolve inconsistencies that may exist, so that answers are supported by interpretable chains of reasoning drawn from a consistent network of beliefs. Our approach, which we call REFLEX, is to add a rational, self-reflecting layer on top of the LLM. First, given a question, we construct a belief graph using a backward-chaining process to materialize relevant model beliefs (including beliefs about answer candidates) and their inferential relationships. Second, we identify and minimize contradictions in that graph using a formal constraint reasoner. We find that REFLEX significantly improves consistency (by 8%-11% absolute) without harming overall answer accuracy, resulting in answers supported by faithful chains of reasoning drawn from a more consistent belief system. This suggests a new style of system architecture in which an LLM extended with a rational layer can provide an interpretable window into system beliefs, add a systematic reasoning capability, and repair latent inconsistencies present in the LLM.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

Predictive models often need to work with incomplete information in real-world tasks. Consequently, they must provide reliable probability or confidence estimation, especially in large-scale decision-making and planning tasks. Current large language models (LLMs) are insufficient for accurate estimations, but they can generate relevant factors that may affect the probabilities, produce coarse-grained probabilities when the information is more complete, and help determine which factors are relevant to specific downstream contexts. In this paper, we make use of these capabilities of LLMs to provide a significantly more accurate probabilistic estimation. We propose BIRD, a novel probabilistic inference framework that aligns a Bayesian network with LLM abductions and then estimates more accurate probabilities in a deduction step. We show BIRD provides reliable probability estimations that are 30% better than those provided directly by LLM baselines. These estimates further contribute to better and more trustworthy decision making.

Language models can store vast amounts of factual knowledge, but their ability to use this knowledge for logical reasoning remains questionable. This paper explores a language model's ability to manipulate its stored knowledge during inference. We focus on four manipulation types: retrieval (e.g., "What is person A's attribute X"), classification (e.g., "Is A's attribute X even or odd?"), comparison (e.g., "Is A greater than B in attribute X?") and inverse search (e.g., "Which person's attribute X equals T?") We observe that pre-trained language models like GPT2/3/4 excel in knowledge retrieval but struggle with simple classification or comparison tasks unless Chain of Thoughts (CoTs) are employed during both training and inference. They also perform poorly in inverse knowledge search, irrespective of the prompts. Our primary contribution is a synthetic dataset for a controlled experiment that confirms these inherent weaknesses: a language model cannot efficiently manipulate knowledge from pre-training data, even when such knowledge is perfectly stored and fully extractable in the models, and despite adequate instruct fine-tuning.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Knowledge distillation aims at transferring knowledge acquired in one model (a teacher) to another model (a student) that is typically smaller. Previous approaches can be expressed as a form of training the student to mimic output activations of individual data examples represented by the teacher. We introduce a novel approach, dubbed relational knowledge distillation (RKD), that transfers mutual relations of data examples instead. For concrete realizations of RKD, we propose distance-wise and angle-wise distillation losses that penalize structural differences in relations. Experiments conducted on different tasks show that the proposed method improves educated student models with a significant margin. In particular for metric learning, it allows students to outperform their teachers' performance, achieving the state of the arts on standard benchmark datasets.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

Multi-agent interactions, such as communication, teaching, and bluffing, often rely on higher-order social inference, i.e., understanding how others infer oneself. Such intricate reasoning can be effectively modeled through nested multi-agent reasoning. Nonetheless, the computational complexity escalates exponentially with each level of reasoning, posing a significant challenge. However, humans effortlessly perform complex social inferences as part of their daily lives. To bridge the gap between human-like inference capabilities and computational limitations, we propose a novel approach: leveraging neural networks to amortize high-order social inference, thereby expediting nested multi-agent reasoning. We evaluate our method in two challenging multi-agent interaction domains. The experimental results demonstrate that our method is computationally efficient while exhibiting minimal degradation in accuracy.

The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of how semantic relations can be learned from non-relational word embeddings, we present a new computational model of mapping between two analogs. The model adopts a Bayesian framework for probabilistic graph matching, operating on semantic relation networks constructed from distributed representations of individual concepts and of relations between concepts. Through comparisons of model predictions with human performance in a novel mapping task requiring integration of multiple relations, as well as in several classic studies, we demonstrate that the model accounts for a broad range of phenomena involving analogical mapping by both adults and children. We also show the potential for extending the model to deal with analog retrieval. Our approach demonstrates that human-like analogical mapping can emerge from comparison mechanisms applied to rich semantic representations of individual concepts and relations.

One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also that they cannot naturally model uncertainty. Here, we present BetaE, a probabilistic embedding framework for answering arbitrary FOL queries over KGs. BetaE is the first method that can handle a complete set of first-order logical operations: conjunction (wedge), disjunction (vee), and negation (neg). A key insight of BetaE is to use probabilistic distributions with bounded support, specifically the Beta distribution, and embed queries/entities as distributions, which as a consequence allows us to also faithfully model uncertainty. Logical operations are performed in the embedding space by neural operators over the probabilistic embeddings. We demonstrate the performance of BetaE on answering arbitrary FOL queries on three large, incomplete KGs. While being more general, BetaE also increases relative performance by up to 25.4% over the current state-of-the-art KG reasoning methods that can only handle conjunctive queries without negation.

Reasoning and inference are central to human and artificial intelligence. Modeling inference in human language is very challenging. With the availability of large annotated data (Bowman et al., 2015), it has recently become feasible to train neural network based inference models, which have shown to be very effective. In this paper, we present a new state-of-the-art result, achieving the accuracy of 88.6% on the Stanford Natural Language Inference Dataset. Unlike the previous top models that use very complicated network architectures, we first demonstrate that carefully designing sequential inference models based on chain LSTMs can outperform all previous models. Based on this, we further show that by explicitly considering recursive architectures in both local inference modeling and inference composition, we achieve additional improvement. Particularly, incorporating syntactic parsing information contributes to our best result---it further improves the performance even when added to the already very strong model.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

Graphs offer unique insights into relationships between entities, complementing data modalities like text and images and enabling AI models to extend their capabilities beyond traditional tasks. However, learning from graphs often involves handling sensitive relationships in the data, raising significant privacy concerns. Existing privacy-preserving methods, such as DP-SGD, rely on gradient decoupling assumptions and are incompatible with relational learning due to the inherent dependencies between training samples. To address this challenge, we propose a privacy-preserving pipeline for relational learning that decouples dependencies in sampled relations for training, ensuring differential privacy through a tailored application of DP-SGD. We apply this approach to fine-tune large language models (LLMs), such as Llama2, on sensitive graph data while addressing the associated computational complexities. Our method is evaluated on four real-world text-attributed graphs, demonstrating significant improvements in relational learning tasks while maintaining robust privacy guarantees. Additionally, we analyze the trade-offs between privacy, utility, and computational efficiency, offering insights into the practical deployment of our approach for privacy-preserving relational learning. Code is available at https://github.com/Graph-COM/PvGaLM.

When prompted with a few examples and intermediate steps, large language models (LLMs) have demonstrated impressive performance in various reasoning tasks. However, prompting methods that rely on implicit knowledge in an LLM often generate incorrect answers when the implicit knowledge is wrong or inconsistent with the task. To tackle this problem, we present Hypotheses-to-Theories (HtT), a framework that learns a rule library for reasoning with LLMs. HtT contains two stages, an induction stage and a deduction stage. In the induction stage, an LLM is first asked to generate and verify rules over a set of training examples. Rules that appear and lead to correct answers sufficiently often are collected to form a rule library. In the deduction stage, the LLM is then prompted to employ the learned rule library to perform reasoning to answer test questions. Experiments on relational reasoning, numerical reasoning and concept learning problems show that HtT improves existing prompting methods, with an absolute gain of 10-30% in accuracy. The learned rules are also transferable to different models and to different forms of the same problem.

Relational Deep Learning (RDL) models multi-tabular databases as temporal heterogeneous graphs for end-to-end representation learning. While RDL is evolving rapidly, existing approaches face significant generalization obstacles. They are either schema-specific, requiring training from scratch for every new database, or they rely on monolithic architectures that entangle feature encoding with graph message-passing. Analyzing these limitations, we establish four core pillars for building foundational relational models: semantic granularity, structural topology, temporal causality, and unified optimization. Addressing these pillars, we propose a modular approach that decouples row encoding from graph message-passing. We introduce the Universal Row Encoder, a transformer-based module that integrates raw cell data with schema metadata-including column semantics, table names, and global distribution statistics-to produce table-width invariant row embeddings. By explicitly feeding global statistics to an intra-row self-attention mechanism, the encoder natively contextualizes unseen features and handles sparse data. Serving as a flexible "backend" for any downstream graph architecture, our pretrained encoder enhances cross-database knowledge transfer on the established RelBench benchmarks while improving learning convergence and memory footprint.

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

We present RelBench, a public benchmark for solving predictive tasks over relational databases with graph neural networks. RelBench provides databases and tasks spanning diverse domains and scales, and is intended to be a foundational infrastructure for future research. We use RelBench to conduct the first comprehensive study of Relational Deep Learning (RDL) (Fey et al., 2024), which combines graph neural network predictive models with (deep) tabular models that extract initial entity-level representations from raw tables. End-to-end learned RDL models fully exploit the predictive signal encoded in primary-foreign key links, marking a significant shift away from the dominant paradigm of manual feature engineering combined with tabular models. To thoroughly evaluate RDL against this prior gold-standard, we conduct an in-depth user study where an experienced data scientist manually engineers features for each task. In this study, RDL learns better models whilst reducing human work needed by more than an order of magnitude. This demonstrates the power of deep learning for solving predictive tasks over relational databases, opening up many new research opportunities enabled by RelBench.

While current deep learning systems excel at tasks such as object classification, language processing, and gameplay, few can construct or modify a complex system such as a tower of blocks. We hypothesize that what these systems lack is a "relational inductive bias": a capacity for reasoning about inter-object relations and making choices over a structured description of a scene. To test this hypothesis, we focus on a task that involves gluing pairs of blocks together to stabilize a tower, and quantify how well humans perform. We then introduce a deep reinforcement learning agent which uses object- and relation-centric scene and policy representations and apply it to the task. Our results show that these structured representations allow the agent to outperform both humans and more naive approaches, suggesting that relational inductive bias is an important component in solving structured reasoning problems and for building more intelligent, flexible machines.

The reversal curse -- a language model's (LM) inability to infer an unseen fact ``B is A'' from a learned fact ``A is B'' -- is widely considered a fundamental limitation. We show that this is not an inherent failure but an artifact of how models encode knowledge. By training LMs from scratch on a synthetic dataset of relational knowledge graphs, we demonstrate that bilinear relational structure emerges in their hidden representations. This structure substantially alleviates the reversal curse, enabling LMs to infer unseen reverse facts. Crucially, we also find that this bilinear structure plays a key role in consistent model editing. When a fact is updated in a LM with this structure, the edit correctly propagates to its reverse and other logically dependent facts. In contrast, models lacking this representation not only suffer from the reversal curse but also fail to generalize edits, further introducing logical inconsistencies. Our results establish that training on a relational knowledge dataset induces the emergence of bilinear internal representations, which in turn enable LMs to behave in a logically consistent manner after editing. This implies that the success of model editing depends critically not just on editing algorithms but on the underlying representational geometry of the knowledge being modified.

Causal inference is one of the hallmarks of human intelligence. While the field of CausalNLP has attracted much interest in the recent years, existing causal inference datasets in NLP primarily rely on discovering causality from empirical knowledge (e.g., commonsense knowledge). In this work, we propose the first benchmark dataset to test the pure causal inference skills of large language models (LLMs). Specifically, we formulate a novel task Corr2Cause, which takes a set of correlational statements and determines the causal relationship between the variables. We curate a large-scale dataset of more than 400K samples, on which we evaluate seventeen existing LLMs. Through our experiments, we identify a key shortcoming of LLMs in terms of their causal inference skills, and show that these models achieve almost close to random performance on the task. This shortcoming is somewhat mitigated when we try to re-purpose LLMs for this skill via finetuning, but we find that these models still fail to generalize -- they can only perform causal inference in in-distribution settings when variable names and textual expressions used in the queries are similar to those in the training set, but fail in out-of-distribution settings generated by perturbing these queries. Corr2Cause is a challenging task for LLMs, and would be helpful in guiding future research on improving LLMs' pure reasoning skills and generalizability. Our data is at https://huggingface.co/datasets/causalnlp/corr2cause. Our code is at https://github.com/causalNLP/corr2cause.

Relational deep learning (RDL) has emerged as a powerful paradigm for learning directly on relational databases by modeling entities and their relationships across multiple interconnected tables. As this paradigm evolves toward larger models and relational foundation models, scalable and realistic benchmarks are essential for enabling systematic evaluation and progress. In this paper, we introduce RelBench v2, a major expansion of the RelBench benchmark for RDL. RelBench v2 adds four large-scale relational datasets spanning scholarly publications, enterprise resource planning, consumer platforms, and clinical records, increasing the benchmark to 11 datasets comprising over 22 million rows across 29 tables. We further introduce autocomplete tasks, a new class of predictive objectives that require models to infer missing attribute values directly within relational tables while respecting temporal constraints, expanding beyond traditional forecasting tasks constructed via SQL queries. In addition, RelBench v2 expands beyond its native datasets by integrating external benchmarks and evaluation frameworks: we translate event streams from the Temporal Graph Benchmark into relational schemas for unified relational-temporal evaluation, interface with ReDeLEx to provide uniform access to 70+ real-world databases suitable for pretraining, and incorporate 4DBInfer datasets and tasks to broaden multi-table prediction coverage. Experimental results demonstrate that RDL models consistently outperform single-table baselines across autocomplete, forecasting, and recommendation tasks, highlighting the importance of modeling relational structure explicitly.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.

The growing popularity of neuro symbolic reasoning has led to the adoption of various forms of differentiable (i.e., fuzzy) first order logic. We introduce PyReason, a software framework based on generalized annotated logic that both captures the current cohort of differentiable logics and temporal extensions to support inference over finite periods of time with capabilities for open world reasoning. Further, PyReason is implemented to directly support reasoning over graphical structures (e.g., knowledge graphs, social networks, biological networks, etc.), produces fully explainable traces of inference, and includes various practical features such as type checking and a memory-efficient implementation. This paper reviews various extensions of generalized annotated logic integrated into our implementation, our modern, efficient Python-based implementation that conducts exact yet scalable deductive inference, and a suite of experiments. PyReason is available at: github.com/lab-v2/pyreason.

Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review of knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models, and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference, and logical rule reasoning, are reviewed. We further explore several emerging topics, including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.

Large language models (LLMs) have majorly advanced NLP and AI, and next to their ability to perform a wide range of procedural tasks, a major success factor is their internalized factual knowledge. Since Petroni et al. (2019), analyzing this knowledge has gained attention. However, most approaches investigate one question at a time via modest-sized pre-defined samples, introducing an ``availability bias'' (Tversky&Kahnemann, 1973) that prevents the analysis of knowledge (or beliefs) of LLMs beyond the experimenter's predisposition. To address this challenge, we propose a novel methodology to comprehensively materialize an LLM's factual knowledge through recursive querying and result consolidation. Our approach is a milestone for LLM research, for the first time providing constructive insights into the scope and structure of LLM knowledge (or beliefs). As a prototype, we build GPTKB, a knowledge base (KB) comprising 101 million relational triples for over 2.9 million entities from GPT-4o-mini. We use GPTKB to exemplarily analyze GPT-4o-mini's factual knowledge in terms of scale, accuracy, bias, cutoff and consistency, at the same time. GPTKB is accessible at https://gptkb.org

The ability to perform causal reasoning is widely considered a core feature of intelligence. In this work, we investigate whether large language models (LLMs) can coherently reason about causality. Much of the existing work in natural language processing (NLP) focuses on evaluating commonsense causal reasoning in LLMs, thus failing to assess whether a model can perform causal inference in accordance with a set of well-defined formal rules. To address this, we propose a new NLP task, causal inference in natural language, inspired by the "causal inference engine" postulated by Judea Pearl et al. We compose a large dataset, CLadder, with 10K samples: based on a collection of causal graphs and queries (associational, interventional, and counterfactual), we obtain symbolic questions and ground-truth answers, through an oracle causal inference engine. These are then translated into natural language. We evaluate multiple LLMs on our dataset, and we introduce and evaluate a bespoke chain-of-thought prompting strategy, CausalCoT. We show that our task is highly challenging for LLMs, and we conduct an in-depth analysis to gain deeper insights into the causal reasoning abilities of LLMs. Our data is open-sourced at https://huggingface.co/datasets/causalNLP/cladder, and our code can be found at https://github.com/causalNLP/cladder.

Foundation models in language and vision have the ability to run inference on any textual and visual inputs thanks to the transferable representations such as a vocabulary of tokens in language. Knowledge graphs (KGs) have different entity and relation vocabularies that generally do not overlap. The key challenge of designing foundation models on KGs is to learn such transferable representations that enable inference on any graph with arbitrary entity and relation vocabularies. In this work, we make a step towards such foundation models and present ULTRA, an approach for learning universal and transferable graph representations. ULTRA builds relational representations as a function conditioned on their interactions. Such a conditioning strategy allows a pre-trained ULTRA model to inductively generalize to any unseen KG with any relation vocabulary and to be fine-tuned on any graph. Conducting link prediction experiments on 57 different KGs, we find that the zero-shot inductive inference performance of a single pre-trained ULTRA model on unseen graphs of various sizes is often on par or better than strong baselines trained on specific graphs. Fine-tuning further boosts the performance.

We seek a hierarchical resolution of residual error under a composite learning objective as a principled mechanism for identifying and exploiting additional information, particularly under distribution shift and perturbation. Inspired by the System 1/System 2 paradigm, we formulate this principle as a two-loop mechanism serving a common inference goal. A fast, System 1-like loop resolves the residual addressable by the available evidence; the remaining epistemic residual triggers a medium speed, System 2-like loop that actively acquires additional evidence and measures its informational value through residual reduction. Over nested solution spaces, the medium-loop optimum is provably no worse than the fast-loop optimum. Experiments show that the resulting two-loop model consistently improves upon the fast loop at approximately half the computation of the medium loop, including under unseen corruptions, and, when provided a cleaner observation, outperforms staged classifiers and learning-to-defer methods at equal computational cost.

In this paper, we propose a new deep learning approach, called neural association model (NAM), for probabilistic reasoning in artificial intelligence. We propose to use neural networks to model association between any two events in a domain. Neural networks take one event as input and compute a conditional probability of the other event to model how likely these two events are to be associated. The actual meaning of the conditional probabilities varies between applications and depends on how the models are trained. In this work, as two case studies, we have investigated two NAM structures, namely deep neural networks (DNN) and relation-modulated neural nets (RMNN), on several probabilistic reasoning tasks in AI, including recognizing textual entailment, triple classification in multi-relational knowledge bases and commonsense reasoning. Experimental results on several popular datasets derived from WordNet, FreeBase and ConceptNet have all demonstrated that both DNNs and RMNNs perform equally well and they can significantly outperform the conventional methods available for these reasoning tasks. Moreover, compared with DNNs, RMNNs are superior in knowledge transfer, where a pre-trained model can be quickly extended to an unseen relation after observing only a few training samples. To further prove the effectiveness of the proposed models, in this work, we have applied NAMs to solving challenging Winograd Schema (WS) problems. Experiments conducted on a set of WS problems prove that the proposed models have the potential for commonsense reasoning.

While moral reasoning has emerged as a promising research direction for large language models (LLMs), achieving robust generalization remains a critical challenge. This challenge arises from the gap between what is said and what is morally implied. In this paper, we build on metapragmatic links and the moral foundations theory to close the gap. Specifically, we develop a pragmatic-inference approach that facilitates LLMs, for a given moral situation, to acquire the metapragmantic links between moral reasoning objectives and the social variables that affect them. This approach is adapted to three different moral reasoning tasks to demonstrate its adaptability and generalizability. Experimental results demonstrate that our approach significantly enhances LLMs' generalization in moral reasoning, paving the road for future research to utilize pragmatic inference in various moral reasoning tasks.

We address whether neural models for Natural Language Inference (NLI) can learn the compositional interactions between lexical entailment and negation, using four methods: the behavioral evaluation methods of (1) challenge test sets and (2) systematic generalization tasks, and the structural evaluation methods of (3) probes and (4) interventions. To facilitate this holistic evaluation, we present Monotonicity NLI (MoNLI), a new naturalistic dataset focused on lexical entailment and negation. In our behavioral evaluations, we find that models trained on general-purpose NLI datasets fail systematically on MoNLI examples containing negation, but that MoNLI fine-tuning addresses this failure. In our structural evaluations, we look for evidence that our top-performing BERT-based model has learned to implement the monotonicity algorithm behind MoNLI. Probes yield evidence consistent with this conclusion, and our intervention experiments bolster this, showing that the causal dynamics of the model mirror the causal dynamics of this algorithm on subsets of MoNLI. This suggests that the BERT model at least partially embeds a theory of lexical entailment and negation at an algorithmic level.

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if P and Q, then R" for some propositions P, Q, and R. Next, we prove that although small transformers can faithfully follow such rules, maliciously crafted prompts can still mislead both theoretical constructions and models learned from data. Furthermore, we demonstrate that popular attack algorithms on LLMs find adversarial prompts and induce attention patterns that align with our theory. Our novel logic-based framework provides a foundation for studying LLMs in rule-based settings, enabling a formal analysis of tasks like logical reasoning and jailbreak attacks.

Humans do not just see attribute similarity -- we also see relational similarity. An apple is like a peach because both are reddish fruit, but the Earth is also like a peach: its crust, mantle, and core correspond to the peach's skin, flesh, and pit. This ability to perceive and recognize relational similarity, is arguable by cognitive scientist to be what distinguishes humans from other species. Yet, all widely used visual similarity metrics today (e.g., LPIPS, CLIP, DINO) focus solely on perceptual attribute similarity and fail to capture the rich, often surprising relational similarities that humans perceive. How can we go beyond the visible content of an image to capture its relational properties? How can we bring images with the same relational logic closer together in representation space? To answer these questions, we first formulate relational image similarity as a measurable problem: two images are relationally similar when their internal relations or functions among visual elements correspond, even if their visual attributes differ. We then curate 114k image-caption dataset in which the captions are anonymized -- describing the underlying relational logic of the scene rather than its surface content. Using this dataset, we finetune a Vision-Language model to measure the relational similarity between images. This model serves as the first step toward connecting images by their underlying relational structure rather than their visible appearance. Our study shows that while relational similarity has a lot of real-world applications, existing image similarity models fail to capture it -- revealing a critical gap in visual computing.

Tabular representation learning has recently gained a lot of attention. However, existing approaches only learn a representation from a single table, and thus ignore the potential to learn from the full structure of relational databases, including neighboring tables that can contain important information for a contextualized representation. Moreover, current models are significantly limited in scale, which prevents that they learn from large databases. In this paper, we thus introduce our vision of relational representation learning, that can not only learn from the full relational structure, but also can scale to larger database sizes that are commonly found in real-world. Moreover, we also discuss opportunities and challenges we see along the way to enable this vision and present initial very promising results. Overall, we argue that this direction can lead to foundation models for relational databases that are today only available for text and images.

Knowledge graph (KG) reasoning is an important problem for knowledge graphs. In this paper, we propose a novel and principled framework called RulE (stands for {Rul}e {E}mbedding) to effectively leverage logical rules to enhance KG reasoning. Unlike knowledge graph embedding (KGE) methods, RulE learns rule embeddings from existing triplets and first-order {rules} by jointly representing entities, relations and logical rules in a unified embedding space. Based on the learned rule embeddings, a confidence score can be calculated for each rule, reflecting its consistency with the observed triplets. This allows us to perform logical rule inference in a soft way, thus alleviating the brittleness of logic. On the other hand, RulE injects prior logical rule information into the embedding space, enriching and regularizing the entity/relation embeddings. This makes KGE alone perform better too. RulE is conceptually simple and empirically effective. We conduct extensive experiments to verify each component of RulE. Results on multiple benchmarks reveal that our model outperforms the majority of existing embedding-based and rule-based approaches.

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.

Recent advances in Neural Variational Inference allowed for a renaissance in latent variable models in a variety of domains involving high-dimensional data. While traditional variational methods derive an analytical approximation for the intractable distribution over the latent variables, here we construct an inference network conditioned on the symbolic representation of entities and relation types in the Knowledge Graph, to provide the variational distributions. The new framework results in a highly-scalable method. Under a Bernoulli sampling framework, we provide an alternative justification for commonly used techniques in large-scale stochastic variational inference, which drastically reduce training time at a cost of an additional approximation to the variational lower bound. We introduce two models from this highly scalable probabilistic framework, namely the Latent Information and Latent Fact models, for reasoning over knowledge graph-based representations. Our Latent Information and Latent Fact models improve upon baseline performance under certain conditions. We use the learnt embedding variance to estimate predictive uncertainty during link prediction, and discuss the quality of these learnt uncertainty estimates. Our source code and datasets are publicly available online at https://github.com/alexanderimanicowenrivers/Neural-Variational-Knowledge-Graphs.

Most state-of-the-art Visual-Language Models (VLMs) are seemingly limited by the linear separabilty of their visual embeddings on abstract reasoning tasks. This work investigates this "linear reasoning bottleneck" by introducing the Linear Separability Ceiling (LSC), the performance of a simple linear classifier on a VLM's visual embeddings. We find this bottleneck is widespread and stems not from poor perception, but from failures in the language model's reasoning pathways. We demonstrate this is a solvable alignment issue. The required intervention, however, is task-dependent: activating existing pathways suffices for semantic concepts, while complex relational reasoning requires adapting core model weights. Using postfix tuning as a methodological control, we find strong evidence for powerful, dormant reasoning pathways within VLMs. However, for complex relational tasks requiring deeper adaptation, explicitly improving representation quality causes the model to fail on new prompt formats despite its embeddings remaining well separated. Ultimately, this work provides a new lens for VLM analysis, showing that robust reasoning is a matter of targeted alignment, not simply improved representation learning.

The web provides a rich, open-domain environment with textual, structural, and spatial properties. We propose a new task for grounding language in this environment: given a natural language command (e.g., "click on the second article"), choose the correct element on the web page (e.g., a hyperlink or text box). We collected a dataset of over 50,000 commands that capture various phenomena such as functional references (e.g. "find who made this site"), relational reasoning (e.g. "article by john"), and visual reasoning (e.g. "top-most article"). We also implemented and analyzed three baseline models that capture different phenomena present in the dataset.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.