The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models

Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an important expressivity gap. In this work, we compare PCs and LLMs under a unified autoregressive formulation. First, an output bottleneck: PCs parameterize predictions as convex combinations in probability space, which struggles to represent the sharp distributions typical of language; adopting a logit-space parameterization substantially narrows this gap. Second, a context-encoding bottleneck: we prove that structured-decomposable PCs can match Transformer separation rank on vtree-aligned partitions, but show, both theoretically and empirically, that this capacity is limited to partitions aligned with the fixed routing structure, leading to severe degradation when the data exhibits heterogeneous dependency topologies. We further prove that decomposable PCs are strictly more expressive than structured-decomposable ones, though effectively optimizing them remains an open challenge.

SAGE: A Self-Evolving Agentic Graph-Memory Engine for Structure-Aware Associative Memory

Long-term memory is becoming a central bottleneck for language agents. Exsting RAG and GraphRAG systems largely treat memory graphs as static retrieval middleware, which limits their ability to recover complete evidence chains from partial cues, exploit reusable graph-structrual roles, and improve the memory itself through downstream feedback. We introduce SAGE, a Self-evolving Agentic Graph-memory Engine that models graph memory as a dynamic long-term memory substrate. SAGE couples two roles: a memory writer that incrementally constucts structured graph memory from interaction histories, and a Graph Foundation Model-based memory reader to perform retrieval and provide feedback to the memory writer. We provide rigorooous theoretical annalyses supporting the framework. Across multi-hop QA, open-domain retireval, domain-specific review QA, and long-term agent-memory benchmarks, SAGE improves evidence recovery, answer grounding, and retrieval efficiency: after two self-evolution rounds, it achieves the best average rank on multi-hop QA; in zero-shot open-domain transfer, it reaches 82.5/91.6 Recall@2/5 on NQ. Further results on LongMemEval and HaluMem show that traning and reader-writer feedback improve multiple long-term memory and hallucination-diagnostic metrics, suggesting that self-evolving, structure-aware graph memory is a promising foundation for robust long-horizon language agents.

Position: How can Graphs Help Large Language Models?

With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encoding of textual features, more efficient construction of graphs from text, and enhanced reasoning over knowledge graphs. In this paper, we ask a complementary question: How can graphs help LLMs? We address this question from three perspectives: 1) graphs provide an up-to-date knowledge source that helps reduce LLM hallucinations, 2) graph-based prompting techniques-such as Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT)-enhance LLM reasoning capabilities, and 3) integrating graphs into LLMs improves their understanding of structured data, expanding their applicability to domains such as e-commerce, code, and relational databases (RDBs). We further outlook some future directions including designing sparse LLM architectures based on graphs and brain-inspired memory systems.

HISA: Efficient Hierarchical Indexing for Fine-Grained Sparse Attention

Token-level sparse attention mechanisms, exemplified by DeepSeek Sparse Attention (DSA), achieve fine-grained key selection by scoring every historical key for each query through a lightweight indexer, then computing attention only on the selected subset. While the downstream sparse attention itself scales favorably, the indexer must still scan the entire prefix for every query, introducing an per-layer bottleneck that grows prohibitively with context length. We propose HISA (Hierarchical Indexed Sparse Attention), a plug-and-play replacement for the indexer that rewrites the search path from a flat token scan into a two-stage hierarchical procedure: (1) a block-level coarse filtering stage that scores pooled block representations to discard irrelevant regions, followed by (2) a token-level refinement stage that applies the original indexer exclusively within the retained candidate blocks. HISA preserves the identical token-level top-sparse pattern consumed by the downstream Sparse MLA operator and requires no additional training. On kernel-level benchmarks, HISA achieves up to speedup at 64K context. On Needle-in-a-Haystack and LongBench, we directly replace the indexer in DeepSeek-V3.2 and GLM-5 with our HISA indexer, without any finetuning. HISA closely matches the original DSA in quality, while substantially outperforming block-sparse baselines.

VecMol: Vector-Field Representations for 3D Molecule Generation

Generative modeling of three-dimensional (3D) molecules is a fundamental yet challenging problem in drug discovery and materials science. Existing approaches typically represent molecules as 3D graphs and co-generate discrete atom types with continuous atomic coordinates, leading to intrinsic learning difficulties such as heterogeneous modality entanglement and geometry-chemistry coherence constraints. We propose VecMol, a paradigm-shifting framework that reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, where vectors point toward nearby atoms and implicitly encode molecular structure. The vector field is parameterized by a neural field and generated using a latent diffusion model, avoiding explicit graph generation and decoupling structure learning from discrete atom instantiation. Experiments on the QM9 and GEOM-Drugs benchmarks validate the feasibility of this novel approach, suggesting vector-field-based representations as a promising new direction for 3D molecular generation.

Relational In-Context Learning via Synthetic Pre-training with Structural Prior

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 $\textbf{RDB-PFN}$, the first relational foundation model trained purely via $\textbf{synthetic data}$. Inspired by Prior-Data Fitted Networks (PFNs) where synthetic data generated from Structural Causal Models (SCMs) enables reasoning on single tables, we design a $\textbf{Relational Prior Generator}$ to create an infinite stream of diverse RDBs from scratch. Pre-training on $\textbf{over 2 million}$ synthetic single-table and relational tasks, RDB-PFN learns to adapt to any new database instantly via genuine $\textbf{in-context learning}$. 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

TabDLM: Free-Form Tabular Data Generation via Joint Numerical-Language Diffusion

Synthetic tabular data generation has attracted growing attention due to its importance for data augmentation, foundation models, and privacy. However, real-world tabular datasets increasingly contain free-form text fields (e.g., reviews or clinical notes) alongside structured numerical and categorical attributes. Generating such heterogeneous tables with joint modeling of different modalities remains challenging. Existing approaches broadly fall into two categories: diffusion-based methods and LLM-based methods. Diffusion models can capture complex dependencies over numerical and categorical features in continuous or discrete spaces, but extending them to open-ended text is nontrivial and often leads to degraded text quality. In contrast, LLM-based generators naturally produce fluent text, yet their discrete tokenization can distort precise or wide-range numerical values, hindering accurate modeling of both numbers and language. In this work, we propose TabDLM, a unified framework for free-form tabular data generation via a joint numerical--language diffusion model built on masked diffusion language models (MDLMs). TabDLM models textual and categorical features through masked diffusion, while modeling numerical features with a continuous diffusion process through learned specialized numeric tokens embedding; bidirectional attention then captures cross-modality interactions within a single model. Extensive experiments on diverse benchmarks demonstrate the effectiveness of TabDLM compared to strong diffusion- and LLM-based baselines.

Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.

GREPO: A Benchmark for Graph Neural Networks on Repository-Level Bug Localization

Repository-level bug localization-the task of identifying where code must be modified to fix a bug-is a critical software engineering challenge. Standard Large Language Modles (LLMs) are often unsuitable for this task due to context window limitations that prevent them from processing entire code repositories. As a result, various retrieval methods are commonly used, including keyword matching, text similarity, and simple graph-based heuristics such as Breadth-First Search. Graph Neural Networks (GNNs) offer a promising alternative due to their ability to model complex, repository-wide dependencies; however, their application has been hindered by the lack of a dedicated benchmark. To address this gap, we introduce GREPO, the first GNN benchmark for repository-scale bug localization tasks. GREPO comprises 86 Python repositories and 47294 bug-fixing tasks, providing graph-based data structures ready for direct GNN processing. Our evaluation of various GNN architectures shows outstanding performance compared to established information retrieval baselines. This work highlights the potential of GNNs for bug localization and established GREPO as a foundation resource for future research, The code is available at https://github.com/qingpingmo/GREPO.

SHINE: A Scalable In-Context Hypernetwork for Mapping Context to LoRA in a Single Pass

We propose SHINE (Scalable Hyper In-context NEtwork), a scalable hypernetwork that can map diverse meaningful contexts into high-quality LoRA adapters for large language models (LLM). By reusing the frozen LLM's own parameters in an in-context hypernetwork design and introducing architectural innovations, SHINE overcomes key limitations of prior hypernetworks and achieves strong expressive power with a relatively small number of parameters. We introduce a pretraining and instruction fine-tuning pipeline, and train our hypernetwork to generate high quality LoRA adapters from diverse meaningful contexts in a single forward pass. It updates LLM parameters without any fine-tuning, and immediately enables complex question answering tasks related to the context without directly accessing the context, effectively transforming in-context knowledge to in-parameter knowledge in one pass. Our work achieves outstanding results on various tasks, greatly saves time, computation and memory costs compared to SFT-based LLM adaptation, and shows great potential for scaling. Our code is available at https://github.com/Yewei-Liu/SHINE