Graph of States: Solving Abductive Tasks with Large Language Models

Logical reasoning encompasses deduction, induction, and abduction. However, while Large Language Models (LLMs) have effectively mastered the former two, abductive reasoning remains significantly underexplored. Existing frameworks, predominantly designed for static deductive tasks, fail to generalize to abductive reasoning due to unstructured state representation and lack of explicit state control. Consequently, they are inevitably prone to Evidence Fabrication, Context Drift, Failed Backtracking, and Early Stopping. To bridge this gap, we introduce Graph of States (GoS), a general-purpose neuro-symbolic framework tailored for abductive tasks. GoS grounds multi-agent collaboration in a structured belief states, utilizing a causal graph to explicitly encode logical dependencies and a state machine to govern the valid transitions of the reasoning process. By dynamically aligning the reasoning focus with these symbolic constraints, our approach transforms aimless, unconstrained exploration into a convergent, directed search. Extensive evaluations on two real-world datasets demonstrate that GoS significantly outperforms all baselines, providing a robust solution for complex abductive tasks. Code repo and all prompts: https://anonymous.4open.science/r/Graph-of-States-5B4E.

Advancing Multimodal Agent Reasoning with Long-Term Neuro-Symbolic Memory

Recent advances in large language models have driven the emergence of intelligent agents operating in open-world, multimodal environments. To support long-term reasoning, such agents are typically equipped with external memory systems. However, most existing multimodal agent memories rely primarily on neural representations and vector-based retrieval, which are well-suited for inductive, intuitive reasoning but fundamentally limited in supporting analytical, deductive reasoning critical for real-world decision making. To address this limitation, we propose NS-Mem, a long-term neuro-symbolic memory framework designed to advance multimodal agent reasoning by integrating neural memory with explicit symbolic structures and rules. Specifically, NS-Mem is operated around three core components of a memory system: (1) a three-layer memory architecture that consists episodic layer, semantic layer and logic rule layer, (2) a memory construction and maintenance mechanism implemented by SK-Gen that automatically consolidates structured knowledge from accumulated multimodal experiences and incrementally updates both neural representations and symbolic rules, and (3) a hybrid memory retrieval mechanism that combines similarity-based search with deterministic symbolic query functions to support structured reasoning. Experiments on real-world multimodal reasoning benchmarks demonstrate that Neural-Symbolic Memory achieves an average 4.35% improvement in overall reasoning accuracy over pure neural memory systems, with gains of up to 12.5% on constrained reasoning queries, validating the effectiveness of NS-Mem.

Modality Gap-Driven Subspace Alignment Training Paradigm For Multimodal Large Language Models

Despite the success of multimodal contrastive learning in aligning visual and linguistic representations, a persistent geometric anomaly, the Modality Gap, remains: embeddings of distinct modalities expressing identical semantics occupy systematically offset regions. Prior approaches to bridge this gap are largely limited by oversimplified isotropic assumptions, hindering their application in large-scale scenarios. In this paper, we address these limitations by precisely characterizing the geometric shape of the modality gap and leveraging it for efficient model scaling. First, we propose the Fixed-frame Modality Gap Theory, which decomposes the modality gap within a frozen reference frame into stable biases and anisotropic residuals. Guided by this precise modeling, we introduce ReAlign, a training-free modality alignment strategy. Utilizing statistics from massive unpaired data, ReAlign aligns text representation into the image representation distribution via a three-step process comprising Anchor, Trace, and Centroid Alignment, thereby explicitly rectifying geometric misalignment. Building on ReAlign, we propose ReVision, a scalable training paradigm for Multimodal Large Language Models (MLLMs). ReVision integrates ReAlign into the pretraining stage, enabling the model to learn the distribution of visual representations from unpaired text before visual instruction tuning, without the need for large-scale, high-quality image-text pairs. Our framework demonstrates that statistically aligned unpaired data can effectively substitute for expensive image-text pairs, offering a robust path for the efficient scaling of MLLMs.

Small Shifts, Large Gains: Unlocking Traditional TSP Heuristic Guided-Sampling via Unsupervised Neural Instance Modification

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest Insertion, are computationally efficient and highly practical, but their deterministic behavior limits exploration and often leads to local optima. In contrast, neural-based heuristic tour constructors alleviate this issue through guided-sampling and typically achieve superior solution quality, but at the cost of extensive training and reliance on ground-truth supervision, hindering their practical use. To bridge this gap, we propose TSP-MDF, a novel instance modification framework that equips traditional deterministic heuristic tour constructors with guided-sampling capability. Specifically, TSP-MDF introduces a neural-based instance modifier that strategically shifts node coordinates to sample multiple modified instances, on which the base traditional heuristic tour constructor constructs tours that are mapped back to the original instance, allowing traditional tour constructors to explore higher-quality tours and escape local optima. At the same time, benefiting from our instance modification formulation, the neural-based instance modifier can be trained efficiently without any ground-truth supervision, ensuring the framework maintains practicality. Extensive experiments on large-scale TSP benchmarks and real-world benchmarks demonstrate that TSP-MDF significantly improves the performance of traditional heuristics tour constructors, achieving solution quality comparable to neural-based heuristic tour constructors, but with an extremely short training time.

PrivGemo: Privacy-Preserving Dual-Tower Graph Retrieval for Empowering LLM Reasoning with Memory Augmentation

Knowledge graphs (KGs) provide structured evidence that can ground large language model (LLM) reasoning for knowledge-intensive question answering. However, many practical KGs are private, and sending retrieved triples or exploration traces to closed-source LLM APIs introduces leakage risk. Existing privacy treatments focus on masking entity names, but they still face four limitations: structural leakage under semantic masking, uncontrollable remote interaction, fragile multi-hop and multi-entity reasoning, and limited experience reuse for stability and efficiency. To address these issues, we propose PrivGemo, a privacy-preserving retrieval-augmented framework for KG-grounded reasoning with memory-guided exposure control. PrivGemo uses a dual-tower design to keep raw KG knowledge local while enabling remote reasoning over an anonymized view that goes beyond name masking to limit both semantic and structural exposure. PrivGemo supports multi-hop, multi-entity reasoning by retrieving anonymized long-hop paths that connect all topic entities, while keeping grounding and verification on the local KG. A hierarchical controller and a privacy-aware experience memory further reduce unnecessary exploration and remote interactions. Comprehensive experiments on six benchmarks show that PrivGemo achieves overall state-of-the-art results, outperforming the strongest baseline by up to 17.1%. Furthermore, PrivGemo enables smaller models (e.g., Qwen3-4B) to achieve reasoning performance comparable to that of GPT-4-Turbo.

Beyond Homophily: Community Search on Heterophilic Graphs

Community search aims to identify a refined set of nodes that are most relevant to a given query, supporting tasks ranging from fraud detection to recommendation. Unlike homophilic graphs, many real-world networks are heterophilic, where edges predominantly connect dissimilar nodes. Therefore, structural signals that once reflected smooth, low-frequency similarity now appear as sharp, high-frequency contrasts. However, both classical algorithms (e.g., k-core, k-truss) and recent ML-based models struggle to achieve effective community search on heterophilic graphs, where edge signs or semantics are generally unknown. Algorithm-based methods often return communities with mixed class labels, while GNNs, built on homophily, smooth away meaningful signals and blur community boundaries. Therefore, we propose Adaptive Community Search (AdaptCS), a unified framework featuring three key designs: (i) an AdaptCS Encoder that disentangles multi-hop and multi-frequency signals, enabling the model to capture both smooth (homophilic) and contrastive (heterophilic) relations; (ii) a memory-efficient low-rank optimization that removes the main computational bottleneck and ensures model scalability; and (iii) an Adaptive Community Score (ACS) that guides online search by balancing embedding similarity and topological relations. Extensive experiments on both heterophilic and homophilic benchmarks demonstrate that AdaptCS outperforms the best-performing baseline by an average of 11% in F1-score, retains robustness across heterophily levels, and achieves up to 2 orders of magnitude speedup.

HyperJoin: LLM-augmented Hypergraph Link Prediction for Joinable Table Discovery

As a pivotal task in data lake management, joinable table discovery has attracted widespread interest. While existing language model-based methods achieve remarkable performance by combining offline column representation learning with online ranking, their design insufficiently accounts for the underlying structural interactions: (1) offline, they directly model tables into isolated or pairwise columns, thereby struggling to capture the rich inter-table and intra-table structural information; and (2) online, they rank candidate columns based solely on query-candidate similarity, ignoring the mutual interactions among the candidates, leading to incoherent result sets. To address these limitations, we propose HyperJoin, a large language model (LLM)-augmented Hypergraph framework for Joinable table discovery. Specifically, we first construct a hypergraph to model tables using both the intra-table hyperedges and the LLM-augmented inter-table hyperedges. Consequently, the task of joinable table discovery is formulated as link prediction on this constructed hypergraph. We then design HIN, a Hierarchical Interaction Network that learns expressive column representations through bidirectional message passing over columns and hyperedges. To strengthen coherence and internal consistency in the result columns, we cast online ranking as a coherence-aware top-k column selection problem. We then introduce a reranking module that leverages a maximum spanning tree algorithm to prune noisy connections and maximize coherence. Experiments demonstrate the superiority of HyperJoin, achieving average improvements of 21.4% (Precision@15) and 17.2% (Recall@15) over the best baseline.

MiST: Understanding the Role of Mid-Stage Scientific Training in Developing Chemical Reasoning Models

Large Language Models can develop reasoning capabilities through online fine-tuning with rule-based rewards. However, recent studies reveal a critical constraint: reinforcement learning succeeds only when the base model already assigns non-negligible probability to correct answers -- a property we term 'latent solvability'. This work investigates the emergence of chemical reasoning capabilities and what these prerequisites mean for chemistry. We identify two necessary conditions for RL-based chemical reasoning: 1) Symbolic competence, and 2) Latent chemical knowledge. We propose mid-stage scientific training (MiST): a set of mid-stage training techniques to satisfy these, including data-mixing with SMILES/CIF-aware pre-processing, continued pre-training on 2.9B tokens, and supervised fine-tuning on 1B tokens. These steps raise the latent-solvability score on 3B and 7B models by up to 1.8x, and enable RL to lift top-1 accuracy from 10.9 to 63.9% on organic reaction naming, and from 40.6 to 67.4% on inorganic material generation. Similar results are observed for other challenging chemical tasks, while producing interpretable reasoning traces. Our results define clear prerequisites for chemical reasoning training and highlight the broader role of mid-stage training in unlocking reasoning capabilities.

RP-CATE: Recurrent Perceptron-based Channel Attention Transformer Encoder for Industrial Hybrid Modeling

Nowadays, industrial hybrid modeling which integrates both mechanistic modeling and machine learning-based modeling techniques has attracted increasing interest from scholars due to its high accuracy, low computational cost, and satisfactory interpretability. Nevertheless, the existing industrial hybrid modeling methods still face two main limitations. First, current research has mainly focused on applying a single machine learning method to one specific task, failing to develop a comprehensive machine learning architecture suitable for modeling tasks, which limits their ability to effectively represent complex industrial scenarios. Second, industrial datasets often contain underlying associations (e.g., monotonicity or periodicity) that are not adequately exploited by current research, which can degrade model's predictive performance. To address these limitations, this paper proposes the Recurrent Perceptron-based Channel Attention Transformer Encoder (RP-CATE), with three distinctive characteristics: 1: We developed a novel architecture by replacing the self-attention mechanism with channel attention and incorporating our proposed Recurrent Perceptron (RP) Module into Transformer, achieving enhanced effectiveness for industrial modeling tasks compared to the original Transformer. 2: We proposed a new data type called Pseudo-Image Data (PID) tailored for channel attention requirements and developed a cyclic sliding window method for generating PID. 3: We introduced the concept of Pseudo-Sequential Data (PSD) and a method for converting industrial datasets into PSD, which enables the RP Module to capture the underlying associations within industrial dataset more effectively. An experiment aimed at hybrid modeling in chemical engineering was conducted by using RP-CATE and the experimental results demonstrate that RP-CATE achieves the best performance compared to other baseline models.

FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation

Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. However, existing Transformer- and diffusion-based models lack explicit inductive biases and frequency awareness, limiting their generalization under structured missing patterns and distribution shifts. We propose FADTI, a diffusion-based framework that injects frequency-informed feature modulation via a learnable Fourier Bias Projection (FBP) module and combines it with temporal modeling through self-attention and gated convolution. FBP supports multiple spectral bases, enabling adaptive encoding of both stationary and non-stationary patterns. This design injects frequency-domain inductive bias into the generative imputation process. Experiments on multiple benchmarks, including a newly introduced biological time series dataset, show that FADTI consistently outperforms state-of-the-art methods, particularly under high missing rates. Code is available at https://anonymous.4open.science/r/TimeSeriesImputation-52BF