Theorem-of-Thought: A Multi-Agent Framework for Abductive, Deductive, and Inductive Reasoning in Language Models

Large language models (LLMs) have shown strong performance across natural language reasoning tasks, yet their reasoning processes remain brittle and difficult to interpret. Prompting techniques like Chain-of-Thought (CoT) enhance reliability by eliciting intermediate reasoning steps or aggregating multiple outputs. However, they lack mechanisms for enforcing logical structure and assessing internal coherence. We introduce Theorem-of-Thought (ToTh), a novel framework that models reasoning as collaboration among three parallel agents, each simulating a distinct mode of inference: abductive, deductive, and inductive. Each agent produces a reasoning trace, which is structured into a formal reasoning graph. To evaluate consistency, we apply Bayesian belief propagation guided by natural language inference (NLI), assigning confidence scores to each step. The most coherent graph is selected to derive the final answer. Experiments on symbolic (WebOfLies) and numerical (MultiArith) reasoning benchmarks show that ToTh consistently outperforms CoT, Self-Consistency, and CoT-Decoding across multiple LLMs, while producing interpretable and logically grounded reasoning chains. Our findings suggest a promising direction for building more robust and cognitively inspired LLM reasoning. The implementation is available at https://github.com/KurbanIntelligenceLab/theorem-of-thought.

PhysicsNeRF: Physics-Guided 3D Reconstruction from Sparse Views

PhysicsNeRF is a physically grounded framework for 3D reconstruction from sparse views, extending Neural Radiance Fields with four complementary constraints: depth ranking, RegNeRF-style consistency, sparsity priors, and cross-view alignment. While standard NeRFs fail under sparse supervision, PhysicsNeRF employs a compact 0.67M-parameter architecture and achieves 21.4 dB average PSNR using only 8 views, outperforming prior methods. A generalization gap of 5.7-6.2 dB is consistently observed and analyzed, revealing fundamental limitations of sparse-view reconstruction. PhysicsNeRF enables physically consistent, generalizable 3D representations for agent interaction and simulation, and clarifies the expressiveness-generalization trade-off in constrained NeRF models.

Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting

Time series forecasting remains a challenging task for foundation models due to temporal heterogeneity, high dimensionality, and the lack of inherent symbolic structure. In this work, we propose DRAGON (Discrete Representation and Augmented Graph encoding Over deBruijN Graphs), a novel encoder that introduces Multivariate de Bruijn Graphs (MdBGs) to bridge the gap between symbolic representations and neural modeling. DRAGON discretizes continuous input sequences and maps them onto a fixed graph structure, enabling dynamic context recovery via graph-based attention. Integrated as an auxiliary module within a dual-branch architecture, DRAGON augments conventional CNN-based encoders with symbolic, structure-aware representations. All code developed for this study is available at: https://github.com/KurbanIntelligenceLab/MultdBG-Time-Series-Library

Understanding the Capabilities of Molecular Graph Neural Networks in Materials Science Through Multimodal Learning and Physical Context Encoding

Molecular graph neural networks (GNNs) often focus exclusively on XYZ-based geometric representations and thus overlook valuable chemical context available in public databases like PubChem. This work introduces a multimodal framework that integrates textual descriptors, such as IUPAC names, molecular formulas, physicochemical properties, and synonyms, alongside molecular graphs. A gated fusion mechanism balances geometric and textual features, allowing models to exploit complementary information. Experiments on benchmark datasets indicate that adding textual data yields notable improvements for certain electronic properties, while gains remain limited for others. Furthermore, the GNN architectures display similar performance patterns (improving and deteriorating on analogous targets), suggesting they learn comparable representations rather than distinctly different physical insights.

Exploring Various Sequential Learning Methods for Deformation History Modeling

Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to transformer-based architectures. However, it is unknown which NN architectures will perform the best on datasets containing deformation history due to mechanical loading. Thus, this study ascertains the appropriateness of 1D-convolutional, recurrent, and transformer-based architectures for predicting deformation localization based on the earlier states in the form of deformation history. Following this investigation, the crucial incompatibility issues between the mathematical computation of the prediction process in the best-performing NN architectures and the actual values derived from the natural physical properties of the deformation paths are examined in detail.

HalluVerse25: Fine-grained Multilingual Benchmark Dataset for LLM Hallucinations

Large Language Models (LLMs) are increasingly used in various contexts, yet remain prone to generating non-factual content, commonly referred to as "hallucinations". The literature categorizes hallucinations into several types, including entity-level, relation-level, and sentence-level hallucinations. However, existing hallucination datasets often fail to capture fine-grained hallucinations in multilingual settings. In this work, we introduce HalluVerse25, a multilingual LLM hallucination dataset that categorizes fine-grained hallucinations in English, Arabic, and Turkish. Our dataset construction pipeline uses an LLM to inject hallucinations into factual biographical sentences, followed by a rigorous human annotation process to ensure data quality. We evaluate several LLMs on HalluVerse25, providing valuable insights into how proprietary models perform in detecting LLM-generated hallucinations across different contexts.

SINdex: Semantic INconsistency Index for Hallucination Detection in LLMs

Large language models (LLMs) are increasingly deployed across diverse domains, yet they are prone to generating factually incorrect outputs - commonly known as "hallucinations." Among existing mitigation strategies, uncertainty-based methods are particularly attractive due to their ease of implementation, independence from external data, and compatibility with standard LLMs. In this work, we introduce a novel and scalable uncertainty-based semantic clustering framework for automated hallucination detection. Our approach leverages sentence embeddings and hierarchical clustering alongside a newly proposed inconsistency measure, SINdex, to yield more homogeneous clusters and more accurate detection of hallucination phenomena across various LLMs. Evaluations on prominent open- and closed-book QA datasets demonstrate that our method achieves AUROC improvements of up to 9.3% over state-of-the-art techniques. Extensive ablation studies further validate the effectiveness of each component in our framework.

SAFE: A Sparse Autoencoder-Based Framework for Robust Query Enrichment and Hallucination Mitigation in LLMs

Despite the state-of-the-art performance of Large Language Models (LLMs), these models often suffer from hallucinations, which can undermine their performance in critical applications. In this work, we propose SAFE, a novel method for detecting and mitigating hallucinations by leveraging Sparse Autoencoders (SAEs). While hallucination detection techniques and SAEs have been explored independently, their synergistic application in a comprehensive system, particularly for hallucination-aware query enrichment, has not been fully investigated. To validate the effectiveness of SAFE, we evaluate it on two models with available SAEs across three diverse cross-domain datasets designed to assess hallucination problems. Empirical results demonstrate that SAFE consistently improves query generation accuracy and mitigates hallucinations across all datasets, achieving accuracy improvements of up to 29.45%.