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 framework 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 four 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%.

Evaluating foundation models for crystallographic reasoning requires benchmarks that isolate generalization behavior while enforcing physical constraints. This work introduces, xCrysAlloys, a multiscale multicrystal dataset with two physically grounded evaluation protocols to stress-test multimodal generative models. The Spatial-Exclusion benchmark withholds all supercells of a given radius from a diverse dataset, enabling controlled assessments of spatial interpolation and extrapolation. The Compositional-Exclusion benchmark omits all samples of a specific chemical composition, probing generalization across stoichiometries. Nine vision–language foundation models are prompted with crystallographic images and textual context to generate structural annotations. Responses are evaluated via (i) relative errors in lattice parameters and density, (ii) a physics-consistency index penalizing volumetric violations, and (iii) a hallucination score capturing geometric outliers and invalid space-group predictions. These benchmarks establish a reproducible, physically informed framework for assessing generalization, consistency, and reliability in large-scale multimodal models. Dataset and implementation are available at https://github.com/KurbanIntelligenceLab/StressTestingMMFMinCR.

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.