SCALAR: Quantifying Structural Hallucination, Consistency, and Reasoning Gaps in Materials Foundation Models

Large language models are increasingly applied to materials science reasoning, yet their behavior under physically structured distribution shifts remains poorly understood. We introduce SCALAR (Structural Consistency And Logic Across Regimes), a benchmark for evaluating geometric scale generalization and its connection to structural hallucination, consistency, and reasoning in materials foundation models. Given canonical crystal representations, models must reason about derived nanoparticle structures obtained through supercell expansion and geometric truncation across length scales spanning a few atoms to over 18,000 atoms, totaling $\approx$100,000 structures from DFT-validated unit cells. SCALAR defines three tasks. (i) CIF to property prediction. (ii) A Chain-of-Thought variant with explicit physics-grounded reasoning. (iii) Inverse retrieval identifying crystals from candidates given target properties. Outputs are evaluated via structured metrics capturing numeric error, hallucination, cross-prompt consistency, monotonic reasoning, output validity, and retrieval regret. Experiments across diverse foundation models reveal large, model-dependent shifts under explicit reasoning, often reducing hallucination and error, but frequently destabilizing consistency or validity. These results demonstrate that geometric scale generalization cannot be inferred from accuracy alone. Supplementary materials are available at https://github.com/KurbanIntelligenceLab/SCALAR.

C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation

Generative models for materials have achieved strong performance on periodic bulk crystals, yet their ability to generalize across scale transitions to finite nanostructures remains largely untested. We introduce Crystal-to-Nanoparticle (C2NP), a systematic benchmark for evaluating generative models when moving between infinite crystalline unit cells and finite nanoparticles, where surface effects and size-dependent distortions dominate. C2NP defines two complementary tasks: (i) generating nanoparticles of specified radii from periodic unit cells, testing whether models capture surface truncation and geometric constraints; and (ii) recovering bulk lattice parameters and space-group symmetry from finite particle configurations, assessing whether models can infer underlying crystallographic order despite surface perturbations. Using diverse materials as a structurally consistent testbed, we construct over 170,000 nanoparticle configurations by carving particles from supercells derived from DFT-relaxed crystal unit cells, and introduce size-based splits that separate interpolation from extrapolation regimes. Experiments with state-of-the-art approaches, including diffusion, flow-matching, and variational models, show that even when losses are low, models often fail geometrically under distribution shift, yielding large lattice-recovery errors and near-zero joint accuracy on structure and symmetry. Overall, our results suggest that current methods rely on template memorization rather than scalable physical generalization. C2NP offers a controlled, reproducible framework for diagnosing these failures, with immediate applications to nanoparticle catalyst design, nanostructured hydrides for hydrogen storage, and materials discovery. Dataset and code are available at https://github.com/KurbanIntelligenceLab/C2NP.

Temporal Realism Evaluation of Generated Videos Using Compressed-Domain Motion Vectors

Temporal realism remains a central weakness of current generative video models, as most evaluation metrics prioritize spatial appearance and offer limited sensitivity to motion. We introduce a scalable, model-agnostic framework that assesses temporal behavior using motion vectors (MVs) extracted directly from compressed video streams. Codec-generated MVs from standards such as H.264 and HEVC provide lightweight, resolution-consistent descriptors of motion dynamics. We quantify realism by computing Kullback-Leibler, Jensen-Shannon, and Wasserstein divergences between MV statistics of real and generated videos. Experiments on the GenVidBench dataset containing videos from eight state-of-the-art generators reveal systematic discrepancies from real motion: entropy-based divergences rank Pika and SVD as closest to real videos, MV-sum statistics favor VC2 and Text2Video-Zero, and CogVideo shows the largest deviations across both measures. Visualizations of MV fields and class-conditional motion heatmaps further reveal center bias, sparse and piecewise constant flows, and grid-like artifacts that frame-level metrics do not capture. Beyond evaluation, we investigate MV-RGB fusion through channel concatenation, cross-attention, joint embedding, and a motion-aware fusion module. Incorporating MVs improves downstream classification across ResNet, I3D, and TSN backbones, with ResNet-18 and ResNet-34 reaching up to 97.4% accuracy and I3D achieving 99.0% accuracy on real-versus-generated discrimination. These findings demonstrate that compressed-domain MVs provide an effective temporal signal for diagnosing motion defects in generative videos and for strengthening temporal reasoning in discriminative models. The implementation is available at: https://github.com/KurbanIntelligenceLab/Motion-Vector-Learning

Evaluating Multilingual and Code-Switched Alignment in LLMs via Synthetic Natural Language Inference

Large language models (LLMs) are increasingly applied in multilingual contexts, yet their capacity for consistent, logically grounded alignment across languages remains underexplored. We present a controlled evaluation framework for multilingual natural language inference (NLI) that generates synthetic, logic-based premise-hypothesis pairs and translates them into a typologically diverse set of languages. This design enables precise control over semantic relations and allows testing in both monolingual and mixed-language (code-switched) conditions. Surprisingly, code-switching does not degrade, and can even improve, performance, suggesting that translation-induced lexical variation may serve as a regularization signal. We validate semantic preservation through embedding-based similarity analyses and cross-lingual alignment visualizations, confirming the fidelity of translated pairs. Our findings expose both the potential and the brittleness of current LLM cross-lingual reasoning, and identify code-switching as a promising lever for improving multilingual robustness. Code available at: https://github.com/KurbanIntelligenceLab/nli-stress-testing

EMPATHIA: Multi-Faceted Human-AI Collaboration for Refugee Integration

Current AI approaches to refugee integration optimize narrow objectives such as employment and fail to capture the cultural, emotional, and ethical dimensions critical for long-term success. We introduce EMPATHIA (Enriched Multimodal Pathways for Agentic Thinking in Humanitarian Immigrant Assistance), a multi-agent framework addressing the central Creative AI question: how do we preserve human dignity when machines participate in life-altering decisions? Grounded in Kegan's Constructive Developmental Theory, EMPATHIA decomposes integration into three modules: SEED (Socio-cultural Entry and Embedding Decision) for initial placement, RISE (Rapid Integration and Self-sufficiency Engine) for early independence, and THRIVE (Transcultural Harmony and Resilience through Integrated Values and Engagement) for sustained outcomes. SEED employs a selector-validator architecture with three specialized agents - emotional, cultural, and ethical - that deliberate transparently to produce interpretable recommendations. Experiments on the UN Kakuma dataset (15,026 individuals, 7,960 eligible adults 15+ per ILO/UNHCR standards) and implementation on 6,359 working-age refugees (15+) with 150+ socioeconomic variables achieved 87.4% validation convergence and explainable assessments across five host countries. EMPATHIA's weighted integration of cultural, emotional, and ethical factors balances competing value systems while supporting practitioner-AI collaboration. By augmenting rather than replacing human expertise, EMPATHIA provides a generalizable framework for AI-driven allocation tasks where multiple values must be reconciled.

Geometric-k-means: A Bound Free Approach to Fast and Eco-Friendly k-means

This paper introduces Geometric-k-means (or Gk-means for short), a novel approach that significantly enhances the efficiency and energy economy of the widely utilized k-means algorithm, which, despite its inception over five decades ago, remains a cornerstone in machine learning applications. The essence of Gk-means lies in its active utilization of geometric principles, specifically scalar projection, to significantly accelerate the algorithm without sacrificing solution quality. This geometric strategy enables a more discerning focus on data points that are most likely to influence cluster updates, which we call as high expressive data (HE). In contrast, low expressive data (LE), does not impact clustering outcome, is effectively bypassed, leading to considerable reductions in computational overhead. Experiments spanning synthetic, real-world and high-dimensional datasets, demonstrate Gk-means is significantly better than traditional and state of the art (SOTA) k-means variants in runtime and distance computations (DC). Moreover, Gk-means exhibits better resource efficiency, as evidenced by its reduced energy footprint, placing it as more sustainable alternative.

Stress-Testing Multimodal Foundation Models for Crystallographic Reasoning

Evaluating foundation models for crystallographic reasoning requires benchmarks that isolate generalization behavior while enforcing physical constraints. This work introduces 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 code are available at https://github.com/KurbanIntelligenceLab/StressTestingMMFMinCR.

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