We study fundamental connections between coalition formation games and clustering, illustrating the cross-disciplinary relevance of these concepts. We focus on graphical hedonic games where agents' preferences are compactly represented by a friendship graph and an enmity graph. In the context of clustering, friendship relations naturally align with data point similarities, whereas enmity corresponds to dissimilarities. We consider two stability notions based on single-agent deviations: local popularity and local stability.

Post-training compression has been a widely employed approach to scale down large language model (LLM) and facilitate efficient inference. In various proposed compression methods, including pruning and quantization, calibration data plays a vital role by informing the weight importance and activation dynamic ranges. However, how calibration data impacts the LLM capability after compression is less explored. Few of the existing works, though recognizing the significance of this study, only investigate the language modeling or commonsense reasoning performance degradation from limited angles, like the data sources or sample amounts. More systematic research is still needed to examine the impacts on different LLM capabilities in terms of compositional properties and domain correspondence of calibration data.

Forecasting real-world time series requires modeling both short-term fluctuations and long-term evolutions, as these signals typically exhibit multiscale temporal structures. A core challenge lies in reconciling such dynamics: high-frequency seasonality demands local precision, while low-frequency trends require global robustness. However, most existing methods adopt a unified loss function across all temporal components, overlooking their structural differences. This misalignment often causes overfitting to seasonal noise or underfitting of long-term trends, leading to suboptimal forecasting performance. To address this issue, we propose a Physics-guided Multiscale Loss Framework (PMLF) that decomposes time series into seasonal and trend components and assigns component-specific objectives grounded in the distinct energy responses of oscillatory and drift dynamics. Specifically, we assign a quadratic loss to seasonal components, reflecting the quadratic potential energy profile of molecular vibration, while a logarithmic loss is used for trend components to capture the sublinear energy profile of molecular drift under sustained external forces. Furthermore, we introduce a softmax-based strategy that adaptively balances the unequal energetic responses of these two physical processes. Experiments on different public benchmarks show that PMLF improves the performance of diverse baselines, demonstrating the effectiveness of physics-guided loss design in modeling structural heterogeneity in time series forecasting.

Local SGD, or Federated Averaging, is one of the most widely used algorithms for distributed optimization. Although it often outperforms alternatives such as mini-batch SGD, existing theory has not fully explained this advantage under realistic assumptions about data heterogeneity. Recent work has suggested that a second-order heterogeneity assumption may suffice to justify the empirical gains of local SGD. We confirm this conjecture by establishing new upper and lower bounds on the convergence of local SGD. These bounds demonstrate how a low secondorder heterogeneity, combined with third-order smoothness, enables local SGD to interpolate between heterogeneous and homogeneous regimes while maintaining communication efficiency. Our main technical contribution is a refined analysis of the consensus error, a central quantity in such results. We validate our theory with experiments on a distributed linear regression task.

While end-to-end adaptive graph learning methods have demonstrated promising results in capturing latent spatiotemporal dependencies, they often suffer from high computational complexity and limited expressive capacity. In this paper, we propose MAGE for efficient spatiotemporal forecasting. We first conduct a theoretical analysis demonstrating that the ReLU activation function employed in existing methods amplifies edgelevel noise during graph topology learning, thereby compromising the fidelity of the learned graph structures. To enhance model expressiveness, we introduce a sparse yet balanced mixture-of-experts strategy, where each expert perceives the unique underlying graph through kernel-based functions and operates with linear complexity relative to the number of nodes. The sparsity mechanism ensures that each node interacts exclusively with compatible experts, while the balancing mechanism promotes uniform activation across all experts, enabling diverse and adaptive graph representations. Furthermore, we theoretically establish that a single graph convolution using the learned graph in MAGE is mathematically equivalent to multiple convolutional steps under conventional graphs. We evaluate MAGE against advanced baselines on multiple real-world spatiotemporal datasets, and MAGE achieves competitive performance while maintaining strong computational efficiency. Our code is available at official repository.

Neural scaling laws are observed in a range of domains, to date with no universal understanding of why they occur. Recent theories suggest that loss power laws arise from Zipf's law, a power law observed in domains like natural language. One theory suggests that language scaling laws emerge when Zipf-distributed task quanta are learned in descending order of frequency. In this paper we examine power-law scaling in AlphaZero, a reinforcement learning algorithm, using a model of language-model scaling. We find that game states in training and inference data scale with Zipf's law, which is known to arise from the tree structure of the environment, and examine the correlation between scaling-law and Zipf'slaw exponents. In agreement with the quanta scaling model, we find that agents optimize state loss in descending order of frequency, even though this order scales inversely with modelling complexity. We also find that inverse scaling, the failure of models to improve with size, is correlated with unusual Zipf curves where end-game states are among the most frequent states. We show evidence that larger models shift their focus to these less-important states, sacrificing their understanding of important early-game states.

Biomedical research data portals are essential resources for scientific inquiry, and interactive exploratory visualizations are an integral component for querying such data repositories. Increasingly, machine learning is being integrated into visualization systems to create natural language interfaces where questions about data can be answered with visualizations, and follow-up questions can build on the previous state. This paper introduces a framework that takes abstract low-level questions about data and a visualization grammar specification that can answer such a question, reifies them with data entities and fields that meet certain constraints, and paraphrases the question language to produce the final collection of realized data-question-visualization triplets. Furthermore, we can link these foundational elements together to construct chains of queries, visualizations, and follow-up queries. We developed an open-source review interface for evaluating the results of these datasets. We applied this framework to five biomedical research data repositories, resulting in DQVis, a dataset of 1.08 million dataquestion-visualization triplets and 11.4 thousand two-step question samples. Five visualization experts provided feedback on the generated dataset through our review interface. We present a summary of their input and publish the full reviews as an additional resource alongside the dataset.

What does it truly mean for a language model to "reason" strategically, and can scaling up alone guarantee intelligent, context-aware decisions? Strategic decisionmaking requires adaptive reasoning, where agents anticipate and respond to others' actions under uncertainty. Yet, most evaluations of large language models (LLMs) for strategic decision-making often rely heavily on Nash Equilibrium (NE) benchmarks, overlook reasoning depth, and fail to reveal the mechanisms behind model behavior. To address this gap, we introduce a behavioral game-theoretic evaluation framework that disentangles intrinsic reasoning from contextual influence. Using this framework, we evaluate 22 state-of-the-art LLMs across diverse strategic scenarios. We find models like GPT-o3-mini, GPT-o1, and DeepSeek-R1 lead in reasoning depth. Through thinking chain analysis, we identify distinct reasoning styles--such as maximin or belief-based strategies--and show that longer reasoning chains do not consistently yield better decisions. Furthermore, embedding demographic personas reveals context-sensitive shifts: some models (e.g., GPT4o, Claude-3-Opus) improve when assigned female identities, while others (e.g., Gemini 2.0) show diminished reasoning under minority sexuality personas. These findings underscore that technical sophistication alone is insufficient; alignment with ethical standards, human expectations, and situational nuance is essential for the responsible deployment of LLMs in interactive settings.

The AlphaFold Protein Structure Database (AFDB) offers unparalleled structural coverage at near-experimental accuracy, positioning it as a valuable resource for data-driven protein design. However, its direct use in training deep models that are sensitive to fine-grained atomic geometry--such as inverse folding--exposes a critical limitation. Comparative analysis of structural feature distributions reveals that AFDB structures exhibit distinct statistical regularities, reflecting a systematic geometric bias that deviates from the conformational diversity found in experimentally determined structures from the Protein Data Bank (PDB). While AFDB structures are cleaner and more idealized, PDB structures capture the intrinsic variability and physical realism essential for generalization in downstream tasks. To address this discrepancy, we introduce a Debiasing Structure AutoEncoder (DeSAE) that learns to reconstruct native-like conformations from intentionally corrupted backbone geometries. By training the model to recover plausible structural states, DeSAE implicitly captures a more robust and natural structural manifold. At inference, applying DeSAE to AFDB structures produces debiased representations that significantly improve inverse folding performance across multiple benchmarks, and also enhance other structure-conditioned modeling tasks. This work highlights the critical impact of subtle systematic biases in predicted structures and presents a principled framework for debiasing, significantly boosting the performance of structure-based learning tasks like inverse folding.

Prompt tuning has emerged as a key technique for adapting large pre-trained Decision Transformers (DTs) in offline Reinforcement Learning (RL), particularly in multi-task and few-shot settings. The Prompting Decision Transformer (PDT) enables task generalization via trajectory prompts sampled uniformly from expert demonstrations - without accounting for prompt informativeness. In this work, we propose a bandit-based prompt-tuning method that learns to construct optimal trajectory prompts from demonstration data at inference time. We devise a structured bandit architecture operating in the trajectory prompt space, achieving linear rather than combinatorial scaling with prompt size. Additionally, we show that the pretrained PDT itself can serve as a powerful feature extractor for the bandit, enabling efficient reward modeling across various environments. We theoretically establish regret bounds and demonstrate empirically that our method consistently enhances performance across a wide range of tasks, high-dimensional environments, and out-of-distribution scenarios, outperforming existing baselines in prompt tuning.