The rapid advancements in large language models (LLMs), particularly in their reasoning capabilities, hold transformative potential for addressing complex challenges and boosting scientific discovery in atmospheric science. However, leveraging LLMs effectively in this domain requires a robust and comprehensive evaluation benchmark. Toward this end, we present ATMOSSCI-BENCH, a novel benchmark designed to systematically assess LLM performance across five core categories of atmospheric science problems: hydrology, atmospheric dynamics, atmospheric physics, geophysics, and physical oceanography. ATMOSSCI-BENCH features a dual-format design comprising both multiple-choice questions (MCQs) and open-ended questions (OEQs), enabling scalable automated evaluation alongside deeper analysis of conceptual understanding. We employ a template-based MCQ generation framework to create diverse, graduate-level problems with symbolic perturbation, while OEQs are used to probe open-ended reasoning. We conduct a comprehensive evaluation of representative LLMs, categorized into four groups: instruction-tuned models, advanced reasoning models, math-augmented models, and domain-specific climate models. Our analysis provides some interesting insights into the reasoning and problem-solving capabilities of LLMs in atmospheric science. We believe ATMOSSCI-BENCH can serve as a critical step toward advancing LLM applications in climate services by offering a standard and rigorous evaluation framework.

The capabilities of large language models (LLMs) significantly depend on training data drawn from various domains. Optimizing domain-specific mixture ratios can be modeled as a bi-level optimization problem, which we simplify into a singlelevel penalized form and solve with twin networks: a proxy model trained on primary data and a dynamically updated reference model trained with additional data. Our proposed method, Twin Networks for bi-level DatA mixturE optiMization (TANDEM), measures the data efficacy through the difference between the twin models and up-weights domains that benefit more from the additional data. TANDEM provides theoretical guarantees and wider applicability, compared to prior approaches. Furthermore, our bi-level perspective suggests new settings to study domain reweighting such as data-restricted scenarios and supervised finetuning, where optimized mixture ratios significantly improve the performance.

Continual Structured Knowledge Reasoning (CSKR) focuses on training models to handle sequential tasks, where each task involves translating natural language questions into structured queries grounded in structured knowledge. Existing general continual learning approaches face significant challenges when applied to this task, including poor generalization to heterogeneous structured knowledge and inefficient reasoning due to parameter growth as tasks increase. To address these limitations, we propose a novel CSKR framework, K-DECORE, which operates with a fixed number of tunable parameters. Unlike prior methods, K-DECORE introduces a knowledge decoupling mechanism that disentangles the reasoning process into task-specific and task-agnostic stages, effectively bridging the gaps across diverse tasks. Building on this foundation, K-DECORE integrates a dualperspective memory consolidation mechanism for distinct stages and introduces a structure-guided pseudo-data synthesis strategy to further enhance the model's generalization capabilities. Extensive experiments on four benchmark datasets demonstrate the superiority of K-DECORE over existing continual learning methods across multiple metrics, leveraging various backbone large language models.

Large Language Models (LLMs) show strong generalization across diverse tasks, yet the internal decision-making processes behind their predictions remain opaque. In this work, we study the geometry of hidden representations in LLMs through the lens of intrinsic dimension (ID), focusing specifically on decision-making dynamics in a multiple-choice question answering (MCQA) setting. We perform a large-scale study, with 28 open-weight transformer models and estimate ID across layers using multiple estimators, while also quantifying per-layer performance on MCQA tasks. Our findings reveal a consistent ID pattern across models: early layers operate on low-dimensional manifolds, middle layers expand this space, and later layers compress it again, converging to decision-relevant representations. Together, these results suggest LLMs implicitly learn to project linguistic inputs onto structured, low-dimensional manifolds aligned with task-specific decisions, providing new geometric insights into how generalization and reasoning emerge in language models.

We investigate congested assignment problems where agents have preferences over both resources and their associated congestion levels. These agents are averse towards congestion, i.e., consistently preferring lower congestion for identical resources. Such scenarios are ubiquitous across domains including traffic management and school choice, where fair resource allocation is essential. We focus on the concept of competitiveness, recently introduced by Bogomolnaia and Moulin [6], and contribute a polynomial-time algorithm that determines competitiveness, resolving their open question. Additionally, we explore two optimization variants of congested assignments by examining the problem of finding envy-free or maximally competitive assignments that guarantee a certain amount of social welfare for every agent, termed top-guarantees [6]. While we prove that both problems are NP-hard, we develop parameterized algorithms with respect to the number of agents or resources.

As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning in a straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As a result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial tracking--capabilities that humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, a novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations, including annotating bounding boxes and drawing auxiliary lines, we empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the performance ceiling imposed by specialized perception tools in previous tool-integrated reasoning approaches. To cultivate this capability, we develop a three-stage training framework: cold-start training with synthetic data to establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and reinforcement learning to directly optimize for target rewards. Extensive experiments demonstrate that our model, named VILASR, consistently outperforms existing methods across diverse spatial reasoning benchmarks, involving maze navigation, static spatial reasoning, video-based reasoning, and multi-view-based reasoning tasks, with an average improvement of 18.4%. Ablation studies reveal the critical role of each training stage, where reflective rejection sampling strengthens the model's self-correction capabilities, and reinforcement learning effectively unlocks its reasoning potential.

Effective data selection is critical for efficient training of modern Large Language Models (LLMs). This paper introduces Influence Distillation, a novel, mathematically-justified framework for data selection that employs second-order information to optimally weight training samples. By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data for LLM fine-tuning, guiding it toward strong performance on the target domain. We derive these optimal weights for both Gradient Descent and Adam optimizers. To ensure scalability and reduce computational cost, we propose a landmark-based approximation: influence is precisely computed for a small subset of "landmark" samples and then efficiently propagated to all other samples to determine their weights.

However, deploying these models can be unreliable when significant distribution gaps exist between training and test data, while fine-tuning for diverse scenarios is often costly. This creates a need for methods that can efficiently adapt to new data at test time without expensive retraining. Cache-based test-time adapters serve this purpose by storing representative test samples to guide subsequent classifications. Yet, these methods typically employ naive cache management with limited capacity, leading to severe catastrophic forgetting when samples are inevitably dropped during updates. In this paper, we propose Dota(DistributiOnal Test-time Adaptation), a simple yet effective method addressing this limitation. Crucially, instead of merely memorizing individual test samples, Dotacontinuously estimates the underlying distribution of the test data stream. Test-time posterior probabilities are then computed using these dynamically estimated distributions via Bayes' theorem for adaptation. This distribution-centric approach enables the model to continually learn and adapt to the deployment environment. Extensive experiments validate that Dota significantly mitigates forgetting and achieves state-of-the-art performance compared to existing methods.

We study Online Convex Optimization with adversarial constraints (COCO). At each round a learner selects an action from a convex decision set and then an adversary reveals a convex cost and a convex constraint function. The goal of the learner is to select a sequence of actions to minimize both regret and the cumulative constraint violation (CCV) over a horizon of length T. The best-known policy for this problem achieves O( T)regret and O( T)CCV. In this paper, we improve this by trading off regret to achieve substantially smaller CCV. This trade-off is especially important in safety-critical applications, where satisfying the safety constraints is non-negotiable. Specifically, for any bounded convex cost and constraint functions, we propose an online policy that achieves O( dT+Tβ)regret and O(dT1 β)CCV, where dis the dimension of the decision set and β [0,1]is a tunable parameter. We begin with a special case, called the CONSTRAINEDEXPERT problem, where the decision set is a probability simplex and the cost and constraint functions are linear. Leveraging a new adaptive small-loss regret bound, we propose a computationally efficient policy for the CONSTRAINEDEXPERT problem, that attains O( T lnN+Tβ)regret and O(T1 β lnN)CCV for N number of experts.

Lifelong knowledge editing enables continuous, precise updates to outdated knowledge in large language models (LLMs) without computationally expensive full retraining. However, existing methods often accumulate errors throughout the editing process, causing a gradual decline in both editing accuracy and generalization. To tackle this problem, we propose Neuron-Specific Masked Knowledge Editing (NMKE), a novel fine-grained editing framework that combines neuron-level attribution with dynamic sparse masking. Leveraging neuron functional attribution, we identify two key types of knowledge neurons, with knowledge-general neurons activating consistently across prompts and knowledge-specific neurons activating to specific prompts. NMKE further introduces an entropy-guided dynamic sparse mask, locating relevant neurons to the target knowledge. This strategy enables precise neuron-level knowledge editing with fewer parameter modifications. Experimental results from thousands of sequential edits demonstrate that NMKE outperforms existing methods in maintaining high editing success rates and preserving model general capabilities in lifelong editing.