We analyze task orderings in continual learning for linear regression, assuming joint realizability of training data. We focus on orderings that greedily maximize dissimilarity between consecutive tasks, a concept briefly explored in prior work but still surrounded by open questions. Using tools from the Kaczmarz method literature, we formalize such orderings and develop geometric and algebraic intuitions around them. Empirically, we demonstrate that greedy orderings converge faster than random ones in terms of the average loss across tasks, both for linear regression with random data and for linear probing on CIFAR-100 classification tasks. Analytically, in a high-rank regression setting, we prove a loss bound for greedy orderings analogous to that of random ones. However, under general rank, we establish a repetition-dependent separation. Specifically, while prior work showed that for random orderings, with or without replacement, the average loss after $k$ iterations is bounded by $\mathcal{O}(1/\sqrt{k})$, we prove that single-pass greedy orderings may fail catastrophically, whereas those allowing repetition converge at rate $\mathcal{O}(1/\sqrt[3]{k})$. Overall, we reveal nuances within and between greedy and random orderings.

The integration of Large Language Models (LLMs) with optimization modeling offers a promising avenue for advancing decision-making in operations research (OR). Traditional optimization methods,such as linear programming, mixed integer programming, and simulation depend heavily on domain expertise to translate real-world problems into solvable mathematical models. While solvers like Gurobi and COPT are powerful, expert input remains essential for defining objectives, constraints, and variables. This research investigates the potential of LLMs, specifically the DeepSeek-R1 model, to bridge this formulation gap using natural language understanding and code generation. Although prior models like GPT-4, Claude, and Bard have shown strong performance in NLP and reasoning tasks, their high token costs and tendency toward hallucinations limit real-world applicability in supply chain contexts. In contrast, DeepSeek-R1, a cost-efficient and high-performing model trained with reinforcement learning, presents a viable alternative. Despite its success in benchmarks such as LiveCodeBench and Math-500, its effectiveness in applied OR scenarios remains under explored. This study systematically evaluates DeepSeek-R1 across four key OR benchmarks: NL4OPT, IndustryOR, EasyLP, and ComplexOR. Our methodology includes baseline assessments, the development of a hallucination taxonomy, and the application of mitigation strategies like LLM-as-a-Judge, Few-shot Learning (FSL), Tool Calling, and a Multi-agent Framework. These techniques aim to reduce hallucinations, enhance formulation accuracy, and better align model outputs with user intent.

This study evaluates the pedagogical soundness and usability of AI-generated lesson plans across five leading large language models: ChatGPT (GPT-5), Claude Sonnet 4.5, Gemini 2.5 Flash, DeepSeek V3.2, and Grok 4. Beyond model choice, three structured prompt frameworks were tested: TAG (Task, Audience, Goal), RACE (Role, Audience, Context, Execution), and COSTAR (Context, Objective, Style, Tone, Audience, Response Format). Fifteen lesson plans were generated for a single high-school physics topic, The Electromagnetic Spectrum. The lesson plans were analyzed through four automated computational metrics: (1) readability and linguistic complexity, (2) factual accuracy and hallucination detection, (3) standards and curriculum alignment, and (4) cognitive demand of learning objectives. Results indicate that model selection exerted the strongest influence on linguistic accessibility, with DeepSeek producing the most readable teaching plan (FKGL = 8.64) and Claude generating the densest language (FKGL = 19.89). The prompt framework structure most strongly affected the factual accuracy and pedagogical completeness, with the RACE framework yielding the lowest hallucination index and the highest incidental alignment with NGSS curriculum standards. Across all models, the learning objectives in the fifteen lesson plans clustered at the Remember and Understand tiers of Bloom's taxonomy. There were limited higher-order verbs in the learning objectives extracted. Overall, the findings suggest that readability is significantly governed by model design, while instructional reliability and curricular alignment depend more on the prompt framework. The most effective configuration for lesson plans identified in the results was to combine a readability-optimized model with the RACE framework and an explicit checklist of physics concepts, curriculum standards, and higher-order objectives.

Comprehending natural language and following human instructions are critical capabilities for intelligent agents. However, the flexibility of linguistic instructions induces substantial ambiguity across language-conditioned tasks, severely degrading algorithmic performance. To address these limitations, we present a novel method named DAIL (Distributional Aligned Learning), featuring two key components: distributional policy and semantic alignment. Specifically, we provide theoretical results that the value distribution estimation mechanism enhances task differentiability. Meanwhile, the semantic alignment module captures the correspondence between trajectories and linguistic instructions. Extensive experimental results on both structured and visual observation benchmarks demonstrate that DAIL effectively resolves instruction ambiguities, achieving superior performance to baseline methods. Our implementation is available at https://github.com/RunpengXie/Distributional-Aligned-Learning.

Extending Named Entity Recognition (NER) models to new PII entities in noisy spoken-language data is a common need. We find that jointly fine-tuning a BERT model on standard semantic entities (PER, LOC, ORG) and new pattern-based PII (EMAIL, PHONE) results in minimal degradation for original classes. We investigate this "peaceful coexistence," hypothesizing that the model uses independent semantic vs. morphological feature mechanisms. Using an incremental learning setup as a diagnostic tool, we measure semantic drift and find two key insights. First, the LOC (location) entity is uniquely vulnerable due to a representation overlap with new PII, as it shares pattern-like features (e.g., postal codes). Second, we identify a "reverse O-tag representation drift." The model, initially trained to map PII patterns to 'O', blocks new learning. This is resolved only by unfreezing the 'O' tag's classifier, allowing the background class to adapt and "release" these patterns. This work provides a mechanistic diagnosis of NER model adaptation, highlighting feature independence, representation overlap, and 'O' tag plasticity. Work done based on data gathered by https://www.papernest.com

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In particular, given a hypergraph $\mathcal{H}=(\mathcal{V},\mathcal{E})$, we prove that the naive $2^{\mathcal{O}(|\mathcal{V}|)}$-time algorithm is asymptotically tight under the Exponential Time Hypothesis (ETH). We then prove that the problem admits a $1$-additive fixed-parameter approximation algorithm when parameterized by the maximum degree of $\mathcal{H}$ and a fixed-parameter algorithm when parameterized by its dimension, and that these are essentially the only such exploitable structural parameters. Lastly, we consider a generalization of the problem, formulated using graphs, which captures the VC-dimension of both set systems and graphs. We design a $2^{\mathcal{O}(\rm{tw}\cdot \log \rm{tw})}\cdot |V|$-time algorithm for any graph $G=(V,E)$ of treewidth $\rm{tw}$ (which, for a set system, applies to the treewidth of its incidence graph). This is in contrast with closely related problems that require a double-exponential dependency on the treewidth (assuming the ETH).

We present DexCanvas, a large-scale hybrid real-synthetic human manipulation dataset containing 7,000 hours of dexterous hand-object interactions seeded from 70 hours of real human demonstrations, organized across 21 fundamental manipulation types based on the Cutkosky taxonomy (Feix et al., 2016). Each entry combines synchronized multi-view RGB-D, high-precision mocap with MANO hand parameters, and per-frame contact points with physically consistent force profiles. Our real-to-sim pipeline uses reinforcement learning to train policies that control an actuated MANO hand in physics simulation, reproducing human demonstrations while discovering the underlying contact forces that generate the observed object motion. DexCanvas is the first manipulation dataset to combine large-scale real demonstrations, systematic skill coverage based on established taxonomies, and physics-validated contact annotations. The dataset can facilitate research in robotic manipulation learning, contact-rich control, and skill transfer across different hand morphologies. Dexterous manipulation with high-DoF anthropomorphic hands is fundamental to robot learning: it enables the most general form of object interaction and is essential for robots to achieve human-level autonomy in unstructured environments (Y u & Wang, 2022; Ozawa & Tahara, 2017). The field has witnessed rapid advancement along two dimensions: diverse learning paradigms including reinforcement learning for contact-rich control (Chen et al., 2024; 2023) and diffusion-based methods for handling multimodal action distributions (Weng et al., 2024; Wu et al., 2024), alongside dramatic scale expansion from task-specific models to billion-parameter foundation models (Wen et al., 2025; Kim et al., 2024; Zitkovich et al., 2023). However, current flagship manipulation systems predominantly rely on parallel-jaw grippers, while generalizable control of anthropomorphic hands remains limited to simulation or narrow real-world scenarios. This gap highlights an opportunity: to unlock the full potential of dexterous manipulation, we need large-scale datasets that capture diverse human manipulation strategies with physically accurate contact dynamics and force profiles, the crucial signals for learning robust dexterous control. Building such datasets requires careful consideration of data sources and collection methodologies. The choice between robot-generated and human-sourced data presents fundamental tradeoffs for learning manipulation.

Multi-class wine classification presents fundamental trade-offs between model accuracy, feature dimensionality, and interpretability - critical factors for production deployment in analytical chemistry. This paper presents a comprehensive empirical study of One-vs-Rest logistic regression on the UCI Wine dataset (178 samples, 3 cultivars, 13 chemical features), comparing from-scratch gradient descent implementation against scikit-learn's optimized solvers and quantifying L1 regularization effects on feature sparsity. Manual gradient descent achieves 92.59 percent mean test accuracy with smooth convergence, validating theoretical foundations, though scikit-learn provides 24x training speedup and 98.15 percent accuracy. Class-specific analysis reveals distinct chemical signatures with heterogeneous patterns where color intensity varies dramatically (0.31 to 16.50) across cultivars. L1 regularization produces 54-69 percent feature reduction with only 4.63 percent accuracy decrease, demonstrating favorable interpretability-performance trade-offs. We propose an optimal 5-feature subset achieving 62 percent complexity reduction with estimated 92-94 percent accuracy, enabling cost-effective deployment with 80 dollars savings per sample and 56 percent time reduction. Statistical validation confirms robust generalization with sub-2ms prediction latency suitable for real-time quality control. Our findings provide actionable guidelines for practitioners balancing comprehensive chemical analysis against targeted feature measurement in resource-constrained environments.

Aging is a highly complex and heterogeneous process that progresses at different rates across individuals, making biological age (BA) a more accurate indicator of physiological decline than chronological age. While previous studies have built aging clocks using single-omics data, they often fail to capture the full molecular complexity of human aging. In this work, we leveraged the Human Phenotype Project, a large-scale cohort of 10,000 adults aged 40-70 years, with extensive longitudinal profiling that includes clinical, behavioral, environmental, and multi-omics datasets spanning transcriptomics, lipidomics, metabolomics, and the microbiome. By employing advanced machine learning frameworks capable of modeling nonlinear biological dynamics, we developed and rigorously validated a multi-omics aging clock that robustly predicts diverse health outcomes and future disease risk. Unsupervised clustering of the integrated molecular profiles from multi-omics uncovered distinct biological subtypes of aging, revealing striking heterogeneity in aging trajectories and pinpointing pathway-specific alterations associated with different aging patterns. These findings demonstrate the power of multi-omics integration to decode the molecular landscape of aging and lay the groundwork for personalized healthspan monitoring and precision strategies to prevent age-related diseases.

In cooperative Multi-Agent Reinforcement Learning (MARL), it is a common practice to tune hyperparameters in ideal simulated environments to maximize cooperative performance. However, policies tuned for cooperation often fail to maintain robustness and resilience under real-world uncertainties. Building trustworthy MARL systems requires a deep understanding of robustness, which ensures stability under uncertainties, and resilience, the ability to recover from disruptions--a concept extensively studied in control systems but largely overlooked in MARL. In this paper, we present a large-scale empirical study comprising over 82,620 experiments to evaluate cooperation, robustness, and resilience in MARL across 4 real-world environments, 13 uncertainty types, and 15 hyperparameters. Our key findings are: (1) Under mild uncertainty, optimizing cooperation improves robustness and resilience, but this link weakens as perturbations intensify. Robustness and resilience also varies by algorithm and uncertainty type. (2) Robustness and resilience do not generalize across uncertainty modalities or agent scopes: policies robust to action noise for all agents may fail under observation noise on a single agent. (3) Hyperparameter tuning is critical for trustworthy MARL: surprisingly, standard practices like parameter sharing, GAE, and PopArt can hurt robustness, while early stopping, high critic learning rates, and Leaky ReLU consistently help. By optimizing hyperparameters only, we observe substantial improvement in cooperation, robustness and resilience across all MARL backbones, with the phenomenon also generalizing to robust MARL methods across these backbones. Code and results available at https://github.com/BUAA-TrustworthyMARL/adv_marl_benchmark .