High-quality prompts are crucial for eliciting outstanding performance from large language models (LLMs) on complex tasks. Existing research has explored model-driven strategies for prompt optimization. However, these methods often suffer from high computational overhead or require strong optimization capabilities from the model itself, which limits their broad applicability.To address these challenges, we propose ORPP (Optimized Role-Playing Prompt),a framework that enhances model performance by optimizing and generating role-playing prompts. The core idea of ORPP is to confine the prompt search space to role-playing scenarios, thereby fully activating the model's intrinsic capabilities through carefully crafted, high-quality role-playing prompts. Specifically, ORPP first performs iterative optimization on a small subset of training samples to generate high-quality role-playing prompts. Then, leveraging the model's few-shot learning capability, it transfers the optimization experience to efficiently generate suitable prompts for the remaining samples.Our experimental results show that ORPP not only matches but in most cases surpasses existing mainstream prompt optimization methods in terms of performance. Notably, ORPP demonstrates superior "plug-and-play" capability. In most cases, it can be integrated with various other prompt methods and further enhance their effectiveness.

Optimization remains a fundamental pillar of machine learning, yet existing methods often struggle to maintain stability and adaptability in dynamic, non linear systems, especially under uncertainty. We introduce AERO (Adversarial Energy-based Redirection Optimization), a novel framework inspired by the redirection principle in Judo, where external disturbances are leveraged rather than resisted. AERO reimagines optimization as a redirection process guided by 15 interrelated axioms encompassing adversarial correction, energy conservation, and disturbance-aware learning. By projecting gradients, integrating uncertainty driven dynamics, and managing learning energy, AERO offers a principled approach to stable and robust model updates. Applied to probabilistic solar energy forecasting, AERO demonstrates substantial gains in predictive accuracy, reliability, and adaptability, especially in noisy and uncertain environments. Our findings highlight AERO as a compelling new direction in the theoretical and practical landscape of optimization.

Diffusion models achieve strong generative performance but often rely on large datasets that may include sensitive content. This challenge is compounded by the models' tendency to memorize training data, raising privacy concerns. SFBD (Lu et al., 2025) addresses this by training on corrupted data and using limited clean samples to capture local structure and improve convergence. However, its iterative denoising and fine-tuning loop requires manual coordination, making it burdensome to implement. We reinterpret SFBD as an alternating projection algorithm and introduce a continuous variant, SFBD flow, that removes the need for alternating steps. We further show its connection to consistency constraint-based methods, and demonstrate that its practical instantiation, Online SFBD, consistently outperforms strong baselines across benchmarks.

Model extraction attacks aim to replicate the functionality of a black-box model through query access, threatening the intellectual property (IP) of machine-learning-as-a-service (MLaaS) providers. Defending against such attacks is challenging, as it must balance efficiency, robustness, and utility preservation in the real-world scenario. Despite the recent advances, most existing defenses presume that attacker queries have out-of-distribution (OOD) samples, enabling them to detect and disrupt suspicious inputs. However, this assumption is increasingly unreliable, as modern models are trained on diverse datasets and attackers often operate under limited query budgets. As a result, the effectiveness of these defenses is significantly compromised in realistic deployment scenarios. To address this gap, we propose MISLEADER (enseMbles of dIStiLled modEls Against moDel ExtRaction), a novel defense strategy that does not rely on OOD assumptions. MISLEADER formulates model protection as a bilevel optimization problem that simultaneously preserves predictive fidelity on benign inputs and reduces extractability by potential clone models. Our framework combines data augmentation to simulate attacker queries with an ensemble of heterogeneous distilled models to improve robustness and diversity. We further provide a tractable approximation algorithm and derive theoretical error bounds to characterize defense effectiveness. Extensive experiments across various settings validate the utility-preserving and extraction-resistant properties of our proposed defense strategy. Our code is available at https://github.com/LabRAI/MISLEADER.

The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical phenomena are often neglected making the reinterpretation of the learned models in a physically meaningful sense very challenging. In this work, we present three data-driven modeling approaches for the construction of dynamical systems with second-order differential structure directly from frequency domain data. Based on the second-order structured barycentric form, we extend the well-known Adaptive Antoulas-Anderson algorithm to the case of second-order systems. Depending on the available computational resources, we propose variations of the proposed method that prioritize either higher computation speed or greater modeling accuracy, and we present a theoretical analysis for the expected accuracy and performance of the proposed methods. Three numerical examples demonstrate the effectiveness of our new structured approaches in comparison to classical unstructured data-driven modeling.

Decomposing weight matrices into quantization and low-rank components ($\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$) is a widely used technique for compressing large language models (LLMs). Existing joint optimization methods iteratively alternate between quantization and low-rank approximation. However, these methods tend to prioritize one component at the expense of the other, resulting in suboptimal decompositions that fail to leverage each component's unique strengths. In this work, we introduce Outlier-Driven Low-Rank Initialization (ODLRI), which assigns low-rank components the specific role of capturing activation-sensitive weights. This structured decomposition mitigates outliers' negative impact on quantization, enabling more effective balance between quantization and low-rank approximation. Experiments on Llama2 (7B, 13B, 70B), Llama3-8B, and Mistral-7B demonstrate that incorporating ODLRI into the joint optimization framework consistently reduces activation-aware error, minimizes quantization scale, and improves perplexity and zero-shot accuracy in low-bit settings.

The field of health informatics has been profoundly influenced by the development of random forest models, which have led to significant advances in the interpretability of feature interactions. These models are characterized by their robustness to overfitting and parallelization, making them particularly useful in this domain. However, the increasing number of features and estimators in random forests can prevent domain experts from accurately interpreting global feature interactions, thereby compromising trust and regulatory compliance. A method called the surrogate interpretability graph has been developed to address this issue. It uses graphs and mixed-integer linear programming to analyze and visualize feature interactions. This improves their interpretability by visualizing the feature usage per decision-feature-interaction table and the most dominant hierarchical decision feature interactions for predictions. The implementation of a surrogate interpretable graph enhances global interpretability, which is critical for such a high-stakes domain.

Mixed-Integer Linear Programming (MILP) is fundamental to solving complex decision-making problems. The proliferation of MILP instance generation methods, driven by machine learning's demand for diverse optimization datasets and the limitations of static benchmarks, has significantly outpaced standardized evaluation techniques. Consequently, assessing the fidelity and utility of synthetic MILP instances remains a critical, multifaceted challenge. This paper introduces a comprehensive benchmark framework designed for the systematic and objective evaluation of MILP instance generation methods. Our framework provides a unified and extensible methodology, assessing instance quality across crucial dimensions: mathematical validity, structural similarity, computational hardness, and utility in downstream machine learning tasks. A key innovation is its in-depth analysis of solver-internal features -- particularly by comparing distributions of key solver outputs including root node gap, heuristic success rates, and cut plane usage -- leveraging the solver's dynamic solution behavior as an `expert assessment' to reveal nuanced computational resemblances. By offering a structured approach with clearly defined solver-independent and solver-dependent metrics, our benchmark aims to facilitate robust comparisons among diverse generation techniques, spur the development of higher-quality instance generators, and ultimately enhance the reliability of research reliant on synthetic MILP data. The framework's effectiveness in systematically comparing the fidelity of instance sets is demonstrated using contemporary generative models.

Large Language Models (LLMs) generate functionally correct solutions but often fall short in code efficiency, a critical bottleneck for real-world deployment. In this paper, we introduce a novel test-time iterative optimization framework to address this, employing a closed-loop system where LLMs iteratively refine code based on empirical performance feedback from an execution sandbox. We explore three training strategies: Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and Group Relative Policy Optimization (GRPO). Experiments on our Venus dataset and the APPS benchmark show that SFT and DPO rapidly saturate in efficiency gains. In contrast, GRPO, using reinforcement learning (RL) with execution feedback, continuously optimizes code performance, significantly boosting both pass@1 (from 47% to 62%) and the likelihood of outperforming human submissions in efficiency (from 31% to 45%). Our work demonstrates effective test-time code efficiency improvement and critically reveals the power of RL in teaching LLMs to truly self-improve code efficiency.

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of ($L_0$,$L_1$)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal $O(n^{-1/4})$ convergence rate by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning and demonstrate their properties on image classification and language modeling.