Functional constrained optimization (FCO) has emerged as a powerful tool for solving various machine learning problems. However, with the rapid increase in applications of neural networks in recent years, it has become apparent that both the objective and constraints often involve nonconvex functions, which poses significant challenges in obtaining high-quality solutions. In this work, we focus on a class of nonconvex FCO problems with nonconvex constraints, where the two optimization variables are nonlinearly coupled in the inequality constraint. Leveraging the primal-dual optimization framework, we propose a smoothed first-order Lagrangian method (SLM) for solving this class of problems. We establish the theoretical convergence guarantees of SLM to the Karush-Kuhn-Tucker (KKT) solutions through quantifying dual error bounds. By establishing connections between this structured FCO and equilibrium-constrained nonconvex problems (also known as bilevel optimization), we apply the proposed SLM to tackle bilevel optimization oriented problems where the lower-level problem is nonconvex. Numerical results obtained from both toy examples and hyper-data cleaning problems demonstrate the superiority of SLM compared to benchmark methods.

Sentence scoring aims at measuring the likelihood score of a sentence and is widely usedinnatural language processing scenarios, likereranking, which isto select the best sentence from multiple candidates.

Commonly used classification algorithms in machine learning, such as support vector machines, minimize a convex surrogate loss on training examples. In practice, these algorithms are surprisingly robusttoerrors inthe training data.

What are small language models and how do they differ from large ones? Microsoft recently released its latest small language model that can operate directly on the user's computer. If you haven't followed the AI industry closely, you might be asking: what exactly a small language model (SLM)? As AI becomes increasingly central to how we work, learn and solve problems, understanding the different types of AI models has never been more important. Large language models (LLMs) such as ChatGPT, Claude, Gemini and others are in widespread use.

Functional constrained optimization (FCO) has emerged as a powerful tool for solving various machine learning problems. However, with the rapid increase in applications of neural networks in recent years, it has become apparent that both the objective and constraints often involve nonconvex functions, which poses significant challenges in obtaining high-quality solutions. In this work, we focus on a class of nonconvex FCO problems with nonconvex constraints, where the two optimization variables are nonlinearly coupled in the inequality constraint. Leveraging the primal-dual optimization framework, we propose a smoothed first-order Lagrangian method (SLM) for solving this class of problems. We establish the theoretical convergence guarantees of SLM to the Karush-Kuhn-Tucker (KKT) solutions through quantifying dual error bounds. By establishing connections between this structured FCO and equilibrium-constrained nonconvex problems (also known as bilevel optimization), we apply the proposed SLM to tackle bilevel optimization oriented problems where the lower-level problem is nonconvex. Numerical results obtained from both toy examples and hyper-data cleaning problems demonstrate the superiority of SLM compared to benchmark methods.

New York City reports over one hundred thousand motor vehicle collisions each year, creating substantial injury and public health burden. We present RaX-Crash, a resource efficient and explainable small model pipeline for structured injury severity prediction on the official NYC Motor Vehicle Collisions dataset. RaX-Crash integrates three linked tables with tens of millions of records, builds a unified feature schema in partitioned storage, and trains compact tree based ensembles (Random Forest and XGBoost) on engineered tabular features, which are compared against locally deployed small language models (SLMs) prompted with textual summaries. On a temporally held out test set, XGBoost and Random Forest achieve accuracies of 0.7828 and 0.7794, clearly outperforming SLMs (0.594 and 0.496); class imbalance analysis shows that simple class weighting improves fatal recall with modest accuracy trade offs, and SHAP attribution highlights human vulnerability factors, timing, and location as dominant drivers of predicted severity. Overall, RaX-Crash indicates that interpretable small model ensembles remain strong baselines for city scale injury analytics, while hybrid pipelines that pair tabular predictors with SLM generated narratives improve communication without sacrificing scalability.

Analysts in Security Operations Centers routinely query massive telemetry streams using Kusto Query Language (KQL). Writing correct KQL requires specialized expertise, and this dependency creates a bottleneck as security teams scale. This paper investigates whether Small Language Models (SLMs) can enable accurate, cost-effective natural-language-to-KQL translation for enterprise security. We propose a three-knob framework targeting prompting, fine-tuning, and architecture design. First, we adapt existing NL2KQL framework for SLMs with lightweight retrieval and introduce error-aware prompting that addresses common parser failures without increasing token count. Second, we apply LoRA fine-tuning with rationale distillation, augmenting each NLQ-KQL pair with a brief chain-of-thought explanation to transfer reasoning from a teacher model while keeping the SLM compact. Third, we propose a two-stage architecture that uses an SLM for candidate generation and a low-cost LLM judge for schema-aware refinement and selection. We evaluate nine models (five SLMs and four LLMs) across syntax correctness, semantic accuracy, table selection, and filter precision, alongside latency and token cost. On Microsoft's NL2KQL Defender Evaluation dataset, our two-stage approach achieves 0.987 syntax and 0.906 semantic accuracy. We further demonstrate generalizability on Microsoft Sentinel data, reaching 0.964 syntax and 0.831 semantic accuracy. These results come at up to 10x lower token cost than GPT-5, establishing SLMs as a practical, scalable foundation for natural-language querying in security operations.