Low-Complexity Algorithm for Stackelberg Prediction Games with Global Optimality

Stackelberg prediction games (SPGs) model strategic data manipulation in adversarial learning via a leader--follower interaction between a learner and a self-interested data provider, leading to challenging bilevel optimization problems. Focusing on the least-squares setting (SPG-LS), recent work shows that the bilevel program admits an equivalent spherically constrained least-squares (SCLS) reformulation, which avoids costly conic programming and enables scalable algorithms. In this paper, we develop a simple and efficient alternating direction method of multiplier (ADMM) based solver for the SCLS problem. By introducing a consensus splitting that separates the quadratic objective from the spherical constraint, we obtain an augmented Lagrangian formulation with closed-form updates: the primal quadratic step reduces to solving a fixed shifted linear system, the constraint step is a projection onto the unit sphere, and the dual step is a lightweight scaled ascent. The resulting method has low per-iteration complexity and allows pre-factorization of the constant system matrix for substantial speedups. Experiments demonstrate that the proposed ADMM approach achieves competitive solution quality with significantly improved computational efficiency compared with existing global solvers for SCLS, particularly in sparse and high-dimensional regimes.

The Necessity of Setting Temperature in LLM-as-a-Judge

LLM-as-a-Judge has emerged as an effective and low-cost paradigm for evaluating text quality and factual correctness. Prior studies have shown substantial agreement between LLM judges and human experts, even on tasks that are difficult to assess automatically. In practice, researchers commonly employ fixed temperature configurations during the evaluation process-with values of 0.1 and 1.0 being the most prevalent choices-a convention that is largely empirical rather than principled. However, recent researches suggest that LLM performance exhibits non-trivial sensitivity to temperature settings, that lower temperatures do not universally yield optimal outcomes, and that such effects are highly task-dependent. This raises a critical research question: does temperature influence judge performance in LLM centric evaluation? To address this, we systematically investigate the relationship between temperature and judge performance through a series of controlled experiments, and further adopt a causal inference framework within our empirical statistical analysis to rigorously examine the direct causal effect of temperature on judge behavior, offering actionable engineering insights for the design of LLM-centric evaluation pipelines.

Agent Skill Framework: Perspectives on the Potential of Small Language Models in Industrial Environments

Agent Skill framework, now widely and officially supported by major players such as GitHub Copilot, LangChain, and OpenAI, performs especially well with proprietary models by improving context engineering, reducing hallucinations, and boosting task accuracy. Based on these observations, an investigation is conducted to determine whether the Agent Skill paradigm provides similar benefits to small language models (SLMs). This question matters in industrial scenarios where continuous reliance on public APIs is infeasible due to data-security and budget constraints requirements, and where SLMs often show limited generalization in highly customized scenarios. This work introduces a formal mathematical definition of the Agent Skill process, followed by a systematic evaluation of language models of varying sizes across multiple use cases. The evaluation encompasses two open-source tasks and a real-world insurance claims data set. The results show that tiny models struggle with reliable skill selection, while moderately sized SLMs (approximately 12B - 30B) parameters) benefit substantially from the Agent Skill approach. Moreover, code-specialized variants at around 80B parameters achieve performance comparable to closed-source baselines while improving GPU efficiency. Collectively, these findings provide a comprehensive and nuanced characterization of the capabilities and constraints of the framework, while providing actionable insights for the effective deployment of Agent Skills in SLM-centered environments.