Startups and Big Ag are using Crispr gene editing to create crops that taste better and grow on a hotter planet. But will they find a market? If you wanted to create better blackberries, you could try to breed a variety without the seeds that get stuck in your teeth. Or one without the thorns that make the berries hard to pick. Or you could aim for more environmentally efficient plants that produce more berries per acre with less water and fewer chemicals.

Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the same benchmark can be analyzed under multiple ranking assumptions. We describe the package design, position it relative to existing Julia tools, and report pilot experiments on synthetic rank recovery, stability under limited trials, and runtime scaling.

We also introduce anew on-average stability measure to develop optimistic bounds in a low noise setting.

Representative problems include AUC maximization [14, 25, 42, 63, 66], metric learning [8, 31], ranking [1, 13] and learning with minimum error entropy loss functions [29]. For example, in supervised metric learning we wish to find a distance function between pairs of examples so that examples within the same class are relatively close while examples from different classes are far apartfromeachother.

Recently, there is a growing interest in studying pairwise learning since it includes many important machine learning tasks as specific examples, e.g., metric learning, AUC maximization and ranking. While stochastic gradient descent (SGD) is an efficient method, there is a lacking study on its generalization behavior for pairwise learning. In this paper, we present a systematic study on the generalization analysis of SGD for pairwise learning to understand the balance between generalization and optimization. We develop a novel high-probability generalization bound for uniformly-stable algorithms to incorporate the variance information for better generalization, based on which we establish the first nonsmooth learning algorithm to achieve almost optimal high-probability and dimension-independent generalization bounds in linear time. We consider both convex and nonconvex pairwise learning problems. Our stability analysis for convex problems shows how the interpolation can help generalization. We establish a uniform convergence of gradients, and apply it to derive the first generalization bounds on population gradients for nonconvex problems. Finally, we develop better generalization bounds for gradient-dominated problems.

Large Language Models (LLMs) are widely used as judges to evaluate response quality, providing a scalable alternative to human evaluation. However, most LLM judges operate solely on intrinsic text-based reasoning, limiting their ability to verify complex constraints or perform accurate computation. Motivated by the success of tool-integrated reasoning (TIR) in numerous tasks, we propose TIR-Judge, an end-to-end RL framework for training LLM judges that integrates a code executor for precise evaluation. TIR-Judge is built on three principles: (i) diverse training across verifiable and non-verifiable domains, (ii) flexible judgment formats (pointwise, pairwise, listwise), and (iii) iterative RL that bootstraps directly from the initial model without distillation. On seven public benchmarks, TIR-Judge surpasses strong reasoning-based judges by up to 6.4% (pointwise) and 7.7% (pairwise), and achieves listwise performance comparable to Claude-Opus-4 despite having only 8B parameters. Remarkably, TIR-Judge-Zero - trained entirely without distilled judge trajectories, matches the performance of distilled variants, demonstrating that tool-augmented judges can self-evolve through iterative reinforcement learning.

In this paper, we formalize the active set ordering problem, which involves actively discovering a set of inputs based on their orderings determined by expensive evaluations of a blackbox function.