DAJ: Data-Reweighted LLM Judge for Test-Time Scaling in Code Generation

Test-time scaling for code generation commonly relies on Best-of-N selection, in which multiple candidate solutions are sampled from a base model, and the best one is selected by an LLM judge. However, training reliable LLM judges is challenging due to severe distribution shifts, including imbalances between easy and hard problems, mismatches between training tasks and evaluation benchmarks, and trajectory mismatch arising from training data generated by cheaper models whose behavior differs from that of inference-time models. We propose DAJ, a reasoning-based LLM judge trained with verifiable rewards under a bi-level data-reweighted learning framework. The proposed framework learns data-importance weights (either domain-level or instance-level) to optimize generalization performance on a held-out meta set aligned with target benchmarks. To the best of our knowledge, this is the first application of data reweighting to LLM-as-a-Judge training for test-time scaling. Our approach automatically emphasizes hard problems, in-distribution samples, and trajectory-aligned data, without relying on hand-crafted heuristics. Empirically, DAJ achieves state-of-the-art performance on LiveCodeBench and BigCodeBench, outperforming strong test-time scaling baselines as well as leading proprietary models.

Models Under SCOPE: Scalable and Controllable Routing via Pre-hoc Reasoning

Model routing chooses which language model to use for each query. By sending easy queries to cheaper models and hard queries to stronger ones, it can significantly reduce inference cost while maintaining high accuracy. However, most existing routers treat this as a fixed choice among a small set of models, which makes them hard to adapt to new models or changing budget constraints. In this paper, we propose SCOPE (Scalable and Controllable Outcome Performance Estimator), a routing framework that goes beyond model selection by predicting their cost and performance. Trained with reinforcement learning, SCOPE makes reasoning-based predictions by retrieving how models behave on similar problems, rather than relying on fixed model names, enabling it to work with new, unseen models. Moreover, by explicitly predicting how accurate and how expensive a model will be, it turns routing into a dynamic decision problem, allowing users to easily control the trade-off between accuracy and cost. Experiments show that SCOPE is more than just a cost-saving tool. It flexibly adapts to user needs: it can boost accuracy by up to 25.7% when performance is the priority, or cut costs by up to 95.1% when efficiency matters most.

FunPRM: Function-as-Step Process Reward Model with Meta Reward Correction for Code Generation

Code generation is a core application of large language models (LLMs), yet LLMs still frequently fail on complex programming tasks. Given its success in mathematical reasoning, test-time scaling approaches such as Process Reward Model (PRM)-based Best-of-N selection offer a promising way to improve performance. However, existing PRMs remain ineffective for code generation due to the lack of meaningful step decomposition in code and the noise of Monte Carlo-estimated partial-solution correctness scores (rewards). To address these challenges, we propose FunPRM. FunPRM prompts LLMs to encourage modular code generation organized into functions, with functions treated as PRM reasoning steps. Furthermore, FunPRM introduces a novel meta-learning-based reward correction mechanism that leverages clean final-solution rewards obtained via a unit-test-based evaluation system to purify noisy partial-solution rewards. Experiments on LiveCodeBench and BigCodeBench demonstrate that FunPRM consistently outperforms existing test-time scaling methods across five base LLMs, notably achieving state-of-the-art performance on LiveCodeBench when combined with O4-mini. Furthermore, FunPRM produces code that is more readable and reusable for developers.

DreamPRM-Code: Function-as-Step Process Reward Model with Label Correction for LLM Coding

Process Reward Models (PRMs) have become essential for improving Large Language Models (LLMs) via test-time scaling, yet their effectiveness in coding remains limited due to the lack of meaningful step decompositions in code and the noise of Monte-Carlo-generated partial labels. We propose DreamPRM-Code, a coding-focused PRM that treats functions as reasoning steps using a Chain-of-Function prompting strategy to induce modular code generation, enabling PRM training and application analogous to mathematical reasoning tasks. To address label noise, DreamPRM-Code introduces a meta-learning-based correction mechanism that leverages clean final-solution unit-test labels and performs bi-level optimization to refine intermediate labels. Applying on test-time scaling, DreamPRM-Code achieved state-of-the-art performance on LiveCodeBench with 80.9 pass@1 rate, surpassing OpenAI o4-mini.

Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems

Predictor feedback designs are critical for delay-compensating controllers in nonlinear systems. However, these designs are limited in practical applications as predictors cannot be directly implemented, but require numerical approximation schemes. These numerical schemes, typically combining finite difference and successive approximations, become computationally prohibitive when the dynamics of the system are expensive to compute. To alleviate this issue, we propose approximating the predictor mapping via a neural operator. In particular, we introduce a new perspective on predictor designs by recasting the predictor formulation as an operator learning problem. We then prove the existence of an arbitrarily accurate neural operator approximation of the predictor operator. Under the approximated-predictor, we achieve semiglobal practical stability of the closed-loop nonlinear system. The estimate is semiglobal in a unique sense - namely, one can increase the set of initial states as large as desired but this will naturally increase the difficulty of training a neural operator approximation which appears practically in the stability estimate. Furthermore, we emphasize that our result holds not just for neural operators, but any black-box predictor satisfying a universal approximation error bound. From a computational perspective, the advantage of the neural operator approach is clear as it requires training once, offline and then is deployed with very little computational cost in the feedback controller. We conduct experiments controlling a 5-link robotic manipulator with different state-of-the-art neural operator architectures demonstrating speedups on the magnitude of $10^2$ compared to traditional predictor approximation schemes.

BiDoRA: Bi-level Optimization-Based Weight-Decomposed Low-Rank Adaptation

Parameter-efficient fine-tuning (PEFT) of large language models (LLMs) has gained considerable attention as a flexible and efficient way of adapting LLMs to downstream tasks. Among these methods, weighted decomposed low-rank adaptation (DoRA) has emerged as a promising approach. DoRA bridges the gap between low-rank adaptation (LoRA) and full fine-tuning (FT) by decomposing the weight matrices into magnitude and direction components, thereby maintaining learning behavior similar to FT. Although DoRA shows encouraging performance, it introduces additional parameters compared to LoRA, which potentially increases the risk of overfitting. Moreover, optimizing magnitude and direction simultaneously leads to a coupled gradient updating pattern for both components, limiting its learning capacity. To overcome these limitations, we propose BiDoRA, a bi-level optimization-based PEFT method. In BiDoRA, the direction and magnitude components are optimized on two distinct datasets at different optimization levels, mitigating the risk of overfitting. Additionally, the asynchronous optimization of the two components promotes their decoupling, allowing for more flexible gradient updates suitable for various downstream tasks. Evaluation of BiDoRA on fourteen datasets spanning natural language understanding, natural language generation, and token classification reveals that it significantly outperforms DoRA and other PEFT methods. The superior performance of BiDoRA underscores its effectiveness. The code for BiDoRA is available at https://anonymous.4open.science/r/BiDoRA-5D31.