The order of training samples plays a crucial role in large language models (LLMs), significantly impacting both their external performance and internal learning dynamics. Traditional methods for investigating this effect generally require retraining the model with various sample orders, which is computationally infeasible for LLMs. In this work, we improve traditional methods by designing a retraining-free framework. By approximating Adam optimizer updates with first- and second-order Taylor expansions and utilizing random projection methods to store intermediate checkpoints, our framework can efficiently estimate model parameters for arbitrary training sample orders. Next, we apply our framework to two downstream research problems: (1) Training curriculum design for LLMs — We base our retraining-free framework to propose a novel curriculum learning strategy that augments curriculum proposals with estimated model performances, enabling more informed sample scheduling. (2) LLMs’ memorization and generalization effect analysis — We use our retraining-free framework to estimate how the positions of training samples influence LLMs’ capacity for memorization and generalization. We conduct extensive experiments to validate the effectiveness of our retraining-free framework in reproducing the true model performances, and further demonstrate its potential in optimizing LLM training curricula and analyzing the memorization and generalization effects of LLMs.

The saturation of high-quality pre-training data has shifted research focus toward evolutionary systems capable of continuously generating novel artifacts, leading to the success of AlphaEvolve. However, the progress of such systems is hindered by the lack of rigorous, quantitative evaluation. To tackle this challenge, we introduce CreativeBench, a benchmark for evaluating machine creativity in code generation, grounded in a classical cognitive framework. Comprising two subsets – CreativeBench-Combo and CreativeBench-Explore – the benchmark targets combinatorial and exploratory creativity through an automated pipeline utilizing reverse engineering and self-play. By leveraging executable code, CreativeBench objectively distinguishes creativity from hallucination via a unified metric defined as the product of quality and novelty. Our analysis of state-of-the-art models reveals distinct behaviors: (1) scaling significantly improves combinatorial creativity but yields diminishing returns for exploration; (2) larger models exhibit “convergence-by-scaling,” becoming more correct but less divergent; and (3) reasoning capabilities primarily benefit constrained exploration rather than combination. Finally, we propose EvoRePE, a plug-and-play inference-time steering strategy that internalizes evolutionary search patterns to consistently enhance machine creativity.

Large Language Models (LLMs) have advanced reasoning ability, yet conventional alignment remains dominated by outcome reward models (ORMs) that judge only final answers. Process Reward Models(PRMs) address this gap by evaluating and guiding reasoning at the step or trajectory level. This survey provides a systematic overview of PRMs through the full loop: how to generate process data, build PRMs, and use PRMs for test-time scaling and reinforcement learning. We summarize applications across math, code, text, multimodal reasoning, robotics, and agents, and review emerging benchmarks. Our goal is to clarify design spaces, reveal open challenges, and guide future research toward fine-grained, robust reasoning alignment.