Jiarui Yao, Shweta Parihar, Nghia Tuan Bui, Guergana K Savova, Lijing Wang
Language model assistants sometimes change a correct answer when the user suggests a wrong one. The behavior, called sycophancy, is usually attributed to preference-based post-training, yet early measurements found it in pretrained models. We ask where it comes from by measuring it at every available stage of training: 13 open checkpoints from 5 lineages, from base model through supervised fine-tuning and preference optimization to release. We separate how far an injected claim moves a model's answer from how firmly the answer was held, and vary who makes the claim, how reliable they are said to be, and how strongly they make it. Two sycophancy behaviors with different origins emerge, and both replicate across datasets. Deference to a claim in the prompt is already present in every base model, which ranks sources in the same order as its post-trained descendants. Capitulation in conversation, dropping a stated answer when the user objects, is largely absent from base models and present in every post-trained checkpoint. When the objection names an alternative, most post-trained models give up firmly held answers as often as loosely held ones. We discuss the implications of these measurements for evaluating sycophancy and approaches for addressing each behavior.
Large language models (LLMs) have shown increasing promise in research-level problem solving, yet a comprehensive collection of such problems is still missing, and evaluating them on research-level problems remains challenging. We introduce OpenFrontiers, a cross-disciplinary resource that combines a structured corpus of open research problems with a retrospective benchmark of recently resolved problems in mathematics. The corpus records problem statements, context, progress, and other information for 12,151 problems. The benchmark contains 200 problems, 110 resolved in 2026 and 90 still open, each with a Lean~4 statement checked by automated probes and two independent reviews; a subset HQ-50 further filters based on quality score, etc. Our evaluation protocol grades formal proofs with two independent checkers in an isolated sandbox under closed-book, frozen-retrieval, and live-web conditions. Evaluating seven LLM agents on the HQ-50 subset under a standardized budget, we find that closed-book rediscovery is rare, at most 7 of 40 resolved problems, whereas live-web success mostly reflects retrieval of published solutions. By linking a broad research-problem corpus to a formally graded evaluation subset with documented solutions, OpenFrontiers provides a foundation for measuring research-level rediscovery and studying progress toward solving currently open scientific problems. The dataset and benchmark could be found in https://huggingface.co/collections/FlippyDora/openfrontiers.