In knowledge-intensive creative tasks, Large Language Models (LLMs) often generate outputs that extend beyond established knowledge, making direct verification against current evidence impractical. Unlike factual hallucinations checked against ground truth, such outputs arise naturally in creative generation, where extending beyond current knowledge is often the goal. Yet prior work debates whether hallucination should be suppressed or embraced without empirically analyzing this unverifiable subclass. On the ideation evaluation side, existing work focuses on individual outputs without characterizing the unverifiable space as a whole. To address this gap, we propose a novelty-verifiability characterization that distinguishes Creative Synthesis (Region A) from Groundless Fabrication (Region B), and study it through a conceptual creation task where LLMs synthesize novel scientific concepts. Through 32,400 generations across three technical domains and 1,080 human judgments, we find that Region A is non-negligible (4.7%) and robust, persisting across generation strategies, models, domains, and embedding choices. A retrospective recovery experiment further shows that LLMs can approximate post-cutoff scientific concepts in controlled combinatorial settings. Our findings suggest that the unverifiable space is not uniformly noise but exhibits empirically distinguishable internal structure, providing an empirical basis for more selective hallucination governance.[<https://github.com/YuLab1/llm-concept-creation>]

Large language models with search capabilities frequently exhibit miscalibrated confidence, producing incorrect answers with high certainty. We present Deliberative Searcher, a reasoning-primary framework that integrates search operations into chain-of-thought generation while maintaining explicit confidence calibration. Our method employs constrained reinforcement learning with adaptive Lagrangian multipliers to jointly optimize correctness and reliability. Experiments across five benchmarks demonstrate substantial improvements: our 7B model reduces average false-certain rates from 54% in baselines to 2%, while our 72B variant achieves competitive accuracy with closed-source models and reduces false-certain rates to 9%. The well-calibrated confidence scores also enable more efficient test-time compute: instead of standard majority voting, we use confidence-weighted aggregation and match the performance of 16-sample majority voting with only 4 samples, a 4× reduction in inference compute. These results establish calibrated confidence as a foundation for both trustworthy outputs and adaptive test-time compute, demonstrating the value of the proposed constrained RL framework in search-augmented language models.

Large language models (LLMs) garner significant attention for their unprecedented performance, leading to an increasing number of researches evaluating LLMs. However, these evaluation benchmarks are limited to assessing the instruction-following capabilities, overlooking the fundamental abilities that emerge during the pre-training stage. Previous subjective evaluation methods mainly reply on scoring by API models. However, in the absence of references, large models have shown limited ability to discern subtle differences. To bridge the gap, we propose F-Eval, a bilingual evaluation benchmark to evaluate the fundamental abilities, including expression, commonsense and logic. The tasks in F-Eval include multi-choice objective tasks, open-ended objective tasks, reference-based subjective tasks and reference-free subjective tasks. For reference-free subjective tasks, we devise new evaluation methods, serving as alternatives to scoring by API models. We conduct evaluations on 13 advanced LLMs. Results show that our evaluation methods show higher correlation coefficients and larger distinction than other evaluators. Additionally, we discuss the influence of different model sizes, dimensions, and normalization methods. We anticipate that F-Eval will facilitate the study of LLMs’ fundamental abilities.