Automatically solving optimization problems from natural language descriptions with both efficiency and reliability is highly desirable but remains challenging. Language model hallucinations and the limited availability of labeled datasets often result in misaligned formulations, code errors, and feasibility failures We propose UMCTS, an Uncertainty-aware Monte Carlo Tree Search framework that combines the language understanding capability of large language models with the reliability of well-established solvers. UMCTS structures the solution process into four stages: global instruction, assumptions, mathematical formulation, and solver code generation. It employs Monte Carlo Tree Search with semantic-equivalence pruning, prior-guided exploration, and solver-based feasibility checks. An LLM judge provides numerical reward signals, qualitative error information, and uncertainty estimates. These signals are backpropagated to guide the search and flag unreliable outputs. Across six public benchmarks, UMCTS achieves state-of-the-art solution accuracy, improves efficiency by reducing token usage.

Sequential labeling is a task predicting labels for each token in a sequence, such as Named Entity Recognition (NER). NER tasks aim to extract entities and predict their labels given a text, which is important in information extraction. Although previous works have shown great progress in improving NER performance, uncertainty estimation on NER (UE-NER) is still underexplored but essential. This work focuses on UE-NER, which aims to estimate uncertainty scores for the NER predictions. Previous uncertainty estimation models often overlook two unique characteristics of NER: the connection between entities (i.e., one entity embedding is learned based on the other ones) and wrong span cases in the entity extraction subtask. Therefore, we propose a Sequential Labeling Posterior Network (SLPN) to estimate uncertainty scores for the extracted entities, considering uncertainty transmitted from other tokens. Moreover, we have defined an evaluation strategy to address the specificity of wrong-span cases. Our SLPN has achieved significant improvements on three datasets, such as a 5.54-point improvement in AUPR on the MIT-Restaurant dataset. Our code is available at https://github.com/he159ok/UncSeqLabeling_SLPN.

Text summarization, a key natural language generation (NLG) task, is vital in various domains. However, the high cost of inaccurate summaries in risk-critical applications, particularly those involving human-in-the-loop decision-making, raises concerns about the reliability of uncertainty estimation on text summarization (UE-TS) evaluation methods. This concern stems from the dependency of uncertainty model metrics on diverse and potentially conflicting NLG metrics. To address this issue, we introduce a comprehensive UE-TS benchmark incorporating 31 NLG metrics across four dimensions. The benchmark evaluates the uncertainty estimation capabilities of two large language models and one pre-trained language model on three datasets, with human-annotation analysis incorporated where applicable. We also assess the performance of 14 common uncertainty estimation methods within this benchmark. Our findings emphasize the importance of considering multiple uncorrelated NLG metrics and diverse uncertainty estimation methods to ensure reliable and efficient evaluation of UE-TS techniques. Our code and data are available: https://github.com/he159ok/Benchmark-of-Uncertainty-Estimation-Methods-in-Text-Summarization.