Using LLMs for Knowledge Component-level Correctness Labeling in Open-ended Coding Problems

Despite strong performance in competitive programming, the role of Large Language Models (LLMs) in supporting human learning in the same setting remains largely unexplored. In this work, we introduce UOJ-Bench, a benchmark designed to evaluate not only the problem-solving ability of LLMs, but also their ability to identify errors in human-written code -- a crucial educational activity traditionally supported by running test cases over online judge systems. UOJ-Bench consists of three distinct tasks: code generation, code hacking, and code repair, all constructed from real-world code submissions on the Universal Online Judge (UOJ) and evaluated through UOJ's native judging infrastructure. Our results show that under one-shot evaluation, even the strongest models fail to identify errors in more than 50% of a set of submissions that have been found to be incorrect by UOJ users. While test-time scaling improves success rates to above 90%, the substantial computational costs incurred from model inference limit its practicality for large-scale deployment. Despite these limitations, we find that the best-performing models under test-time scaling can uncover errors in over 5% of full-score submissions across roughly 30 problems, suggesting that frontier LLMs can already provide complementary signals beyond standard judging systems.

Recent advances in large language models (LLMs) have shown that test-time scaling can substantially improve model performance on complex tasks, particularly in the coding domain. Under this paradigm, models use a larger token budget during inference to generate intermediate reasoning traces before producing a final answer. However, current evaluations primarily rely on competitive programming benchmarks, which may not capture the full range of reasoning abilities. In this work, we perform a systematic study of frontier reasoning models to understand their performance on real-world coding benchmarks. To gain more insights into the performance of such models, we devise a programmatic way to {\em automatically generate} coding tasks of arbitrary difficulty and structure from existing benchmarks. Using this framework, our analysis reveals that the structure of a reasoning trace, not just its contents, is a strong predictor of correctness. Motivated by this, we propose structured thought-trees as means to represent reasoning traces. To illustrate their use, we train a lightweight classifier on features extracted from thought-trees to predict trace correctness, and demonstrate that flagging and retrying structurally anomalous traces based on the extracted features yields consistent gains at lower complexity levels.

Large Language Models (LLMs) are increasingly used for code generation but can produce fluent yet functionally incorrect outputs, which limits trust in their usage for practical software engineering workflows. This thesis investigates whether Introspective Uncertainty Estimation (IUE), based on internal hidden-state representations of LLMs, can reliably indicate correctness at the response and line levels for code generation tasks. The objective is to determine the extent to which hidden states encode information about functional code correctness and how this can be leveraged for practical risk assessment and fault localization. Methodologically, this thesis combines response-level evaluation on LiveCodeBench (LCB) and BigCodeBench (BCB) with an augmentation pipeline that derives token- and line-level labels from incorrect programs. In this setup, it compares static and dynamic response-level features, evaluates generalization across tasks, programming domains, and token positions, and studies line-level fault localization. The results show that hidden states contain a strong response-level correctness signal. Static single-token probes perform best, while more elaborate dynamic strategies yield no consistent gains. While generalization across tasks, domains, and token positions is feasible, setting-dependent degradation largely remains for real-world software projects. At a fine granularity, line-level prediction is substantially harder than response-level estimation. However, in a conditional localization setup with known-incorrect programs, Top-K point-of-failure ranking remains effective. Overall, the findings suggest that hidden states are a robust and informative resource for estimating functional code correctness, supporting a two-stage workflow that combines response-level risk screening with targeted line-level prioritization.