Joshua Ong Jun Leang
Publications
Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Models
While plan-and-infill decoding in Masked Diffusion Models (MDMs) shows promise for mathematical and code reasoning, performance remains highly sensitive to slot infilling order, often yielding substantial output variance. We introduce McDiffuSE, a framework that formulates slot selection as decision making and optimises infilling orders through Monte Carlo Tree Search (MCTS). McDiffuSE uses look-ahead simulations to evaluate partial completions before commitment, systematically exploring the combinatorial space of generation orders. Experiments show an average improvement of 3.2% over autoregressive baselines and 8.0% over baseline plan-and-infill, with notable gains of 19.5% on MBPP and 4.9% on MATH500. Our analysis reveals that while McDiffuSE predominantly follows sequential ordering, incorporating non-sequential generation is essential for maximising performance. We observe that larger exploration constants, rather than increased simulations, are necessary to overcome model confidence biases and discover effective orderings. These findings establish MCTS-based planning as an effective approach for enhancing generation quality in MDMs.
Neural Theorem Proving for Verification Conditions: A Real-World Benchmark
Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem Provers (ATPs) cannot prove, leading to a critical need for extensive manual proofs that burden practical application. While Neural Theorem Proving (NTP) has achieved significant success in mathematical competitions, demonstrating the potential of machine learning approaches to formal reasoning, its application to program verification--particularly VC proving--remains largely unexplored. Despite existing work on annotation synthesis and verification-related theorem proving, no benchmark has specifically targeted this fundamental bottleneck: automated VC proving. This work introduces Neural Theorem Proving for Verification Conditions (NTP4VC), presenting the first real-world multi-language benchmark for this task. From real-world projects such as Linux and Contiki-OS kernel, our benchmark leverages industrial pipelines (Why3 and Frama-C) to generate semantically equivalent test cases across formal languages of Isabelle, Lean, and Rocq. We evaluate large language models (LLMs), both general-purpose and those fine-tuned for theorem proving, on NTP4VC. Results indicate that although LLMs show promise in VC proving, significant challenges remain for program verification, highlighting a large gap and opportunity for future research.