Liangliang Shi

Author directory

2026

Formal theorem proving provides executable verification signals from proof assistants, making it a key domain for improving the reliable reasoning ability of large language models through reinforcement learning (RL). However, RL-based prover training is increasingly bottlenecked by the scarcity of high-quality hard tasks: many existing Lean instances are either already solvable by current provers or too uninformative to drive further improvement. We propose ProofFrontier, a proof-structure-guided method for generating statement-preserving boundary-hard training tasks from verified Lean proofs. Instead of synthesizing open-ended problems that may be ill-posed or unverifiable, ProofFrontier starts from existing theorems with Lean-certified proofs, preserving task completeness and formal verifiability. It selectively withholds proof-structural guidance around important local nodes, encouraging the prover to rediscover nontrivial intermediate reasoning while keeping the original theorem statement unchanged. We further introduce capability-aware filtering to retain tasks that are solvable in principle but not easily solved by the base prover, yielding hard yet rewardable RL data. Training with GRPO on ProofFrontier-generated tasks consistently improves DeepSeek-Prover-V2 and Goedel-Prover-V2 on miniF2F, ProofNet, and PutnamBench. Notably, these gains are achieved using only hundreds of synthesized tasks, showing that complete boundary-hard tasks can be more data-efficient than simply scaling weak or already-solved proof data for theorem-proving RL.

2018

This paper describes our speech translation system for the IWSLT 2018 Speech Translation of lectures and TED talks from English to German task. The pipeline approach is employed in our work, which mainly includes the Automatic Speech Recognition (ASR) system, a post-processing module, and the Neural Machine Translation (NMT) system. Our ASR system is an ensemble system of Deep-CNN, BLSTM, TDNN, N-gram Language model with lattice rescoring. We report average results on tst2013, tst2014, tst2015. Our best combination system has an average WER of 6.73. The machine translation system is based on Google’s Transformer architecture. We achieved an improvement of 3.6 BLEU over baseline system by applying several techniques, such as cleaning parallel corpus, fine tuning of single model, ensemble models and re-scoring with additional features. Our final average result on speech translation is 31.02 BLEU.