Thang Luong, Dawsen Hwang, Hoang H Nguyen, Golnaz Ghiasi, Yuri Chervonyi, Insuk Seo, Junsu Kim, Garrett Bingham, Jonathan Lee, Swaroop Mishra, Alex Zhai, Huiyi Hu, Henryk Michalewski, Jimin Kim, Jeonghyun Ahn, Junhwi Bae, Xingyou Song, Trieu Hoang Trinh, Quoc V Le, Junehyuk Jung. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Nature, 625 (7995):476, 2024, which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with support for non-constructive problems, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that enables effective communication between search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry to 84% on all geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved the silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Finally, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems from natural language input. Code: https://github.com/google-deepmind/alphageometry2.

Long Phan, Tai Dang, Hieu Tran, Trieu H. Trinh, Vy Phan, Lam D. Chau, Minh-Thang Luong. Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics. 2023.

Despite recent advances in training recurrent neural networks (RNNs), capturing long-term dependencies in sequences remains a fundamental challenge. Most approaches use backpropagation through time (BPTT), which is difficult to scale to very long sequences. This paper proposes a simple method that improves the ability to capture long term dependencies in RNNs by adding an unsupervised auxiliary loss to the original objective. This auxiliary loss forces RNNs to either reconstruct previous events or predict next events in a sequence, making truncated backpropagation feasible for long sequences and also improving full BPTT. We evaluate our method on a variety of settings, including pixel-by-pixel image classification with sequence lengths up to 16000, and a real document classification benchmark. Our results highlight good performance and resource efficiency of this approach over competitive baselines, including other recurrent models and a comparable sized Transformer. Further analyses reveal beneficial effects of the auxiliary loss on optimization and regularization, as well as extreme cases where there is little to no backpropagation.