Despite the striking success of general protein folding models such as AlphaFold2 (AF2), the accurate computational modeling of antibody-antigen complexes remains a challenging task. In this paper, we first analyze AF2’s primary loss function, known as the Frame Aligned Point Error (FAPE), and raise a previously overlooked issue that FAPE tends to face gradient vanishing problem on high-rotational-error targets. To address this fundamental limitation, we propose a novel geodesic loss called Frame Aligned Frame Error (FAFE, denoted as F2E to distinguish from FAPE), which enables the model to better optimize both the rotational and translational errors between two frames. We then prove that F2E can be reformulated as a group-aware geodesic loss, which translates the optimization of the residue-to-residue error to optimizing group-to-group geodesic frame distance. By fine-tuning AF2 with our proposed new loss function, we attain a correct rate of 52.3% (DockQ $>$ 0.23) on an evaluation set and 43.8% correct rate on a subset with low homology, with improvement over AF2 by 182% and 100% respectively.

Predicting the effects of protein mutations is crucial for analyzing protein functions and understanding genetic diseases. However, existing models struggle to effectively extract mutation-related local structure motifs from protein databases, which hinders their predictive accuracy and robustness. To tackle this problem, we design a novel retrieval-augmented framework for incorporating similar structure information in known protein structures. We create a vector database consisting of local structure motif embeddings from a pre-trained protein structure encoder, which allows for efficient retrieval of similar local structure motifs during mutation effect prediction. Our findings demonstrate that leveraging this method results in the SOTA performance across multiple protein mutation prediction datasets, and offers a scalable solution for studying mutation effects.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learning complex reasoning, we propose *Difficulty-Aware Rejection Tuning* (`DART`), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing `DART`, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called `DART-Math`. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, `DART-Math` outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving. Our datasets, models and code are publicly available at https://github.com/hkust-nlp/dart-math.

Protein structure prediction helps to understand gene translation and protein function, which is of growing interest and importance in structural biology. The AlphaFold model, which used transformer architecture to achieve atomic-level accuracy in protein structure prediction, was a significant breakthrough. However, training and inference of AlphaFold model are challenging due to its high computation and memory cost. In this work, we present FastFold, an efficient implementation of AlphaFold for both training and inference. We propose Dynamic Axial Parallelism (DAP) as a novel model parallelism method. Additionally, we have implemented a series of low-level optimizations aimed at reducing communication, computation, and memory costs. These optimizations include Duality Async Operations, highly optimized kernels, and AutoChunk (an automated search algorithm finds the best chunk strategy to reduce memory peaks). Experimental results show that FastFold can efficiently scale to more GPUs using DAP and reduces overall training time from 11 days to 67 hours and achieves 7.5 ~ 9.5× speedup for long-sequence inference. Furthermore, AutoChunk can reduce memory cost by over 80% during inference by automatically partitioning the intermediate tensors during the computation.

Ruidong Wu, Yuan Yao, Xu Han, Ruobing Xie, Zhiyuan Liu, Fen Lin, Leyu Lin, Maosong Sun. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.