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.

We present a method to formulate algorithm discovery as program search, and apply it to discover optimization algorithms for deep neural network training. We leverage efficient search techniques to explore an infinite and sparse program space. To bridge the large generalization gap between proxy and target tasks, we also introduce program selection and simplification strategies. Our method discovers a simple and effective optimization algorithm, $\textbf{Lion}$ ($\textit{Evo$\textbf{L}$ved S$\textbf{i}$gn M$\textbf{o}$me$\textbf{n}$tum}$). It is more memory-efficient than Adam as it only keeps track of the momentum. Different from adaptive optimizers, its update has the same magnitude for each parameter calculated through the sign operation. We compare Lion with widely used optimizers, such as Adam and Adafactor, for training a variety of models on different tasks. On image classification, Lion boosts the accuracy of ViT by up to 2\% on ImageNet and saves up to 5x the pre-training compute on JFT. On vision-language contrastive learning, we achieve 88.3\% $\textit{zero-shot}$ and 91.1\% $\textit{fine-tuning}$ accuracy on ImageNet, surpassing the previous best results by 2\% and 0.1\%, respectively. On diffusion models, Lion outperforms Adam by achieving a better FID score and reducing the training compute by up to 2.3x. For autoregressive, masked language modeling, and fine-tuning, Lion exhibits a similar or better performance compared to Adam. Our analysis of Lion reveals that its performance gain grows with the training batch size. It also requires a smaller learning rate than Adam due to the larger norm of the update produced by the sign function. Additionally, we examine the limitations of Lion and identify scenarios where its improvements are small or not statistically significant.

Despite recent successes, most contrastive self-supervised learning methods are domain-specific, relying heavily on data augmentation techniques that require knowledge about a particular domain, such as image cropping and rotation. To overcome such limitation, we propose a domain-agnostic approach to contrastive learning, named DACL, that is applicable to problems where domain-specific data augmentations are not readily available. Key to our approach is the use of Mixup noise to create similar and dissimilar examples by mixing data samples differently either at the input or hidden-state levels. We theoretically analyze our method and show advantages over the Gaussian-noise based contrastive learning approach. To demonstrate the effectiveness of DACL, we conduct experiments across various domains such as tabular data, images, and graphs. Our results show that DACL not only outperforms other domain-agnostic noising methods, such as Gaussian-noise, but also combines well with domain-specific methods, such as SimCLR, to improve self-supervised visual representation learning.

The vast majority of deep models use multiple gradient signals, typically corresponding to a sum of multiple loss terms, to update a shared set of trainable weights. However, these multiple updates can impede optimal training by pulling the model in conflicting directions. We present Gradient Sign Dropout (GradDrop), a probabilistic masking procedure which samples gradients at an activation layer based on their level of consistency. GradDrop is implemented as a simple deep layer that can be used in any deep net and synergizes with other gradient balancing approaches. We show that GradDrop outperforms the state-of-the-art multiloss methods within traditional multitask and transfer learning settings, and we discuss how GradDrop reveals links between optimal multiloss training and gradient stochasticity.

Semi-supervised learning lately has shown much promise in improving deep learning models when labeled data is scarce. Common among recent approaches is the use of consistency training on a large amount of unlabeled data to constrain model predictions to be invariant to input noise. In this work, we present a new perspective on how to effectively noise unlabeled examples and argue that the quality of noising, specifically those produced by advanced data augmentation methods, plays a crucial role in semi-supervised learning. By substituting simple noising operations with advanced data augmentation methods such as RandAugment and back-translation, our method brings substantial improvements across six language and three vision tasks under the same consistency training framework. On the IMDb text classification dataset, with only 20 labeled examples, our method achieves an error rate of 4.20, outperforming the state-of-the-art model trained on 25,000 labeled examples. On a standard semi-supervised learning benchmark, CIFAR-10, our method outperforms all previous approaches and achieves an error rate of 5.43 with only 250 examples. Our method also combines well with transfer learning, e.g., when finetuning from BERT, and yields improvements in high-data regime, such as ImageNet, whether when there is only 10% labeled data or when a full labeled set with 1.3M extra unlabeled examples is used. Code is available at https://github.com/google-research/uda.

The softmax bottleneck has been shown to limit the expressiveness of neural lan- guage models. Mixture of Softmaxes (MoS) is an effective approach to address such a theoretical limitation, but are expensive compared to softmax in terms of both memory and time. We propose Mixtape, an output layer that breaks the softmax bottleneck more efficiently with three novel techniques—logit space vector gating, sigmoid tree decomposition, and gate sharing. On four benchmarks including language modeling and machine translation, the Mixtape layer substantially improves the efficiency over the MoS layer by 3.5x to 10.5x while obtaining similar performance. A network equipped with Mixtape is only 20% to 34% slower than a softmax-based network with 10-30K vocabulary sizes, and outperforms softmax in perplexity and translation quality.

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.

Thang Luong, Ilya Sutskever, Quoc Le, Oriol Vinyals, Wojciech Zaremba. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2015.

Neural language models (NLMs) have been able to improve machine translation (MT) thanks to their ability to generalize well to long contexts.Despite recent successes of deep neural networks in speech and vision, the general practice in MT is to incorporate NLMs with only one or two hidden layers and there have not been clear results on whether having more layers helps.In this paper, we demonstrate that deep NLMs with three or four layers outperform those with fewer layers in terms of both the perplexity and the translation quality.We combine various techniques to successfully train deep NLMs that jointly condition on both the source and target contexts.When reranking nbest lists of a strong web-forum baseline, our deep models yield an average boost of 0.5 TER / 0.5 BLEU points compared to using a shallow NLM.Additionally, we adapt our models to a new sms-chat domain and obtain a similar gain of 1.0 TER / 0.5 BLEU points. 1

Recursive neural models, which use syntactic parse trees to recursively generate representations bottom-up, are a popular architecture.However there have not been rigorous evaluations showing for exactly which tasks this syntax-based method is appropriate.In this paper, we benchmark recursive neural models against sequential recurrent neural models, enforcing applesto-apples comparison as much as possible.We investigate 4 tasks: (1) sentiment classification at the sentence level and phrase level; (2) matching questions to answerphrases; (3) discourse parsing; (4) semantic relation extraction.Our goal is to understand better when, and why, recursive models can outperform simpler models.We find that recursive models help mainly on tasks (like semantic relation extraction) that require longdistance connection modeling, particularly on very long sequences.We then introduce a method for allowing recurrent models to achieve similar performance: breaking long sentences into clause-like units at punctuation and processing them separately before combining.Our results thus help understand the limitations of both classes of models, and suggest directions for improving recurrent models.

An attentional mechanism has lately been used to improve neural machine translation (NMT) by selectively focusing on parts of the source sentence during translation.However, there has been little work exploring useful architectures for attention-based NMT.This paper examines two simple and effective classes of attentional mechanism: a global approach which always attends to all source words and a local one that only looks at a subset of source words at a time.We demonstrate the effectiveness of both approaches on the WMT translation tasks between English and German in both directions.With local attention, we achieve a significant gain of 5.0 BLEU points over non-attentional systems that already incorporate known techniques such as dropout.Our ensemble model using different attention architectures yields a new state-of-the-art result in the WMT'15 English to German translation task with 25.9 BLEU points, an improvement of 1.0 BLEU points over the existing best system backed by NMT and an n-gram reranker.1