Alex Zhai

Jian Ding, Yuval Peres, Gireeja Ranade et al.

We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if the system growth is large enough, then the system cannot be stabilized in a second-moment sense. This is done by showing that the probability that the state magnitude remains bounded must go to zero with time. Our proof technique recursively bounds the conditional density of the system state (instead of focusing on the second moment) to bound the progress the controller can make. This sidesteps the difficulty encountered in using the standard data-rate theorem style approach; that approach does not work because the mutual information per round between the system state and the observation is potentially unbounded. It was known that a system with multiplicative observation noise can be stabilized using a simple memoryless linear strategy if the system growth is suitably bounded. In this paper, we show that while memory cannot improve the performance of a linear scheme, a simple non-linear scheme that uses one-step memory can do better than the best linear scheme.

Thang Luong, Dawsen Hwang, Hoang H. Nguyen et al.

Finding the right north-star metrics is highly critical for advancing the mathematical reasoning capabilities of foundation models, especially given that existing evaluations are either too easy or only focus on getting correct short answers. To address these issues, we present IMO-Bench, a suite of advanced reasoning benchmarks, vetted by a panel of top specialists and that specifically targets the level of the International Mathematical Olympiad (IMO), the most prestigious venue for young mathematicians. IMO-AnswerBench first tests models on 400 diverse Olympiad problems with verifiable short answers. IMO-Proof Bench is the next-level evaluation for proof-writing capabilities, which includes both basic and advanced IMO level problems as well as detailed grading guidelines to facilitate automatic grading. These benchmarks played a crucial role in our historic achievement of the gold-level performance at IMO 2025 with Gemini Deep Think (Luong and Lockhart, 2025). Our model achieved 80.0% on IMO-AnswerBench and 65.7% on the advanced IMO-Proof Bench, surpassing the best non-Gemini models by large margins of 6.9% and 42.4% respectively. We also showed that autograders built with Gemini reasoning correlate well with human evaluations and construct IMO-GradingBench, with 1000 human gradings on proofs, to enable further progress in automatic evaluation of long-form answers. We hope that IMO-Bench will help the community towards advancing robust mathematical reasoning and release it at https://imobench.github.io/.

Chengxu Zhuang, Alex Lin Zhai, Daniel Yamins

Unsupervised approaches to learning in neural networks are of substantial interest for furthering artificial intelligence, both because they would enable the training of networks without the need for large numbers of expensive annotations, and because they would be better models of the kind of general-purpose learning deployed by humans. However, unsupervised networks have long lagged behind the performance of their supervised counterparts, especially in the domain of large-scale visual recognition. Recent developments in training deep convolutional embeddings to maximize non-parametric instance separation and clustering objectives have shown promise in closing this gap. Here, we describe a method that trains an embedding function to maximize a metric of local aggregation, causing similar data instances to move together in the embedding space, while allowing dissimilar instances to separate. This aggregation metric is dynamic, allowing soft clusters of different scales to emerge. We evaluate our procedure on several large-scale visual recognition datasets, achieving state-of-the-art unsupervised transfer learning performance on object recognition in ImageNet, scene recognition in Places 205, and object detection in PASCAL VOC.