FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI

We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. Solving a typical problem requires multiple hours of effort from a researcher in the relevant branch of mathematics, and for the upper end questions, multiple days. FrontierMath uses new, unpublished problems and automated verification to reliably evaluate models while minimizing risk of data contamination. Current state-of-the-art AI models solve under 2% of problems, revealing a vast gap between AI capabilities and the prowess of the mathematical community. As AI systems advance toward expert-level mathematical abilities, FrontierMath offers a rigorous testbed that quantifies their progress.

Hierarchical Federated Learning with Multi-Timescale Gradient Correction

While traditional federated learning (FL) typically focuses on a star topology where clients are directly connected to a central server, real-world distributed systems often exhibit hierarchical architectures. Hierarchical FL (HFL) has emerged as a promising solution to bridge this gap, leveraging aggregation points at multiple levels of the system. However, existing algorithms for HFL encounter challenges in dealing with multi-timescale model drift, i.e., model drift occurring across hierarchical levels of data heterogeneity. In this paper, we propose a multi-timescale gradient correction (MTGC) methodology to resolve this issue. Our key idea is to introduce distinct control variables to (i) correct the client gradient towards the group gradient, i.e., to reduce client model drift caused by local updates based on individual datasets, and (ii) correct the group gradient towards the global gradient, i.e., to reduce group model drift caused by FL over clients within the group. We analytically characterize the convergence behavior of MTGC under general non-convex settings, overcoming challenges associated with couplings between correction terms. We show that our convergence bound is immune to the extent of data heterogeneity, confirming the stability of the proposed algorithm against multi-level non-i.i.d. data. Through extensive experiments on various datasets and models, we validate the effectiveness of MTGC in diverse HFL settings. The code for this project is available at \href{https://github.com/wenzhifang/MTGC}{https://github.com/wenzhifang/MTGC}.

Cross-Resolution Flow Propagation for Foveated Video Super-Resolution

The demand of high-resolution video contents has grown over the years. However, the delivery of high-resolution video is constrained by either computational resources required for rendering or network bandwidth for remote transmission. To remedy this limitation, we leverage the eye trackers found alongside existing augmented and virtual reality headsets. We propose the application of video super-resolution (VSR) technique to fuse low-resolution context with regional high-resolution context for resource-constrained consumption of high-resolution content without perceivable drop in quality. Eye trackers provide us the gaze direction of a user, aiding us in the extraction of the regional high-resolution context. As only pixels that falls within the gaze region can be resolved by the human eye, a large amount of the delivered content is redundant as we can't perceive the difference in quality of the region beyond the observed region. To generate a visually pleasing frame from the fusion of high-resolution region and low-resolution region, we study the capability of a deep neural network of transferring the context of the observed region to other regions (low-resolution) of the current and future frames. We label this task a Foveated Video Super-Resolution (FVSR), as we need to super-resolve the low-resolution regions of current and future frames through the fusion of pixels from the gaze region. We propose Cross-Resolution Flow Propagation (CRFP) for FVSR. We train and evaluate CRFP on REDS dataset on the task of 8x FVSR, i.e. a combination of 8x VSR and the fusion of foveated region. Departing from the conventional evaluation of per frame quality using SSIM or PSNR, we propose the evaluation of past foveated region, measuring the capability of a model to leverage the noise present in eye trackers during FVSR. Code is made available at https://github.com/eugenelet/CRFP.

Meta-rPPG: Remote Heart Rate Estimation Using a Transductive Meta-Learner

Remote heart rate estimation is the measurement of heart rate without any physical contact with the subject and is accomplished using remote photoplethysmography (rPPG) in this work. rPPG signals are usually collected using a video camera with a limitation of being sensitive to multiple contributing factors, e.g. variation in skin tone, lighting condition and facial structure. End-to-end supervised learning approach performs well when training data is abundant, covering a distribution that doesn't deviate too much from the distribution of testing data or during deployment. To cope with the unforeseeable distributional changes during deployment, we propose a transductive meta-learner that takes unlabeled samples during testing (deployment) for a self-supervised weight adjustment (also known as transductive inference), providing fast adaptation to the distributional changes. Using this approach, we achieve state-of-the-art performance on MAHNOB-HCI and UBFC-rPPG.