Shaping the Future of Mathematics in the Age of AI

Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching, technology, and ethics. We offer recommendations on safeguarding our intellectual autonomy, rethinking our practice, broadening curricula, building academically oriented infrastructure, and developing shared ethical principles - with the aim of ensuring that the future of mathematics is shaped by the community itself.

Universal Facial Encoding of Codec Avatars from VR Headsets

Faithful real-time facial animation is essential for avatar-mediated telepresence in Virtual Reality (VR). To emulate authentic communication, avatar animation needs to be efficient and accurate: able to capture both extreme and subtle expressions within a few milliseconds to sustain the rhythm of natural conversations. The oblique and incomplete views of the face, variability in the donning of headsets, and illumination variation due to the environment are some of the unique challenges in generalization to unseen faces. In this paper, we present a method that can animate a photorealistic avatar in realtime from head-mounted cameras (HMCs) on a consumer VR headset. We present a self-supervised learning approach, based on a cross-view reconstruction objective, that enables generalization to unseen users. We present a lightweight expression calibration mechanism that increases accuracy with minimal additional cost to run-time efficiency. We present an improved parameterization for precise ground-truth generation that provides robustness to environmental variation. The resulting system produces accurate facial animation for unseen users wearing VR headsets in realtime. We compare our approach to prior face-encoding methods demonstrating significant improvements in both quantitative metrics and qualitative results.

Cross-domain Variational Capsules for Information Extraction

In this paper, we present a characteristic extraction algorithm and the Multi-domain Image Characteristics Dataset of characteristic-tagged images to simulate the way a human brain classifies cross-domain information and generates insight. The intent was to identify prominent characteristics in data and use this identification mechanism to auto-generate insight from data in other unseen domains. An information extraction algorithm is proposed which is a combination of Variational Autoencoders (VAEs) and Capsule Networks. Capsule Networks are used to decompose images into their individual features and VAEs are used to explore variations on these decomposed features. Thus, making the model robust in recognizing characteristics from variations of the data. A noteworthy point is that the algorithm uses efficient hierarchical decoding of data which helps in richer output interpretation. Noticing a dearth in the number of datasets that contain visible characteristics in images belonging to various domains, the Multi-domain Image Characteristics Dataset was created and made publicly available. It consists of thousands of images across three domains. This dataset was created with the intent of introducing a new benchmark for fine-grained characteristic recognition tasks in the future.