Hyperbolic Space is particularly interesting and promising in machine learning due to its non-Euclidean properties. For example, volume of a ball in the hyperbolic space increases exponentially w.r.t. the radius (polynomially in Euclidean space). This imitates a tree, where the number of nodes increases exponentially over the depth (with a fixed branch factor).
We propose HyLa, a completely different approach to using hyperbolic space in graph learning: HyLa maps once from a learned hyperbolic-space embedding to Euclidean space via the eigenfunctions of the Laplacian operator in the hyperbolic space. HyLa is inspired by the random Fourier feature methodology, which uses the eigenfunctions of the Laplacian in Euclidan space. HyLa shows significant improvements over (hyperbolic) GCNs on downstream tasks including node classification and text classification.
We also look into a critical issue of using hyperbolic space: the NaN problem. We proposed tiling-based models and multi-component floats models to solve the NaN problem both theoretically and empirically, currently we are working on a Library to use these techniques easily in ML.

Despite of the great success of Machine learning, there are also some concerns calling for attention, namely, the security and privacy concern. On the one hand, Machine Learning models are vulnerable to imperceptible adversarial perturbations, which alter the model's decision entirely, it's necessary and worthwhile to design robust and secure models for various applications. On the other hand, Machine Learning models also suffer from information leakage, attacks such as membership inference and model inversion are able to infer information of the dataset. Hence, it's important to measure the information leakage and design privacy-preserving models and algorithms. However, both aspects may degrade the model's performace. What's more, it's particularly interesting to ask whether there is a tradeoff between robustness and privacy, we are currently looking at these tradeoffs in detail.

Federated learning is proposed for collaborative Machine Learning without centralized training data. Users will be able to collaboratively learn a shared model while keeping all the data on device. Latest FL approaches use differential privacy or robust aggregation to ensure privacy and integrity of the federated model, however, we show that these approaches will destroy the accuracy of the federated model for many participants. Thus, we propose local adaptation of federated models, our evaluatation of different techniques demonstrate that all participants benefit from local adaptation.