Rotating Majorana Zero Modes in a disk geometry

We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor, in order to understand their use as a building block for topological quantum computers. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied, and calculate their dynamical evolution when rotating the magnetic field, with special emphasis on non-adiabatic effects. We characterize the phase transition between high-frequency and near-adiabatic evolution using Floquet analysis. We show that oscillations persist even in the adiabatic phase because of a frequency dependent coupling between zero modes and excited states, which we have quantified numerically and analytically. These results show that controlling the rotation frequency can be a simple method to avoid the non-adiabatic errors originated from this coupling and thus increase the robustness of topological quantum computation.

Practical and Secure Federated Recommendation with Personalized Masks

Federated recommendation is a new notion of private distributed recommender systems. It aims to address the data silo and privacy problems altogether. Current federated recommender systems mainly utilize homomorphic encryption and differential privacy methods to protect the intermediate computational results. However, the former comes with extra communication and computation costs, the latter damages model accuracy. Neither of them could simultaneously satisfy the real-time feedback and accurate personalization requirements of recommender systems. In this paper, we proposed a new federated recommendation framework, named federated masked matrix factorization. Federated masked matrix factorization could protect the data privacy in federated recommender systems without sacrificing efficiency or efficacy. Instead of using homomorphic encryption and differential privacy, we utilize the secret sharing technique to incorporate the secure aggregation process of federated matrix factorization. Compared with homomorphic encryption, secret sharing largely speeds up the whole training process. In addition, we introduce a new idea of personalized masks and apply it in the proposed federated masked matrix factorization framework. On the one hand, personalized masks could further improve efficiency. On the other hand, personalized masks also benefit efficacy. Empirically, we show the superiority of the designed model on different real-world data sets. Besides, we also provide the privacy guarantee and discuss the extension of the personalized mask method to the general federated learning tasks.

Learning Functional Priors and Posteriors from Data and Physics

We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physics-informed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field. The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, and can be extended to big data problems using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

Passage Retrieval for Outside-Knowledge Visual Question Answering

In this work, we address multi-modal information needs that contain text questions and images by focusing on passage retrieval for outside-knowledge visual question answering. This task requires access to outside knowledge, which in our case we define to be a large unstructured passage collection. We first conduct sparse retrieval with BM25 and study expanding the question with object names and image captions. We verify that visual clues play an important role and captions tend to be more informative than object names in sparse retrieval. We then construct a dual-encoder dense retriever, with the query encoder being LXMERT, a multi-modal pre-trained transformer. We further show that dense retrieval significantly outperforms sparse retrieval that uses object expansion. Moreover, dense retrieval matches the performance of sparse retrieval that leverages human-generated captions.

Natural Language Understanding with Privacy-Preserving BERT

Privacy preservation remains a key challenge in data mining and Natural Language Understanding (NLU). Previous research shows that the input text or even text embeddings can leak private information. This concern motivates our research on effective privacy preservation approaches for pretrained Language Models (LMs). We investigate the privacy and utility implications of applying dx-privacy, a variant of Local Differential Privacy, to BERT fine-tuning in NLU applications. More importantly, we further propose privacy-adaptive LM pretraining methods and show that our approach can boost the utility of BERT dramatically while retaining the same level of privacy protection. We also quantify the level of privacy preservation and provide guidance on privacy configuration. Our experiments and findings lay the groundwork for future explorations of privacy-preserving NLU with pretrained LMs.

Distributionally Robust Optimization with Moment Ambiguity Sets

This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with equivalent moment conic constraints. Under some general assumptions, we prove the DRO is equivalent to a linear optimization problem with moment and psd polynomial cones. A moment-SOS relaxation method is proposed to solve it. Its asymptotic and finite convergence are shown under certain assumptions. Numerical examples are presented to show how to solve DRO problems.

Weakly-Supervised Open-Retrieval Conversational Question Answering

Recent studies on Question Answering (QA) and Conversational QA (ConvQA) emphasize the role of retrieval: a system first retrieves evidence from a large collection and then extracts answers. This open-retrieval ConvQA setting typically assumes that each question is answerable by a single span of text within a particular passage (a span answer). The supervision signal is thus derived from whether or not the system can recover an exact match of this ground-truth answer span from the retrieved passages. This method is referred to as span-match weak supervision. However, information-seeking conversations are challenging for this span-match method since long answers, especially freeform answers, are not necessarily strict spans of any passage. Therefore, we introduce a learned weak supervision approach that can identify a paraphrased span of the known answer in a passage. Our experiments on QuAC and CoQA datasets show that the span-match weak supervisor can only handle conversations with span answers, and has less satisfactory results for freeform answers generated by people. Our method is more flexible as it can handle both span answers and freeform answers. Moreover, our method can be more powerful when combined with the span-match method which shows it is complementary to the span-match method. We also conduct in-depth analyses to show more insights on open-retrieval ConvQA under a weak supervision setting.

Flow-based Generative Models for Learning Manifold to Manifold Mappings

Many measurements or observations in computer vision and machine learning manifest as non-Euclidean data. While recent proposals (like spherical CNN) have extended a number of deep neural network architectures to manifold-valued data, and this has often provided strong improvements in performance, the literature on generative models for manifold data is quite sparse. Partly due to this gap, there are also no modality transfer/translation models for manifold-valued data whereas numerous such methods based on generative models are available for natural images. This paper addresses this gap, motivated by a need in brain imaging -- in doing so, we expand the operating range of certain generative models (as well as generative models for modality transfer) from natural images to images with manifold-valued measurements. Our main result is the design of a two-stream version of GLOW (flow-based invertible generative models) that can synthesize information of a field of one type of manifold-valued measurements given another. On the theoretical side, we introduce three kinds of invertible layers for manifold-valued data, which are not only analogous to their functionality in flow-based generative models (e.g., GLOW) but also preserve the key benefits (determinants of the Jacobian are easy to calculate). For experiments, on a large dataset from the Human Connectome Project (HCP), we show promising results where we can reliably and accurately reconstruct brain images of a field of orientation distribution functions (ODF) from diffusion tensor images (DTI), where the latter has a $5times$ faster acquisition time but at the expense of worse angular resolution.

Divide-and-Shuffle Synchronization for Distributed Machine Learning

Distributed Machine Learning suffers from the bottleneck of synchronization to all-reduce workers updates. Previous works mainly consider better network topology, gradient compression, or stale updates to speed up communication and relieve the bottleneck. However, all these works ignore the importance of reducing the scale of synchronized elements and inevitable serial executed operators. To address the problem, our work proposes the Divide-and-Shuffle Synchronization(DS-Sync), which divides workers into several parallel groups and shuffles group members. DS-Sync only synchronizes the workers in the same group so that the scale of a group is much smaller. The shuffle of workers maintains the algorithms convergence speed, which is interpreted in theory. Comprehensive experiments also show the significant improvements in the latest and popular models like Bert, WideResnet, and DeepFM on challenging datasets.

B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINN posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Lo`eve (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.