We show in the table below the notations grouped by the modules. The values used in our implementation are shown if applicable. The necessity of a two-layer hierarchy is briefly discussed in Section 3.3. In short, it is difficult for a single-layer hierarchy to capture long-time dependencies and variations. This section describes an empirical study where we compare MCAE with its single-layer correspondence.

Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based Transformers is largely unexplored. In this work, we mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. One may naturally assume the answer is in the affirmative--RPE-based Transformers are universal function approximators. However, we present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is.

Most of the medical observational studies estimate the causal treatment effects using electronic health records (EHR), where a patient's covariates and outcomes are both observed longitudinally. However, previous methods focus only on adjusting for the covariates while neglecting the temporal structure in the outcomes. To bridge the gap, this paper develops a new method, SyncTwin, that learns a patient-specific time-constant representation from the pre-treatment observations. SyncTwin issues counterfactual prediction of a target patient by constructing a synthetic twin that closely matches the target in representation. The reliability of the estimated treatment effect can be assessed by comparing the observed and synthetic pre-treatment outcomes. The medical experts can interpret the estimate by examining the most important contributing individuals to the synthetic twin. In the real-data experiment, SyncTwin successfully reproduced the findings of a randomized controlled clinical trial using observational data, which demonstrates its usability in the complex real-world EHR.

The main purpose of this research is to provide the user of DNN classifiers with a method to detect if the model is backdoor attacked without access to the training set. All attacks used to evaluate our detection method in this paper are created by published backdoor attack strategies on public datasets. Thus, we did not create new threats to society. Moreover, our work provides a new perspective on backdoor defense, as it is the first to address the certification of backdoor detection. It helps other researchers to understand the behavior of deep learning systems facing malicious activities. While existing backdoor detectors are all empirical [67, 20, 75, 41, 69, 6, 56, 13], our work initiates a new research direction - backdoor detection with certification. Moreover, we first exposed that certified backdoor detectors and certified robustness against backdoor attacks complement each other [86, 71, 27, 53].

We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous function over time, hence the name Neural Motion Fields (NeMF). Specifically, we use a neural network to learn this function for miscellaneous sets of motions, which is designed to be a generative model conditioned on a temporal coordinate t and a random vector z for controlling the style. The model is then trained as a Variational Autoencoder (VAE) with motion encoders to sample the latent space. We train our model with a diverse human motion dataset and quadruped dataset to prove its versatility, and finally deploy it as a generic motion prior to solve task-agnostic problems and show its superiority in different motion generation and editing applications, such as motion interpolation, in-betweening, and re-navigating. More details can be found on our project page: https://cs.yale.edu/homes/