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.

To enable large-scale machine learning in bandwidth-hungry environments such as wireless networks, significant progress has been made recently in designing communication-efficient federated learning algorithms with the aid of communication compression. On the other end, privacy-preserving, especially at the client level, is another important desideratum that has not been addressed simultaneously in the presence of advanced communication compression techniques yet. In this paper, we propose a unified framework that enhances the communication efficiency of private federated learning with communication compression. Exploiting both general compression operators and local differential privacy, we first examine a simple algorithm that applies compression directly to differentially-private stochastic gradient descent, and identify its limitations. We then propose a unified framework SoteriaFL for private federated learning, which accommodates a general family of local gradient estimators including popular stochastic variance-reduced gradient methods and the state-of-the-art shifted compression scheme. We provide a comprehensive characterization of its performance trade-offs in terms of privacy, utility, and communication complexity, where SoteriaFL is shown to achieve better communication complexity without sacrificing privacy nor utility than other private federated learning algorithms without communication compression.

We study the problem of list-decodable linear regression, where an adversary can corrupt a majority of the examples. Specifically, we are given a set T of labeled examples (x,y) Rd R and a parameter 0 <α<1/2 such that an α-fraction of the points in T are i.i.d.

A.2: Comparison of the causal assumptions A.3: Comparison of allowed temporal covariates A.4: Unrelated works with similar terminology The SyncTwin algorithm. A.5: The generality of SyncTwin's assumed DGP A.6: Estimation for control and new individuals A.7: Algorithmic details and pseudocode A.8: Optimization for the matching loss Lm Simulation study.

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].