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.

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.

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.

Motivated by neuroscientific and clinical applications, we empirically examine whether observational measures of information flow can suggest interventions. We do so by performing experiments on artificial neural networks in the context of fairness in machine learning, where the goal is to induce fairness in the system through interventions. Using our recently developed M-information flow framework, we measure the flow of information about the true label (responsible for accuracy, and hence desirable), and separately, the flow of information about a protected attribute (responsible for bias, and hence undesirable) on the edges of a trained neural network. We then compare the flow magnitudes against the effect of intervening on those edges by pruning. We show that pruning edges that carry larger information flows about the protected attribute reduces bias at the output to a greater extent. This demonstrates that M-information flow can meaningfully suggest targets for interventions, answering the title's question in the affirmative. We also evaluate bias-accuracy tradeoffs for different intervention strategies, to analyze how one might use estimates of desirable and undesirable information flows (here, accuracy and bias flows) to inform interventions that preserve the former while reducing the latter.

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/