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Abstract A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a realspace lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84 Sr atom, we demonstrate a syntheticdimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and onsite potentials are set by the millimeterwave amplitudes and detunings respectively. Alternating weak and strong tunneling in a onedimensional configuration realizes the singleparticle SuSchriefferHeeger (SSH) Hamiltonian,more »Free, publiclyaccessible full text available December 1, 2023

Within machine learning, active learning studies the gains in performance made possible by adaptively selecting data points to label. In this work, we show through upper and lower bounds, that for a simple benign setting of wellspecified logistic regression on a uniform distribution over a sphere, the expected excess error of both active learning and random sampling have the same inverse proportional dependence on the number of samples. Importantly, due to the nature of lower bounds, any more general setting does not allow a better dependence on the number of samples. Additionally, we show a variant of uncertainty sampling canmore »Free, publiclyaccessible full text available January 1, 2023

We prove asymptotic convergence for a general class of kmeans algorithms performed over streaming data from a distribution— the centers asymptotically converge to the set of stationary points of the kmeans objective function. To do so, we show that online kmeans over a distribution can be interpreted as stochastic gradient descent with a stochastic learning rate schedule. Then, we prove convergence by extending techniques used in optimization literature to handle settings where centerspecific learning rates may depend on the past trajectory of the centers.Free, publiclyaccessible full text available January 1, 2023

Recent work introduced the model of learning from discriminative feature feedback, in which a human annotator not only provides labels of instances, but also identifies discriminative features that highlight important differences between pairs of instances. It was shown that such feedback can be conducive to learning, and makes it possible to efficiently learn some concept classes that would otherwise be in tractable. However, these results all relied upon perfect annotator feedback. In this pa per, we introduce a more realistic, robust ver sion of the framework, in which the annotator is allowed to make mistakes. We show how such errorsmore »

Detecting overfitting in generative models is an important challenge in machine learning. In this work, we formalize a form of overfitting that we call datacopying – where the gener ative model memorizes and outputs training samples or small variations thereof. We pro vide a three sample nonparametric test for detecting datacopying that uses the training set, a separate sample from the target dis tribution, and a generated sample from the model, and study the performance of our test on several canonical models and datasets.

We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.

Detecting overfitting in generative models is an important challenge in machine learning. In this work, we formalize a form of overfitting that we call datacopying – where the gener ative model memorizes and outputs training samples or small variations thereof. We pro vide a three sample test for detecting data copying that uses the training set, a separate sample from the target distribution, and a generated sample from the model, and study the performance of our test on several canon ical models and datasets.

We introduce a variant of the knearest neighbor classifier in which k is chosen adaptively for each query, rather than being supplied as a parameter. The choice of k depends on properties of each neighborhood, and therefore may significantly vary between different points. For example, the algorithm will use larger k for predicting the labels of points in noisy regions. We provide theory and experiments that demonstrate that the algorithm performs comparably to, and sometimes better than, kNN with an optimal choice of k. In particular, we bound the convergence rate of our classifier in terms of a lo calmore »

One widelystudied model of teaching calls for a teacher to provide the minimal set of labeled examples that uniquely specifies a target concept. The assumption is that the teacher knows the learner’s hypothesis class, which is often not true of reallife teaching scenarios. We consider the problem of teaching a learner whose representation and hypothesis class are unknown—that is, the learner is a black box. We show that a teacher who does not interact with the learner can do no better than providing random examples. We then prove, however, that with interaction, a teacher can efficiently find a set ofmore »