arXiv research

The paper tests properties of trees in graphical models using covariance queries.

Efficient sparse modern Hopfield models are introduced for memory retrieval and learning tasks.

We analyze computational limits of modern Hopfield models based on pattern norms.

New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.

Study shows uniqueness of solutions on complex manifolds without requiring solution decay.

New findings on gradient expanding Ricci solitons with finite scalar curvature ratio.

We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under certain assumptions, expected run time O(N^(3/2)) in R^d where N is the set size, making it the first sub-quadratic exact m…

A new framework for efficient sequence maps using Bayesian filtering and covariance.

We consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvature and the squared inverse of the injectivity radius. We show the existence on such a manifold of a distance-like function with bounded gradi…

Single-head transformers with a single self-attention layer can approximate any sequence-to-sequence function and are efficient under certain conditions.

The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$ operations. When $n,p$ are large, this computation may be prohibitively slow. Moreover, …

We study manifolds satisfying a weighed Poincare inequality, which was first introduced by Li-Wang. We generalized one of their results by relaxing the Ricci curvature bound condition only being satisfied outside a compact set and established a finitely many ends result. We proved a vanishing result for $L^2$ harmonic …

Study sharp convergence rates of empirical UOT for spatio-temporal point processes.

Quadratic regression involves modeling the response as a (generalized) linear function of not only the features $x^{j_1}$ but also of quadratic terms $x^{j_1}x^{j_2}$. The inclusion of such higher-order "interaction terms" in regression often provides an easy way to increase accuracy in already-high-dimensional problem…

Max-convolution is an important problem closely resembling standard convolution; as such, max-convolution occurs frequently across many fields. Here we extend the method with fastest known worst-case runtime, which can be applied to nonnegative vectors by numerically approximating the Chebyshev norm $\| \cdot \|_\infty…

Improved MMD test for two-sample testing with random Fourier features.

The so-called {\it kissing number} for hyperbolic surfaces is the maximum number of homotopically distinct systoles a surface of given genus $g$ can have. These numbers, first studied (and named) by Schmutz Schaller by analogy with lattice sphere packings, are known to grow, as a function of genus, at least like $g^{\s…

Study calculates stable norm of slit tori using Farey sequence.

Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the pe…

Solves TOD systems' query annotation problem without explicit annotations.

Study exact community recovery in noisy SBM with limited queries.

Efficiently classifies binary labels with XOR queries, even under noisy conditions.

Proposes a new query autocompletion method that maximizes retrieval performance.

A new method for private query release using Johnson-Lindenstrauss projection.

LAZO reduces query complexity and variance in ZO methods.

We consider the problem of adaptively PAC-learning a probability distribution $\mathcal{P}$'s mode by querying an oracle for information about a sequence of i.i.d. samples $X_1, X_2, \ldots$ generated from $\mathcal{P}$. We consider two different query models: (a) each query is an index $i$ for which the oracle reveals…

Estimates heavy hitters in data streams with queries, balancing accuracy and efficiency.

Query2box embeds complex queries as boxes to handle logical operations in large KGs.

Survey of statistical queries and their applications.

We study the query complexity of a learner-private sequential learning problem, motivated by the privacy and security concerns due to eavesdropping that arise in practical applications such as pricing and Federated Learning. A learner tries to estimate an unknown scalar value, by sequentially querying an external datab…

Source coding is the canonical problem of data compression in information theory. In a locally encodable source coding, each compressed bit depends on only few bits of the input. In this paper, we show that a recently popular model of semi-supervised clustering is equivalent to locally encodable source coding. In this …

A new query embedding method improves KB performance on complex queries.

We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices to sample sm…

In this paper we study the adaptive learnability of decision trees of depth at most $d$ from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^…

We study black-box attacks on machine learning classifiers where each query to the model incurs some cost or risk of detection to the adversary. We focus explicitly on minimizing the number of queries as a major objective. Specifically, we consider the problem of attacking machine learning classifiers subject to a budg…

Fairly allocate items with noisy queries, reducing envy.

This paper models the crowdsourced labeling/classification problem as a sparsely encoded source coding problem, where each query answer, regarded as a code bit, is the XOR of a small number of labels, as source information bits. In this paper we leverage the connections between this problem and well-studied codes with …

In query learning, the goal is to identify an unknown object while minimizing the number of "yes" or "no" questions (queries) posed about that object. A well-studied algorithm for query learning is known as generalized binary search (GBS). We show that GBS is a greedy algorithm to optimize the expected number of querie…

We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful enough to enough to give new and very short proofs of the efficient learnability…

The paper tackles learning smooth distance functions using query-based methods.

Understanding search queries is critical for shopping search engines to deliver a satisfying customer experience. Popular shopping search engines receive billions of unique queries yearly, each of which can depict any of hundreds of user preferences or intents. In order to get the right results to customers it must be …

Efficiently tests two distributions with few label queries.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately est…

This work sets lower bounds on the number of score queries needed for diffusion sampling.

Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a…

Improves model classification accuracy in black-box settings.

Improved algorithm for selecting a hypothesis locally privately with fewer queries.

Discrete integration in a high dimensional space of n variables poses fundamental challenges. The WISH algorithm reduces the intractable discrete integration problem into n optimization queries subject to randomized constraints, obtaining a constant approximation guarantee. The optimization queries are expensive, which…