arXiv subjects

Nathan White

Publications and source records attributed to Nathan White.

10 recordsLinked to original sources

arXiv2026

Approximate Nearest Neighbor in Ultra-High Dimensional $\ell_\infty$

We study the approximate nearest neighbor problem under $\ell_\infty$ in the ultra-high dimensional setting where the dimension $d$ is significantly larger than the number of points $n$. Thus, we desire data structures with no dependence on $d$ in the query time. [Herold-Nanongkai-Spoerhase-Varma-Wu, SoCG 2025] introduce this problem and give data structures in $\ell_p$: for $p=1,2$, they give $(1+\varepsilon)$-approximation data structures with space $\tilde{O}(n\log d/\text{poly}(\varepsilon))$ and query time $\tilde{O}(n/\text{poly}(\varepsilon))$. Since any data structure must have query time $\Omega(\min \{n,d\})$, this query time is nearly tight. However, their results are inefficient for $\ell_\infty$, with query time $\Omega(nd)$. In order to handle the challenges of $\ell_\infty$, we introduce a notion of subset embeddings, which embed points by simply selecting a subset of dimensions. In particular, we show one may preserve all pairwise distances of an $n$ point dataset up to a factor of $O(c)$ by computing distances on only $n^{1+1/c}$ coordinates. We also show a matching lower bound: for any $c > 1$, there exists a set of $n$ points in $\mathbb{R}^{d}$ such that any subset embedding for the set with approximation $c$ must have at least $n^{1+\Omega(1/c)}$ coordinates. Using our subset embeddings, we give data structures for approximate nearest neighbor in $\ell_\infty$ with space $O(n^2\log d)$, query time $\tilde{O}(n^{1+1/c})$, and approximation $O(c\log\log n)$ for any $c \geq 1$. Finally, we give another data structure for the approximate nearest neighbor under $\ell_\infty$ with the same space and query time as our subset embedding approach, but with approximation $O(c^{\log_2 3}) \approx O(c^{1.58})$. This allows us to achieve $O(1)$-approximation with query time e.g.~$n^{1.01}$

cs.DS↗

arXiv2026

Inner Product Aware Quantization: Provably Fast, Accurate, and Adaptive Algorithms

Quantization is a fundamental tool used to compress datasets, neural network weights, and memory usage in a range of computational tasks. Many downstream applications of vector quantization perform inner products with arbitrary inputs. This motivates the study of inner product aware quantization schemes that approximately preserve inner products with unseen vectors -- in contrast to simply minimizing the mean-squared error. In this work, we formulate objectives that capture natural desiderata and develop adaptive and unbiased quantization methods that approximately preserve inner products with worst-case and average-case inputs. An analysis of these objectives shows a tight connection with the well-studied notion of Adaptive Stochastic Quantization (ASQ). We develop provably fast exact and approximate algorithms for our objectives. Our theoretical results inspire efficient practical algorithms that perform well across a variety of workload distributions. They also lead to practical algorithms for standard ASQ which are 2-10$\times$ faster than prior state-of-the-art methods while maintaining quality. These theoretical and empirical results contribute towards making adaptive quantization techniques more efficient and tractable in practical settings.

cs.LG↗

arXiv2026

Detector-in-the-Loop Tracking: Active Memory Rectification for Stable Glottic Opening Localization

Temporal stability in glottic opening localization remains challenging due to the complementary weaknesses of single-frame detectors and foundation-model trackers: the former lacks temporal context, while the latter suffers from memory drift. Specifically, in video laryngoscopy, rapid tissue deformation, occlusions, and visual ambiguities in emergency settings require a robust, temporally aware solution that can prevent progressive tracking errors. We propose Closed-Loop Memory Correction (CL-MC), a detector-in-the-loop framework that supervises Segment Anything Model 2(SAM2) through confidence-aligned state decisions and active memory rectification. High-confidence detections trigger semantic resets that overwrite corrupted tracker memory, effectively mitigating drift accumulation with a training-free foundation tracker in complex endoscopic scenes. On emergency intubation videos, CL-MC achieves state-of-the-art performance, significantly reducing drift and missing rate compared with the SAM2 variants and open loop based methods. Our results establish memory correction as a crucial component for reliable clinical video tracking. Our code will be available in https://github.com/huayuww/CL-MR.

cs.CV↗

arXiv2025

Testing noisy low-degree polynomials for sparsity

We consider the problem of testing whether an unknown low-degree polynomial $p$ over $\mathbb{R}^n$ is sparse versus far from sparse, given access to noisy evaluations of the polynomial $p$ at \emph{randomly chosen points}. This is a property-testing analogue of classical problems on learning sparse low-degree polynomials with noise, extending the work of Chen, De, and Servedio (2020) from noisy \emph{linear} functions to general low-degree polynomials. Our main result gives a \emph{precise characterization} of when sparsity testing for low-degree polynomials admits constant sample complexity independent of dimension, together with a matching constant-sample algorithm in that regime. For any mean-zero, variance-one finitely supported distribution $\boldsymbol{X}$ over the reals, degree $d$, and any sparsity parameters $s \leq T$, we define a computable function $\mathrm{MSG}_{\boldsymbol{X},d}(\cdot)$, and: - For $T \ge \mathrm{MSG}_{\boldsymbol{X},d}(s)$, we give an $O_{s,\boldsymbol{X},d}(1)$-sample algorithm that distinguishes whether a multilinear degree-$d$ polynomial over $\mathbb{R}^n$ is $s$-sparse versus $\varepsilon$-far from $T$-sparse, given examples $(\boldsymbol{x},\, p(\boldsymbol{x}) + \mathrm{noise})_{\boldsymbol{x} \sim \boldsymbol{X}^{\otimes n}}$. Crucially, the sample complexity is \emph{completely independent} of the ambient dimension $n$. - For $T \leq \mathrm{MSG}_{\boldsymbol{X},d}(s) - 1$, we show that even without noise, any algorithm given samples $(\boldsymbol{x},p(\boldsymbol{x}))_{\boldsymbol{x} \sim \boldsymbol{X}^{\otimes n}}$ must use $\Omega_{\boldsymbol{X},d,s}(\log n)$ examples. Our techniques employ a generalization of the results of Dinur et al. (2007) on the Fourier tails of bounded functions over $\{0,1\}^n$ to a broad range of finitely supported distributions, which may be of independent interest.

cs.DS↗

arXiv2024

Average-Distortion Sketching

We introduce average-distortion sketching for metric spaces. As in (worst-case) sketching, these algorithms compress points in a metric space while approximately recovering pairwise distances. The novelty is studying average-distortion: for any fixed (yet, arbitrary) distribution $\mu$ over the metric, the sketch should not over-estimate distances, and it should (approximately) preserve the average distance with respect to draws from $\mu$. The notion generalizes average-distortion embeddings into $\ell_1$ [Rabinovich '03, Kush-Nikolov-Tang '21] as well as data-dependent locality-sensitive hashing [Andoni-Razenshteyn '15, Andoni-Naor-Nikolov-et-al. '18], which have been recently studied in the context of nearest neighbor search. $\bullet$ For all $p \in (2, \infty)$ and any $c$ larger than a fixed constant, we give an average-distortion sketch for $([\Delta]^d, \ell_p)$ with approximation $c$ and bit-complexity $\text{poly}(2^{p/c} \cdot \log(d\Delta))$, which is provably impossible in (worst-case) sketching. $\bullet$ As an application, we improve on the approximation of sublinear-time data structures for nearest neighbor search over $\ell_p$ (for large $p > 2$). The prior best approximation was $O(p)$ [Andoni-Naor-Nikolov-et-al. '18, Kush-Nikolov-Tang '21], and we show it can be any $c$ larger than a fixed constant (irrespective of $p$) by using $n^{O(p/c)}$ space. We give some evidence that $2^{\Omega(p/c)}$ space may be necessary by giving a lower bound on average-distortion sketches which produce a certain probabilistic certificate of farness (which our sketches crucially rely on).

cs.DS↗

arXiv2024

Parallel Approximate Maximum Flows in Near-Linear Work and Polylogarithmic Depth

We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3} \text{polylog} n)$ work in the PRAM model. Although near-linear time sequential algorithms for this problem have been known for almost a decade, no parallel algorithms that simultaneously achieved polylogarithmic depth and near-linear work were known. At the heart of our result is a polylogarithmic depth, near-linear work recursive algorithm for computing congestion approximators. Our algorithm involves a recursive step to obtain a low-quality congestion approximator followed by a "boosting" step to improve its quality which prevents a multiplicative blow-up in error. Similar to Peng [SODA'16], our boosting step builds upon the hierarchical decomposition scheme of R\"acke, Shah, and T\"aubig [SODA'14]. A direct implementation of this approach, however, leads only to an algorithm with $n^{o(1)}$ depth and $m^{1+o(1)}$ work. To get around this, we introduce a new hierarchical decomposition scheme, in which we only need to solve maximum flows on subgraphs obtained by contracting vertices, as opposed to vertex-induced subgraphs used in R\"acke, Shah, and T\"aubig [SODA'14]. In particular, we are able to directly extract congestion approximators for the subgraphs from a congestion approximator for the entire graph, thereby avoiding additional recursion on those subgraphs. Along the way, we also develop a parallel flow-decomposition algorithm that is crucial to achieving polylogarithmic depth and may be of independent interest.

cs.DS↗

arXiv2023

Designing Parent-child-robot Interactions to Facilitate In-Home Parental Math Talk with Young Children

Parent-child interaction is critical for child development, yet parents may need guidance in some aspects of their engagement with their children. Current research on educational math robots focuses on child-robot interactions but falls short of including the parents and integrating the critical role they play in children's learning. We explore how educational robots can be designed to facilitate parent-child conversations, focusing on math talk, a predictor of later math ability in children. We prototyped capabilities for a social robot to support math talk via reading and play activities and conducted an exploratory Wizard-of-Oz in-home study for parent-child interactions facilitated by a robot. Our findings yield insights into how parents were inspired by the robot's prompts, their desired interaction styles and methods for the robot, and how they wanted to include the robot in the activities, leading to guidelines for the design of parent-child-robot interaction in educational contexts.

cs.RO↗

arXiv2023

Learning to Maximize Mutual Information for Dynamic Feature Selection

Feature selection helps reduce data acquisition costs in ML, but the standard approach is to train models with static feature subsets. Here, we consider the dynamic feature selection (DFS) problem where a model sequentially queries features based on the presently available information. DFS is often addressed with reinforcement learning, but we explore a simpler approach of greedily selecting features based on their conditional mutual information. This method is theoretically appealing but requires oracle access to the data distribution, so we develop a learning approach based on amortized optimization. The proposed method is shown to recover the greedy policy when trained to optimality, and it outperforms numerous existing feature selection methods in our experiments, thus validating it as a simple but powerful approach for this problem.

cs.LG↗

arXiv2022

Understanding Factors that Shape Children's Long Term Engagement with an In-Home Learning Companion Robot

Social robots are emerging as learning companions for children, and research shows that they facilitate the development of interest and learning even through brief interactions. However, little is known about how such technologies might support these goals in authentic environments over long-term periods of use and interaction. We designed a learning companion robot capable of supporting children reading popular-science books by expressing social and informational commentaries. We deployed the robot in homes of 14 families with children aged 10-12 for four weeks during the summer. Our analysis revealed critical factors that affected children's long-term engagement and adoption of the robot, including external factors such as vacations, family visits, and extracurricular activities; family/parental involvement; and children's individual interests. We present four in-depth cases that illustrate these factors and demonstrate their impact on children's reading experiences and discuss the implications of our findings for robot design.

cs.RO↗

arXiv2019

Socially Inspired Communication in Swarm Robotics

Localized communication in swarms has been shown to increase swarm effectiveness in some situations by allowing for additional opportunities for cooperation. However, communication and utilization of potentially outdated information is also a concern. We present an explicit non-directional goal-based communication model and message accept/reject scheme, and test our model in a set of object gathering experiments with a swarm of robots. The results of the experiments indicate that even low levels of communication regarding the swarm's goal outperform high levels of random information communication.

cs.RO↗