Related papers: Space lower bounds for linear prediction in the st…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
In this paper, we focus on lower bounds and algorithms for some basic geometric problems in the one-pass (insertion only) streaming model. The problems considered are grouped into three categories: (i) Klee's measure (ii) Convex body…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a…
In this paper we introduce and study the \textsc{StreamingCycles} problem, a random order streaming version of the Boolean Hidden Hypermatching problem that has been instrumental in streaming lower bounds over the past decade. In this…
We study streaming algorithms for the fundamental geometric problem of computing the cost of the Euclidean Minimum Spanning Tree (MST) on an $n$-point set $X \subset \mathbb{R}^d$. In the streaming model, the points in $X$ can be added and…
We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
A few models have tried to tackle the link prediction problem, also known as knowledge graph completion, by embedding knowledge graphs in comparably lower dimensions. However, the state-of-the-art results are attained at the cost of…
We identify a sharp separation in the streaming space complexity of Maximum Cut when the algorithm must output an approximate cut (rather than only the approximate value). For dense graphs, we show that $O(n/\varepsilon^2)$ space is…
We consider the problem of performing linear regression over a stream of $d$-dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without…
Previous research has explored the computational expressivity of Transformer models in simulating Boolean circuits or Turing machines. However, the learnability of these simulators from observational data has remained an open question. Our…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
Recent feed-forward reconstruction models like VGGT and $\pi^3$ achieve impressive reconstruction quality but cannot process streaming videos due to quadratic memory complexity, limiting their practical deployment. While existing streaming…
In this column, we overview recent progress by many authors on understanding the approximability of constraint satisfaction problems (CSPs) in low-space streaming models. Inspired by this recent progress, we collate nine conjectural lower…
An autoassociative memory model is a function that, given a set of data points, takes as input an arbitrary vector and outputs the most similar data point from the memorized set. However, popular memory models fail to retrieve images even…
We present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum…