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The transformer has revolutionized modern AI across language, vision, and beyond. It consists of $L$ layers, each running $H$ attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input…
We construct examples of contingency tables on $n$ binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
In this paper, we present the case for a declarative foundation for data-intensive machine learning systems. Instead of creating a new system for each specific flavor of machine learning task, or hardcoding new optimizations, we argue for…
Industrial transfer learning increases the adaptability of deep learning algorithms towards heterogenous and dynamic industrial use cases without high manual efforts. The appropriate selection of what to transfer can vastly improve a…
In machine learning, correlation clustering is an important problem whose goal is to partition the individuals into groups that correlate with their pairwise similarities as much as possible. In this work, we revisit the correlation…
We introduce a bisimulation learning algorithm for non-deterministic transition systems. We generalise bisimulation learning to systems with bounded branching and extend its applicability to model checking branching-time temporal logic,…
Tabled evaluation is an implementation technique that solves some problems of traditional Prolog systems in dealing with recursion and redundant computations. Most tabling engines determine if a tabled subgoal will produce or consume…
In many data analysis pipelines, a basic and time-consuming process is to produce join results and feed them into downstream tasks. Numerous enumeration algorithms have been developed for this purpose. To be a statistically meaningful…
The growing demand for intelligent services on resource-constrained edge devices has spurred the development of collaborative inference systems that distribute workloads across end devices, edge servers, and the cloud. While most existing…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
Given a graph $G$ that can be partitioned into $k$ disjoint expanders with outer conductance upper bounded by $\epsilon\ll 1$, can we efficiently construct a small space data structure that allows quickly classifying vertices of $G$…
A tight $\Omega((n/\sqrt{M})^{\log_2 7}M)$ lower bound is derived on the \io complexity of Strassen's algorithm to multiply two $n \times n$ matrices, in a two-level storage hierarchy with $M$ words of fast memory. A proof technique is…
We present Universal Conditional Logic (UCL), a mathematical framework for prompt optimization that transforms prompt engineering from heuristic practice into systematic optimization. Through systematic evaluation (N=305, 11 models, 4…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
Modern NLP systems require high-quality annotated data. In specialized domains, expert annotations may be prohibitively expensive. An alternative is to rely on crowdsourcing to reduce costs at the risk of introducing noise. In this paper we…
VQ (Vendor Qualification) and IOQ (Installation and Operation Qualification) audits are implemented in warehouses to ensure all equipment being turned over in the fulfillment network meets the quality standards. Audit checks are likely to…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…
In the bi-objective branch-and-bound literature, a key ingredient is objective branching, i.e. to create smaller and disjoint sub-problems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound…
Given a next-to-leading order calculation, we show how to set up a computer program, which generates a sequence of unweighted momentum configurations, each configuration containing either n or n+1 four-vectors, such that for any infrared…