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We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn…

We consider an efficient two-party protocol for securely computing the similarity of strings w.r.t. an extended edit distance measure. Here, two parties possessing strings $x$ and $y$, respectively, want to jointly compute an approximate…

Measuring the in-context computational effort of language models is a key challenge, as metrics like next-token loss fail to capture reasoning complexity. Prior methods based on latent state compressibility can be invasive and unstable. We…

Modern day computing increasingly relies on specialization to satiate growing performance and efficiency requirements. A core challenge in designing such specialized hardware architectures is how to perform mapping space search, i.e.,…

Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two…

Word embeddings are trained to predict word cooccurrence statistics, which leads them to possess different lexical properties (syntactic, semantic, etc.) depending on the notion of context defined at training time. These properties manifest…

The sliding window approach provides an elegant way to handle contexts of sizes larger than the Transformer's input window, for tasks like language modeling. Here we extend this approach to the sequence-to-sequence task of document parsing.…

Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$.…

Computing optimal transport (OT) distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. In this paper, we study the problem of approximating the general OT distance…

Audio alignment is a fundamental preprocessing step in many MIR pipelines. For two audio clips with M and N frames, respectively, the most popular approach, dynamic time warping (DTW), has O(MN) requirements in both memory and computation,…

The standard bag-of-words vector space model (VSM) is efficient, and ubiquitous in information retrieval, but it underestimates the similarity of documents with the same meaning, but different terminology. To overcome this limitation,…

Loss functions are fundamental to learning accurate 3D point cloud models, yet common choices trade geometric fidelity for computational cost. Chamfer Distance is efficient but permits many-to-one correspondences, while Earth Mover Distance…

Given two point sets $S$ and $T$, the minimum-cost many-to-many matching with demands (MMD) problem is the problem of finding a minimum-cost many-to-many matching between $S$ and $T$ such that each point of $S$ (respectively $T$) is matched…

Optimal transport (OT) and maximum mean discrepancies (MMD) are now routinely used in machine learning to compare probability measures. We focus in this paper on \emph{Sinkhorn divergences} (SDs), a regularized variant of OT distances which…

Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…

A measure of similarity between text embeddings can be considered adequate only if it adheres to the human perception of similarity between texts. In this paper, we introduce the distance-to-distance ratio (DDR), a novel measure of…

Lexical semantic change detection (LSCD) increasingly relies on contextualised language model embeddings, yet most approaches still quantify change using a small set of semantic change metrics, primarily Average Pairwise Distance (APD) and…

Document parsing is a fine-grained task where image resolution significantly impacts performance. While advanced research leveraging vision-language models benefits from high-resolution input to boost model performance, this often leads to…

Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…

We consider the Maximum-weight Matching (MWM) problem in the streaming sliding window model of computation. In this model, the input consists of a sequence of weighted edges on a given vertex set $V$ of size $n$. The objective is to…