Related papers: A Triangle Inequality for Cosine Similarity

We show that the gradient of the cosine similarity between two points goes to zero in two under-explored settings: (1) if a point has large magnitude or (2) if the points are on opposite ends of the latent space. Counterintuitively, we…

Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…

Datasets often contain values that naturally reside in a metric space: numbers, strings, geographical locations, machine-learned embeddings in a Euclidean space, and so on. We study the computational complexity of repairing inconsistent…

Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The…

Word Embeddings have recently imposed themselves as a standard for representing word meaning in NLP. Semantic similarity between word pairs has become the most common evaluation benchmark for these representations, with vector cosine being…

We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…

Similarity search in math is to find mathematical expressions that are similar to a user's query. We conceptualized the similarity factors between mathematical expressions, and proposed an approach to math similarity search (MSS) by…

Accurately evaluating the similarity of object vector embeddings is of critical importance for natural language processing, information retrieval and classification tasks. Popular similarity scores (e.g cosine similarity) are based on pairs…

In this paper we study an application of an information distance between two measurements to the problem of non-contextuality and local realism. We postulate the triangle principle which states that any information distance is well defined…

Similarity search finds objects that are similar to a given query object based on a similarity metric. As the amount and variety of data continue to grow, similarity search in metric spaces has gained significant attention. Metric spaces…

Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications.…

In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly…

In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…

Measuring the similarity of images is a fundamental problem to computer vision for which no universal solution exists. While simple metrics such as the pixel-wise L2-norm have been shown to have significant flaws, they remain popular. One…

Embedding-based retrieval aims to learn a shared semantic representation space for both queries and items, enabling efficient and effective item retrieval through approximate nearest neighbor (ANN) algorithms. In current industrial…

Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…

To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…

Graph similarity search has received considerable attention in many applications, such as bioinformatics, data mining, pattern recognition, and social networks. Existing methods for this problem have limited scalability because of the huge…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

Determining the interaction partners among protein/domain families poses hard computational problems, in particular in the presence of paralogous proteins. Available approaches aim to identify interaction partners among protein/domain…