Related papers: Similarity Learning with neural networks

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…

The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…

An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological…

Similarity query is the family of queries based on some similarity metrics. Unlike the traditional database queries which are mostly based on value equality, similarity queries aim to find targets "similar enough to" the given data objects,…

Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…

Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…

Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

This paper presents a deep nonlinear metric learning framework for data visualization on an image dataset. We propose the Triangular Similarity and prove its equivalence to the Cosine Similarity in measuring a data pair. Based on this novel…

We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We…

What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…

In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns : the gauge symmetry Z 2 . This symmetry is present in physical problems from topological transitions to QCD, and controls the…

Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

Graph neural network (GNN) has gained increasing popularity in recent years owing to its capability and flexibility in modeling complex graph structure data. Among all graph learning methods, hypergraph learning is a technique for exploring…

We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…

Deep metric learning for vision is trained by optimizing a representation network to map (non-)matching image pairs to (non-)similar representations. During testing, which typically corresponds to image retrieval, both database and query…