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Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of Gerstewitz function [1], a vectorizing function is defined to replace a given set-valued…
In mathematics, many notations have been invented for the concise representation of mathematical formulae. Tensor index notation is one of such notations and has been playing a crucial role in describing formulae in mathematical physics.…
In this paper, we address the challenges faced by Value Iteration Networks (VIN) in handling larger input maps and mitigating the impact of accumulated errors caused by increased iterations. We propose a novel approach, Value Iteration…
Evaluation metric of visual captioning is important yet not thoroughly explored. Traditional metrics like BLEU, METEOR, CIDEr, and ROUGE often miss semantic depth, while trained metrics such as CLIP-Score, PAC-S, and Polos are limited in…
Background: Biological networks have a growing importance for the interpretation of high-throughput omics data. Integrative network analysis makes use of statistical and combinatorial methods to extract smaller subnetwork modules, and…
Annotations are central to effective data communication, yet most visualization tools treat them as secondary constructs -- manually defined, difficult to reuse, and loosely coupled to the underlying visualization grammar. We propose a…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
Second-order optimization approaches like the generalized Gauss-Newton method are considered more powerful as they utilize the curvature information of the objective function with preconditioning matrices. Albeit offering tempting…
In this position paper, we consider the state of computer vision research with respect to invariance to the horizontal orientation of an image -- what we term reflection invariance. We describe why we consider reflection invariance to be an…
Automating the conversion of user interface design into code (image-to-code or image-to-UI) is an active area of software engineering research. However, the state-of-the-art solutions do not achieve high fidelity to the original design, as…
Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. However, GNNs lack transparency as they cannot provide understandable explanations for their predictions. To…
Human-annotated datasets with explicit difficulty ratings are essential in intelligent educational systems. Although embedding vector spaces are widely used to represent semantic closeness and are promising for analyzing text difficulty,…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
Lexically constrained neural machine translation (NMT), which controls the generation of NMT models with pre-specified constraints, is important in many practical scenarios. Due to the representation gap between discrete constraints and…
The Global Vectors for word representation (GloVe), introduced by Jeffrey Pennington et al. is reported to be an efficient and effective method for learning vector representations of words. State-of-the-art performance is also provided by…
Learning vector representation for words is an important research field which may benefit many natural language processing tasks. Two limitations exist in nearly all available models, which are the bias caused by the context definition and…
Most network embedding algorithms consist in measuring co-occurrences of nodes via random walks then learning the embeddings using Skip-Gram with Negative Sampling. While it has proven to be a relevant choice, there are alternatives, such…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…