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With the rapid progress of Multimodal LLMs, evaluating their mathematical reasoning capabilities has become an increasingly important research direction. In particular, visual-textual mathematical reasoning serves as a key indicator of an…
Current critical systems commonly use a lot of floating-point computations, and thus the testing or static analysis of programs containing floating-point operators has become a priority. However, correctly defining the semantics of common…
We propose a light-weight video frame interpolation algorithm. Our key innovation is an instance-level supervision that allows information to be learned from the high-resolution version of similar objects. Our experiment shows that the…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
The inherent heavy computation of deep neural networks prevents their widespread applications. A widely used method for accelerating model inference is quantization, by replacing the input operands of a network using fixed-point values.…
This article presents a detailed introduction to density-based topology optimisation of fluid flow problems. The goal is to allow new students and researchers to quickly get started in the research area and to skip many of the initial…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
Very large volumes of spatial data increasingly become available and demand effective management. While there has been decades of research on spatial data management, few works consider the current state of commodity hardware, having…
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
The concept of a Point Cloud has played an increasingly important role in many areas of Engineering, Science, and Mathematics. Examples are: LIDAR, 3D-Printing, Data Analysis, Computer Graphics, Machine Learning, Mathematical Visualization,…
We extend the Stainless deductive verifier with floating-point support, providing the first automated verification support for floating-point numbers for a subset of Scala that includes polymorphism, recursion and higher-order functions. We…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
ExaScale systems will be a key driver for simulations that are essential for advance of science and economic growth. We aim to present a new concept of microprocessor for floating-point computations useful for being a basic building block…
Despite strong results on many tasks, multimodal large language models (MLLMs) still underperform on visual mathematical problem solving, especially in reliably perceiving and interpreting diagrams. Inspired by human problem-solving, we…
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
Multilayer perceptrons (MLPs) remain fundamental to modern deep learning, yet their algorithmic details are rarely presented in complete, explicit \emph{batch matrix-form}. Rather, most references express gradients per sample or rely on…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…