Related papers: Summer Research Report: Towards Incremental Lazard…
Large language models often fail on multi-step reasoning due to fixed reasoning strategies that ignore problem specific difficulty. We introduce CARD (Complexity Agnostic Recursive Decomposition), a framework that predicts problem…
We introduce beyond-worst-case analysis into symbolic computation. This is an extensive field which almost entirely relies on worst-case bit complexity, and we start from a basic problem in the field: isolating the real roots of univariate…
Aligning theoretical atomistic structural models of materials with available experimental data presents a significant challenge for disordered systems. The configurational space to navigate is vast, and faithful realizations require large…
Ashenhurst-Curtis decomposition (ACD) is a decomposition technique used, in particular, to map combinational logic into lookup tables (LUTs) structures when synthesizing hardware designs. However, available implementations of ACD suffer…
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an…
The ever-increasing quantity of multivariate process data is driving a need for skilled engineers to analyze, interpret, and build models from such data. Multivariate data analytics relies heavily on linear algebra, optimization, and…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
Lithography modeling is a crucial problem in chip design to ensure a chip design mask is manufacturable. It requires rigorous simulations of optical and chemical models that are computationally expensive. Recent developments in machine…
This paper addresses the unrealistic aspect of the commonly adopted Continuous Incremental Semantic Segmentation (CISS) scenario, termed overlapped. We point out that overlapped allows the same image to reappear in future tasks with…
This paper proposes an incremental solution to Fast Subclass Discriminant Analysis (fastSDA). We present an exact and an approximate linear solution, along with an approximate kernelized variant. Extensive experiments on eight image…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
Causal structure discovery (CSD) models are making inroads into several domains, including Earth system sciences. Their widespread adaptation is however hampered by the fact that the resulting models often do not take into account the…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems and medium-scale nonlinear systems. Chordal decomposition…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
The Winograd Schema Challenge (WSC) is a natural language understanding task proposed as an alternative to the Turing test in 2011. In this work we attempt to solve WSC problems by reasoning with additional knowledge. By using an approach…
The rapid advances in Vision Transformer (ViT) refresh the state-of-the-art performances in various vision tasks, overshadowing the conventional CNN-based models. This ignites a few recent striking-back research in the CNN world showing…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…