Related papers: Polynomial diagrams for microstructure modelling

Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical-computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a…

It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…

In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…

From AlexNet to Inception, autoencoders to diffusion models, the development of novel and powerful deep learning models and learning algorithms has proceeded at breakneck speeds. In part, we believe that rapid iteration of model…

Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…

Continuous-time deep learning models, such as neural ordinary differential equations (ODEs), offer a promising framework for surrogate modeling of complex physical systems. A central challenge in training these models lies in learning…

Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…

Simulations with an explicit description of intermolecular forces using electronic structure methods are still not feasible for many systems of interest. As a result, empirical methods such as force fields (FF) have become an established…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes,…

The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on…

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…

The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous…

Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…