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Bounded treewidth is one of the most cited combinatorial invariants, which was applied in the literature for solving several counting problems efficiently. A canonical counting problem is #SAT, which asks to count the satisfying assignments…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
Domain randomization is a popular technique for improving domain transfer, often used in a zero-shot setting when the target domain is unknown or cannot easily be used for training. In this work, we empirically examine the effects of domain…
The tree-width of a multivariate polynomial is the tree-width of the hypergraph with hyperedges corresponding to its terms. Multivariate polynomials of bounded tree-width have been studied by Makowsky and Meer as a new sparsity condition…
The treewidth boundedness problem for a logic asks for the existence of an upper bound on the treewidth of the models of a given formula in that logic. This problem is found to be undecidable for first order logic. We consider a…
We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a set $S$ of vertices such…
Overparameterization refers to the important phenomenon where the width of a neural network is chosen such that learning algorithms can provably attain zero loss in nonconvex training. The existing theory establishes such global convergence…
Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR…
Batch Normalization (BN) is extensively employed in various network architectures by performing standardization within mini-batches. A full understanding of the process has been a central target in the deep learning communities. Unlike…
Open-set single-source domain generalization aims to use a single-source domain to learn a robust model that can be generalized to unknown target domains with both domain shifts and label shifts. The scarcity of the source domain and the…
Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…
The existing internet-scale image and video datasets cover a wide range of everyday objects and tasks, bringing the potential of learning policies that generalize in diverse scenarios. Prior works have explored visual pre-training with…
Generative Flow Networks (GFlowNets) have emerged as an innovative learning paradigm designed to address the challenge of sampling from an unnormalized probability distribution, called the reward function. This framework learns a policy on…
Building an AI agent that can design on its own has been a goal since the 1980s. Recently, deep learning has shown the ability to learn from large-scale data, enabling significant advances in data-driven design. However, learning over prior…
A breakthrough result of Cygan et al. (FOCS 2011) showed that connectivity problems parameterized by treewidth can be solved much faster than the previously best known time $\mathcal{O}^*(2^{\mathcal{O}(tw \log(tw))})$. Using their inspired…
The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
We introduce tree-width for first order formulae \phi, fotw(\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed…
Multi-Source Domain Generalization (DG) is the task of training on multiple source domains and achieving high classification performance on unseen target domains. Recent methods combine robust features from web-scale pretrained backbones…
The data-driven approach to robot control has been gathering pace rapidly, yet generalization to unseen task domains remains a critical challenge. We argue that the key to generalization is representations that are (i) rich enough to…