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Polycube layouts for 3D models effectively support a wide variety of applications such as hexahedral mesh construction, seamless texture mapping, spline fitting, and multi-block grid generation. However, the automated construction of valid polycube layouts suffers from robustness issues: the state-of-the-art deformation-based methods are not guaranteed to find a valid solution. In this paper we present a novel approach which is guaranteed to return a valid polycube layout for 3D models of genus 0. Our algorithm is based on a dual representation of polycubes; we construct polycube layouts by iteratively adding or removing dual loops. The iterative nature of our algorithm facilitates a seamless trade-off between quality and complexity of the solution. Our method is efficient and can be implemented using comparatively simple algorithmic building blocks. We experimentally compare the results of our algorithm against state-of-the-art methods. Our fully automated method always produces provably valid polycube layouts whose quality - assessed via the quality of derived hexahedral meshes - is on par with state-of-the-art deformation methods.

In statistical mechanics, computing the partition function is generally difficult. An approximation method using a variational autoregressive network (VAN) has been proposed recently. This approach offers the advantage of directly calculating the generation probabilities while obtaining a significantly large number of samples. The present study introduces a novel approximation method that employs samples derived from quantum annealing machines in conjunction with VAN, which are empirically assumed to adhere to the Gibbs-Boltzmann distribution. When applied to the finite-size Sherrington-Kirkpatrick model, the proposed method demonstrates enhanced accuracy compared to the traditional VAN approach and other approximate methods, such as the widely utilized naive mean field.

We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and the decision variables. We call such problems conditional stochastic optimization problems. They arise in many applications, such as uplift modeling, reinforcement learning, and contextual optimization. We propose a specialized single time-scale stochastic method for nonconvex constrained conditional stochastic optimization problems with a Lipschitz smooth outer function and a generalized differentiable inner function. In the method, we approximate the inner conditional expectation with a rich parametric model whose mean squared error satisfies a stochastic version of a {\L}ojasiewicz condition. The model is used by an inner learning algorithm. The main feature of our approach is that unbiased stochastic estimates of the directions used by the method can be generated with one observation from the joint distribution per iteration, which makes it applicable to real-time learning. The directions, however, are not gradients or subgradients of any overall objective function. We prove the convergence of the method with probability one, using the method of differential inclusions and a specially designed Lyapunov function, involving a stochastic generalization of the Bregman distance. Finally, a numerical illustration demonstrates the viability of our approach.

We experimentally evaluated the accuracy with which material properties can be estimated through object compression by two standard parallel jaw grippers and a force/torque sensor mounted at the robot wrist, with a professional biaxial compression device used as reference. Gripper effort versus position curves were obtained and transformed into stress/strain curves. The modulus of elasticity was estimated at different strain points and the effect of multiple compression cycles (precycling), compression speed, and the gripper surface area on estimation was studied. Viscoelasticity was estimated using the energy absorbed in a compression/decompression cycle, the Kelvin-Voigt, and Hunt-Crossley models. We found that: (1) slower compression speeds improved elasticity estimation, while precycling or surface area did not; (2) the robot grippers, even after calibration, were found to have a limited capability of delivering accurate estimates of absolute values of Young's modulus and viscoelasticity; (3) relative ordering of material characteristics was largely consistent across different grippers; (4) despite the nonlinear characteristics of deformable objects, fitting linear stress/strain approximations led to more stable results than local estimates of Young's modulus; (5) the Hunt-Crossley model worked best to estimate viscoelasticity, from a single object compression. A two-dimensional space formed by elasticity and viscoelasticity estimates obtained from a single grasp is advantageous for the discrimination of the object material properties. We demonstrated the applicability of our findings in a mock single stream recycling scenario, where plastic, paper, and metal objects were correctly separated from a single grasp, even when compressed at different locations on the object. The data and code are publicly available.

It is well known that the spectral gap of the down-up walk over an $n$-partite simplicial complex (also known as Glauber dynamics) cannot be better than $O(1/n)$ due to natural obstructions such as coboundaries. We study an alternative random walk over partite simplicial complexes known as the sequential sweep or the systematic scan Glauber dynamics: Whereas the down-up walk at each step selects a random coordinate and updates it based on the remaining coordinates, the sequential sweep goes through each of the coordinates one by one in a deterministic order and applies the same update operation. It is natural, thus, to compare $n$-steps of the down-up walk with a single step of the sequential sweep. Interestingly, while the spectral gap of the $n$-th power of the down-up walk is still bounded from above by a constant, under a strong enough local spectral assumption (in the sense of Gur, Lifschitz, Liu, STOC 2022) we can show that the spectral gap of this walk can be arbitrarily close to 1. We also study other isoperimetric inequalities for these walks, and show that under the assumptions of local entropy contraction (related to the considerations of Gur, Lifschitz, Liu), these walks satisfy an entropy contraction inequality.

We introduce an algorithm that simplifies the construction of efficient estimators, making them accessible to a broader audience. 'Dimple' takes as input computer code representing a parameter of interest and outputs an efficient estimator. Unlike standard approaches, it does not require users to derive a functional derivative known as the efficient influence function. Dimple avoids this task by applying automatic differentiation to the statistical functional of interest. Doing so requires expressing this functional as a composition of primitives satisfying a novel differentiability condition. Dimple also uses this composition to determine the nuisances it must estimate. In software, primitives can be implemented independently of one another and reused across different estimation problems. We provide a proof-of-concept Python implementation and showcase through examples how it allows users to go from parameter specification to efficient estimation with just a few lines of code.

Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based methods, such as physics-informed neural networks (PINNs) and neural operators, exhibit deficiencies in robustness and generalization. To address these issues, numerous studies have integrated classical numerical frameworks with machine learning techniques, incorporating neural networks into parts of traditional numerical methods. In this study, we focus on hyperbolic conservation laws by replacing traditional numerical fluxes with neural operators. To this end, we developed loss functions inspired by established numerical schemes related to conservation laws and approximated numerical fluxes using Fourier neural operators (FNOs). Our experiments demonstrated that our approach combines the strengths of both traditional numerical schemes and FNOs, outperforming standard FNO methods in several respects. For instance, we demonstrate that our method is robust, has resolution invariance, and is feasible as a data-driven method. In particular, our method can make continuous predictions over time and exhibits superior generalization capabilities with out-of-distribution (OOD) samples, which are challenges that existing neural operator methods encounter.

Adaptive experiments use preliminary analyses of the data to inform further course of action and are commonly used in many disciplines including medical and social sciences. Because the null hypothesis and experimental design are not pre-specified, it has long been recognized that statistical inference for adaptive experiments is not straightforward. Most existing methods only apply to specific adaptive designs and rely on strong assumptions. In this work, we propose selective randomization inference as a general framework for analyzing adaptive experiments. In a nutshell, our approach applies conditional post-selection inference to randomization tests. By using directed acyclic graphs to describe the data generating process, we derive a selective randomization p-value that controls the selective type-I error without requiring independent and identically distributed data or any other modelling assumptions. We show how rejection sampling and Markov Chain Monte Carlo can be used to compute the selective randomization p-values and construct confidence intervals for a homogeneous treatment effect. To mitigate the risk of disconnected confidence intervals, we propose the use of hold-out units. Lastly, we demonstrate our method and compare it with other randomization tests using synthetic and real-world data.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.