Neural fields are a highly effective representation across visual computing. This work observes that fitting these fields is greatly improved by incorporating spatial stochasticity during training, and that this simple technique can replace or even outperform custom-designed hierarchies and frequency space constructions. The approach is formalized as implicitly operating on a blurred version of the field, evaluated in-expectation by sampling with Gaussian-distributed offsets. Querying the blurred field during optimization greatly improves convergence and robustness, akin to the role of preconditioners in numerical linear algebra. This implicit, sampling-based perspective fits naturally into the neural field paradigm, comes at no additional cost, and is extremely simple to implement. We describe the basic theory of this technique, including details such as handling boundary conditions, and extending to a spatially-varying blur. Experiments demonstrate this approach on representations including coordinate MLPs, neural hashgrids, triplanes, and more, across tasks including surface reconstruction and radiance fields. In settings where custom-designed hierarchies have already been developed, stochastic preconditioning nearly matches or improves their performance with a simple and unified approach; in settings without existing hierarchies it provides an immediate boost to quality and robustness.

Increasingly complex and autonomous systems require machine ethics to maximize the benefits and minimize the risks to society arising from the new technology. It is challenging to decide which type of ethical theory to employ and how to implement it effectively. This survey provides a threefold contribution. Firstly, it introduces a taxonomy to analyze the field of machine ethics from an ethical, implementational, and technical perspective. Secondly, an exhaustive selection and description of relevant works is presented. Thirdly, applying the new taxonomy to the selected works, dominant research patterns and lessons for the field are identified, and future directions for research are suggested.

One of the best ways for developers to test and improve their skills in a fun and challenging way are programming challenges, offered by a plethora of websites. For the inexperienced ones, some of the problems might appear too challenging, requiring some suggestions to implement a solution. On the other hand, tagging problems can be a tedious task for problem creators. In this paper, we focus on automating the task of tagging a programming challenge description using machine and deep learning methods. We observe that the deep learning methods implemented outperform well-known IR approaches such as tf-idf, thus providing a starting point for further research on the task.

Over the last few decades, many distinct lines of research aimed at automating mathematics have been developed, including computer algebra systems (CASs) for mathematical modelling, automated theorem provers for first-order logic, SAT/SMT solvers aimed at program verification, and higher-order proof assistants for checking mathematical proofs. More recently, some of these lines of research have started to converge in complementary ways. One success story is the combination of SAT solvers and CASs (SAT+CAS) aimed at resolving mathematical conjectures. Many conjectures in pure and applied mathematics are not amenable to traditional proof methods. Instead, they are best addressed via computational methods that involve very large combinatorial search spaces. SAT solvers are powerful methods to search through such large combinatorial spaces---consequently, many problems from a variety of mathematical domains have been reduced to SAT in an attempt to resolve them. However, solvers traditionally lack deep repositories of mathematical domain knowledge that can be crucial to pruning such large search spaces. By contrast, CASs are deep repositories of mathematical knowledge but lack efficient general search capabilities. By combining the search power of SAT with the deep mathematical knowledge in CASs we can solve many problems in mathematics that no other known methods seem capable of solving. We demonstrate the success of the SAT+CAS paradigm by highlighting many conjectures that have been disproven, verified, or partially verified using our tool MathCheck. These successes indicate that the paradigm is positioned to become a standard method for solving problems requiring both a significant amount of search and deep mathematical reasoning. For example, the SAT+CAS paradigm has recently been used by Heule, Kauers, and Seidl to find many new algorithms for $3\times3$ matrix multiplication.

Figures are an important channel for scientific communication, used to express complex ideas, models and data in ways that words cannot. However, this visual information is mostly ignored in analyses of the scientific literature. In this paper, we demonstrate the utility of using scientific figures as markers of knowledge domains in science, which can be used for classification, recommender systems, and studies of scientific information exchange. We encode sets of images into a visual signature, then use distances between these signatures to understand how patterns of visual communication compare with patterns of jargon and citation structures. We find that figures can be as effective for differentiating communities of practice as text or citation patterns. We then consider where these metrics disagree to understand how different disciplines use visualization to express ideas. Finally, we further consider how specific figure types propagate through the literature, suggesting a new mechanism for understanding the flow of ideas apart from conventional channels of text and citations. Our ultimate aim is to better leverage these information-dense objects to improve scientific communication across disciplinary boundaries.