Neural Information Processing Systems http://nips.cc/

Learning general-purpose representations from perceptual inputs is a hallmark of human intelligence. For example, people can write out numbers or characters, or even draw doodles, by characterizing these tasks as different instantiations of the same generic underlying process---compositional arrangements of different forms of pen strokes. Crucially, learning to do one task, say writing, implies reasonable competence at another, say drawing, on account of this shared process. We present Drawing out of Distribution (DooD), a neuro-symbolic generative model of stroke-based drawing that can learn such general-purpose representations. In contrast to prior work, DooD operates directly on images, requires no supervision or expensive test-time inference, and performs unsupervised amortized inference with a symbolic stroke model that better enables both interpretability and generalization. We evaluate DooD on its ability to generalize across both data and tasks. We first perform zero-shot transfer from one dataset (e.g.

Deep generative models have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that deep generative networks can efficiently generate high-dimensional complex data from a low-dimensional easy-to-sample distribution. However, this phenomenon can not be justified by existing theories. The widely held manifold hypothesis speculates that real-world data sets, such as natural images and signals, exhibit low-dimensional geometric structures. In this paper, we take such low-dimensional data structures into consideration by assuming that data distributions are supported on a low-dimensional manifold. We prove approximation and estimation theories of deep generative networks for estimating distributions on a low-dimensional manifold under the Wasserstein-1 loss. We show that the Wasserstein-1 loss converges to zero at a fast rate depending on the intrinsic dimension instead of the ambient data dimension. Our theory leverages the low-dimensional geometric structures in data sets and justifies the practical power of deep generative models. We require no smoothness assumptions on the data distribution which is desirable in practice.

We categorize meta-learning evaluation into two settings: $\textit{in-distribution}$ [ID], in which the train and test tasks are sampled $\textit{iid}$ from the same underlying task distribution, and $\textit{out-of-distribution}$ [OOD], in which they are not. While most meta-learning theory and some FSL applications follow the ID setting, we identify that most existing few-shot classification benchmarks instead reflect OOD evaluation, as they use disjoint sets of train (base) and test (novel) classes for task generation. This discrepancy is problematic because -- as we show on numerous benchmarks -- meta-learning methods that perform better on existing OOD datasets may perform significantly worse in the ID setting. In addition, in the OOD setting, even though current FSL benchmarks seem befitting, our study highlights concerns in 1) reliably performing model selection for a given meta-learning method, and 2) consistently comparing the performance of different methods. To address these concerns, we provide suggestions on how to construct FSL benchmarks to allow for ID evaluation as well as more reliable OOD evaluation. Our work aims to inform the meta-learning community about the importance and distinction of ID vs. OOD evaluation, as well as the subtleties of OOD evaluation with current benchmarks.

We study the general problem of testing whether an unknown discrete distribution belongs to a specified family of distributions. More specifically, given a distribution family P and sample access to an unknown discrete distribution D, we want to distinguish (with high probability) between the case that D in P and the case that D is ε-far, in total variation distance, from every distribution in P . This is the prototypical hypothesis testing problem that has received significant attention in statistics and, more recently, in computer science. The main contribution of this work is a simple and general testing technique that is applicable to all distribution families whose Fourier spectrum satisfies a certain approximate sparsity property. We apply our Fourier-based framework to obtain near sample-optimal and computationally efficient testers for the following fundamental distribution families: Sums of Independent Integer Random Variables (SIIRVs), Poisson Multinomial Distributions (PMDs), and Discrete Log-Concave Distributions. For the first two, ours are the first non-trivial testers in the literature, vastly generalizing previous work on testing Poisson Binomial Distributions. For the third, our tester improves on prior work in both sample and time complexity.

Outline of Appendices Appendix A describes Chroma-V AE's model and training procedure in detail. Appendix B describes the experimental details in Sections 3 and 5. Appendix C contains Appendix D is a statement on the societal impact of our work. Figure 6 depicts Chroma-V AE and its training procedure. Section 3: CelebA (Synthetic Patch) We use standard CNN architecture. Section 5: ColouredMNIST We use standard CNN architecture.

Physics-informed machine learning provides an approach to combining data and governing physics laws for solving complex partial differential equations (PDEs). However, efficiently solving PDEs with varying parameters and changing initial conditions and boundary conditions (ICBCs) with theoretical guarantees remains an open challenge. We propose a hybrid framework that uses a neural network to learn B-spline control points to approximate solutions to PDEs with varying system and ICBC parameters. The proposed network can be trained efficiently as one can directly specify ICBCs without imposing losses, calculate physics-informed loss functions through analytical formulas, and requires only learning the weights of B-spline functions as opposed to both weights and basis as in traditional neural operator learning methods. We provide theoretical guarantees that the proposed B-spline networks serve as universal approximators for the set of solutions of PDEs with varying ICBCs under mild conditions and establish bounds on the generalization errors in physics-informed learning. We also demonstrate in experiments that the proposed B-spline network can solve problems with discontinuous ICBCs and outperforms existing methods, and is able to learn solutions of 3D dynamics with diverse initial conditions.

In mobile robot navigation, despite advancements, the generation of optimal paths often disrupts pedestrian areas. To tackle this, we propose three key contributions to improve human-robot coexistence in shared spaces. Firstly, we have established a comprehensive framework to understand disturbances at individual and flow levels. Our framework provides specialized computational strategies for in-depth studies of human-robot interactions from both micro and macro perspectives. By employing novel penalty terms, namely Flow Disturbance Penalty (FDP) and Individual Disturbance Penalty (IDP), our framework facilitates a more nuanced assessment and analysis of the robot navigation's impact on pedestrians. Secondly, we introduce an innovative sampling-based navigation system that adeptly integrates a suite of safety measures with the predictability of robotic movements. This system not only accounts for traditional factors such as trajectory length and travel time but also actively incorporates pedestrian awareness. Our navigation system aims to minimize disturbances and promote harmonious coexistence by considering safety protocols, trajectory clarity, and pedestrian engagement. Lastly, we validate our algorithm's effectiveness and real-time performance through simulations and real-world tests, demonstrating its ability to navigate with minimal pedestrian disturbance in various environments.

Here we describe well-known chaotic sequences, including new generalizations, with application to random number generation, highly non-linear auto-regressive models for times series, simulation, random permutations, and the use of big numbers (libraries available in programming languages to work with numbers with hundreds of decimals) as standard computer precision almost always produces completely erroneous results after a few iterations -- a fact rarely if ever mentioned in the scientific literature, but illustrated here, together with a solution. It is possible that all scientists who published on chaotic processes, used faulty numbers because of this issue. This article is accessible to non-experts, even though we solve a special stochastic equation for the first time, providing an unexpected exact solution, for a new chaotic process that generalizes the logistic map. We also describe a general framework for continuous random number generators, and investigate the interesting auto-correlation structure associated with some of these sequences. References are provided, as well as fast source code to process big numbers accurately, and even an elegant mathematical proof in the last section.

While companies like Amazon pour considerable resources into finding ways of using drones to deliver such things as shoes and dog treats, Zipline has been saving lives in Rwanda since October 2016 with drones that deliver blood. Zipline's autonomous fixed-wing drones now form an integral part of Rwanda's medical-supply infrastructure, transporting blood products from a central distribution center to hospitals across the country. And in 2018, Zipline's East African operations will expand to include Tanzania, a much larger country. Delivering critical medical supplies in this region typically involves someone spending hours (or even days) driving a cooler full of life-saving medicine or blood along windy dirt roads. Such deliveries can become dangerous or even impossible to make if roads and bridges get washed out.