**Lightweight Probabilistic Deep Network**

Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical CNN architectures in computer vision only compound this problem. Uncertainty in neural networks has thus been largely ignored in practice, despite the fact that it may provide important information about the reliability of predictions and the inner workings of the network. In this paper, we introduce two lightweight approaches to making supervised learning with probabilistic deep networks practical: First, we suggest probabilistic output layers for classification and regression that require only minimal changes to existing networks. Second, we employ assumed density filtering and show that activation uncertainties can be propagated in a practical fashion through the entire network, again with minor changes. Both probabilistic networks retain the predictive power of the deterministic counterpart, but yield uncertainties that correlate well with the empirical error induced by their predictions. Moreover, the robustness to adversarial examples is significantly increased. … **Proto-MAML**

Few-shot classification refers to learning a classifier for new classes given only a few examples. While a plethora of models have emerged to tackle this recently, we find the current procedure and datasets that are used to systematically assess progress in this setting lacking. To address this, we propose Meta-Dataset: a new benchmark for training and evaluating few-shot classifiers that is large-scale, consists of multiple datasets, and presents more natural and realistic tasks. The aim is to measure the ability of state-of-the-art models to leverage diverse sources of data to achieve higher generalization, and to evaluate that generalization ability in a more challenging setting. We additionally measure robustness of current methods to variations in the number of available examples and the number of classes. Finally our extensive empirical evaluation leads us to identify weaknesses in Prototypical Networks and MAML, two popular few-shot classification methods, and to propose a new method, Proto-MAML, which achieves improved performance on our benchmark. … **STROOPWAFEL**

Gravitational-wave observations of double compact object (DCO) mergers are providing new insights into the physics of massive stars and the evolution of binary systems. Making the most of expected near-future observations for understanding stellar physics will rely on comparisons with binary population synthesis models. However, the vast majority of simulated binaries never produce DCOs, which makes calculating such populations computationally inefficient. We present an importance sampling algorithm, STROOPWAFEL, that improves the computational efficiency of population studies of rare events, by focusing the simulation around regions of the initial parameter space found to produce outputs of interest. We implement the algorithm in the binary population synthesis code COMPAS, and compare the efficiency of our implementation to the standard method of Monte Carlo sampling from the birth probability distributions. STROOPWAFEL finds $\sim$25-200 times more DCO mergers than the standard sampling method with the same simulation size, and so speeds up simulations by up to two orders of magnitude. Finding more DCO mergers automatically maps the parameter space with far higher resolution than when using the traditional sampling. This increase in efficiency also leads to a decrease of a factor $\sim$3-10 in statistical sampling uncertainty for the predictions from the simulations. This is particularly notable for the distribution functions of observable quantities such as the black hole and neutron star chirp mass distribution, including in the tails of the distribution functions where predictions using standard sampling can be dominated by sampling noise. … **Neural Logic Machine (NLM)**

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks—as function approximators, and logic programming—as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone. …

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May 2021

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