**SelectionNet**

Recent years have witnessed growing interests in designing efficient neural networks and neural architecture search (NAS). Although remarkable efficiency and accuracy have been achieved, existing expert designed and NAS models neglect that input instances are of varying complexity thus different amount of computation is required. Therefore, inference with a fixed model that processes all instances through the same transformations would waste plenty of computational resources. Customizing the model capacity in an instance-aware manner is highly demanded. In this paper, we introduce a novel network ISBNet to address this issue, which supports efficient instance-level inference by selectively bypassing transformation branches of infinitesimal importance weight. We also propose lightweight hypernetworks SelectionNet to generate these importance weights instance-wisely. Extensive experiments have been conducted to evaluate the efficiency of ISBNet and the results show that ISBNet achieves extremely efficient inference comparing to existing networks. For example, ISBNet takes only 12.45% parameters and 45.79% FLOPs of the state-of-the-art efficient network ShuffleNetV2 with comparable accuracy. … **Nonlinear Dimensionality Reduction (NLDR)**

High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space. Top-left: a 3D dataset of 1000 points in a spiraling band (a.k.a. the Swiss roll) with a rectangular hole in the middle. Top-right: the original 2D manifold used to generate the 3D dataset. Bottom left and right: 2D recoveries of the manifold respectively using the LLE and Hessian LLE algorithms as implemented by the Modular Data Processing toolkit. Below is a summary of some of the important algorithms from the history of manifold learning and nonlinear dimensionality reduction (NLDR). Many of these non-linear dimensionality reduction methods are related to the linear methods listed below. Non-linear methods can be broadly classified into two groups: those that provide a mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa), and those that just give a visualisation. In the context of machine learning, mapping methods may be viewed as a preliminary feature extraction step, after which pattern recognition algorithms are applied. Typically those that just give a visualisation are based on proximity data – that is, distance measurements.

➚ “Manifold Learning” … **dynesty**

We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested Sampling has the benefits of Markov Chain Monte Carlo algorithms that focus exclusively on posterior estimation while retaining Nested Sampling’s ability to estimate evidences and sample from complex, multi-modal distributions. We provide an overview of Nested Sampling, its extension to Dynamic Nested Sampling, the algorithmic challenges involved, and the various approaches taken to solve them. We then examine dynesty’s performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to Nested Sampling are also included in the Appendix. … **Lagrange Policy Gradient**

Most algorithms for reinforcement learning work by estimating action-value functions. Here we present a method that uses Lagrange multipliers, the costate equation, and multilayer neural networks to compute policy gradients. We show that this method can find solutions to time-optimal control problems, driving nonlinear mechanical systems quickly to a target configuration. On these tasks its performance is comparable to that of deep deterministic policy gradient, a recent action-value method. …

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