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X-ray polarimetry will soon open a new window on the high energy universe with the launch of NASA's Imaging X-ray Polarimetry Explorer (IXPE). Polarimeters are currently limited by their track reconstruction algorithms, which typically use linear estimators and do not consider individual event quality. We present a modern deep learning method for maximizing the sensitivity of X-ray telescopic observations with imaging polarimeters, with a focus on the gas pixel detectors (GPDs) to be flown on IXPE. We use a weighted maximum likelihood combination of predictions from a deep ensemble of ResNets, trained on Monte Carlo event simulations. We derive and apply the optimal event weighting for maximizing the polarization signal-to-noise ratio (SNR) in track reconstruction algorithms. For typical power-law source spectra, our method improves on the current state of the art, providing a ~40% decrease in required exposure times for a given SNR.

Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a challenging computational bottleneck. Compared to conventional neural networks, physical-model devices offer a fast, efficient and inherently parallel substrate capable of related forms of Markov chain Monte Carlo sampling. Here, we demonstrate the ability of a neuromorphic chip to represent the ground states of quantum spin models by variational energy minimization. We develop a training algorithm and apply it to the transverse field Ising model, showing good performance at moderate system sizes ($N\leq 10$). A systematic hyperparameter study shows that scalability to larger system sizes mainly depends on sample quality, which is limited by temporal parameter variations on the analog neuromorphic chip. Our work thus provides an important step towards harnessing the capabilities of neuromorphic hardware for tackling the curse of dimensionality in quantum many-body problems.

Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW is that the IPW estimator can be remarkably unstable if some probabilities are very close to zero. To overcome this problem, at least three remedies have been developed in the literature: stabilizing, thresholding, and trimming. However the final estimators are still IPW type estimators, and inevitably inherit certain weaknesses of the naive IPW estimator: they may still be unstable or biased. We propose a biased-sample empirical likelihood weighting (ELW) method to serve the same general purpose as IPW, while completely overcoming the instability of IPW-type estimators by circumventing the use of inverse probabilities. The ELW weights are always well defined and easy to implement. We show theoretically that the ELW estimator is asymptotically normal and more efficient than the IPW estimator and its stabilized version for missing data problems and unequal probability sampling without replacement. Its asymptotic normality is also established under unequal probability sampling with replacement. Our simulation results and a real data analysis indicate that the ELW estimator is shift-equivariant, nearly unbiased, and usually outperforms the IPW-type estimators in terms of mean square error.

This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These neural networks are simple because they are designed with a simple and computable continuous activation function $\sigma$ leveraging a triangular-wave function and a softsign function. We prove that $\sigma$-activated networks with width $36d(2d+1)$ and depth $11$ can approximate any continuous function on a $d$-dimensioanl hypercube within an arbitrarily small error. Hence, for supervised learning and its related regression problems, the hypothesis space generated by these networks with a size not smaller than $36d(2d+1)\times 11$ is dense in the space of continuous functions. Furthermore, classification functions arising from image and signal classification are in the hypothesis space generated by $\sigma$-activated networks with width $36d(2d+1)$ and depth $12$, when there exist pairwise disjoint closed bounded subsets of $\mathbb{R}^d$ such that the samples of the same class are located in the same subset.

Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.

To rapidly learn a new task, it is often essential for agents to explore efficiently -- especially when performance matters from the first timestep. One way to learn such behaviour is via meta-learning. Many existing methods however rely on dense rewards for meta-training, and can fail catastrophically if the rewards are sparse. Without a suitable reward signal, the need for exploration during meta-training is exacerbated. To address this, we propose HyperX, which uses novel reward bonuses for meta-training to explore in approximate hyper-state space (where hyper-states represent the environment state and the agent's task belief). We show empirically that HyperX meta-learns better task-exploration and adapts more successfully to new tasks than existing methods.

Neural Architecture Search (NAS) was first proposed to achieve state-of-the-art performance through the discovery of new architecture patterns, without human intervention. An over-reliance on expert knowledge in the search space design has however led to increased performance (local optima) without significant architectural breakthroughs, thus preventing truly novel solutions from being reached. In this work we 1) are the first to investigate casting NAS as a problem of finding the optimal network generator and 2) we propose a new, hierarchical and graph-based search space capable of representing an extremely large variety of network types, yet only requiring few continuous hyper-parameters. This greatly reduces the dimensionality of the problem, enabling the effective use of Bayesian Optimisation as a search strategy. At the same time, we expand the range of valid architectures, motivating a multi-objective learning approach. We demonstrate the effectiveness of this strategy on six benchmark datasets and show that our search space generates extremely lightweight yet highly competitive models.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.

Meta learning is a promising solution to few-shot learning problems. However, existing meta learning methods are restricted to the scenarios where training and application tasks share the same out-put structure. To obtain a meta model applicable to the tasks with new structures, it is required to collect new training data and repeat the time-consuming meta training procedure. This makes them inefficient or even inapplicable in learning to solve heterogeneous few-shot learning tasks. We thus develop a novel and principled HierarchicalMeta Learning (HML) method. Different from existing methods that only focus on optimizing the adaptability of a meta model to similar tasks, HML also explicitly optimizes its generalizability across heterogeneous tasks. To this end, HML first factorizes a set of similar training tasks into heterogeneous ones and trains the meta model over them at two levels to maximize adaptation and generalization performance respectively. The resultant model can then directly generalize to new tasks. Extensive experiments on few-shot classification and regression problems clearly demonstrate the superiority of HML over fine-tuning and state-of-the-art meta learning approaches in terms of generalization across heterogeneous tasks.

Network embedding has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accelerated by distributed computing schemes. To address these problems, we propose RandNE, a novel and simple billion-scale network embedding method. Specifically, we propose a Gaussian random projection approach to map the network into a low-dimensional embedding space while preserving the high-order proximities between nodes. To reduce the time complexity, we design an iterative projection procedure to avoid the explicit calculation of the high-order proximities. Theoretical analysis shows that our method is extremely efficient, and friendly to distributed computing schemes without any communication cost in the calculation. We demonstrate the efficacy of RandNE over state-of-the-art methods in network reconstruction and link prediction tasks on multiple datasets with different scales, ranging from thousands to billions of nodes and edges.