In this paper, we propose a control synthesis method for signal temporal logic (STL) specifications with neural networks (NNs). Most of the previous works consider training a controller for only a given STL specification. These approaches, however, require retraining the NN controller if a new specification arises and needs to be satisfied, which results in large consumption of memory and inefficient training. To tackle this problem, we propose to construct NN controllers by introducing encoder-decoder structured NNs with an attention mechanism. The encoder takes an STL formula as input and encodes it into an appropriate vector, and the decoder outputs control signals that will meet the given specification. As the encoder, we consider three NN structures: sequential, tree-structured, and graph-structured NNs. All the model parameters are trained in an end-to-end manner to maximize the expected robustness that is known to be a quantitative semantics of STL formulae. We compare the control performances attained by the above NN structures through a numerical experiment of the path planning problem, showing the efficacy of the proposed approach.

We extend best-subset selection to linear Multi-Task Learning (MTL), where a set of linear models are jointly trained on a collection of datasets (``tasks''). Allowing the regression coefficients of tasks to have different sparsity patterns (i.e., different supports), we propose a modeling framework for MTL that encourages models to share information across tasks, for a given covariate, through separately 1) shrinking the coefficient supports together, and/or 2) shrinking the coefficient values together. This allows models to borrow strength during variable selection even when the coefficient values differ markedly between tasks. We express our modeling framework as a Mixed-Integer Program, and propose efficient and scalable algorithms based on block coordinate descent and combinatorial local search. We show our estimator achieves statistically optimal prediction rates. Importantly, our theory characterizes how our estimator leverages the shared support information across tasks to achieve better variable selection performance. We evaluate the performance of our method in simulations and two biology applications. Our proposed approaches outperform other sparse MTL methods in variable selection and prediction accuracy. Interestingly, penalties that shrink the supports together often outperform penalties that shrink the coefficient values together. We will release an R package implementing our methods.

卷积神经网络（CNN）的鲁棒性存在一些问题。例如，可以通过向输入中添加少量噪声来更改CNN的预测，当输入分布通过在训练过程中从未见过的转换移动时，CNN的性能会降解（例如，模糊效应）。有一些方法可以用二进制嵌入替代像素值，以解决对抗性扰动的问题，从而成功改善了鲁棒性。在这项工作中，我们将像素提出到二进制嵌入（P2BE）以提高CNN的鲁棒性。P2BE是一种可学习的二进制嵌入方法，而不是先前的手工编码的二进制嵌入方法。P2BE在训练过程中未显示的对抗性扰动和视觉损坏方面的其他二进制嵌入方法优于其他二进制嵌入方法。