Neural processes (NPs) learn stochastic processes and predict the distribution of target output adaptively conditioned on a context set of observed input-output pairs. Furthermore, Attentive Neural Process (ANP) improved the prediction accuracy of NPs by incorporating attention mechanism among contexts and targets. In a number of real-world applications such as robotics, finance, speech, and biology, it is critical to learn the temporal order and recurrent structure from sequential data. However, the capability of NPs capturing these properties is limited due to its permutation invariance instinct. In this paper, we proposed the Recurrent Attentive Neural Process (RANP), or alternatively, Attentive Neural Process-Recurrent Neural Network(ANP-RNN), in which the ANP is incorporated into a recurrent neural network. The proposed model encapsulates both the inductive biases of recurrent neural networks and also the strength of NPs for modeling uncertainty. We demonstrate that RANP can effectively model sequential data and outperforms NPs and LSTMs remarkably in a 1D regression toy example as well as autonomous driving applications.
We report on the fabrication and characterization of nanopatterned superconducting quantum interference devices (SQUIDs) based on grain boundary Josephson junctions in epitaxially grown multilayer YBa2Cu3O7 (YBCO)/SiTrO3 (STO) thin films. Nanopatterning is performed by Ga+ focused ion beam milling. The evolution of the electric transport and noise properties of the YBCO nanoSQUIDs over a time span of more than one year are recorded and analyzed. We find that the multilayer YBCO/STO nanoSQUIDs show stable and high performance over time. The critical current decreases within ∼40 days by 30%–50% and then remains almost constant without obvious decline trend for nanoSQUIDs with STO layer as the interface even more than 380 days, which demonstrates the superiority of STO as the capping layer. Moreover, we find that the multilayer nanoSQUIDs have about an order of magnitude smaller low-frequency excess flux noise (compared to similar single layer devices) with root-mean-square spectral density ∼5–6 µΦ0/Hz1/2 at 1 Hz. For one device, we show that the low-frequency excess noise does not degrade within three months.
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