Statistical models for spatial processes play a central role in statistical analyses of spatial data. Yet, it is the simple, interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network; it is tailored to a spatial setting by incorporating a spatial "embedding layer" into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we have many realisations from it. We propose several variants of SBNNs, most of which are able to match the finite-dimensional distribution of the target process at the selected grid better than conventional BNNs of similar complexity. We also show that a single SBNN can be used to represent a variety of spatial processes often used in practice, such as Gaussian processes and lognormal processes. We briefly discuss the tools that could be used to make inference with SBNNs, and we conclude with a discussion of their advantages and limitations.

Binary neural networks (BNNs) are an attractive solution for developing and deploying deep neural network (DNN)-based applications in resource constrained devices. Despite their success, BNNs still suffer from a fixed and limited compression factor that may be explained by the fact that existing pruning methods for full-precision DNNs cannot be directly applied to BNNs. In fact, weight pruning of BNNs leads to performance degradation, which suggests that the standard binarization domain of BNNs is not well adapted for the task. This work proposes a novel more general binary domain that extends the standard binary one that is more robust to pruning techniques, thus guaranteeing improved compression and avoiding severe performance losses. We demonstrate a closed-form solution for quantizing the weights of a full-precision network into the proposed binary domain. Finally, we show the flexibility of our method, which can be combined with other pruning strategies. Experiments over CIFAR-10 and CIFAR-100 demonstrate that the novel approach is able to generate efficient sparse networks with reduced memory usage and run-time latency, while maintaining performance.

During the first part of life, the brain develops while it learns through a process called synaptogenesis. The neurons, growing and interacting with each other, create synapses. However, eventually the brain prunes those synapses. While previous work focused on learning and pruning independently, in this work we propose a biologically plausible model that, thanks to a combination of Hebbian learning and pruning, aims to simulate the synaptogenesis process. In this way, while learning how to solve the task, the agent translates its experience into a particular network structure. Namely, the network structure builds itself during the execution of the task. We call this approach Self-building Neural Network (SBNN). We compare our proposed SBNN with traditional neural networks (NNs) over three classical control tasks from OpenAI. The results show that our model performs generally better than traditional NNs. Moreover, we observe that the performance decay while increasing the pruning rate is smaller in our model than with NNs. Finally, we perform a validation test, testing the models over tasks unseen during the learning phase. In this case, the results show that SBNNs can adapt to new tasks better than the traditional NNs, especially when over $80\%$ of the weights are pruned.