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This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the point pattern over a large area. It is shown how the presence of covariates allows to borrow information from far away locations in the observation window, enabling consistent inference in the growing domain asymptotics. In particular, optimal posterior contraction rates under both global and point-wise loss functions are derived. The rates in global loss are obtained under conditions on the prior distribution resembling those in the well established theory of Bayesian nonparametrics, here combined with concentration inequalities for functionals of stationary processes to control certain random covariate-dependent loss functions appearing in the analysis. The local rates are derived with an ad-hoc study that builds on recent advances in the theory of P\'olya tree priors, extended to the present multivariate setting with a novel construction that makes use of the random geometry induced by the covariates.

Aircraft are composed of many electronic systems: sensors, displays, navigation equipment and communication elements. These elements require a reliable interconnection, which is a major challenge for communication networks as high reliability and predictability requirements must be verified for safe operation. In addition, their verification via hardware deployments is limited because these are costly and make difficult to try different architectures and configurations, thus delaying the design and development in this area. Therefore, verification at early stages in the design process is of great importance and must be supported by simulation. In this context, this work presents an event-driven link level framework and simulator for the validation of avionics networks. The presented tool supports communication protocols such as Avionics Full-Duplex Switched Ethernet (AFDX), which is a common protocol in avionics, as well as Ethernet, used with static routing. Alsa, accurate results are facilitated by the simulator through the utilization of realistic models for the different devices. The proposed platform is evaluated in Clean Sky's Disruptive Cockpit for Large Passenger Aircraft architecture scenario showing capabilities of the simulator. The speed of the verification is a key factor in its application, so the computational cost is analysed, proving that the execution time is linearly dependent on the number of messages sent.

We investigate the descriptive complexity of a class of neural networks with unrestricted topologies and piecewise polynomial activation functions. We consider the general scenario where the running time is unlimited and floating-point numbers are used for simulating reals. We characterize these neural networks with a rule-based logic for Boolean networks. In particular, we show that the sizes of the neural networks and the corresponding Boolean rule formulae are polynomially related. In fact, in the direction from Boolean rules to neural networks, the blow-up is only linear. We also analyze the delays in running times due to the translations. In the translation from neural networks to Boolean rules, the time delay is polylogarithmic in the neural network size and linear in time. In the converse translation, the time delay is linear in both factors. We also obtain translations between the rule-based logic for Boolean networks, the diamond-free fragment of modal substitution calculus and a class of recursive Boolean circuits where the number of input and output gates match.

The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving ill-posed inverse problems and high-dimensional parameter spaces, the scheme has shown promising success. However, in its general form, the EKI does not take constraints into account, which are essential and often stem from physical limitations or specific requirements. Based on a log-barrier approach, we suggest adapting the continuous-time formulation of EKI to incorporate convex inequality constraints. We underpin this adaptation with a theoretical analysis that provides lower and upper bounds on the ensemble collapse, as well as convergence to the constraint optimum for general nonlinear forward models. Finally, we showcase our results through two examples involving partial differential equations (PDEs).

Speech bandwidth extension (BWE) has demonstrated promising performance in enhancing the perceptual speech quality in real communication systems. Most existing BWE researches primarily focus on fixed upsampling ratios, disregarding the fact that the effective bandwidth of captured audio may fluctuate frequently due to various capturing devices and transmission conditions. In this paper, we propose a novel streaming adaptive bandwidth extension solution dubbed BAE-Net, which is suitable to handle the low-resolution speech with unknown and varying effective bandwidth. To address the challenges of recovering both the high-frequency magnitude and phase speech content blindly, we devise a dual-stream architecture that incorporates the magnitude inpainting and phase refinement. For potential applications on edge devices, this paper also introduces BAE-NET-lite, which is a lightweight, streaming and efficient framework. Quantitative results demonstrate the superiority of BAE-Net in terms of both performance and computational efficiency when compared with existing state-of-the-art BWE methods.

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic processes to model approximate samples from these target densities. The main drawback of these approaches is that the training objective requires full trajectories to compute, resulting in sluggish credit assignment issues due to use of entire trajectories and a learning signal present only at the terminal time. In this work, we present Diffusion Generative Flow Samplers (DGFS), a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments, via parameterizing an additional "flow function". Our method takes inspiration from the theory developed for generative flow networks (GFlowNets), allowing us to make use of intermediate learning signals. Through various challenging experiments, we demonstrate that DGFS achieves more accurate estimates of the normalization constant than closely-related prior methods.

We establish explicit dynamics for neural networks whose training objective has a regularising term that constrains the parameters to remain close to their initial value. This keeps the network in a lazy training regime, where the dynamics can be linearised around the initialisation. The standard neural tangent kernel (NTK) governs the evolution during the training in the infinite-width limit, although the regularisation yields an additional term appears in the differential equation describing the dynamics. This setting provides an appropriate framework to study the evolution of wide networks trained to optimise generalisation objectives such as PAC-Bayes bounds, and hence potentially contribute to a deeper theoretical understanding of such networks.

Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent variables and data interact through more complex designs. In this work, we study empirical Bayes estimation of an i.i.d. prior in Bayesian linear models, via the nonparametric maximum likelihood estimator (NPMLE). We introduce and study a system of gradient flow equations for optimizing the marginal log-likelihood, jointly over the prior and posterior measures in its Gibbs variational representation using a smoothed reparametrization of the regression coefficients. A diffusion-based implementation yields a Langevin dynamics MCEM algorithm, where the prior law evolves continuously over time to optimize a sequence-model log-likelihood defined by the coordinates of the current Langevin iterate. We show consistency of the NPMLE as $n, p \rightarrow \infty$ under mild conditions, including settings of random sub-Gaussian designs when $n \asymp p$. In high noise, we prove a uniform log-Sobolev inequality for the mixing of Langevin dynamics, for possibly misspecified priors and non-log-concave posteriors. We then establish polynomial-time convergence of the joint gradient flow to a near-NPMLE if the marginal negative log-likelihood is convex in a sub-level set of the initialization.

In the past few years, the emergence of pre-training models has brought uni-modal fields such as computer vision (CV) and natural language processing (NLP) to a new era. Substantial works have shown they are beneficial for downstream uni-modal tasks and avoid training a new model from scratch. So can such pre-trained models be applied to multi-modal tasks? Researchers have explored this problem and made significant progress. This paper surveys recent advances and new frontiers in vision-language pre-training (VLP), including image-text and video-text pre-training. To give readers a better overall grasp of VLP, we first review its recent advances from five aspects: feature extraction, model architecture, pre-training objectives, pre-training datasets, and downstream tasks. Then, we summarize the specific VLP models in detail. Finally, we discuss the new frontiers in VLP. To the best of our knowledge, this is the first survey on VLP. We hope that this survey can shed light on future research in the VLP field.

Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.