Neural Bayesian Information Processing

Abstract

Deep learning is developed as a learning process from source inputs to target outputs where the inference or optimization is performed over an assumed deterministic model with deep structure. A wide range of temporal and spatial data in language and vision are treated as the inputs or outputs to build such a complicated mapping in different information systems. A systematic and elaborate transfer is required to meet the mapping between source and target domains. Also, the semantic structure in natural language and computer vision may not be well represented or trained in mathematical logic or computer programs. The distribution function in discrete or continuous latent variable model for words, sentences, images or videos may not be properly decomposed or estimated. The system robustness to heterogeneous environments may not be assured. This tutorial addresses the fundamentals and advances in statistical models and neural networks, and presents a series of deep Bayesian solutions including variational Bayes, sampling method, Bayesian neural network, variational auto-encoder (VAE), stochastic recurrent neural network, sequence-to-sequence model, attention mechanism, end-to-end network, stochastic temporal convolutional network, temporal difference VAE, normalizing flow and neural ordinary differential equation. Enhancing the prior/posterior representation is addressed in different latent variable models. We illustrate how these models are connected and why they work for a variety of applications on complex patterns in language and vision. The word, sentence and image embeddings are merged with semantic constraint or structural information. Bayesian learning is formulated in the optimization procedure where the posterior collapse is tackled. An informative latent space is trained to incorporate deep Bayesian learning in various information systems.

Incomplete to complete multiphysics forecasting: a hybrid approach for learning unknown phenomena

“…These tools provide differentiable functions for physical simulations, which enable close integration with deep learning frameworks by leveraging their automatic differentiation functionality. Hybrid approaches that combine machine learning techniques with numerical PDE solvers (Wang et al, 2020; Illarramendi et al, 2022), have attracted a significant amount of interest due to their capabilities for generalization (Chen et al, 2018). In this context, neural networks are typically used to model or replace a part of the conventional PDE solver to improve aspects of the solving process.…”