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With few exceptions, neural networks have been relying on backpropagation andgradient descent as the inference engine in order to learn the modelparameters, because the closed-form Bayesian inference for neural networks hasbeen considered to be intractable. In this paper, we show how we can leveragethe tractable approximate Gaussian inference's (TAGI) capabilities to inferhidden states, rather than only using it for inferring the network'sparameters. One novel aspect it allows is to infer hidden states through theimposition of constraints designed to achieve specific objectives, asillustrated through three examples: (1) the generation of adversarial-attackexamples, (2) the usage of a neural network as a black-box optimization method,and (3) the application of inference on continuous-action reinforcementlearning. These applications showcase how tasks that were previously reservedto gradient-based optimization approaches can now be approached withanalytically tractable inference

Analytically Tractable Hidden-States Inference in Bayesian Neural Networks