The brain performs probabilistic Bayesian inference to interpret the external world. The sampling-based view assumes that the brain represents the stimulus posterior distribution via samples of stochastic neuronal responses. Although the idea of sampling-based inference is appealing, it faces a critical challenge of whether stochastic sampling is fast enough to match the rapid computation of the brain. In this study, we explore how latent stimulus sampling can be accelerated in neural circuits. Specifically, we consider a canonical neural circuit model called continuous attractor neural networks (CANNs) and investigate how sampling-based inference of latent continuous variables is accelerated in CANNs.

The brain performs probabilistic Bayesian inference to interpret the external world. The sampling-based view assumes that the brain represents the stimulus posterior distribution via samples of stochastic neuronal responses. Although the idea of sampling-based inference is appealing, it faces a critical challenge of whether stochastic sampling is fast enough to match the rapid computation of the brain. In this study, we explore how latent stimulus sampling can be accelerated in neural circuits. Specifically, we consider a canonical neural circuit model called continuous attractor neural networks (CANNs) and investigate how sampling-based inference of latent continuous variables is accelerated in CANNs.

Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 outputs x 50k datapoints), with ResNet-50 on Imagenet (50M parameters, 1000 outputs x 1.2M datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output~dimensions).