A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of sampling Bayesian posteriors over many parameters inhibits the use of Bayesian methods where they are most needed. Thermodynamic computing has emerged as a paradigm for accelerating operations used in machine learning, such as matrix inversion, and is based on the mapping of Langevin equations to the dynamics of noisy physical systems. Hence, it is natural to consider the implementation of Langevin sampling algorithms on thermodynamic devices. In this work we propose electronic analog devices that sample from Bayesian posteriors by realizing Langevin dynamics physically. Circuit designs are given for sampling the posterior of a Gaussian-Gaussian model and for Bayesian logistic regression, and are validated by simulations. It is shown, under reasonable assumptions, that the Bayesian posteriors for these models can be sampled in time scaling with $\ln(d)$, where $d$ is dimension. For the Gaussian-Gaussian model, the energy cost is shown to scale with $ d \ln(d)$. These results highlight the potential for fast, energy-efficient Bayesian inference using thermodynamic computing.

In this paper we describe the architecture, implementation and experimental resultsfor an Intracardiac Electrogram (ICEG) classification and compression chip. The chip processes and vector-quantises 30 dimensional analoguevectors while consuming a maximum of 2.5 J-tW power for a heart rate of 60 beats per minute (1 vector per second) from a 3.3 V supply. This represents a significant advance on previous work which achieved ultra low power supervised morphology classification since the template matching scheme used in this chip enables unsupervised blind classification of abnonnal rhythms and the computational support for low bit rate data compression. The adaptive template matching scheme used is tolerant to amplitude variations, and inter-and intra-sample time shifts.

In this paper we describe the architecture, implementation and experimental results for an Intracardiac Electrogram (ICEG) classification and compression chip. The chip processes and vector-quantises 30 dimensional analogue vectors while consuming a maximum of 2.5 J-tW power for a heart rate of 60 beats per minute (1 vector per second) from a 3.3 V supply. This represents a significant advance on previous work which achieved ultra low power supervised morphology classification since the template matching scheme used in this chip enables unsupervised blind classification of abnonnal rhythms and the computational support for low bit rate data compression. The adaptive template matching scheme used is tolerant to amplitude variations, and inter-and intra-sample time shifts.

In this paper we describe the architecture, implementation and experimental results for an Intracardiac Electrogram (ICEG) classification and compression chip. The chip processes and vector-quantises 30 dimensional analogue vectors while consuming a maximum of 2.5 J-tW power for a heart rate of 60 beats per minute (1 vector per second) from a 3.3 V supply. This represents a significant advance on previous work which achieved ultra low power supervised morphology classification since the template matching scheme used in this chip enables unsupervised blind classification of abnonnal rhythms and the computational support for low bit rate data compression. The adaptive template matching scheme used is tolerant to amplitude variations, and inter-and intra-sample time shifts.

The vestibulo-ocular reflex (VOR) is the primary mechanism that controls the compensatory eye movements that stabilize retinal images duringrapid head motion. The primary pathways of this system are feed-forward, with inputs from the semicircular canals and outputs to the oculomotor system. Since visual feedback is not used directly in the VOR computation, the system must exploit motor learning to perform correctly. Lisberger(1988) has proposed a model for adapting the VOR gain using image-slip information from the retina. We have designed and tested analog very largescale integrated(VLSI) circuitry that implements a simplified version of Lisberger's adaptive VOR model.

The vestibulo-ocular reflex (VOR) is the primary mechanism that controls the compensatory eye movements that stabilize retinal images during rapid head motion. The primary pathways of this system are feed-forward, with inputs from the semicircular canals and outputs to the oculomotor system. Since visual feedback is not used directly in the VOR computation, the system must exploit motor learning to perform correctly. Lisberger(1988) has proposed a model for adapting the VOR gain using image-slip information from the retina. We have designed and tested analog very largescale integrated (VLSI) circuitry that implements a simplified version of Lisberger's adaptive VOR model.

The vestibulo-ocular reflex (VOR) is the primary mechanism that controls the compensatory eye movements that stabilize retinal images during rapid head motion. The primary pathways of this system are feed-forward, with inputs from the semicircular canals and outputs to the oculomotor system. Since visual feedback is not used directly in the VOR computation, the system must exploit motor learning to perform correctly. Lisberger(1988) has proposed a model for adapting the VOR gain using image-slip information from the retina. We have designed and tested analog very largescale integrated (VLSI) circuitry that implements a simplified version of Lisberger's adaptive VOR model.