The marginal likelihood, or model evidence, is a key quantity in Bayesian parameter estimation and model comparison.

The marginal likelihood, or model evidence, is a key quantity in Bayesian parameter estimation and model comparison. For many probabilistic models, computation of the marginal likelihood is challenging, because it involves a sum or integral over an enormous parameter space. Markov chain Monte Carlo (MCMC) is a powerful approach to compute marginal likelihoods. Various MCMC algorithms and evidence estimators have been proposed in the literature. Here we discuss the use of nonequilibrium techniques for estimating the marginal likelihood. Nonequilibrium estimators build on recent developments in statistical physics and are known as annealed importance sampling (AIS) and reverse AIS in probabilistic machine learning. We introduce estimators for the model evidence that combine forward and backward simulations and show for various challenging models that the evidence estimators outperform forward and reverse AIS.

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interest from industrial application, but a complete picture about inherent mechanisms is still lacking. In this paper, we provide a transparent physics analysis of the diffusion models, deriving the fluctuation theorem, entropy production, Franz-Parisi potential to understand the intrinsic phase transitions discovered recently. Our analysis is rooted in non-equlibrium physics and concepts from equilibrium physics, i.e., treating both forward and backward dynamics as a Langevin dynamics, and treating the reverse diffusion generative process as a statistical inference, where the time-dependent state variables serve as quenched disorder studied in spin glass theory. This unified principle is expected to guide machine learning practitioners to design better algorithms and theoretical physicists to link the machine learning to non-equilibrium thermodynamics.

Consciousness continues to be of one of the most important, interesting and complex question to focus upon. While the study of consciousness has a long and rich history in the field of philosophy, the scientific study of consciousness has become less taboo recently, and made tremendous progress in the field over the last couple of decades, due to significant contributions from disciplines like neuroscience, cognitive science and computer science. Though research interests have continued to grow, fueled by the recent artificial intelligence/machine learning (AI/ML) revolution (reigniting questions around artificial consciousness), the topic of consciousness itself has generally been ignored or dismissed by a majority of those who work in mainstream AI as either an unimportant factor for their research goals or accusing work in (artificial) consciousness as distracting flights of fantasy. It seems as this trend might change in the near future as leaders in the field of AI recognize the importance of mechanisms of higher level cognition for making progress in AI, their relationship to the'easy problems' of consciousness and the important work that has been conducted in the field of cognitive science to understand these better (Yoshua Bengio's keynote address at NEURIPS 2019 being an important example of this [1]). While this might not satisfy those who are interested in the phenomenal aspects of our conscious experience, it represents a step forward in the right direction by the larger AI community. In keeping with the (beginnings of a) trend, the author will look to make the case for a non-equilibrium thermodynamic framework of consciousness, it's relationship to the field of AI and the crucial role that computer hardware engineers might have to play in the scientific study of consciousness. The author would like to take a brief moment (to digress) and explain the journey towards these ideas, hoping that it would elucidate their motivations as an engineer to study and understand the field of consciousness from a more physics based approach. The author's primary research interests lie in the field of artificial intelligence and was lucky

The pioneering paper [Ito and Sagawa, 2013] analyzed the non-equilibrium statistical physics of a set of multiple interacting systems, S, whose joint discrete-time evolution is specified by a Bayesian network. The major result of [Ito and Sagawa, 2013] was an integral fluctuation theorem (IFT) governing the sum of two quantities: the entropy production (EP) of an arbitrary single v in S, and the transfer entropy from v to the other systems. Here I extend the analysis in [Ito and Sagawa, 2013]. I derive several detailed fluctuation theorems (DFTs), concerning arbitrary subsets of all the systems (including the full set). I also derive several associated IFTs, concerning an arbitrary subset of the systems, thereby extending the IFT in [Ito and Sagawa, 2013]. In addition I derive "conditional" DFTs and IFTs, involving conditional probability distributions rather than (as in conventional fluctuation theorems) unconditioned distributions. I then derive thermodynamic uncertainty relations relating the total EP of the Bayes net to the set of all the precisions of probability currents within the individual systems. I end with an example of that uncertainty relation.

The marginal likelihood, or model evidence, is a key quantity in Bayesian parameter estimation and model comparison. For many probabilistic models, computation of the marginal likelihood is challenging, because it involves a sum or integral over an enormous parameter space. Markov chain Monte Carlo (MCMC) is a powerful approach to compute marginal likelihoods. Various MCMC algorithms and evidence estimators have been proposed in the literature. Here we discuss the use of nonequilibrium techniques for estimating the marginal likelihood. Nonequilibrium estimators build on recent developments in statistical physics and are known as annealed importance sampling (AIS) and reverse AIS in probabilistic machine learning. We introduce estimators for the model evidence that combine forward and backward simulations and show for various challenging models that the evidence estimators outperform forward and reverse AIS.