Summary and Contributions: The paper proposes a method for utilizing ODEs to represent dynamics for continuous-time decision-making problems with the aim of They also target filling a perceived gap in the literature of Deep RL for continuous-time problems, where most publications are model-free and discretize time if it is continuous. They claim that their approach leads to lower dependence on vast amounts of training data, better performance and that the model-based approach is well-founded. I tend to agree, although this is not exactly my area. I also believe the importance of connecting ODEs and other explicit models is critical for extending RL methods to important problems in physics, chemistry, epidemiology and population modelling.

The reviewers all found the paper to make a reasonable contribution. While there are some limitations that were pointed out, the rebuttal addressed them well and the experiments were appreciated.

SUMMARY Hamiltonian MCMC methods sample from a probability distribution by treating its log as a "potential energy" function over the state space, augmenting the space with extra "momentum variables" and their associated "kinetic energy", and evolving the state of the Markov process by integrating the physical Hamiltonian equations of motion of the system. Each step of the Markov chain is accomplished by numerically integrating the Hamiltonian equations forward in time. However, if the energy function is non-differentiable, the integral is not well-defined. The rejection step that is used to counteract numerical inaccuracies in the integration also accounts for such non-differentiable regions, but at the cost of slowing down the mixing rate of the Markov chain. This paper suggests physically-inspired "reflections" and "refractions" of the trajectory of the system that occur whenever the state crosses a discontinuity in the energy function. It applies to target distributions that are differentiable everywhere except on the boundaries of certain polytopes; the reflection or refraction occurs whenever the trajectory of the system crosses such a boundary.

This paper is about a new Bayesian method for multi label learning. The goal is to classify accurately in settings where there are many potential labels but only a few of them apply to each data point. The basis of the new results is a new generative model for the label vector of each example. Specifically the label vector y_n of the n-th example is generated as y_n f(V(\sigma(Wx_n)), where Wx_n is a lower dimensional projection of the n-th instance x_n, followed by an element-wise sigmoid activation \sigma. The final operation f corresponds to drawing Poisson random variables with rates given by V(\sigma(Wx_n)) and thresholding these so-called latent counts by taking the minimum with 1.

The paper presents a latent variable model for modeling spectral energy distribution of quasars, given stereoscopic and photometric observations. The joint modeling of stereoscopic and photometric measurements allows the model to make inferences about stereoscopic properties of quasars leveraging the more broadly available photometric data. Clarity: The paper for the most part is well written and easy to follow. I have some minor complaints about the exposition, see detailed comments below. The authors develop a well motivated, non trivial latent variable model for capturing the salient properties of distributions of noisy quasar measurements. The use of parallel tempering in the inference procedure is interesting as well.

This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time t_{mix} of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time t_{relax}, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a \sqrt{n} rate, where n is the length of the sample path. Upper and lower bounds are given on the number of samples required to achieve constant-factor multiplicative accuracy.

The paper describes a new class of Bayes nets for which inference and structure learning can be done in polynomial time. This is the class of Bayes nets with a bounded vertex cover number. So far, the only other class of Bayes nets for which inference and structure learning is tractable is the class of trees. Hence, this is an important contribution that advances our understanding of tractable probabilistic graphical models. The paper also describes two algorithms to find the best Bayes net structure for a bounded vertex cover k, however it is not clear whether practitioners would want to use those algorithms.

Weaknesses: This manuscript contains a highly theoretical analysis of modern Hopfield networks and their relationship to the attention mechanism of a transformer model. It also contains a deep model that addresses the machine learning task of immune repertoire classification. The major issue with this submission is that the connection between the two topics addressed in this paper, (i) classification of immune repertoires, and (ii) equivalence of the update rule of modern Hopfield networks and the attention mechanism of the transformer, is at best unclear. It feels as though two distinct papers have been condensed into one. Overall, combining these two results into one paper results in a main text manuscript that does not provide sufficient detail about either.

The reviewers find the application compelling, to a timely topic, and with interesting theoretical connections that they now understand will primarily be presented elsewhere, and thus can now be cited in this NeurIPS paper, thereby enabling a cleaner exposition.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.