Weaknesses: The specific empirical evaluation chosen is the primary weakness of the paper. From a neuroscience perspective, the validation of parameter recovery on synthetic data is a necessary first step, but not a sufficient one. Given that [a] the task is primarily of neuroscientific interest and [b] a simpler (though also bayesian belief-updating) fit model is given in the cited prior work, the lack of comparison of cross-validated performance against that prior model is surprising. We should either see better cross-validation performance to the models in prior work, or similar performance but more insight / explanation of the underlying mental computation. This would show us a real payoff of the new insights here.

The paper describes a novel technique for inverse rational control. The reviewers all agree that this is great work that makes an important contribution. There is one important weakness though: the experiments. More comprehensive experiments would be desirable to increase the impact of the work. Nevertheless, this is still good work.

Equation 7 in Section 4 is the log density of the distribution obtained by applying the normalizing flow models to the finite-dimensional distribution of Wiener process on a given time grid. We refer the reader to Chapter 2 of [5] for more details. We drop the subscript of π for the simplicity of notation. We base the justification on the following two propositions. Work developed during an internship at Borealis AI. We describe the details on synthetic dataset generation, real-world dataset pre-processing, model architecture as well as training and evaluation settings in this section.

Weaknesses: No Explanation of Transformations of Stochastic Processes: I was under the impression that transforming / reparameterizing a stochasic process is non-trivial. Thus, I was expecting Equation 7 to include a second derivative term. I'm not saying that Equation 7 is wrong, per se---transforming just the increments agrees with intuition. However, the problem is that the paper provides no explanation or mathematical references for stochastic processes and their transformations. There are *zero* citations in both Section 2.2 and Section 3.1.

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by a differential deformation of the Wiener process. As a result, we obtain a rich time series model whose observable process inherits many of the appealing properties of its base process, such as efficient computation of likelihoods and marginals. Furthermore, our continuous treatment provides a natural framework for irregular time series with an independent arrival process, including straightforward interpolation. We illustrate the desirable properties of the proposed model on popular stochastic processes and demonstrate its superior flexibility to variational RNN and latent ODE baselines in a series of experiments on synthetic and realworld data.

One reviewer recommend borderline rejection, but in my opinion the authors successfully addressed his concerns in the rebuttal. Recommendations: The authors are encouraged to clearly explain the reviewers' concern on potential similarities of the approach with the Kalman filter with nonlinear outputs. Also the issues related to background and related work and motivation for continuity.

In this paper, we revisit and improve the convergence of policy gradient (PG), natural PG (NPG) methods, and their variance-reduced variants, under general smooth policy parametrizations. More specifically, with the Fisher information matrix of the policy being positive definite: i) we show that a state-of-the-art variance-reduced PG method, which has only been shown to converge to stationary points, converges to the globally optimal value up to some inherent function approximation error due to policy parametrization; ii) we show that NPG enjoys a lower sample complexity; iii) we propose SRVR-NPG, which incorporates variancereduction into the NPG update. Our improvements follow from an observation that the convergence of (variance-reduced) PG and NPG methods can improve each other: the stationary convergence analysis of PG can be applied to NPG as well, and the global convergence analysis of NPG can help to establish the global convergence of (variance-reduced) PG methods.

In this paper, we revisit and improve the convergence of policy gradient (PG), natural PG (NPG) methods, and their variance-reduced variants, under general smooth policy parametrizations. More specifically, with the Fisher information matrix of the policy being positive definite: i) we show that a state-of-the-art variance-reduced PG method, which has only been shown to converge to stationary points, converges to the globally optimal value up to some inherent function approximation error due to policy parametrization; ii) we show that NPG enjoys a lower sample complexity; iii) we propose SRVR-NPG, which incorporates variancereduction into the NPG update. Our improvements follow from an observation that the convergence of (variance-reduced) PG and NPG methods can improve each other: the stationary convergence analysis of PG can be applied to NPG as well, and the global convergence analysis of NPG can help to establish the global convergence of (variance-reduced) PG methods.

This improves the best known exact gradient methods by a factor of p nnz(A)/n and is faster than fully stochastic gradient methods in the accurate and/or sparse regime apple p n/nnz(A).

The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a critical role in understanding the implicit regularization of SGD. In this paper, we provide an explanation of this striking phenomenon by relating the particular noise structure of SGD to its linear stability (Wu et al., 2018). Specifically, we consider training over-parameterized models with square loss.