This paper studies the problem of learning soft state aggregation of a Markov model, where there are r hidden meta states, each corresponds to a distribution over the observed state of the Markov model. Under the anchor state assumption, the authors propose an algorithm that provably learns the state aggregation model from the Markov chain's trajectory. They evaluated their algorithm on a Manhattan taxi-trip dataset which yields interesting discoveries. There has been lots of work on estimating the low rank transition matrix itself and on matrix factorization in the topic modelling setting, and this work seems to be connecting the two problems. The paper is presented well and easy to follow. I have the following questions regarding the novelty and impact of this paper.

Weaknesses: - The paper's narrative is based around POMDPs, but the experimental evaluation does not really stress the capability of the method in that respect. Evaluation is done on pixel-based control, which is PO of course, but we have know that a lagged observation of a few time-steps can make the state fully observable quickly. Hence, we do not know how the method fares in environments where the state uncertainty has to be actively reduced by the agent. Therefore I think the paper overstates the results. It is easy to get out of this, however, since one can just drop the POMDP claim. For me personally (and the optimal control community) it is obvious that we want some kind of state estimation when we use control, as most–if not all–practical problems are PO.

The method targets a model-based approach to solve POMDPs with high-dimensional observation spaces. This problem is tackle by learning jointly about the dynamics of the POMDP and the optimal policy by maximum likelihood using an "RL as inference" type objective. In more detail, the latent space transitions are predicted by an inference model that is trained to maximise an evidence lower bound. The reviewers are mostly positive about the paper. They mention the theoretical soundness of the approach and the quality of writing as well as the empirical set-up and usefulness of the ablations.

Additional Feedback: The authors propose a Gibbs sampling algorithm that is mentioned to be very efficient. I would expect the parameters to be very correlated, especially in a three-layer model. Could the authors elaborate on this, efficient in what sense? I assume the Gibbs sampler is rather used as a stochastic optimization algorithm than a way to explore the whole posterior? The link activation variable u_k is essentially a variable that will work on the topic level to give strength to individual topics for the links.

The paper, the reviews, the author response and the ensuing discussion were all taken into consideration. All reviewers considered the work marginally above the acceptance threshold. Novelty was a concern for some but other reviewers appreciated it. Lacking comparisons to GCN and others, evaluation of underlying topics, and consideration of topic modeling prior work were also concerns. However, the paper was generally felt to represent good work, and use of a deep model in this context, design of the model, and convincing experiments were appreciated.

The study of learning causal structure with latent variables has advanced the understanding of the world by uncovering causal relationships and latent factors, e.g., Causal Representation Learning (CRL). However, in real-world scenarios, such as those in climate systems, causal relationships are often nonparametric, dynamic, and exist among both observed variables and latent variables. These challenges motivate us to consider a general setting in which causal relations are nonparametric and unrestricted in their occurrence, which is unconventional to current methods. To solve this problem, with the aid of 3-measurement in temporal structure, we theoretically show that both latent variables and processes can be identified up to minor indeterminacy under mild assumptions. Moreover, we tackle the general nonlinear Causal Discovery (CD) from observations, e.g., temperature, as a specific task of learning independent representation, through the principle of functional equivalence. Based on these insights, we develop an estimation approach simultaneously recovering both the observed causal structure and latent causal process in a nontrivial manner. Simulation studies validate the theoretical foundations and demonstrate the effectiveness of the proposed methodology. In the experiments involving climate data, this approach offers a powerful and in-depth understanding of the climate system.

Traditional approaches to studying decision-making in neuroscience focus on simplified behavioral tasks where animals perform repetitive, stereotyped actions to receive explicit rewards. While informative, these methods constrain our understanding of decision-making to short timescale behaviors driven by explicit goals. In natural environments, animals exhibit more complex, long-term behaviors driven by intrinsic motivations that are often unobservable. Recent works in time-varying inverse reinforcement learning (IRL) aim to capture shifting motivations in long-term, freely moving behaviors. However, a crucial challenge remains: animals make decisions based on their history, not just their current state. To address this, we introduce SWIRL (SWitching IRL), a novel framework that extends traditional IRL by incorporating time-varying, history-dependent reward functions. SWIRL models long behavioral sequences as transitions between short-term decision-making processes, each governed by a unique reward function. SWIRL incorporates biologically plausible history dependency to capture how past decisions and environmental contexts shape behavior, offering a more accurate description of animal decision-making. We apply SWIRL to simulated and real-world animal behavior datasets and show that it outperforms models lacking history dependency, both quantitatively and qualitatively. This work presents the first IRL model to incorporate history-dependent policies and rewards to advance our understanding of complex, naturalistic decision-making in animals. Historically, decision making in neuroscience has been studied using simplified assays where animals perform repetitive, stereotyped actions (such as licks, nose pokes, or lever presses) in response to sensory stimuli to obtain an explicit reward. While this approach has its advantages, it has limited our understanding of decision making to scenarios where animals are instructed to achieve an explicit goal over brief timescales, usually no more than tens of seconds.

Hippocampal formation (HF) can rapidly adapt to varied environments and build flexible working memory (WM). To mirror the HF's mechanism on generalization and WM, we propose a model named Generalization and Associative Temporary Encoding (GATE), which deploys a 3-D multi-lamellar dorsoventral (DV) architecture, and learns to build up internally representation from externally driven information layer-wisely. In each lamella, regions of HF: EC3-CA1-EC5-EC3 forms a re-entrant loop that discriminately maintains information by EC3 persistent activity, and selectively readouts the retained information by CA1 neurons. CA3 and EC5 further provides gating function that controls these processes. After learning complex WM tasks, GATE forms neuron representations that align with experimental records, including splitter, lap, evidence, trace, delay-active cells, as well as conventional place cells. Crucially, DV architecture in GATE also captures information, range from detailed to abstract, which enables a rapid generalization ability when cue, environment or task changes, with learned representations inherited. GATE promises a viable framework for understanding the HF's flexible memory mechanisms and for progressively developing brain-inspired intelligent systems.

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.

There are, of course, many other hybrid methods available for learning Bayesian networks and therefore causal structures.