Paper:
In visual planning (VP), an agent learns to plan goal-directed behavior from observations of a dynamical system obtained offline, e.g., images obtained from selfsupervised robot interaction. VP algorithms essentially combine data-driven perception and planning, and are important for robotic manipulation and navigation domains, among others. A recent and promising approach to VP is the semiparametric topological memory (SPTM) method, where image samples are treated as nodes in a graph, and the connectivity in the graph is learned using deep image classification. Thus, the learned graph represents the topological connectivity of the data, and planning can be performed using conventional graph search methods. However, training SPTM necessitates a suitable loss function for the connectivity classifier, which requires non-trivial manual tuning. More importantly, SPTM is constricted in its ability to generalize to changes in the domain, as its graph is constructed from direct observations and thus requires collecting new samples for planning. In this paper, we propose Hallucinative Topological Memory (HTM), which overcomes these shortcomings. In HTM, instead of training a discriminative classifier we train an energy function using contrastive predictive coding. In addition, we learn a conditional VAE model that generates samples given a context image of the domain, and use these hallucinated samples for building the connectivity graph, allowing for zero-shot generalization to domain changes. In simulated domains, HTM outperforms conventional SPTM and visual foresight methods in terms of both plan quality and success in long-horizon planning.

Review:
The paper presents a method for learning agents to solve visual planning, in particular to navigate to a desired goal position in a maze, with a learned topological map, i.e. a graph, where nodes correspond to positions in the maze and edges correspond accessibility (reachability in a certain number of steps). The work extends previous work (semi parametric topological memory, ref. [22]) in several ways. It claims to address a shortcoming of [22], namely the fact that the graph is calculated offline from random rollouts, by using a conditional variational auto-encoder to predict a set of observed images which could lie between the current position and the goal position, and, most importantly from a context image which describes the layout of the environment. These predicted images are then arranged in a graph through a connectivity predictor, which is trained from rollouts through a contrastive loss. Training is performed on multiple environments, and the context vector provides enough information for this connectivity network to generalize to unseen environments.  At test time, the agent navigates using a planner and a policy. The planner calculates the shortest path on a graph where edges are connectivity probabilities, and the policy is an inverse model trained on the output of the planner.
While the idea of a topological memory with dynamic graph creation is certainly interesting, the work is unfortunately not well enough executed and the paper structured written in a way which makes it up to impossible to grasp what has been really done, as much information is missing which would be required for understanding. 
As a first example, we are never really told what the observations are, which the agent sees. The different figures of the paper show very small images with a 2D maze from a bird’s eye view consisting of a walls arranged in a single connected component (mostly 1 to 3 strokes) in red color and an agent shown as a position indicated as a green dot. Are these the observed images? In absence of any other information, this is what we need to assume, and then this problem is fully observable and does not seem to be very challenging. Given the figures, even a handcrafted algorithm should be able to calculate the optimal solution with Dijkstra’s algorithm on a graph calculated from the pixel grid.
This important missing information alone makes it difficult to assess the paper, but the rest of the writing is similarly confusing. The authors focus on very short and dense descriptions of mathematical properties, but seem to have forgotten to ground the different symbols and to connect them to physical entities of the problem. The technical writing is in large parts disconnected from the problem which is addressed by it.
Further examples are:
-	“the data (…) is collected in a self-supervised manner”: what does this mean? Self-supervision is way of creating loss from data without labels, but I am not sure what is meant by collecting data this way.
-	The paragraph on CPC in section 2 can only be understood if the contrastive loss is known. To make the paper self-consistent, this should be properly explained, and tied to a training procedure which details how exactly the positive and negative samples are defined … and collected.
-	The CPC objective in section 2 is only loosely connected to its usage in section 3.2. Barely writing “we optimize a CPC” objective is not sufficient for understanding how this objective is really tied to the different entities of the problem. This paper contains maths (which is always a pleasure to read), but it is not a purely and abstract mathematical problem - a real task is addressed, so it needs to be connected to it. This connection has certainly been done by the authors while they were working on the problem, but they should also communicate it to the reader.
-	The section on ML trajectory is too dense and should be rewritten. I don’t understand what the authors want to tell us here. Basically, a (generalized) Dijkstra is run on a graph, where edge weights are the density or density ratios learned by the CPC objective, and if the edge weights are probabilities, that the shortest path corresponds to a trajectory likelihood. This is known, and this information is buried in a dense set of equations which are difficult to decipher and do not add any further value to the paper.
-	The connection between the planner (generalized Dijkstra) and the policy is never explained. We don’t know how the policy is trained and how it works.
One of the downsides of the method is that it requires a context image. This image is responsible for the generalization to unseen environments, but it is a major drawback, as the image must be created beforehand. The authors claim that the context image must only contain the layout in any format which makes it possible to extract information about navigational space from it, but in the experiments the context image corresponds to the full map – and it is probably equivalent to the observed images, but we can’t be sure as we haven’t been told. In any case, it is far from sure how this could generalize to more complex environments, let alone 3D navigation as is currently addressed in standard simulators like VizDoom, GIBSON, Matterport, Deepmind Lab, Habitat AI etc. 
The authors’ claim that the proposed environment requires long-term planning, but looking at the images this does not seem to be the case. 
The paper claims to perform zero-shot generalization and to adapt to changes in the environment, like the slight changes in camera motion, variations in lightning, but it unclear how the solution solves this claim.
How does the agent determine that a goal has been reached, without ground truth information? 
What happens, if the hallucinated images are disconnected (form several connected components) or are disconnected from the current position and/or from the goal position?
As mentioned, the method is evaluated on an environment, which is too simple. The experiments are difficult to assess, as we don’t really know what the agent observes. An information asymmetry is mentioned (visual foresight having the object’s (=agent’s) position and the others not) … but if the proposed method observes the bird’s eye view, it can infer the agent’s position (as the position of the green dot).
Subjective evaluation by humans on this kind of simple data does not seem to be meaningful, in particular with a very low number of observers (5 people).