First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Beyond representing the position of an animal in a given environment, the activity of neurons in the hippocampus (areas CA1,3) is known to be influenced by a range of task-dependent factors, for instance the presence of a reward at a specific location in the environment; yet we don't fully understand how these representations emerge and what they are good for. The present paper proposes that these observations are a reflection of the circuit implementing a specific algorithm (using a successor representation, SR, initially proposed by Dayan in 1993) for learning state values for reinforcement learning; moreover it suggests that the representation in an upstream region (medial EC) may provide a basis for a hierarchical decomposition of space. Overall, some of the ideas put forward here are intriguing and potentially interesting for theoretical neuroscientists studying hippocampal coding, however the link to the neural data is relatively weak and the presentation of the material is difficult to follow in places. Detailed comments 1. Content: Since the algorithmic part of the paper is not new, the key contribution of this work is the link between the SR representation and the activity of neurons in the hippocampus. Unfortunately, this link between the two is not clear in several aspects: a) it is never spelled out exactly how does the matrix M relate to the firing of the neurons in the corresponding hippocampal circuit.If there is a one-to-one map between firing rates and M(s,s'), how can a downstream circuit compute V(s)?

Hippocampal place fields have been shown to reflect behaviorally relevant aspects of space. For instance, place fields tend to be skewed along commonly traveled directions, they cluster around rewarded locations, and they are constrained by the geometric structure of the environment. We hypothesize a set of design principles for the hippocampal cognitive map that explain how place fields represent space in a way that facilitates navigation and reinforcement learning. In particular, we suggest that place fields encode not just information about the current location, but also predictions about future locations under the current transition distribution. Under this model, a variety of place field phenomena arise naturally from the structure of rewards, barriers, and directional biases as reflected in the transition policy. Furthermore, we demonstrate that this representation of space can support efficient reinforcement learning. We also propose that grid cells compute the eigendecomposition of place fields in part because is useful for segmenting an enclosure along natural boundaries. When applied recursively, this segmentation can be used to discover a hierarchical decomposition of space. Thus, grid cells might be involved in computing subgoals for hierarchical reinforcement learning.

Hippocampal place fields have been shown to reflect behaviorally relevant aspects of space. For instance, place fields tend to be skewed along commonly traveled directions, they cluster around rewarded locations, and they are constrained by the geometric structure of the environment. We hypothesize a set of design principles for the hippocampal cognitive map that explain how place fields represent space in a way that facilitates navigation and reinforcement learning. In particular, we suggest that place fields encode not just information about the current location, but also predictions about future locations under the current transition distribution. Under this model, a variety of place field phenomena arise naturally from the structure of rewards, barriers, and directional biases as reflected in the transition policy.

Hippocampal place fields have been shown to reflect behaviorally relevant aspects of space. For instance, place fields tend to be skewed along commonly traveled directions, they cluster around rewarded locations, and they are constrained by the geometric structure of the environment. We hypothesize a set of design principles for the hippocampal cognitive map that explain how place fields represent space in a way that facilitates navigation and reinforcement learning. In particular, we suggest that place fields encode not just information about the current location, but also predictions about future locations under the current transition distribution. Under this model, a variety of place field phenomena arise naturally from the structure of rewards, barriers, and directional biases as reflected in the transition policy. Furthermore, we demonstrate that this representation of space can support efficient reinforcement learning.

Grid cells are neurons active in multiple fields arranged in a hexagonal lattice and are thought to represent the "universal metric for space." However, they become nonhomogeneously distorted in polarized enclosures, which challenges this view. We found that local changes to the configuration of the enclosure induce individual grid fields to shift in a manner inversely related to their distance from the reconfigured boundary. The grid remained primarily anchored to the unchanged stable walls and showed a nonuniform rescaling. Shifts in simultaneously recorded colocalized grid fields were strongly correlated, which suggests that the readout of the animal's position might still be intact. Similar field shifts were also observed in place and boundary cells--albeit of greater magnitude and more pronounced closer to the reconfigured boundary--which suggests that there is no simple one-to-one relationship between these three different cell types.