Review for NeurIPS paper: Discovering Symbolic Models from Deep Learning with Inductive Biases

Additional Feedback: 0. The notations in the method section especially Section 2 need to be specified, even if it is easy to infer from context,. For example, L_v, v_i, v_j etc. need to be explained. Further, in the case studies sections, the descriptions are not clear, for example, the system should be explained mathematically from a n-body perspective, clearly denoting the particles as nodes at gnn equation level for atleast one case. The authors should discuss the intuitions behind their specific model decisions, for example, as this is a model discovery task, why haven't the authors used generative model frameworks? 2. The input/output dimensionality for eureqa fitting should be explained in Section 3, for example, GNs have multiple layers, how does the proposed method fit equations for the edge/node functions at different layers and put them together? From the simulation dataset, the underlying model does not seem to need multiple layers for GNs. 3. The Hamiltonian Dynamics section is very hard to read, especially to a non-physics person, it would be helpful if the authors add a clear description of the input (like position and momentum) and output for the HGN. 4. What is the intuition behind the sum of pairwise and self for the HGN? Have the authors compared to a model without this assumption? 5. Does the Bottleneck model perform worse simply because its a much smaller model than the other models with a large hidden size? 6. Line 170 states that "models are trained to predict acceleration given current state", do the authors not account for time dependence?