Flexible Neural Representation for Physics Prediction
Humans have a remarkable capacity to understand the physical dynamics of objects in their environment, flexibly capturing complex structures and interactions at multiple levels of detail. Inspired by this ability, we propose a hierarchical particlebased object representation that covers a wide variety of types of three-dimensional objects, including both arbitrary rigid geometrical shapes and deformable materials. We then describe the Hierarchical Relation Network (HRN), an end-to-end differentiable neural network based on hierarchical graph convolution, that learns to predict physical dynamics in this representation. Compared to other neural network baselines, the HRN accurately handles complex collisions and nonrigid deformations, generating plausible dynamics predictions at long time scales in novel settings, and scaling to large scene configurations. These results demonstrate an architecture with the potential to form the basis of next-generation physics predictors for use in computer vision, robotics, and quantitative cognitive science.
object interactions. However, a number of challenges have remained in generalizing this approach to real-world physical dynamics, including representing arbitrary geometric shapes with sufficient resolution to capture complex collisions, working with objects at different scales simultaneously, and handling non-rigid objects of nontrivial complexity .   t  t+1  t+2  t+3  t+4  t+5  t+6  t+7  t+8  t+9 Ground Truth Prediction Figure 1: Predicting physical dynamics. Given past observations the task is to predict the future physical state of a system. In this example, a cube deforms as it collides with the ground. The top row shows the ground truth and the bottom row the prediction of our physics prediction network.
Several of these challenges are illustrated in the fast-moving deformable cube sequence depicted in Figure 1. Humans can flexibly vary the level of detail at which they perceive such objects in motion: The cube may naturally be conceived as an undifferentiated point mass as it moves along its initial kinematic trajectory. But as it collides with and bounces up from the floor, the cube's complex rectilinear substructure and nonrigid material properties become important for understanding what happens and predicting future interactions. The ease with which the human mind handles such complex scenarios is an important explicandum of cognitive science, and also a key challenge for artificial intelligence. Motivated by both of these goals, our aim here is to develop a new class of neural network architectures with this human-like ability to reason flexibly about the physical world.
To this end, it would be natural to extend the interaction network framework by representing each object as a (potentially large) set of connected particles. In such a representation, individual constituent particles could move independently, allowing the object to deform while being constrained by pairwise relations preventing the object from falling apart. However, this type of particle-based representation introduces a number of challenges of its own. Conceptually, it is not immediately clear how to efficiently propagate effects across such an object. Moreover, representing every object with hundreds or thousands of particles would result in an exploding number of pairwise relations, which is both computationally infeasible and cognitively unnatural.
As a solution to these issues, we propose a novel cognitively-inspired hierarchical graph-based object representation that captures a wide variety of complex rigid and deformable bodies (Section 3), and an efficient hierarchical graph-convolutional neural network that learns physics prediction within this representation (Section 4). Evaluating on complex 3D scenarios, we show substantial improvements relative to strong baselines both in quantitative prediction accuracy and qualitative measures of prediction plausibility, and evidence for generalization to complex unseen scenarios (Section 5).
The authors propose a novel hierarchical object representation based on particles to cover both rigid geometrical shapes and deformable materials. Each scene is represented as a graph, with disconnected components corresponding to the objects and the support of the scene. Each graph has a tree-like structure, where higher levels correspond to coarser scales, and the leaves correspond to the original particles placed in the object. They also propose an adapted neural network architecture, called Hierarchical Relation Network, that learns to predict physical dynamics for this representation. This architecture propagates exterior effects (forces, collisions) as well as the effect of past states through the graph, first from the leaves to their ancestors, then among sibling nodes, and finally back to the leaves. This multiscale approach is end to end differentiable, allowing this propagation mechanism to be learned.  The approach is very nicely motivated, and addresses an important problem: learning to model and predict physical states and dynamics of complex objects, and their interactions, in an end to end learnable fashion, so that it could be integrated in larger learning systems. This could be very useful in scenarios of computer vision, (eg. for action recognition tracking and future prediction), robotics (action conditioned future prediction is crucial for navigation) and reinforcement learning. Overall the paper is well written. The authors cite and compare to the most relevant prior work in a convincing manner - although it would be worthwhile citing "Learning Physical Intuition of Block Towers by Example" by Lerer et al. as well as "IntPhys: A Benchmark for Visual Intuitive Physics Reasoning" by Riochet et al. The approach is novel, and the experimental set up they propose is challenging, and would certainly serve future research purposes.   In terms of weaknesses of the approach, the proposed message passing scheme, relying on the hierarchical representation, does not seem very principled. It would be nice to know more precisely what has inspired the authors to make these design choices. Perhaps as a consequence, in qualitative results show sometimes objects seem to rip appart or smoothly deform into independent pieces. Qualitatively, some results are impressive, while some do not conform to our expectations of what would happen; cf my previous comment on unexpected deformations of objects, but also some motions: cubes moving slightly on the ground although they should be still, etc. More importantly, the applicability of the method is questionable, as it requires ground truth for the local and global deltas of each particle for training. Furthermore, even for inference, it would require the initial states of the particles. This would be a huge challenge in computer vision applications, and in any other applications relying on real videos, rather than synthetic videos. This greatly limits the applicability of the proposed representation, and as a consequence of the proposed architecture. Therefore I have doubts at this point that the proposed architecture has "the potential to form the basis of next generation physics predictors for use in computer vision, robotics, and quantitative cognitive science". To claim this, the authors should be able to show preliminary results of how their method could be used, even in very simple, but realistic settings.  Nevertheless I believe that it is worthwhile sharing these results with the community, as well as the code for the method and the environment, as this is an important problem, and the authors attack it with an ambitious and novel (although slightly ad hoc) approach.  To be fully confident that this paper should be accepted, I would like the authors to clarify the following points: - it is not clear how the quantitative results are obtained: what data exactly is used for training, validating and testing ?  - ternary input to the phi network, encoding the type of pairwise relationship -> is this effective ? What happens otherwise, if this is not given, or if weights are not shared ? Also wouldn't it make sense to have categorical input in the form of a one hot vector instead ? - the algorithm described for the creation of the graph G_H is inconsistent with the description of the remaining edges (l.122 to 1.131). According to the algorithm, there should only be edges between siblings, from the root to the leaves and back, and from the root to all intermediate nodes. Maybe this is due to l.127: "each new node taking the place for its child leaves" should be "each new node taking the place of the root" ? This would then also be more consistent with Algorithm 1. Please clarify. In Figure 3b) it is not clear what the red links represent, if the edges are supposed to be directed. - I don't understand the process for learning the r_ij. If it can be different for each pair of particle (or even for each source particle i), how can it be learned using the losses described in 4.3 ? We can obtain their values on the objects of the training set, but then for each new object, we need to gather synthetic videos of the object moving, in order to learn its properties? Wouldn't it be simpler to have fixed parameters ? Furthermore, if the stiffness of the material is to be learned, why not learn the mass as well ? - in the algorithm described for the creation of the graph G_H, it is said that one should "add edges between cluster nodes if the clusters are connected by edges between leaves" - how is there a presence or an absence of an edge in the first place ?  Nitpicking: - are humans really able to predict subtle deformations of masses at different scales ? Or can they simply perceive them and say whether they are plausible or not ?(l.39-44)  Typos: - par(i) should be par(p) l.128 - Figure 3: "is constraint" should be "is constrained" - l.152; l should be p_l ? - l 155 repetition with the following: "Effects are summed together"  -------------------------------- Final decision after rebuttal: The authors have addressed all of my concerns, except for one which I share with R3 that the experimental protocol for the quantitative results is not described.  Overall however I think that the paper presents an ambitious and novel method to a very important problem, which they convincingly test in a challenging experimental set up. I agree with R3 that the qualitative evaluation should include the weaknesses in the main paper and I think it is beneficial that the authors have agreed to do so.  I remain convinced that it would be worth sharing these results with the community. I can only urge the authors to respect their commitment to share the code and environment, and to add the missing details about the experimental protocol, to ease further research in this area and comparison to their work. I stand by my initial decision that the paper should be accepted as the approach is a very well executed stepping stone for others to improve on in the extremely challenging setting proposed by the authors.