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We model a dynamical system as a collection of recurrent modules that interact according to a spatially informed but learned topology.

Spatially Structured Recurrent Modules

ICLR, (2021)

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Abstract

Capturing the structure of a data-generating process by means of appropriate inductive biases can help in learning models that generalise well and are robust to changes in the input distribution. While methods that harness spatial and temporal structures find broad application, recent work has demonstrated the potential of models that lev...More

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Introduction
  • Many spatiotemporal complex systems can be abstracted as a collection of autonomous but sparsely interacting sub-systems, where sub-systems tend to interact if they are in each others’ vicinity.
  • To evaluate the proposed model, the authors choose a problem setting where (a) the task is composed of different sub-systems or processes that locally interact both spatially and temporally, and (b) the environment offers local views into its state paired with their corresponding spatial locations.
Highlights
  • Many spatiotemporal complex systems can be abstracted as a collection of autonomous but sparsely interacting sub-systems, where sub-systems tend to interact if they are in each others’ vicinity
  • To draw fair comparisons between various recurrent neural network (RNN) architectures, we require an architectural scaffolding that is agnostic to the number of observations A, is invariant to the ordering of
  • The resulting model has three components: an encoder, a RNN, and a decoder, which we describe in detail in Appendix D
  • We show results with a Time Travelling Oracle (TTO), which at time-step t has access to the state at t + 1
Results
  • The task here is to model the dynamics of the global state of the environment given local observations made by cooperating agents and their corresponding actions.
  • The output attention mechanism together with the decoder serve as an apparatus to evaluate the world state modeled implicitly by the set of RNNs ({Fm}M m=1) at time t + 1.
  • Recall that the problem setting the authors consider is one where the environment offers local views into its global state paired with the corresponding spatial locations.
  • The authors present a selection of experiments to quantitatively evaluate S2RMs and gauge their performance against strong baselines on two data domains, namely video prediction from crops on the well-known bouncing-balls domain and multi-agent world modelling from partial observations in the challenging Starcraft2 domain.
  • × 11 crops, which the authors use as the local observations corresponding to query central-pixel-positions xqt at a future time-step t > t.
  • In Section 2, the authors formulated the problem of modeling what the authors called the world state o of a dynamical system φ given local observations {(xat , Oat )}Aa=1 where Oat = φ(t, o)(xat ).
  • This problem can be mapped to that of multiagent world modeling from partial and local observations, allowing them to evaluate the proposed model in a rich and challenging setting.
  • The authors only include baselines that achieve similar or better validation scores than S2RMs. Figure 8 shows that S2RMCs remain robust when fewer agents supply their observations to the world model, whereas Table 1 shows that S2GRUs outperforms the baselines in the OOD scenario 1s2z but is matched by RMCs in 5s3z.
Conclusion
  • The authors proposed Spatially Structured Recurrent Modules, a new class of models constructed to jointly leverage both spatial and modular structure in data, and explored its potential in the challenging problem setting of predicting the forward dynamics from partial observations at known spatial locations.
  • In the tasks of video prediction from crops and multi-agent world modeling in the Starcraft2 domain, the authors found that it compares favorably against strong baselines in terms of out-ofdistribution generalization and robustness to the number of available observations.
Tables
  • Table1: Performance metrics on OOD scenarios marker), and (c) four channels marking the 1s2z and 5s3z (larger numbers are better): unithealth, energy, weapon-cooldown and shields type macro F1 score (UT-F1), friendly-marker F1
  • Table2: Hyperparameters used for various models on the Bouncing Ball task. Hyperparameters not listed here were left at their respective default values
  • Table3: Hyperparameters used for various models on the Starcraft2 task. Hyperparameters not listed here were left at their respective default values
  • Table4: Friendly marker F1 scores on the validation set of the training distribution. Larger numbers are better
  • Table5: Unit-type marker (macro averaged) F1 scores on the validation set of the training distribution. Larger numbers are better
  • Table6: HECS Negative MSE on the validation set of the training distribution. Larger numbers are better
  • Table7: Log Likelihood (negative loss) on the validation set of the training distribution. Larger numbers are better
Download tables as Excel
Related work
  • Problem Setting. Recall that the problem setting we consider is one where the environment offers local (partial) views into its global state paired with the corresponding spatial locations. With Generative Query Networks (GQNs), Eslami et al (2018) investigate a similar setting where the 2D images of 3D scenes are paired with the corresponding viewpoint (camera position, yaw, pitch and roll). Given that GQNs are feedforward models, they do not consider the dynamics of the underyling scene and as such cannot be expected to be consistent over time (Kumar et al, 2018). Singh et al (2019) and Kumar et al (2018) propose variants that are temporally consistent, but unlike us, they do not focus on the problem of predicting the future state of the system.

    Modularity. Modularity has been a recurring topic in the context of meta-learning (Alet et al, 2018; Bengio et al, 2019; Ke et al, 2019), sequence modeling (Ghahramani & Jordan, 1996; Henaff et al, 2016; Li et al, 2018; Goyal et al, 2019; Mei et al, 2020; Mittal et al, 2020) and beyond (Jacobs et al, 1991; Shazeer et al, 2017; Parascandolo et al, 2017). In the context of RNNs, Li et al (2018) explore a setting where the recurrent units operate entirely independently of each other. Closer to our work, Goyal et al (2019) explores the setting where autonomous RNN modules interact with each other via the bottleneck of sparse attention. However, instead of leveraging the spatial structure of the environment, they induce sparsity using a scheme inspired by the k-winners-take-all principle (Majani et al, 1988) where only the k modules that attend the most to the input are activated and propagate their state forward, whereas the remaining modules that do not receive an input follow default dynamics in that their hidden states are not updated. This can be contrasted with S2RMs, where the modules that do not receive inputs may still evolve their states forward in time, reflecting that the environment may evolve even when no observations are available.
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