Abstract
A variety of simple models has been proposed to understand the collective motion of animals. These models can be insightful but may lack important elements necessary to predict the motion of each individual in the collective. Adding more detail increases predictability but can make models too complex to be insightful. Here we report that deep attention networks can obtain a model of collective behavior that is simultaneously predictive and insightful thanks to an organization in modules. When using simulated trajectories, the model recovers the ground-truth interaction rule used to generate them, as well as the number of interacting neighbours. For experimental trajectories of large groups of 60-100 zebrafish, Danio rerio, the model obtains that interactions between pairs can approximately be described as repulsive, attractive or as alignment, but only when moving slowly. At high velocities, interactions correspond only to alignment or alignment mixed with repulsion at close distances. The model also shows that each zebrafish decides where to move by aggregating information from the group as a weighted average over neighbours. Weights are higher for neighbours that are close, in a collision path or moving faster in frontal and lateral locations. The network also extracts that the number of interacting individuals is dynamical and typically in the range 8–22, with 1–10 more important ones. Our results suggest that each animal decides by dynamically selecting information from the collective.
Highlights
There is a wide range of models of collective behavior
Simple models have traditionally been very successful, because they usually provide more insight than complicated models. This is true in physics, where simple models can often give highly precise quantitative predictions
To create models that are both precise and insightful, we propose to harness the power of deep neural networks but to confine them into modules with a low number of inputs and outputs
Summary
There is a wide range of models of collective behavior. A useful way to understand the relative merits of these models is to classify them by their accuracy and their complexity (e.g. [1, 2]). If a model has a low parameter-complexity, we can write down the mathematical description and study it in detail, leading to an intuitive grasp of the problem and a better design of new experiments. This simplicity likely misses important biological components. For this reason, these low-parametercomplexity models are not typically tested in their detailed quantitative predictions, using simpler global parameters instead (but see [19, 20])
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