Broken time-reversal symmetry in visual motion detection

Our intuition suggests that when a movie is played in reverse, our perception of motion at each location in the reversed movie will be perfectly inverted compared to the original. This intuition is also reflected in classical theoretical and practical models of motion estimation, in which velocity flow fields invert when inputs are reversed in time. However, here we report that this symmetry of motion perception upon time reversal is broken in real visual systems. We designed a set of visual stimuli to investigate time reversal symmetry breaking in the fruit fly <i>Drosophila</i>'s well-studied optomotor rotation behavior. We identified a suite of stimuli with a wide variety of properties that can uncover broken time reversal symmetry in fly behavioral responses. We then trained neural network models to predict the velocity of scenes with both natural and artificial contrast distributions. Training with naturalistic contrast distributions yielded models that broke time reversal symmetry, even when the training data themselves were time reversal symmetric. We show analytically and numerically that the breaking of time reversal symmetry in the model responses can arise from contrast asymmetry in the training data, but can also arise from other features of the contrast distribution. Furthermore, shallower neural network models can exhibit stronger symmetry breaking than deeper ones, suggesting that less flexible neural networks may be more prone to time reversal symmetry breaking. Overall, these results reveal a surprising feature of biological motion detectors and suggest that it could arise from constrained optimization in natural environments.