Odor cues guide animals to food and mates. Different environmental conditions can create differently patterned odor plumes, making navigation more challenging. Prior work has shown that animals turn upwind when they detect odor and cast crosswind when they lose it. Animals with bilateral olfactory sensors can also detect directional odor cues, such as odor gradient and odor motion. It remains unknown how animals use these two directional odor cues to guide crosswind navigation in odor plumes with distinct statistics. Here, we investigate this problem theoretically and experimentally. We show that these directional odor cues provide complementary information for navigation in different plume environments. We numerically analyzed real plumes to show that odor gradient cues are more informative about crosswind directions in relatively smooth odor plumes, while odor motion cues are more informative in turbulent or complex plumes. Neural networks trained to optimize crosswind turning converge to distinctive network structures that are tuned to odor gradient cues in smooth plumes and to odor motion cues in complex plumes. These trained networks improve the performance of artificial agents navigating plume environments that match the training environment. By recording Drosophila fruit flies as they navigated different odor plume environments, we verified that flies show the same correspondence between informative cues and plume types. Fly turning in the crosswind direction is correlated with odor gradients in smooth plumes and with odor motion in complex plumes. Overall, these results demonstrate that these directional odor cues are complementary across environments, and that animals exploit this relationship.

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 Drosophila’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.

Animals must infer the three-dimensional structure of their environment from two-dimensional images on their retinas. In particular, visual cues like motion parallax and binocular disparity can be used to judge distances to objects. Studies across several animal models have found neural signals that correlate with visual distance, but the causal role of these neurons in distance estimation as well as the range of possible neural properties that can inform distance estimation have remained poorly understood. Here, we developed a novel high-throughput behavioral assay to identify neurons in the Drosophila visual system that are involved in distance estimation during free locomotion. We found that silencing the primary motion detectors in the fly visual system eliminated their ability to perceive distance, consistent with a reliance on motion parallax to judge distance. Through a targeted silencing screen of visual neurons during behavior and through in vivo two-photon microscopy, we identified a visual projection neuron that encodes the parallax signal in the relative motion of foreground and background. Interestingly, it differs from previously identified parallax-tuned neurons in its lack of direction selectivity both to moving bars and to moving backgrounds. This non-canonical tuning is interpretable in the context of parallax signals that the fly would likely encounter during naturalistic walking behavior. Our results demonstrate how both direction selective and non-direction selective feature-detecting neurons can contribute to distance estimation using parallax cues, providing a framework for considering broader classes of parallax-encoding neurons in distance estimation across visual systems.

In selecting appropriate behaviors, animals should weigh sensory evidence both for and against specific beliefs about the world. For instance, animals measure optic flow to estimate and control their own rotation. However, existing models of flow detection can be spuriously triggered by visual motion created by objects moving in the world. Here, we show that stationary patterns on the retina, which constitute evidence against observer rotation, suppress inappropriate stabilizing rotational behavior in the fruit fly Drosophila. In silico experiments show that artificial neural networks (ANNs) that are optimized to distinguish observer movement from external object motion similarly detect stationarity and incorporate negative evidence. Employing neural measurements and genetic manipulations, we identified components of the circuitry for stationary pattern detection, which runs parallel to the fly’s local motion and optic flow detectors. Our results show how the fly brain incorporates negative evidence to improve heading stability, exemplifying how a compact brain exploits geometrical constraints of the visual world.

Animals have evolved sophisticated visual circuits to solve a vital inference problem: detecting whether or not a visual signal corresponds to an object on a collision course. Such events are detected by specific circuits sensitive to visual looming, or objects increasing in size. Various computational models have been developed for these circuits, but how the collision-detection inference problem itself shapes the computational structures of these circuits remains unknown. Here, inspired by the distinctive structures of LPLC2 neurons in the visual system of Drosophila, we build anatomically-constrained shallow neural network models and train them to identify visual signals that correspond to impending collisions. Surprisingly, the optimization arrives at two distinct, opposing solutions, only one of which matches the actual dendritic weighting of LPLC2 neurons. Both solutions can solve the inference problem with high accuracy when the population size is large enough. The LPLC2-like solutions reproduces experimentally observed LPLC2 neuron responses for many stimuli, and reproduces canonical tuning of loom sensitive neurons, even though the models are never trained on neural data. Thus, LPLC2 neuron properties and tuning are predicted by optimizing an anatomically-constrained neural network to detect impending collisions. More generally, these results illustrate how optimizing inference tasks that are important for an animal’s perceptual goals can reveal and explain computational properties of specific sensory neurons.

Although different animal species often exhibit extensive variation in many behaviors, typically scientists examine one or a small number of behaviors in any single study. Here, we propose a new framework to simultaneously study the evolution of many behaviors. We measured the behavioral repertoire of individuals from six species of fruit flies using unsupervised techniques and identified all stereotyped movements exhibited by each species. We then fit a Generalized Linear Mixed Model to estimate the intra- and inter-species behavioral covariances, and, by using the known phylogenetic relationships among species, we estimated the (unobserved) behaviors exhibited by ancestral species. We found that much of intra-specific behavioral variation has a similar covariance structure to previously described long-time scale variation in an individual’s behavior, suggesting that much of the measured variation between individuals of a single species in our assay reflects differences in the status of neural networks, rather than genetic or developmental differences between individuals. We then propose a method to identify groups of behaviors that appear to have evolved in a correlated manner, illustrating how sets of behaviors, rather than individual behaviors, likely evolved. Our approach provides a new framework for identifying co-evolving behaviors and may provide new opportunities to study the mechanistic basis of behavioral evolution.

Traditional theories of sensorimotor learning posit that animals use sensory error signals to find the optimal motor command in the face of Gaussian sensory and motor noise. However, most such theories cannot explain common behavioral observations, for example, that smaller sensory errors are more readily corrected than larger errors and large abrupt (but not gradually introduced) errors lead to weak learning. Here, we propose a theory of sensorimotor learning that explains these observations. The theory posits that the animal controls an entire probability distribution of motor commands rather than trying to produce a single optimal command and that learning arises via Bayesian inference when new sensory information becomes available. We test this theory using data from a songbird, the Bengalese finch, that is adapting the pitch (fundamental frequency) of its song following perturbations of auditory feedback using miniature headphones. We observe the distribution of the sung pitches to have long, non-Gaussian tails, which, within our theory, explains the observed dynamics of learning. Further, the theory makes surprising predictions about the dynamics of the shape of the pitch distribution, which we confirm experimentally.

We investigate the inner structure of a general SU(2) (naturally including SO(3)) symmetry system—the fermion-gauge field interaction system, and achieve naturally a set of gauge invariant spin and orbital angular momentum operators of fermion and gauge fields by Noether theorem in general field theory. Some new relations concerning non-Abelian field strengths are discovered, e.g., the covariant transverse condition, covariant parallel condition ( i.e., non-Abelian divergence, non-Abelian curl ) and simplified SU(2) Coulomb theorem. And we show that the condition that Chen et al obtained to construct their gauge invariant angular momentum operators is a result of some fundamental equations in the general field theory. The results obtained in this paper present a new perspective to look at the overall structure of the gauge field, and provide a new viewpoint to the final resolution of the nucleon spin crisis in the general field theory. Specially, the achieved theory in this paper can calculate the strong interactions with isospin symmetry and solves the serious problem without gauge invariant angular momenta in strong interaction systems with isospin symmetry, and then the achieved predictions in the calculations can be exactly measured by particle physics experiments due to their gauge invariant properties.

We discover an inner structure of the QED system; i.e., by decomposing the gauge potential into two orthogonal components, we obtain a new expansion of the Lagrangian for the electron-photon system, from which, we realize the orthogonal decomposition of the canonical momentum conjugate to the gauge potential with the canonical momentum’s two components conjugate to the gauge potential’s two components, respectively. Using the new expansion of Lagrangian and by the general method of field theory, we naturally derive the gauge invariant separation of the angular momentum of the electron-photon system from Noether theorem, which is the rational one and has the simplest form in mathematics, compared with the other four versions of the angular momentum separation available in literature. We show that it is only the longitudinal component of the gauge potential that is contained in the orbital angular momentum of the electron, as Chen et al. have said. A similar gauge invariant separation of the momentum is given. The decomposed canonical Hamiltonian is derived, from which we construct the gauge invariant energy operator of the electron moving in the external field generated by a proton [Phys. Rev. A 82, 012107 (2010)], where we show that the form of the kinetic energy containing the longitudinal part of the gauge potential is due to the intrinsic requirement of the gauge invariance. Our method provides a new perspective to look on the nucleon spin crisis and indicates that this problem can be solved strictly and systematically.

We discover an inner structure of QED while the gauge potential is decomposed into two orthogonal components. Based on this, the Lagrangian of the electron-photon system is expanded to a new form and by the general method of field theory, the gauge invariant spin and orbital angular momentum operators of the electron and photon are naturally obtained from Noether’s theorem. Our method, which can be generalized to the non-Abelian systems to investigate the inner structure of QCD, provides a new perspective to look on the nucleon spin crisis and opens a window into a strict and systematic resolution of this long-standing problem.