Foraging animals must use decision-making strategies that dynamically adapt to the changing availability of rewards in the environment. A wide diversity of animals do this by distributing their choices in proportion to the rewards received from each option, Herrnstein’s operant matching law. Theoretical work suggests an elegant mechanistic explanation for this ubiquitous behavior, as operant matching follows automatically from simple synaptic plasticity rules acting within behaviorally relevant neural circuits. However, no past work has mapped operant matching onto plasticity mechanisms in the brain, leaving the biological relevance of the theory unclear. Here we discovered operant matching in Drosophila and showed that it requires synaptic plasticity that acts in the mushroom body and incorporates the expectation of reward. We began by developing a novel behavioral paradigm to measure choices from individual flies as they learn to associate odor cues with probabilistic rewards. We then built a model of the fly mushroom body to explain each fly’s sequential choice behavior using a family of biologically-realistic synaptic plasticity rules. As predicted by past theoretical work, we found that synaptic plasticity rules could explain fly matching behavior by incorporating stimulus expectations, reward expectations, or both. However, by optogenetically bypassing the representation of reward expectation, we abolished matching behavior and showed that the plasticity rule must specifically incorporate reward expectations. Altogether, these results reveal the first synaptic level mechanisms of operant matching and provide compelling evidence for the role of reward expectation signals in the fly brain.

Theoretical neuroscientists often try to understand how the structure of a neural network relates to its function by focusing on structural features that would either follow from optimization or occur consistently across possible implementations. Both optimization theories and ensemble modeling approaches have repeatedly proven their worth, and it would simplify theory building considerably if predictions from both theory types could be derived and tested simultaneously. Here we show how tensor formalism from theoretical physics can be used to unify and solve many optimization and ensemble modeling approaches to predicting synaptic connectivity from neuronal responses. We specifically focus on analyzing the solution space of synaptic weights that allow a thresholdlinear neural network to respond in a prescribed way to a limited number of input conditions. For optimization purposes, we compute the synaptic weight vector that minimizes an arbitrary quadratic loss function. For ensemble modeling, we identify synaptic weight features that occur consistently across all solutions bounded by an arbitrary quadratic function. We derive a common solution to this suite of nonlinear problems by showing how each of them reduces to an equivalent linear problem that can be solved analytically. Although identifying the equivalent linear problem is nontrivial, our tensor formalism provides an elegant geometrical perspective that allows us to solve the problem numerically. The final algorithm is applicable to a wide range of interesting neuroscience problems, and the associated geometric insights may carry over to other scientific problems that require constrained optimization.

Both vertebrates and invertebrates perceive illusory motion, known as "reverse-phi," in visual stimuli that contain sequential luminance increments and decrements. However, increment (ON) and decrement (OFF) signals are initially processed by separate visual neurons, and parallel elementary motion detectors downstream respond selectively to the motion of light or dark edges, often termed ON- and OFF-edges. It remains unknown how and where ON and OFF signals combine to generate reverse-phi motion signals. Here, we show that each of Drosophila's elementary motion detectors encodes motion by combining both ON and OFF signals. Their pattern of responses reflects combinations of increments and decrements that co-occur in natural motion, serving to decorrelate their outputs. These results suggest that the general principle of signal decorrelation drives the functional specialization of parallel motion detection channels, including their selectivity for moving light or dark edges.

Modern recording techniques now permit brain-wide sensorimotor circuits to be observed at single neuron resolution in small animals. Extracting theoretical understanding from these recordings requires principles that organize findings and guide future experiments. Here we review theoretical principles that shed light onto brain-wide sensorimotor processing. We begin with an analogy that conceptualizes principles as streetlamps that illuminate the empirical terrain, and we illustrate the analogy by showing how two familiar principles apply in new ways to brain-wide phenomena. We then focus the bulk of the review on describing three more principles that have wide utility for mapping brain-wide neural activity, making testable predictions from highly parameterized mechanistic models, and investigating the computational determinants of neuronal response patterns across the brain.

Goal-directed animal behaviors are typically composed of sequences of motor actions whose order and timing are critical for a successful outcome. Although numerous theoretical models for sequential action generation have been proposed, few have been supported by the identification of control neurons sufficient to elicit a sequence. Here, we identify a pair of descending neurons that coordinate a stereotyped sequence of engagement actions during Drosophila melanogaster male courtship behavior. These actions are initiated sequentially but persist cumulatively, a feature not explained by existing models of sequential behaviors. We find evidence consistent with a ramp-to-threshold mechanism, in which increasing neuronal activity elicits each action independently at successively higher activity thresholds.