Recognition of natural stimuli requires a combination of selectivity and invariance. Classical neurobiological models achieve selectivity and invariance, respectively, by assigning to each cortical neuron either a computation equivalent to the logical "AND" or a computation equivalent to the logical "OR." One powerful OR-like operation is the MAX function, which computes the maximum over input activities. The MAX function is frequently employed in computer vision to achieve invariance and considered a key operation in visual cortex. Here we explore the computations for selectivity and invariance in the auditory system of a songbird, using natural stimuli. We ask two related questions: does the MAX operation exist in auditory system? Is it implemented by specialized "MAX" neurons, as assumed in vision? By analyzing responses of individual neurons to combinations of stimuli we systematically sample the space of implemented feature recombination functions. Although we frequently observe the MAX function, we show that the same neurons that implement it also readily implement other operations, including the AND-like response. We then show that sensory adaptation, a ubiquitous property of neural circuits, causes transitions between these operations in individual neurons, violating the fixed neuron-to-computation mapping posited in the state-of-the-art object-recognition models. These transitions, however, accord with predictions of neural-circuit models incorporating divisive normalization and variable polynomial nonlinearities at the spike threshold. Because these biophysical properties are not tied to a particular sensory modality but are generic, the flexible neuron-to-computation mapping demonstrated in this study in the auditory system is likely a general property.