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Invariant stimulus recognition is a challenging pattern-recognition problem that must be dealt with by all sensory systems. Since neural responses evoked by a stimulus are perturbed in a multitude of ways, how can this computational capability be achieved? We examine this issue in the locust olfactory system. We find that locusts trained in an appetitive-conditioning assay robustly recognize the trained odorant independent of variations in stimulus durations, dynamics, or history, or changes in background and ambient conditions. However, individual- and population-level neural responses vary unpredictably with many of these variations. Our results indicate that linear statistical decoding schemes, which assign positive weights to ON neurons and negative weights to OFF neurons, resolve this apparent confound between neural variability and behavioral stability. Furthermore, simplification of the decoder using only ternary weights ({+1, 0, −1}) (i.e., an “ON-minus-OFF” approach) does not compromise performance, thereby striking a fine balance between simplicity and robustness.