Inspired by the fruit-fly olfactory circuit, the Fly Bloom Filter is able to efficiently summarize the data with a single pass and has been used for novelty detection. We propose a new classifier that effectively encodes the different local neighborhoods for each class with a per-class Fly Bloom Filter. The inference on test data requires an efficient FlyHash operation followed by a high-dimensional, but *very sparse*, dot product with the per-class Bloom Filters. On the theoretical side, we establish conditions under which the predictions of our proposed classifier agrees with the predictions of the nearest neighbor classifier. We extensively evaluate our proposed scheme with 71 data sets of varied data dimensionality to demonstrate that the predictive performance of our proposed neuroscience inspired classifier is competitive to the nearest-neighbor classifiers and other single-pass classifiers.