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Neural network models of categorical perception (compression of withincategory similarity and dilation of between-category differences) are applied to the symbol-grounding problem (of how to connect symbols with meanings) by connecting analogue sensorimotor projections to arbitrary symbolic representations via learned category-invariance detectors in a hybrid symbolic/non-symbolic system. Our nets are trained to categorize and name 50 50 pixel images (eg circles, ellipses, squares and rectangles) projected on to the receptive fi eld of a 7 7 retina. They fi rst learn to do prototype matching and then entry-level naming for the four kinds of stimuli, grounding their names directly in the input patterns via hidden-unit representations (‘sensorimotor toil’). We show that a higher-level categorization (eg ‘symmetric’versus ‘asymmetric’) can be learned in two very different ways: either (1) directly from the input, just as …