In cerebral cortex, ongoing activity absent a stimulus can resemble stimulus-driven activity in size and structure. In particular, spontaneous activity in cat primary visual cortex (V1) has structure significantly correlated with evoked responses to oriented stimuli. This suggests that, from unstructured input, cortical circuits selectively amplify specific activity patterns. Current understanding of selective amplification involves elongation of a neural assembly's lifetime by mutual excitation among its neurons. We introduce a new mechanism for selective amplification without elongation of lifetime: "balanced amplification." Strong balanced amplification arises when feedback inhibition stabilizes strong recurrent excitation, a pattern likely to be typical of cortex. Thus, balanced amplification should ubiquitously contribute to cortical activity. Balanced amplification depends on the fact that individual neurons project only excitatory or only inhibitory synapses. This leads to a hidden feedforward connectivity between activity patterns. We show in a detailed biophysical model that this can explain the cat V1 observations.