Although information theoretic approaches have been used extensively in the analysis of the neural code, they have yet to be used to describe how information is accumulated in time while sensory systems are categorizing dynamic sensory stimuli such as speech sounds or visual objects. Here, we present a novel method to estimate the cumulative information for stimuli or categories. We further define a time-varying categorical information index that, by comparing the information obtained for stimuli versus categories of these same stimuli, quantifies invariant neural representations. We use these methods to investigate the dynamic properties of avian cortical auditory neurons recorded in zebra finches that were listening to a large set of call stimuli sampled from the complete vocal repertoire of this species. We found that the time-varying rates carry 5 times more information than the mean firing rates even in the first 100 ms. We also found that cumulative information has slow time constants (100-600 ms) relative to the typical integration time of single neurons, reflecting the fact that the behaviorally informative features of auditory objects are time-varying sound patterns. When we correlated firing rates and information values, we found that average information correlates with average firing rate but that higher-rates found at the onset response yielded similar information values as the lower-rates found in the sustained response: the onset and sustained response of avian cortical auditory neurons provide similar levels of independent information about call identity and call-type. Finally, our information measures allowed us to rigorously define categorical neurons, these categorical neurons show a high degree of invariance for vocalizations within a call-type. Peak invariance is found around 150 ms after stimulus onset. Surprisingly, call-type invariant neurons were found in both primary and secondary avian auditory areas.