The hippocampus (HPC) is a key structure of the brain's capacity to learn and generalize. One pervasive phenomenon in the brain, but missing in AI, is the presence of different gross brain states. It is known that these different brain states give rise to diverse modes of information processing that are imperative for hippocampus to learn and function, but the mechanisms by which they do so remain unknown. To study this, we harnessed the power of recently developed dimensionality reduction techniques to shed insight on how HPC representations change across brain states. We compared the geometry of HPC neuronal representations when rodents learn to generalize across different environments, and showed that HPC representation could support both pattern separation and generalization. Next, we compared HPC activity during different stages of sleep. Consistent with the literature, we found a robust recapitulation of the previous awake experience during non rapid eye movement sleep (NREM). But interestingly, such geometric correspondence to previous awake experience was not observed during rapid eye movement sleep (REM), suggesting a very different mode of information processing. This is the first known report of UMAP analysis on hippocampal neuronal data during REM sleep. We propose that characterizing and contrasting the geometry of hippocampal representations during different brain states can help understand the brain's mechanisms for learning, and in the future, can even help design next generation of AI that learn and generalize better.