As information about the world is conveyed from the sensory periphery to central neural circuits, it mixes with complex ongoing cortical activity. How do neural populations keep track of sensory signals, separating them from noisy ongoing activity? I will talk about our recent work demonstrating that sensory signals are encoded more reliably in low-dimensional subspaces defined by correlations between neural activity in primary sensory cortex and upstream sensory brain regions. We analytically show that these subspaces can reach optimal limits (without an ideal observer) as noise correlations between cortex and upstream regions are reduced, and that this principle generalizes across diverse sensory stimuli in the olfactory system and the visual system of awake mice. Finally, I will talk about the neural observations that originally motivated our thinking in this area: the difference in the olfactory response between inhale and exhale. This difference is evident early in the olfactory pathway, and we hypothesize that it arises in part because of fluid mechanical forces in the nasal cavity. I will show how we are constructing a phase preference map for mechanical forcing. Our goal is to combine this map with emerging research on receptor zones to produce a unified view of the sensory inputs underlying directional selectivity.