I will review two new approaches for studying cortical representations of sensory stimuli. These exploit maximum likelihood optimization algorithms, deep neural networks, like auto-encoders, and high resolution electrophysiology data. I will show how these approaches can shed new light into the information processing and maintenance taking place in neural populations. First, I will describe a visual perception task with optogenetic activation of the basal forebrain in a mouse. I will discuss how one can infer changes in the precision of error representations of visual stimuli as a result of neuromodulation. These results confirm predictions of hierarchical Bayesian inference. I will also talk about how one can test at which cortical layer these representations might be found. Then, I will describe a spatial delayed response task. I will consider differences in the cortical connectivity underlying memory representations for different cued locations. I will discuss how connectivity patterns might relate to results in psychophysics, like the oblique effect (performance is better for stimuli on than off the horizontal axis). In brief, I hope to show that by marrying detailed biophysical models and modern machine learning algorithms one can answer questions about physiological processes and behavior that are of importance in cognitive neuroscience.