Perception is not a faithful representation of the sensory world; rather, it is an inference of the most likely explanation given sensory evidence. Illusions arise due to rational mistakes in perceptual inference, exemplifying the dichotomy between faithful representation and inferred representation. We utilized illusory contours to ask how and where perceptual inference is encoded in the mouse visual cortex. In illusory contour perception, the perceived whole is greater than the sum of its parts. As such, we hypothesized that brain regions encoding perceptual inference would show enhanced neural activity specific to illusory contours. We employed mesoscale two-photon microscopy to record visual responses from thousands of excitatory neurons across 6 visual areas of the mouse neocortex simultaneously. Contrary to our initial hypothesis, the average neural population activity did not show illusory contour specific enhancement, in neither primary visual cortex (V1) nor any of the higher visual areas (LM, RL, AL, PM, AM). Subsequently, we tested the alternative hypothesis that the inferred illusory contour is represented in the specific pattern of neural activity. To this end, we employed machine learning to decode visual stimulus from visually evoked neural activity (support vector machines, SVM, and artificial neural networks, ANN). Across decoders, the inferred illusory contour was consistently represented in V1 and LM, but not PM. Next, we leveraged our decoding approach to ask how trial-by-trial variability influences perceptual inference. We found that neurons responded with the lowest variability (Fano factor) to visual stimuli that evoked the strongest activity. This sensory specific neural variability facilitated the capacity for inference contained in the neural activity pattern, despite degrading the capacity for faithful discrimination. Such tradeoff between perceptual inference and faithful representation has profound implications for interpreting the neural code.