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Abstract 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? Here, we show that sensory signals are encoded more reliably in certain low-dimensional subspaces. These coding subspaces are defined by correlations between neural activity in the primary sensory cortex and upstream sensory brain regions; the most correlated dimensions were best for decoding. We analytically show that these correlation-based coding subspaces improve, reaching optimal limits (without an ideal observer), as noise correlations between cortex and upstream regions are reduced. We show that this principle generalizes across diverse sensory stimuli in the olfactory system and the visual system of awake mice. Our results demonstrate an algorithm the cortex may use to multiplex different functions, processing sensory input in low-dimensional subspaces separate from other ongoing functions. 

Distinct scientific theories can make similar predictions. To adjudicate between theories, we must design experiments for which the theories make distinct predictions. Here we consider the problem of comparing deep neural networks as models of human visual recognition. To efficiently compare models’ ability to predict human responses, we synthesize controversial stimuli: images for which different models produce distinct responses. We applied this approach to two visual recognition tasks, handwritten digits (MNIST) and objects in small natural images (CIFAR-10). For each task, we synthesized controversial stimuli to maximize the disagreement among models which employed different architectures and recognition algorithms. Human subjects viewed hundreds of these stimuli, as well as natural examples, and judged the probability of presence of each digit/object category in each image. We quantified how accurately each model predicted the human judgments. The best-performing models were a generative analysis-by-synthesis model (based on variational autoencoders) for MNIST and a hybrid discriminative–generative joint energy model for CIFAR-10. These deep neural networks (DNNs), which model the distribution of images, performed better than purely discriminative DNNs, which learn only to map images to labels. None of the candidate models fully explained the human responses. Controversial stimuli generalize the concept of adversarial examples, obviating the need to assume a ground-truth model. Unlike natural images, controversial stimuli are not constrained to the stimulus distribution models are trained on, thus providing severe out-of-distribution tests that reveal the models’ inductive biases. Controversial stimuli therefore provide powerful probes of discrepancies between models and human perception.