Geometric descriptions of deep neural networks (DNNs) have the potential to uncover core principles of computational models in neuroscience, while abstracting over the details of model architectures and training paradigms. Here we examined the geometry of DNN models of visual cortex by quantifying the latent dimensionality of their natural image representations. The prevailing view holds that optimal DNNs compress their representations onto low-dimensional manifolds to achieve invariance and

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... ustness, which suggests that better models of visual cortex should have low-dimensional geometries. Surprisingly, we found a strong trend in the opposite direction---neural networks with high-dimensional image manifolds tend to have better generalization performance when predicting cortical responses to held-out stimuli in both monkey electrophysiology and human fMRI data. These findings held across a diversity of design parameters for DNNs, and they suggest a general principle whereby high-dimensional geometry confers a striking benefit to DNN models of visual cortex.