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Nikolaus Kriegeskorte, Xue-Xin Wei; A unifying framework for understanding neural tuning and representational geometry. Journal of Vision 2020;20(11):235. doi: https://doi.org/10.1167/jov.20.11.235.
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A central goal of visual neuroscience is to understand the representations formed by brain activity patterns and their connection to behavior. The classical approach is to investigate how individual neurons encode the visual stimuli and how their tuning determines the fidelity of the neural representation. Tuning analyses often use the Fisher information to characterize the sensitivity of neural responses to small changes of the stimulus and the mutual information to characterize the information the response conveys about the stimulus. In recent decades, measurements of the activity of large populations of neurons have motivated a complementary approach, which focuses on the information available to linear decoders. A linear decoder projects the representational patterns onto a single dimension. All possible such projections, together, define the representational geometry, i.e., the geometry in multivariate response space of the points that correspond to the stimuli. The relationship between the tuning curves and the representational geometry they give rise to has remained unclear. Here, we clarify this relationship through theoretical analyses and computer simulations. What emerges is a unifying framework, which defines the mathematical relationships between neural tuning, neural noise, representational geometry, Fisher information, mutual information, and perceptual discriminability (Figure 1). We demonstrate several known and some possibly unknown insights: (1) The tuning and the noise co-determine the mutual information and the Fisher information. (2) The tuning and the noise co-determine the geometry. (3) The geometry does not determine the tuning. (4) The geometry and the noise co-determine the Fisher information and the mutual information. (5) The Fisher information does not determine the geometry. (6) The tuning and the noise co-determine the perceptual sensitivity. (7) The geometry and the noise co-determine the perceptual sensitivity. Our framework can help guide future studies aiming to clarify the connections between stimulus, brain activity, and perception.
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