  A central goal of 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 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. In recent decades,
measurements of large populations of neurons have motivated a complementary
approach, which focuses on the information available to linear decoders. The
decodable information is captured by the geometry of the representational
patterns in the multivariate response space. Here we review neural tuning and
representational geometry with the goal of clarifying the relationship between
them. The tuning induces the geometry, but different sets of tuned neurons can
induce the same geometry. The geometry determines the Fisher information, the
mutual information, and the behavioral performance of an ideal observer in a
range of psychophysical tasks. We argue that future studies can benefit from
considering both tuning and geometry to understand neural codes and reveal the
connections between stimulus, brain activity, and behavior.
