  A network of neurons in the central nervous system collectively represents
information by its spiking activity states. Typically observed states, i.e.,
codewords, occupy only a limited portion of the state space due to constraints
imposed by network interactions. Geometrical organization of codewords in the
state space, critical for neural information processing, is poorly understood
due to its high dimensionality. Here, we explore the organization of neural
codewords using retinal data by computing the entropy of codewords as a
function of Hamming distance from a particular reference codeword.
Specifically, we report that the retinal codewords in the state space are
divided into multiple distinct clusters separated by entropy-gaps, and that
this structure is shared with well-known associative memory networks in a
recallable phase. Our analysis also elucidates a special nature of the
all-silent state. The all-silent state is surrounded by the densest cluster of
codewords and located within a reachable distance from most codewords. This
codeword-space structure quantitatively predicts typical deviation of a
state-trajectory from its initial state. Altogether, our findings reveal a
non-trivial heterogeneous structure of the codeword-space that shapes
information representation in a biological network.
