  Conversion of temporal to spatial correlations in the cortex is one of the
most intriguing functions in the brain. The learning at synapses triggering the
correlation conversion can take place in a wide integration window, whose
influence on the correlation conversion remains elusive. Here, we propose a
generalized associative memory model with arbitrary Hebbian length. The model
can be analytically solved, and predicts that a small Hebbian length can
already significantly enhance the correlation conversion, i.e., the
stimulus-induced attractor can be highly correlated with a significant number
of patterns in the stored sequence, thereby facilitating state transitions in
the neural representation space. Moreover, an anti-Hebbian component is able to
reshape the energy landscape of memories, akin to the function of sleep. Our
work thus establishes the fundamental connection between associative memory,
Hebbian length, and correlation conversion in the brain.
