= Symmetric coactivity weights do not distinguish reversed episodes
Suppose storing activities $a_1,\ldots,a_T$ changes a matrix by $\Delta W=\eta\sum_{t=1}^T a_ta_t^T$. Any permutation of the activities leaves this sum unchanged. Therefore the update alone cannot distinguish an episode from its reversal. This is a restriction on the stated order-insensitive update, not on all <Hebbian learning>: <trace learning>, an evolving context or directed transitions can introduce order information.
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