Stability of the replica symmetric solution for the information conveyed by a neural network

Advances in techniques for the formal analysis of neural networks @1‐5# offer insight into the behavior of models of biological interest. Of particular interest are methods which allow the calculation of the information that can be conveyed by a given neural structure, as these offer both useful intuitions and the prospect of conducting pertinent experiments @6#. The replica trick @7# has been used to achieve this in the case of binary units @5# and threshold-linear units @8,9# ,b y appealing to an assumption of replica symmetry. In the case of binary units with continuous inputs, the validity of the replica-symmetric ansatz is justified by the duality with the Gardner calculation of the storage capacity for continuous couplings @2,5,10#. We now analyze the stability of the replica-symmetric solution for mutual information in a network of threshold-linear units.