Organizational Regularities in Recurrent Neural Networks

Claus MetznerAchim SchillingAndreas K MaierPatrick Krauss^*

• University of Erlangen Nuremberg, Erlangen, Germany

Previous work has shown that the dynamical regime of Recurrent Neural Networks (RNNs)—ranging from oscillatory to chaotic and fixed point behavior—can be con-trolled by the global distribution of weights in connection matrices with statistically independent elements. However, it remains unclear how network dynamics respond to organizational regularities in the weight matrix, as often observed in biological neural networks. Here, we investigate three such regularities: (1) monopolar output weights per neuron, in accordance with Dale's principle, (2) reciprocal symmetry between neuron pairs, as in Hopfield networks, and (3) modular structure, where strongly connected blocks are embedded in a background of weaker connectivity. These regularities are studied independently, but as functions of the RNN's general connection strength and its excitatory/inhibitory bias. For this purpose, we construct weight matrices in which the strength of each regularity can be continuously tuned via control parameters, and analyze how key dynamical signatures of the RNN evolve as a function of these pa-rameters. Moreover, using the RNN for actual information processing in a reservoir computing framework, we study how each regularity affects performance. We find that Dale monopolarity and modularity significantly enhance task accuracy, while Hopfield reciprocity tends to reduce it by promoting early saturation, limiting reservoir flexibility.