Extend the DissipNet training algorithm to nonzero lower slope bounds

Extend the DissipNet training algorithm from activation functions with slope restricted to [0, β] to activation functions with a nonzero lower slope bound α ≠ 0, while retaining the dissipativity guarantees.

Background

The proposed dissipative recurrent neural network uses an activation-function slope restriction with lower bound α = 0 and upper bound β. Although the dissipativity condition itself can reportedly be generalized to arbitrary finite values of α and β, the training algorithm developed in the paper is restricted to the α = 0 case, which covers commonly used activations such as tanh, ReLU, and sigmoid under the stated formulation.

The unresolved task is to develop the corresponding training procedure for activation functions whose slopes have a strictly positive or otherwise nonzero lower bound, thereby broadening the class of admissible activations while preserving the network’s dissipativity constraints.

References

While the dissipativity condition proposed in this work can be easily extended for all finite values of α and β, the proposed training algorithm is restricted to the case α = 0. The extension to cases with α ≠ 0 is left for future work.

— Data-driven discrete-time deep recurrent neural network-based modeling for dissipative systems  (2609.27186 - Luong et al., 23 Sep 2026) in Assumption 1, Section 2, subsection “Dissipative Recurrent Neural Networks”