Incorporating Functional Knowledge in Neural Networks

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Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning (2020, background): “This follows since the mixing network is a universal function approximator of monotonic functions (Dugas et al., 2009), and hence can represent any value function that factors into a nonlinear monotonic combination of the agent’s individual value functions.”
Knowledge Infused Learning (K-IL): Towards Deep Incorporation of Knowledge in Deep Learning (2019, methodology): “(Dugas et al. 2009) proposed a modiﬁ-cation in the neural network by adopting Lipschitz functions for its activation function.”
QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning (2018, background): “This allows the mixing network to approximate any monotonic function arbitrarily closely (Dugas et al., 2009).”
Monotonic Calibrated Interpolated Look-Up Tables (2015, background): “Other researchers explicitly proposed constraining the weights to be positive in a single hidden-layer neural network with the sigmoid or other monotonic nonlinear transformation (Wang, 1994; Kay and Ungar, 2000; Dugas et al., 2000, 2009; Minin et al., 2010).”
Fast and Flexible Monotonic Functions with Ensembles of Lattices (2016, background): “Prior knowledge about monotonic relationships can also be an effective regularizer [3].”