Typically, a neural network parameterized by weights $\mathbf{W}$ is a function from an input $x$ to an output $y$. The network has an associated compatibility function $\Psi(y; x, \mathbf{W}) \rightarrow \mathbb{R}^+$ that measures how likely an output y is given an input x under weights $W$.
Source: Gradient-based Inference for Networks with Output Constraints, AAAI 2019 (https://arxiv.org/abs/1707.08608)
What is a compatibility function? What is its utility?
Neural networks are generally deterministic. We are guaranteed to get a specific output for a given input. How do we interpret compatibility function in this context?
