Safe Neurosymbolic Learning with Differentiable Symbolic Execution
This addresses safety-critical domains where neurosymbolic programs are used, but it is incremental as it builds on existing gradient-based safe learning approaches.
The paper tackles the problem of learning worst-case-safe parameters for neurosymbolic programs, which combine neural networks and symbolic code, by introducing Differentiable Symbolic Execution (DSE) that samples control flow paths and backpropagates safety loss gradients, resulting in significant outperformance over the state-of-the-art DiffAI method on synthetic and real-world benchmarks.
We study the problem of learning worst-case-safe parameters for programs that use neural networks as well as symbolic, human-written code. Such neurosymbolic programs arise in many safety-critical domains. However, because they can use nondifferentiable operations, it is hard to learn their parameters using existing gradient-based approaches to safe learning. Our approach to this problem, Differentiable Symbolic Execution (DSE), samples control flow paths in a program, symbolically constructs worst-case "safety losses" along these paths, and backpropagates the gradients of these losses through program operations using a generalization of the REINFORCE estimator. We evaluate the method on a mix of synthetic tasks and real-world benchmarks. Our experiments show that DSE significantly outperforms the state-of-the-art DiffAI method on these tasks.