Extracting Exact Lie Derivatives Without Backpropagation: A Dual Compiler for Neural Control Barrier Functions

This paper presents a dual-algebraic compiler that evaluates neural control barrier functions (CBFs) and their exact Lie derivatives using forward-mode dual-number arithmetic. Emitting self-contained C++ code, the compiler executes a single forward pass to extract the barrier value and Jacobian--vector-field product without backpropagation, alongside a hyper-dual extension for exact second-order Lie derivatives.
Learning-enabled safety filters must operate at kilohertz rates under the strict memory and worst-case execution time (WCET) constraints required for certification. Standard reverse-mode automatic differentiation violates these standards by allocating dynamic graphs on the heap and building depth-dependent activation caches.
Our architecture resolves this conflict by confining the scratch workspace to twice the widest layer, remaining entirely independent of network depth. By eliminating dynamic allocation, the framework makes memory safety verifiable by inspection rather than testing. Validated on a bare-metal ESP32-S3, the compiler assembles the complete safety constraint in sub-millisecond time from a static 768-byte buffer. It bounds WCET within 5% of the median, defeating the 70% jitter of runtime baselines.