Symbolic Neural CPU Offers Interpretable, Low-Precision Program Execution

Neural networks are capable of learning algorithmic input-output mappings, but the internal state transitions that produce these results are typically hidden, making it challenging to fully trust their learned executors. This research addresses this transparency issue by introducing a trace-supervised symbolic neural CPU. This factorized learned execution architecture integrates recurrent control, an explicit operation router over a fixed differentiable arithmetic-logic unit bank, and destination-masked register writeback, all supervised by complete trajectory data. The model is designed to expose the selected operation, source and destination registers, register trajectory, memory signals, and writeback semantics at every step. In non-quantized settings, the executor precisely reproduces reference execution. Even with 8-bit quantization, it preserves the symbolic operation path through programs containing up to 1,000 instructions. The study also compares various controller types and emphasizes that operation-gate supervision is essential for achieving an inspectable execution path, thereby establishing a framework for interpretable, low-precision, and controllable neural execution.