Weights to Code: Extracting Interpretable Algorithms from the Discrete Transformer

Abstract: Algorithm extraction aims to synthesize executable programs directly from models trained on specific algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, extending this paradigm to Transformer is hindered by superposition, where entangled features encoded in overlapping directions obstruct the extraction of symbolic expressions. In this work, we propose the Discrete Transformer, an architecture explicitly engineered to bridge the gap between continuous representations and discrete symbolic logic. By enforcing a strict functional disentanglement, which constrains Numerical Attention to information routing and Numerical MLP to element-wise arithmetic, and employing temperature-annealed sampling, our method effectively facilitates the extraction of human-readable programs. Empirically, the Discrete Transformer not only achieves performance comparable to RNN-based baselines but crucially extends interpretability to continuous variable domains. Moreover, our analysis of the annealing process shows that the efficient discrete search undergoes a clear phase transition from exploration to exploitation. We further demonstrate that our method enables fine-grained control over synthesized programs by imposing inductive biases. Collectively, these findings establish the Discrete Transformer as a robust framework for demonstration-free algorithm discovery, offering a rigorous pathway toward Transformer interpretability.