Zichao Wei
Publications
On the Mirage of Long-Range Dependency, with an Application to Integer Multiplication
Integer multiplication has long been considered a hard problem for neural networks, with the difficulty widely attributed to the O(n) long-range dependency induced by carry chains. We argue that this diagnosis is wrong: long-range dependency is not an intrinsic property of multiplication, but a mirage produced by the choice of computational spacetime. We formalize the notion of mirage and provide a constructive proof: when two n-bit binary integers are laid out as a 2D outer-product grid, every step of long multiplication collapses into a $3 \times 3$ local neighborhood operation. Under this representation, a neural cellular automaton with only 321 learnable parameters achieves perfect length generalization up to $683\times$ the training range. Five alternative architectures -- including Transformer (6,625 params), Transformer+RoPE, and Mamba -- all fail under the same representation. We further analyze how partial successes locked the community into an incorrect diagnosis, and argue that any task diagnosed as requiring long-range dependency should first be examined for whether the dependency is intrinsic to the task or induced by the computational spacetime.
Autoregressive, Yet Revisable: In Decoding Revision for Secure Code Generation
Large Language Model (LLM) based code generation is predominantly formulated as a strictly monotonic process, appending tokens linearly to an immutable prefix. This formulation contrasts to the cognitive process of programming, which is inherently interleaved with forward generation and on-the-fly revision. While prior works attempt to introduce revision via post-hoc agents or external static tools, they either suffer from high latency or fail to leverage the model's intrinsic semantic reasoning. In this paper, we propose Stream of Revision, a paradigm shift that elevates code generation from a monotonic stream to a dynamic, self-correcting trajectory by leveraging model's intrinsic capabilities. We introduce specific action tokens that enable the model to seamlessly backtrack and edit its own history within a single forward pass. By internalizing the revision loop, our framework Stream of Revision allows the model to activate its latent capabilities just-in-time without external dependencies. Empirical results on secure code generation show that Stream of Revision significantly reduces vulnerabilities with minimal inference overhead.