Today's trail

We study the symmetric and antisymmetric parts of bilinear forms in the attention heads of trained large language models. We introduce an orthogonally invariant profile map from real bilinear forms to a three-dimensional simplex and observe that profiles of trained bilinear…

Multilingual code language models transfer skills across programming languages (PLs), but whether any PL occupies a privileged pivot position remains contested: geometric analyses point to C-family languages and Go, while behavioral evidence highlights Python. We revisit this…

Automated operations research (OR) modeling requires LLMs to translate natural-language decision problems into correct mathematical programs. Existing methods can improve individual formulations, but they often solve problems in isolation, retaining little reusable experience…

Physics-informed neural networks (PINNs) use one shared representation over the computational domain, which can become difficult to optimize on long domains and for high-order operators. We study a minimal alternative: multiply the first hidden activation of an otherwise…