pjhkorea/egregore-flat-kernel

This is a pure PyTorch code library aimed at large scale geometric and AI accelerator workloads, built around one central idea: replacing ordinary if-else conditional checks with smooth mathematical formulas that do the same job. The README argues that on GPU hardware, branching logic like if statements can slow things down or cause instability, so this project tries to remove that kind of branching entirely and handle edge cases through continuous math instead. The README describes five specific techniques used to achieve this. First, instead of using an if statement to skip or cap work when the number of active computations exceeds a hardware limit, it uses a smooth exponential formula that gradually shrinks the computation's intensity toward zero as the limit is approached, aiming to avoid running out of memory without interrupting the program. Second, it replaces a hard cutoff near the edges of the inverse cosine function, a place where results can otherwise become invalid or produce NaN values, with a gentler formula that keeps a small, non-zero slope past that boundary so that gradient-based training does not break down. Third, it replaces an integer based table lookup, which normally blocks gradients from flowing backward through the calculation, with linear interpolation between neighboring table values, so gradients keep flowing smoothly. Fourth, it replaces loop based logic for certain matrix operations with a single matrix multiplication against a fixed geometric mask, intended to reduce overhead from repeated control-flow code on the accelerator. Fifth, rather than raising and catching an exception when a NaN or Infinity value appears, it uses PyTorch's where function to permanently replace the faulty values with a fixed placeholder number, so the computation keeps running instead of stopping. The project is written entirely in Python using PyTorch and is aimed at people working on custom GPU-accelerated numerical or geometric computation, particularly where numerical stability and consistent execution speed matter. The README is written in a highly technical, formula heavy style with parallel Korean and English explanations for each rule, and it does not include separate installation instructions, usage examples, or a license section in the portion shown.