The perception of large language models (LLMs) as 'black boxes' is common; users input prompts and receive responses, often relying on fine-tuning or LoRA adjustments for improvements. However, we have taken a different approach. In a prior article, I demonstrated how Schnorr/MuSig2 signatures can be deconstructed into strict affine invariants, treating them as a mathematical framework rather than an enigma. In this new work, we have advanced this methodology by integrating it into a neural network.
Our approach involved utilizing a local MLX distribution: gpt-oss-20b-TurboQuant-MLX-8bit, without retraining it. Instead, we delved into the .safetensors at the level of quantized codes, created a deterministic calibration cache, and extracted real BF16 activations from specific layers. We reduced the task to local integer optimization of quantized weights, implemented a secure patch directly into the model, and incorporated a smoke-check to verify that our mathematical computations align with the actual MLX runtime.
The result is a pipeline where the quantized layer is observable, its behavior measurable, and it can be locally adjusted. Most importantly, we can confirm that the execution environment is not misleading us. For instance, with router.weight, we achieved nearly complete transfer of improvements to the holdout set, while for q_proj, the system clearly indicated that a patch without an external benchmark is meaningless. This insight may prove to be even more significant.