# Constrained Binary Optimization

This work reformulates block removal in large language models as a constrained binary optimization equivalent to finding low-energy states of an Ising glass, using a once-computed approximate-Hessian energy as a cheap proxy for downstream quality so that vast numbers of candidate configurations can be ranked without benchmarking any of them; on Llama-3.3-70B-Instruct at 50% compression (40 of 80 blocks removed) without retraining, MMLU stays near 77 while the strongest baseline, block influence, falls to about 54, with transfer also shown on Llama-3.1-8B-Instruct, Qwen3-14B, and the hybrid NVIDIA-Nemotron-3-Nano-30B-A3B-FP8.

This work reformulates block removal in large language models as a constrained binary optimization equivalent to finding low-energy states of an Ising glass, using a once-computed approximate-Hessian energy as a cheap proxy for downstream quality so that vast numbers of candidate configurations can be ranked without benchmarking any of them; on Llama-3.3-70B-Instruct at 50% compression (40 of 80 blocks removed) without retraining, MMLU stays near 77 while the strongest baseline, block influence, falls to about 54, with transfer also shown on Llama-3.1-8B-Instruct, Qwen3-14B, and the hybrid NVIDIA-Nemotron-3-Nano-30B-A3B-FP8.