Block-Level Weight-Space Structure Persists Under Post-Training: An Empirical Study Across LLM Families

Modern LLMs are deployed as families of post-trained variants (base, instruct, chat, code) derived from a shared set of pre-trained weights. We present an empirical study of how post-training transforms weight-space geometry, covering eight configurations across four architecture families (Qwen2.5, Llama-3.1/3.2, Mistral, Gemma-2). We identify a granularity gap: post-training modifies every tensor (zero of 291-339 tensors remain byte-identical, so hash-based deduplication achieves 0% savings), yet preserves block-level structure (mean cosine similarity exceeds 0.99 and relative Frobenius distance stays below 0.13). Post-training therefore acts as a structured perturbation that shifts every parameter while leaving block-level geometry intact. The property is not universal: independently trained specializations (for example, Qwen2.5-Coder) attain cosine similarity around 0.64 with the general base, indicating a disconnected region of weight space. Perturbation magnitude varies systematically with model scale, architecture family, and post-training recipe. As a practical application, we build LinkerLLM, a lazy loader that aliases shareable blocks across co-resident variants, achieving 18-48% GPU memory savings and enabling up to five 7B-parameter variants on a single 24 GB consumer GPU. Five of eight configurations retain at least 94% of the unshared variant's quality on MMLU, ARC-Challenge, HellaSwag, and WinoGrande; the remaining three (Mistral-7B, Gemma-2-2B, Llama-3.2-1B) have one below-threshold benchmark each (87-91%), which we report transparently rather than gate the block-sharing decision on a single threshold.