Show HN: Fusion Check — a zero-data law that predicts when merging LLMs is safe

Description and use

Fusion Check predicts whether merging two fine-tuned LLMs is safe using a zero-data law, guiding merge decisions and improving performance when models are compatible.

Problem

Blind weight averaging (soup) can dilute performance when merging LLMs trained on different tasks.

Outcome

Fusion Check enables safe merging of fine-tuned LLMs, improving performance in compatible cases and preventing dilution in incompatible ones, with predictions validated analytically, formally, and empirically.

Workflow

• 1. Compute task kernel metrics (cosine of weight deltas and effective dimensionality).
• 2. Apply the zero-data law: check if cos² ≥ 1 − δ²·d_eff/(2(1-α)²).
• 3. If condition satisfied, compute optimal mixing coefficient α* = √γ₁/(√γ₁+√γ₂).
• 4. Decide MERGE, NO_MERGE, PRIORITIZED, REFUSE, or VERIFY based on the law’s output.
• 5. If MERGE, perform weight averaging with α*; otherwise, keep models separate or re-evaluate.

Evidence

Proven three independent ways: Analytic derivation, Formal verification with z3 (28 theorems), Empirical validation (147 combinations, max deviation 1.13%, zero violations).

Source

Real result: Two weak, diverse estimators of the same task (0.762/0.756) → merged soup 0.822 (+6–7 points).

Source