When Do Task Vectors Interfere? Mapping the Validity Boundaries of Weight-Space Composition

2026-08-10

AI Summary

This study investigates when task vector arithmetic in weight space reliably induces predictable functional changes in language models, offering the first systematic distinction between parameter-space geometry and functional geometry. By constructing two-dimensional task vector surfaces and evaluating combinations of response-only fine-tuning, LoRA, and full fine-tuning across multiple models—including Qwen2.5 and Llama-3.1—and scales, the work assesses functional non-additivity under varying input distributions and prompt formats. The authors propose boundaries for functional composability conditioned on inputs and prompt formats, revealing significant non-additivity for code and safety tasks under specific prompts. In a six-task extension, all eight unseen task pairs adhered to predicted signs, supporting internal consistency; however, external evaluation exposed sensitivity to prompt formatting.

Abstract

Task arithmetic treats fine-tuning displacements as composable directions in weight space, yet it remains unclear when parameter addition reflects predictable changes in model function. We separate parameter geometry from functional geometry and measure pairwise functional non-additivity over a two-dimensional task-vector surface, using a first-token predictive-distribution interaction ratio conditioned on an input distribution and evaluated with norm-matched controls, three training seeds, and response-only fine-tuning. On Qwen2.5-1.5B, code+safety is more non-additive than the matched code+math control on code and instruction prompts, but not on math prompts. In a prospectively specified six-task expansion, all eight high-versus-low comparisons of unseen task pairs have the predicted sign. The primary ordering further persists under full-parameter fine-tuning at 0.5B, Qwen2.5 LoRA scale tests up to 7B, and a Llama-3.1-8B cross-architecture audit. External validation exposes a sharper boundary: raw public code, instruction, and safety prompts preserve the continuous contrast, whereas an instruction-style wrapper collapses it on the identical public-code prompts, and EvalPlus pass@1 interactions do not robustly reproduce it. Weight-space composition therefore supports coarse, input- and format-conditioned functional statements across adaptation methods, scales, and one additional model family, not a universal merging-performance predictor.

Problem

• task vectors
• weight-space composition
• functional non-additivity
• parameter interference
• model merging

Innovation

• task arithmetic
• weight-space composition
• functional non-additivity
• parameter geometry
• cross-architecture validation