Learning Task Mixtures from Task Affinities: A Probabilistic Graphical Model for Supervised Fine-Tuning

Fine-tuning Multimodal Large Language Models (MLLMs) on specialized tasks often leads to catastrophic forgetting of their general capabilities. Existing model merging methods to combat this are often heuristic or use sub-optimal objectives. We propose CurvatureGuided Mixing (CGM), a theoretically grounded framework that merges pre-trained and fine-tuned models. CGM formulates a joint optimization objective and uses a second-order (Hessian) approximation of the loss landscapes to analytically derive an optimal, closed-form "soft mixing" ratio. This ratio intelligently blends parameters based on their relative task-specific curvatures. We also introduce CGM$\dagger$, a robust "hard mixing" variant that performs sparse parameter selection guided by a novel, curvature-aware score. Experiments on LLaVA-1.5 and Qwen2.5VL across multiple downstream tasks show that CGM and CGM$\dagger$ consistently improve the trade-off between task specialization and general knowledge retention over existing methods. Code is available at github.com/zzsyjl/CGM-ECCV-2026.

Adapting a language model to a specialized corpus means choosing which instruction-tuning tasks to train on under a fixed budget, and testing one choice costs a fine-tuning run. Common heuristics add more source tasks or pick sources similar to the target. The first assumes transfer is never negative; the second, that it is symmetric. We show that both assumptions fail: task $A$ can help task $B$ while $B$ hurts $A$, so helpfulness is a signed property of ordered source--target pairs. We introduce the transfer map, a signed estimate of how much each source helps or hurts each held-out target. We fit the map in hundreds of fine-tuning runs on Qwen3 and Mistral models from 0.6B to 32B parameters, with all sources drawn from one corpus and no training examples from the target. The map predicts a held-out target's accuracy on unseen mixtures: recorded before those runs, its predictions have less than half the error of a mixture-agnostic baseline. The map is specific to its target and corpus but transfers across model scale: a mixture selected in advance at one size beats training on all source tasks at every other size we tested. Transfer is thus a property of the data. The map selects the tasks that help and drops the one that interferes: accuracy on the reasoning targets (causal explanation, multi-hop questions and methodological critique) rises by up to 14 percentage points over training on all source tasks.

Not all training samples contribute equally to large language model fine-tuning. Selecting informative training samples can reduce the computational cost while preserving downstream performance. Many existing data selection methods rely on indirect heuristics, such as data quality, diversity or reasoning trace length. However, the effectiveness of these fixed criteria is task-dependent and difficult to generalize across diverse downstream tasks. Perplexity-based data selection provides a simple and model-aware solution to estimate the sample difficulty, but existing approaches typically score the entire training sequence and ignore the difference in learning objectives of language modeling and reasoning tasks. In this paper, we propose PPL-Factory, a simple and interpretable data selection framework that combines task-aware perplexity-based scores and data budget-aware selection criteria. Experiments on GSM8K demonstrate that PPL-Factory outperforms other state-of-the-art data selection methods using only $1\%$ of the training set. With $10\%$ of the data, PPL-Factory exceeds full-data fine-tuning accuracy by 0.9 on GSM8K and 4.8 on MATH. Overall, our results demonstrate that task-aware and budget-aware perplexity-based selection provides an effective and applicable approach for efficient fine-tuning.