Task Arithmetic has emerged as a simple yet effective method to merge models without additional training. However, by treating entire networks as flat parameter vectors, it overlooks key structural information and is susceptible to task interference. In this paper, we study task vectors at the layer level, focusing on task layer matrices and their singular value decomposition. In particular, we concentrate on the resulting singular vectors, which we refer to as Task Singular Vectors (TSV). Recognizing that layer task matrices are often low-rank, we propose TSV-Compress (TSV-C), a simple procedure that compresses them to 10% of their original size while retaining 99% of accuracy. We further leverage this low-rank space to define a new measure of task interference based on the interaction of singular vectors from different tasks. Building on these findings, we introduce TSV-Merge (TSV-M), a novel model merging approach that combines compression with interference reduction, significantly outperforming existing methods.

Evolutionary model merging enables the creation of high-performing multi-task models but remains computationally prohibitive for consumer hardware. We introduce MERGE$^3$, an efficient framework that makes evolutionary merging of Large Language Models (LLMs) feasible on a single GPU by reducing fitness computation costs 50$\times$ while retaining a large fraction of the original performance. MERGE$^3$ achieves this by Extracting a reduced dataset for evaluation, Estimating model abilities using Item Response Theory (IRT), and Evolving optimal merges via IRT-based performance estimators. Our method enables state-of-the-art multilingual and cross-lingual merging, transferring knowledge across languages with significantly lower computational overhead. We provide theoretical guarantees and an open-source library, democratizing high-quality model merging.

Foundation models serve as the backbone for numerous specialized models developed through fine-tuning. However, when the underlying pretrained model is updated or retrained (e.g., on larger and more curated datasets), the fine-tuned model becomes obsolete, losing its utility and requiring retraining. This raises the question: is it possible to transfer fine-tuning to a new release of the model? In this work, we investigate how to transfer fine-tuning to a new checkpoint without having to re-train, in a data-free manner. To do so, we draw principles from model re-basin and provide a recipe based on weight permutations to re-base the modifications made to the original base model, often called task vector. In particular, our approach tailors model re-basin for Transformer models, taking into account the challenges of residual connections and multi-head attention layers. Specifically, we propose a two-level method rooted in spectral theory, initially permuting the attention heads and subsequently adjusting parameters within select pairs of heads. Through extensive experiments on visual and textual tasks, we achieve the seamless transfer of fine-tuned knowledge to new pre-trained backbones without relying on a single training step or datapoint. Code is available at https://github.com/aimagelab/TransFusion.

In this paper, we present a novel data-free method for merging neural networks in weight space. Our method optimizes for the permutations of network neurons while ensuring global coherence across all layers, and it outperforms recent layer-local approaches in a set of challenging scenarios. We then generalize the formulation to the $N$-models scenario to enforce cycle consistency of the permutations with guarantees, allowing circular compositions of permutations to be computed without accumulating error along the path. We qualitatively and quantitatively motivate the need for such a constraint, showing its benefits when merging homogeneous sets of models in scenarios spanning varying architectures and datasets. We finally show that, when coupled with activation renormalization, the approach yields the best results in the task.