# Improving Model Fusion by Training-time Neuron Alignment with Fixed Neuron Anchors

arXiv: https://arxiv.org/abs/2402.01342 · HTML: https://mlsanity.com/paper/2402.01342/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 80 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 30 of 55)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [FedBN: Federated Learning on Non-IID Features via Local Batch Normalization](https://mlsanity.com/paper/2102.07623/) (2021)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)

## Built on by (most cited first, 7 of 7)

- [WISE: Rethinking the Knowledge Memory for Lifelong Model Editing of Large Language Models](https://mlsanity.com/paper/2405.14768/) (2024)
- [From Task-Specific Models to Unified Systems: A Review of Model Merging Approaches](https://mlsanity.com/paper/2503.08998/) (2025)
- [Text-to-Model: Text-Conditioned Neural Network Diffusion for Train-Once-for-All Personalization](https://mlsanity.com/paper/2405.14132/) (2024)
- [Sparsity Curse: Understanding RLVR Model Parameter Space from Model Merging](https://mlsanity.com/paper/2606.18521/) (2026)
- [Data-Aware Model Merging in the Essential Subspace for Multi-Task Knowledge Aggregation](https://mlsanity.com/paper/2606.19164/) (2026)
- [FedGuCci: Making Local Models More Connected in Landscape for Federated Learning](https://mlsanity.com/paper/2402.18949/) (2024)
- [Deep Model Merging: The Sister of Neural Network Interpretability -- A Survey](https://mlsanity.com/paper/2410.12927/) (2024)

## Abstract (arXiv)

Model fusion aims to integrate several deep neural network (DNN) models' knowledge into one by fusing parameters, and it has promising applications, such as improving the generalization of foundation models and parameter averaging in federated learning. However, models under different settings (data, hyperparameter, etc.) have diverse neuron permutations; in other words, from the perspective of loss landscape, they reside in different loss basins, thus hindering model fusion performances. To alleviate this issue, previous studies highlighted the role of permutation invariance and have developed methods to find correct network permutations for neuron alignment after training. Orthogonal to previous attempts, this paper studies training-time neuron alignment, improving model fusion without the need for post-matching. Training-time alignment is cheaper than post-alignment and is applicable in various model fusion scenarios. Starting from fundamental hypotheses and theorems, a simple yet lossless algorithm called TNA-PFN is introduced. TNA-PFN utilizes partially fixed neuron weights as anchors to reduce the potential of training-time permutations, and it is empirically validated in reducing the barriers of linear mode connectivity and multi-model fusion. It is also validated that TNA-PFN can improve the fusion of pretrained models under the setting of model soup (vision transformers) and ColD fusion (pretrained language models). Based on TNA-PFN, two federated learning methods, FedPFN and FedPNU, are proposed, showing the prospects of training-time neuron alignment. FedPFN and FedPNU reach state-of-the-art performances in federated learning under heterogeneous settings and can be compatible with the server-side algorithm.