# Null-Space Filtering for Data-Free Continual Model Merging: Preserving Stability, Promoting Plasticity

arXiv: https://arxiv.org/abs/2509.21413 · HTML: https://mlsanity.com/paper/2509.21413/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 78 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 30 of 50)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Overcoming Catastrophic Forgetting by Incremental Moment Matching](https://mlsanity.com/paper/1703.08475/) (2017)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)

## Built on by (most cited first, 8 of 8)

- [Geometry Conflict: Explaining and Controlling Forgetting in LLM Continual Post-Training](https://mlsanity.com/paper/2605.09608/) (2026)
- [Continual Learning with Vision-Language Models via Semantic-Geometry Preservation](https://mlsanity.com/paper/2603.12055/) (2026)
- [From Parameters to Behaviors: A Survey of Model Fusion for Large Language Models](https://mlsanity.com/paper/2609.19553/) (2026)
- [SAFE-Merge: Data-Free Continual Model Merging with General Knowledge Preservation](https://mlsanity.com/paper/2608.01184/) (2026)
- [Dual-Mode Low-Rank Learner with Bridge-Prototype Ensemble for Vision-Language Class-Incremental Learning](https://mlsanity.com/paper/2609.36759/) (2026)
- [BACAM: Behavior-Aware Continual Agent Merging for Multi-Turn Interaction](https://mlsanity.com/paper/2610.04966/) (2026)
- [SuperAI: Merging Capabilities Across Heterogeneous Foundation Models](https://mlsanity.com/paper/2610.15322/) (2026)
- [Geometric Calibration of Supervised Fine-Tuning](https://mlsanity.com/paper/2610.18634/) (2026)

## Abstract (arXiv)

Data-free continual model merging (DFCMM) aims to fuse independently fine-tuned models into a single backbone that evolves with incoming tasks without accessing task data. This paper revisits two fundamental desiderata for DFCMM: stability, avoiding interference with earlier tasks, and plasticity, adapting faithfully to each new task. This poses a challenge that existing approaches fail to address: how to bridge data-level desiderata with parameter-space optimization to ensure stability and plasticity in the absence of task data. To this end, we propose NUFILT (NUll-space FILTering), a data-free framework that directly links these desiderata into parameter-space optimization. Our key observation is that task vectors approximately align with representation subspaces, providing structural surrogates for enforcing stability and plasticity. Accordingly, we design a null-space projector that preserves prior responses by filtering overlapping components of new task vectors, ensuring stability. We further introduce a lightweight LoRA adapter that injects complementary task-specific signals to enable plasticity. The adapter is trained with a projection-based surrogate loss that preserves consistency with prior knowledge while introducing novel directions. This joint filtering-adaptation process enables the backbone to absorb new knowledge while retaining existing behaviors, with updates fused back in a layer-wise linear fashion without extra parameters or inference cost. Theoretically, we establish approximate subspace alignment guarantees that justify null-space filtering. Empirically, NUFILT achieves state-of-the-art performance with minimal forgetting on both vision and NLP benchmarks, improving average accuracy by 4-7% over OPCM and WUDI-Merging, while narrowing the gap to fine-tuning and reducing computation overhead. The code is available at: https://github.com/zihuanqiu/NUFILT