在我们此前的工作中，我们提出了用于神经ODE（神经常微分方程）序列训练的Tuning without Forgetting（TwF，调优不遗忘）原则：训练样本被迭代添加，参数在控制函数子空间内更新，该子空间在一阶近似意义下，保持输出标签流形上已学习样本的端点映射不变。在这篇快报中，我们证明了在非奇异控制下，该参数子空间构成一个有限余维的Banach子流形，并刻画了其切空间。这一结果表明，TwF对应于控制函数沿该Banach子流形切空间的延拓/形变，为其在序列训练中精确（而非仅一阶近似）保持映射不变（即不遗忘）提供了理论基础。
英文摘要：
In our earlier work, we introduced the principle of Tuning without Forgetting (TwF) for sequential training of neural ODEs, where training samples are added iteratively and parameters are updated within the subspace of control functions that preserves the end-point mapping at previously learned samples on the manifold of output labels in the first-order approximation sense. In this letter, we prove that this parameter subspace forms a Banach submanifold of finite codimension under nonsingular controls, and we characterize its tangent space. This reveals that TwF corresponds to a continuation/deformation of the control function along the tangent space of this Banach submanifold, providing a theoretical foundation for its mapping-preserving (not forgetting) during the sequential training exactly, beyond first-order approximation.
Electrical and Computer Engineering Department（电子与计算机工程系）；Coordinated Science Laboratory（协调科学实验室）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
An Empirical Analysis of Forgetting in Pre-trained Models with Incremental Low-Rank Updates
Computer Vision Center, Spain（西班牙计算机视觉中心）；Department of Computer Science, Universitat Autònoma de Barcelona, Spain（西班牙巴塞罗那自治大学计算机科学系）；Department of Information Engineering, University of Florence, Italy（意大利佛罗伦萨大学信息工程系）
Parameter Importance-Driven Continual Learning for Foundation Models
Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University（未来区块链与隐私计算先进创新中心，北京航空航天大学）；School of Artificial Intelligence, Beihang University（人工智能学院，北京航空航天大学）
Department of Mathematics and Mathematical Statistics（数学与统计学系）；Umeå University（乌梅大学）；Department of Mathematical Sciences（数学科学系）；Chalmers University of Technology and Gothenburg University（楚姆勒技术大学和哥德堡大学）
CapTrack: Multifaceted Evaluation of Forgetting in LLM Post-Training
Thomson Reuters Foundational Research（汤姆森路透基础研究）；Tübingen AI Center, University of Tübingen（图宾根人工智能中心，图宾根大学）；Munich Center for Machine Learning (MCML), Technical University Munich（慕尼黑机器学习中心（MCML），慕尼黑技术大学）；Imperial College London（伦敦帝国理工学院）
Few-Shot Continual Learning for 3D Brain MRI with Frozen Foundation Models
Independent Researcher, USA（美国独立研究者）；Indiana University at Bloomington, United States（印第安纳大学布卢明顿分校）；Independent Researcher, Taiwan（台湾独立研究者）；National Taiwan University, Taiwan（台湾国立大学）；Boise State University, United States（博伊西州立大学）；National Yang Ming Chiao Tung University, Taiwan（台湾阳明交通大学）
Fine-tuning Reinforcement Learning Models is Secretly a Forgetting Mitigation Problem
IDEAS NCBR；University of Warsaw（华沙大学）；Warsaw University of Technology（华沙理工大学）；Jagiellonian University（雅盖隆大学）；Google DeepMind（谷歌DeepMind）；Institute of Mathematics, Polish Academy of Sciences（波兰科学院数学研究所）
MEGA: Second-Order Gradient Alignment for Catastrophic Forgetting Mitigation in GFSCIL
Beijing Institute of Technology（北京理工大学）；Department of Biomedical Engineering, Hefei University of Technology（合肥工业大学生物医学工程学院）；School of Artificial Intelligence and Computer Science, Nantong University（南通大学人工智能与计算机科学学院）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）
SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Indian Institute of Technology Delhi（印度理工学院德里分校）；National Center for Supercomputing Applications（国家超级计算应用中心）
Department of Computing（计算系）；Imperial College London（帝国理工学院伦敦分校）；School of Computer and Comm. Sciences (IC)（计算机与通信科学系）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Bisecle: Binding and Separation in Continual Learning for Video Language Understanding
School of Computer Science University of New South Wales（计算机科学学院新南威尔士大学）；School of Computer Science and Engineering University of New South Wales（计算机科学与工程学院新南威尔士大学）；DEVCOM Army Research Laboratory（陆军研究实验室）
FROC: A Unified Framework with Risk-Optimized Control for Machine Unlearning in LLMs
Digital Trust Centre, Nanyang Technological University, Singapore（南洋理工大学数字信任中心）；College of Computing and Data Science, Nanyang Technological University, Singapore（南洋理工大学计算与数据科学学院）
Continual Learning with Foundation Models: An Empirical Study of Latent Replay
ServiceNow（ServiceNow公司）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Heuritech（Heuritech公司）；HEC Montréal（蒙特利尔高等商学院）；Sorbonne University（索邦大学）；Canada CIFAR AI Chair（加拿大CIFAR人工智能讲席）
