# make_continual_learning_stronger_via_cflat__dae91696.pdf Make Continual Learning Stronger via C-Flat Ang Bian 1, Wei Li 1,2, Hangjie Yuan 3,4, Chengrong Yu1, Mang Wang5 Zixiang Zhao6, Aojun Lu1, Pengliang Ji7, Tao Feng 2 1Sichuan University 2Tsinghua University 3DAMO Academy, Alibaba Group 4Zhejiang University 5Byte Dance 6Xi an Jiaotong University 7Carnegie Mellon University hj.yuan@zju.edu.cn, {ymjiii98, fengtao.hi}@gmail.com How to balance the learning sensitivity-stability upon new task training and memory preserving is critical in CL to resolve catastrophic forgetting. Improving model generalization ability within each learning phase is one solution to help CL learning overcome the gap in the joint knowledge space. Zeroth-order loss landscape sharpness-aware minimization is a strong training regime improving model generalization in transfer learning compared with optimizer like SGD. It has also been introduced into CL to improve memory representation or learning efficiency. However, zeroth-order sharpness alone could favors sharper over flatter minima in certain scenarios, leading to a rather sensitive minima rather than a global optima. To further enhance learning stability, we propose a Continual Flatness (C-Flat) method featuring a flatter loss landscape tailored for CL. C-Flat could be easily called with only one line of code and is plug-and-play to any CL methods. A general framework of C-Flat applied to all CL categories and a thorough comparison with loss minima optimizer and flat minima based CL approaches is presented in this paper, showing that our method can boost CL performance in almost all cases. Code is available at https://github.com/Wan Naa/C-Flat. C-Flat: just a line of code suffices for its utilization. 1 from . . . import C_Flat 3 # i n i t i a l i z e o p t i m i z e r f o r CL. 4 C_Flat_optimizer = C_Flat ( params , base_optimizer , model , args ) 1 Introduction Why study Continual Learning (CL)? CL is generally acknowledged as a necessary attribute for Artificial General Intelligence (AGI) [22, 55, 40, 67]. In the open world, CL holds the potential for substantial benefits across many applications: e.g. vision model needs to learn a growing image set [17, 61, 62], or, embodied model needs to incrementally add skills to their repertoire [12]. Challenges. A good CL model is expected to keep the memory of all seen tasks upon learning new knowledge [22]. However, due to the limited access to previous data, the learning phase is naturally sensitive to the current task, hence resulting in a major challenge in CL called catastrophic forgetting [9], which refers to the drastic performance drop on past knowledge after learning new knowledge. This learning sensitivity-stability dilemma is critical in CL, requiring model with strong generalization ability [16] to overcome the knowledge gaps between sequentially arriving tasks. Equal Contribution Corresponding Authors 38th Conference on Neural Information Processing Systems (Neur IPS 2024). Current solutions. A series of works [43, 44, 33, 25] are proposed to improve learning stability by extending data space with dedicated selected and stored exemplars from old tasks, or frozen some network blocks or layers that are strongly related to previous knowledge [68, 24, 69, 57, 24]. Another group of works seeks to preserve model generalization with regularisation onto the training procedure itself [32, 18, 31]. Diverse weight [45, 28, 2] or gradient alignment [22, 9, 35, 26] strategies are designed to encourage the training to efficiently extracting features for the current data space without forgetting. Loss landscape sharpness optimization [23, 19, 65, 70] as an efficient training regime for model generalization starts to gain attentions [27, 63]. Ordinary loss minima based optimizer like SGD can easily lead to suboptimal results [4, 37, 13]. To prevent this, zeroth-order sharpness-aware minimization seeking neighborhood-flat minima [20] has been proven a strong optimizer to improve model generalization ability, especially in transferring learning tasks. It is also introduced into some CL works [49, 30] with dedicated designs to improve old knowledge representation or fewshot learning efficiency. However, given the limited application scenarios[10, 49], the zeroth-order sharpness used in the current work is proved to favor sharper minima than a flat solution [70]. It means zeroth-order only can still lead to a fast gradient descent to the suboptimal in new data space than a more generalizable result for the joint old and new knowledge space. Our solution. Inspired by these works, a beyond zeroth-order sharpness continual optimization method is proposed as demonstrated in 1, where loss landscape flatness is emphasized to strengthen model generalization ability. Thus, the model can always converge to a flat minima in each phase, and then smoothly migrate to the global optimal of the joint knowledge space of the current and next tasks, and hence resolve the catastrophic forgetting in CL. We dub this method Continual Flatness (C-Flat or C ) Moreover, C-Flat is a general method that can be easily plug-and-play into any CL approach with only one line of code, to improve CL. Contribution. A simple and flexible CL-friendly optimization method C-Flat is proposed, which Makes Continual Learning Stronger. A framework of C-Flat covering diverse CL method categories is demonstrated. Experiment results prove that Flatter is Better in nearly all cases. To the best of our knowledge, this work is the first to conduct a thorough comparison of CL approaches with loss landscape aware optimization, and thus can serve as a baseline in CL. 2 Related work Continual learning methods roughly are categorized into three groups: Memory-based methods write experience in memory to alleviate forgetting. Some work [43, 44, 25, 51] design different sampling strategies to establish limited budgets in a memory buffer for rehearsal. However, these methods require access to raw past data, which is discouraged in practice due to privacy concerns. Instead, recently a series of works [10, 34, 46, 33, 50] elaborately construct special subspace of old tasks as the memory. Regularization-based methods aim to realize consolidation of the previous knowledge by introducing additional regularization terms in the loss function. Some works [32, 29, 6] enforce the important weights in the parameter space [45, 28, 2], feature representations [5, 21], or the logits outputs [32, 42] of the current model function to be close to that of the old one. Expansionbased methods dedicate different incremental model structures towards each task to minimize forgetting [68, 39]. Some work [48, 24, 60] exploit modular network architectures (dynamically extending extra components [57, 69], or freeze partial parameters [36, 1]) to overcome forgetting. Trivially, methods in this category implicitly shift the burden of storing numerous raw data into the retention of model [68]. Gradient-based solutions are a main group in CL, including shaping loss landscape, tempering the tug-of-war of gradient, and other learning dynamics [22, 9, 41]. One promising solution is to modify the gradients of different tasks and hence overcome forgetting [7, 38], e.g., aligning the gradients of current and old one [15, 18], or, learning more efficient in the case of conflicting objectives [47, 56, 14]. Other solutions [10, 49] focus on characterizing the generalization from the loss landscape perspectives to improve CL performance and yet are rarely explored. (a) Direct Tuning (b) Regularization loss of old tasks loss of new tasks tolerance line perturb radius well learnt ordinary performance catastrophic forgetting Figure 1: Illustration of C-Flat overcoming catastrophe forgetting by fine-tuning the old model parameter to flat minima of new task. a) loss minima for current task only can cause catastrophe forgetting on previous ones. b) balanced optima aligned by regularization leads to unsatisfying results for both old and new tasks. c) C-Flat seeks global optima for all tasks with flattened loss landscape. Sharpness minimization in CL Many recent works [23, 19, 4] are proposed to optimize neural networks in standard training scenarios towards flat minima. Wide local minima were considered an important regularization in CL to enforce the similarity of important parameters learned from past tasks [6]. Sharpness-aware seeking for loss landscape flat minima starts to gain more attention in CL, especially SAM based zeroth order sharpness is well discussed. An investigation [41] proves SAM can help with addressing forgetting in CL, and [8] proposed a combined SAM for few-shot CL. SAM is also used for boosting the performance of specific methods like DFGP [58] and FS-DGPM [10] designed for GPM. SAM-CL [52] series with loss term gradient alignment for memory-based CL. These efforts kicked off the study of flat minima in CL, however, zeroth-order sharpness may not be enough for flatter optimal [70]. Thus, flatness with a global optima and universal CL framework is further studied. Our solution addresses the learning sensitivity-stability dilemma in CL by improving model generalization for joint learning knowledge obtained from different catalogues domains or tasks. Moreover, a general but stronger optimization method enhanced by the latest gradient landscape flatness is proposed as a plug-and-play tool for any CL approach. Loss landscape flatness. Let B(θ, ρ) = {θ : θ θ < ρ} denotes the neighborhood of θ with radius ρ > 0 in the Euclidean space Θ Rd, the zeroth-order sharpness at point θ is commonly defined by the maximal training loss difference within its neighborhood B(θ, ρ): R0 ρ(θ) = max{l S(θ ) l S(θ) : θ B(θ, ρ)}. (1) where l S(θ) denotes the loss of an arbitrary model with parameter θ on any dataset S with an oracle loss function l( ). The zeroth-order sharpness R0 ρ(θ) regularization can be directly applied to restrain the maximal neighborhood training loss: l R0 ρ S (θ) = l S(θ) + R0 ρ(θ) = max{l S(θ ) : θ B(θ, ρ)}, (2) However, for some fixed ρ, local minima with a lower loss does not always have a lower major hessian eigenvalue [70], which equals to the neighborhood curvature. It means that zeroth-order sharpness optimizer may goes to a sharper suboptimal than to the direction of a flatter global optimal with better generalization ability. Recently, first-order gradient landscape flatness is proposed as a measurement of the maximal neighborhood gradient norm, which reflects landscape curvature, to better describe the smoothness of the loss landscape: R1 ρ(θ) = ρ max{ l S(θ ) 2 : θ B(θ, ρ)}. (3) Unlike zeroth-order sharpness that force the training converging to a local minimal, first-order flatness alone constraining on the neighborhood smoothness can not lead to an optimal with minimal loss. To maximize the generalization ability of loss landscape sharpness for continual learning task, we propose a zeroth-first-order sharpness aware optimizer C-Flat for CL. Considering the data space, model or blocks to be trained are altered regarding the training phase and CL method, (as detailed in the next subsection), we define the the C-Flat loss as follows: l C ST (f T (θT )) = l ST (f T (θT )) + R0 ρ,ST (f T (θT )) + λ R1 ρ,ST (f T (θT )) = l R0 ρ ST (f T (θT )) + λ R1 ρ,ST (f T (θT )), (4) with the minimization objective: minθT {max{l ST (f T (θT 0 )) + λρ l ST (f T (θT 1 )) 2} : θT 0 , θT 1 B(θT , ρ)} (5) where l R0 ρ S (θ) is constructed to replace the original CL loss, while R1 ρ(θ) further regularizes the smoothness of the neighborhood, and hyperparameter λ is to balance the influence of R1 ρ as an additional regularization to loss function l. Hence, the local minima within a flat and smooth neighborhood is calculated for a generalized model possessing both old and new knowledge. Optimization. In our work, the two regularization terms in the proposed C-Flat are resolved correspondingly in each iteration. Assuming the loss function l( ) is differentiable and bounded, the gradient of l R0 ρ S at point θT can be approximated by l R0 ρ S (θT ) l S(θT 0 ) with θT 0 = θT + ρ l S(θT ) l S(θT ) 2 (6) And the gradient of the first-order flatness regularization R1 ρ(θT ) can be approximated by R1 ρ(θT ) ρ l S(θT 1 ) 2 (7) with θT 1 = θT + ρ l S(θT ) 2 l S(θT ) 2 2 where l S(θT ) 2 = 2l S(θT ) l S(θT ) l S(θT ) 2 . The optimization is detailed in Appendix algorithm 1. Note that l is the gradient of l with respect to θ through this paper, and instead of the expensive computation of Hessian matrix 2l, Hessian-vector product calculation is used in our algorithm, where the time and especially space complexity are greatly reduced to o(n) using 1 forward and 1 backward propagation. Thus, the overall calculation in one iteration takes 2 forward and 4 backward propagation in total. Theoretical analysis. Given R0 ρ(θ) measuring the maximal limit of the training loss difference, the first-order flatness is its upper bound by nature. Denoting θ + ϵ B(θ, ρ) the local maximum point, a constant ϵ [0, ϵ] exists according to the mean value theorem that R0 ρ(θ) = max{l S(θ ) l S(θ) : θ B(θ, ρ)} = l S(θ + ϵ) l S(θ) = ( l S(θ + ϵ ))T ϵ l S(θ + ϵ ) 2 ϵ 2 max{ l S(θ ) 2 : θ B(θ, ρ)} ρ = R1 ρ(θ). (8) Assuming the loss function is twice differentiable, bounded by M, obeys the triangle inequality, its gradient has bounded variance σ2, and both the loss function and its second-order gradient are β Lipschitz smooth, we can prove that, according to [3, 63], C-Flat converges in all tasks with η 1/β, ρ 1/4β, and ηT i = η/ i, ρT i = ρ/ 4 i for epoch i in any task T, i=1 E[ l C ST (f T (θT )) 2] 2 i=1 E[ l R0 ρ ST (f T (θT )) 2] i=1 E[ λR1 ρ,ST (f T (θT )) 2] 8Mβ n T + 32λ2(2 n T 1) β2n T . (9) where n T is the total iteration numbers of task T, and b is the batch size. Upper Bound. Let 2l S(θ ) denotes the Hessian matrix at local minimum θ , its maximal eigenvalue λmax( 2l S(θ )) is a proper measure of the landscape curvature. The first-order flatness is proven to be related to the maximal eigenvalue of the Hessian matrix as R1 ρ(θ ) = ρ2 λmax( 2l S(θ )), thus the C-Flat regularization can also be used as an index of model generalization ability, with the following upper bound: RC ρ (θ ) = R0 ρ(θ ) + λR1 ρ(θ ) (1 + λ)ρ2 λmax( 2l S(θ )). (10) 3.1 A Unified CL Framework Using C-Flat This subsection presents an unified CL framework using C-Flat with applications covering Class Incremental Learning (CIL) approaches. To keep focus, the scope of our study is limited in CIL task, which is the most intractable CL scenarios that seek for a lifelong learning model for sequentially arriving class-agnostic data. Most CIL approaches belong to three main families, Memory-based, Regularization-based and Expansion-based methods. Memory-based methods store samples from the previous phases within the memory limit, or produce pseudo-samples by generative approaches to extend the current training data space, thus a memory replay strategy is used to preserve the seen class features with ˆ ST = ST Samplet SAM > C-Flat +2.39%/+1.91% L2 SGD > C-Flat > SAM +1.52%/+1.04% L3 C-Flat > SGD +1.51%/+1.03% To discuss practicality better, we provided a tier guideline, which categorizes C-Flat into L1 to L3 levels, as shown in Table 3, L1 denotes the low-speed version of C-Flat, with a slightly lower speed than SAM and the best performance; L2 follows next; L3 denotes the highspeed version of C-Flat, with a faster speed than SGD and a performance close to L2. 4.7 Ablation Study We perform ablation study in two cases: (i) the influence of λ and ρ on different CL methods; (ii) the influence of ρ and its scheduler on different optimizers. We first present the performance of C-Flat with varying λ and ρ. As described in Eq. 13, λ controls the strength of the C-Flat penalty (when λ is equal to 0, this means that first-order flatness is not implemented). As shown in Figure 6a, compared with vanilla optimizer, C-Flat shows remarkable improvement with varying λ. Moreover, ρ controls the step length of gradient ascent. As shown in Figure 6b, C-Flat with ρ larger than 0 outperforms C-Flat without gradient ascent, showing that C-Flat benefits from the gradient ascent. For each CL task T, same learning rate ηT and neighborhood size ρT initialization are used. By default, ρT i [ρ_, ρ+] is set as a constant, which decays with respect to the learning rate ηT i [η_, η+] by ρT i = ρ_ + (ρ+ ρ_) η+ η_ (ηT i η_). Figure 6c and Figure 6d present a comparison on ρ initialization and {ρ_, ρ+} scheduler. C-Flat outperforms across various settings, and is not oversensitive to hyperparameters in a reasonable range. 4.8 Beyond Not-forgetting As is known to all, forward, and in particular backward transfer, are the desirable conditions for CL [22]. Here, we thoroughly examine the performance of C-Flat in both aspects. Forward Transfer (FT) means better performance on each subsequent task. Backward Transfer (BT) means better Figure 7: Analysis of BT and FT. RR refers to Relative Return on w/o and w/ C-Flat. Method CIFAR-100/ B0_Inc5 w/o C-Flat w/ C-Flat RR i Ca RL [43] old 36.36 37.12 BT+2.10% new 80.25 82.20 FT+2.43% PODNet [11] old 46.32 47.44 BT+2.42% new 62.65 64.75 FT+3.35% FOSTER [54] old 58.50 61.35 BT+2.85% new 62.05 63.05 FT+1.61% 0 25 50 75 100 125 150 175 Epoch MEMO w/ C-Flat 0 25 50 75 100 125 150 175 Epoch Accuracy (old) MEMO w/ C-Flat Figure 8: Loss and forgetting of old tasks. performance on previous tasks, when revisited. We count the performance of new and old tasks on several CL benchmarks before and after using C-Flat. As observed in Table 7, C-Flat consistently improves the learning performance of both new and old tasks. This observation indicates that C-Flat empowers these baselines with robust forward and backward transfer capabilities, that is learning a task should improve related tasks, both past and future. But, thus far, achieving a baseline that maintains perfect recall (by forgetting nothing) remains elusive. Should such a baseline emerge, C-Flat stands poised to empower it with potent backward transfer, potentially transcending the limitations of mere not-forgetting. Moreover, one of our contributions is to prove the positive effect of low curvature on overcoming forgetting. Intuitively, we visualized the change in loss and forgetting of old tasks in CL. Figure 8 shows the lower loss or less forgetting (red line) for old tasks during CL. This is an enlightening finding. 5 Conclusion This paper presents a versatile optimization framework, C-Flat, to confront forgetting. Empirical results demonstrate C-Flat s consistently outperform on all sorts of CL methods, showcasing its plug-and-play feature. Moreover, the exploration of Hessian eigenvalues and traces reaffirms the efficacy of C-Flat in inducing flatter minima to enhance CL. In essence, C-Flat emerges as a simple yet powerful addition to the CL toolkit, making continual learning stronger. 6 Acknowledgments This work was supported in part by the Chunhui Cooperative Research Project from the Ministry of Education of China under Grand HZKY20220560, in part by the National Natural Science Foundation of China under Grant W2433165, and in part by the National Natural Science Foundation of Sichuan Province under Grant 2023YFWZ0009. [1] Davide Abati, Jakub Tomczak, Tijmen Blankevoort, Simone Calderara, Rita Cucchiara, and Babak Ehteshami Bejnordi. Conditional channel gated networks for task-aware continual learning. In CVPR, 2020. [2] Afra Feyza Akyürek, Ekin Akyürek, Derry Tanti Wijaya, and Jacob Andreas. Subspace regularizers for few-shot class incremental learning. ICLR, 2022. [3] Maksym Andriushchenko and Nicolas Flammarion. Towards understanding sharpness-aware minimization. In ICML, 2022. [4] Carlo Baldassi, Fabrizio Pittorino, and Riccardo Zecchina. Shaping the learning landscape in neural networks around wide flat minima. Proceedings of the National Academy of Sciences, 2020. [5] Prashant Bhat, Bahram Zonooz, and Elahe Arani. Task-aware information routing from common representation space in lifelong learning. ICLR, 2023. [6] Sungmin Cha, Hsiang Hsu, Taebaek Hwang, Flavio P Calmon, and Taesup Moon. Cpr: classifier-projection regularization for continual learning. ICLR, 2021. [7] Arslan Chaudhry, Marc Aurelio Ranzato, Marcus Rohrbach, and Mohamed Elhoseiny. Efficient lifelong learning with a-gem. ar Xiv preprint ar Xiv:1812.00420, 2018. [8] Runhang Chen, Xiao-Yuan Jing, Fei Wu, and Haowen Chen. Sharpness-aware gradient guidance for few-shot class-incremental learning. Knowl. Based Syst., 299:112030, 2024. [9] Matthias Delange, Rahaf Aljundi, Marc Masana, Sarah Parisot, Xu Jia, Ales Leonardis, Greg Slabaugh, and Tinne Tuytelaars. A continual learning survey: Defying forgetting in classification tasks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021. [10] Danruo Deng, Guangyong Chen, Jianye Hao, Qiong Wang, and Pheng-Ann Heng. Flattening sharpness for dynamic gradient projection memory benefits continual learning. Neur IPS, 34, 2021. [11] Arthur Douillard, Matthieu Cord, Charles Ollion, Thomas Robert, and Eduardo Valle. Podnet: Pooled outputs distillation for small-tasks incremental learning. In ECCV, 2020. [12] Danny Driess, Fei Xia, Mehdi SM Sajjadi, Corey Lynch, Aakanksha Chowdhery, Brian Ichter, Ayzaan Wahid, Jonathan Tompson, Quan Vuong, Tianhe Yu, et al. Palm-e: An embodied multimodal language model. ar Xiv preprint ar Xiv:2303.03378, 2023. [13] Jiawei Du, Daquan Zhou, Jiashi Feng, Vincent Tan, and Joey Tianyi Zhou. Sharpness-aware training for free. Neur IPS, 2022. [14] Yunshu Du, Wojciech M Czarnecki, Siddhant M Jayakumar, Mehrdad Farajtabar, Razvan Pascanu, and Balaji Lakshminarayanan. Adapting auxiliary losses using gradient similarity. ar Xiv preprint ar Xiv:1812.02224, 2018. [15] Mehrdad Farajtabar, Navid Azizan, Alex Mott, and Ang Li. Orthogonal gradient descent for continual learning. In International Conference on Artificial Intelligence and Statistics, pages 3762 3773. PMLR, 2020. [16] Tao Feng, Kaifan Ji, Ang Bian, Chang Liu, and Jianzhou Zhang. Identifying players in broadcast videos using graph convolutional network. Pattern Recognition, 124:108503, 2022. [17] Tao Feng, Mang Wang, and Hangjie Yuan. Overcoming catastrophic forgetting in incremental object detection via elastic response distillation. In CVPR, 2022. [18] Tao Feng, Hangjie Yuan, Mang Wang, Ziyuan Huang, Ang Bian, and Jianzhou Zhang. Progressive learning without forgetting. ar Xiv preprint ar Xiv:2211.15215, 2022. [19] Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware minimization for efficiently improving generalization. ar Xiv preprint ar Xiv:2010.01412, 2020. [20] Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware minimization for efficiently improving generalization. In ICLR, 2021. [21] Qiankun Gao, Chen Zhao, Bernard Ghanem, and Jian Zhang. R-dfcil: Relation-guided representation learning for data-free class incremental learning. In ECCV, 2022. [22] Raia Hadsell, Dushyant Rao, Andrei A Rusu, and Razvan Pascanu. Embracing change: Continual learning in deep neural networks. Trends in cognitive sciences, 24(12):1028 1040, 2020. [23] Haowei He, Gao Huang, and Yang Yuan. Asymmetric valleys: Beyond sharp and flat local minima. Neur IPS, 32, 2019. [24] Zhiyuan Hu, Yunsheng Li, Jiancheng Lyu, Dashan Gao, and Nuno Vasconcelos. Dense network expansion for class incremental learning. In CVPR, 2023. [25] Kishaan Jeeveswaran, Prashant Bhat, Bahram Zonooz, and Elahe Arani. Birt: Bio-inspired replay in vision transformers for continual learning. ICML, 2023. [26] Xisen Jin, Arka Sadhu, Junyi Du, and Xiang Ren. Gradient-based editing of memory examples for online task-free continual learning. Neur IPS, 2021. [27] Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang. On large-batch training for deep learning: Generalization gap and sharp minima. ar Xiv preprint ar Xiv:1609.04836, 2016. [28] Do-Yeon Kim, Dong-Jun Han, Jun Seo, and Jaekyun Moon. Warping the space: Weight space rotation for class-incremental few-shot learning. In ICLR, 2022. [29] James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaume Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Grabska-Barwinska, et al. Overcoming catastrophic forgetting in neural networks. PNAS, 2017. [30] Yajing Kong, Liu Liu, Huanhuan Chen, Janusz Kacprzyk, and Dacheng Tao. Overcoming catastrophic forgetting in continual learning by exploring eigenvalues of hessian matrix. IEEE Transactions on Neural Networks and Learning Systems, 2023. [31] Tatsuya Konishi, Mori Kurokawa, Chihiro Ono, Zixuan Ke, Gyuhak Kim, and Bing Liu. Parameter-level soft-masking for continual learning. ar Xiv preprint ar Xiv:2306.14775, 2023. [32] Zhizhong Li and Derek Hoiem. Learning without forgetting. IEEE Trans. Pattern Anal. Mach. Intell., 40(12):2935 2947, 2018. [33] Huiwei Lin, Baoquan Zhang, Shanshan Feng, Xutao Li, and Yunming Ye. Pcr: Proxy-based contrastive replay for online class-incremental continual learning. In CVPR, 2023. [34] Sen Lin, Li Yang, Deliang Fan, and Junshan Zhang. Trgp: Trust region gradient projection for continual learning. ar Xiv preprint ar Xiv:2202.02931, 2022. [35] Hao Liu and Huaping Liu. Continual learning with recursive gradient optimization. ICLR, 2022. [36] Yaoyao Liu, Bernt Schiele, and Qianru Sun. Adaptive aggregation networks for class-incremental learning. In CVPR, 2021. [37] Yong Liu, Siqi Mai, Xiangning Chen, Cho-Jui Hsieh, and Yang You. Towards efficient and scalable sharpness-aware minimization. In CVPR, 2022. [38] David Lopez-Paz and Marc Aurelio Ranzato. Gradient episodic memory for continual learning. Neur IPS, 2017. [39] Aojun Lu, Tao Feng, Hangjie Yuan, Xiaotian Song, and Yanan Sun. Revisiting neural networks for continual learning: An architectural perspective. IJCAI, 2024. [40] Marc Masana, Xialei Liu, Bartłomiej Twardowski, Mikel Menta, Andrew D Bagdanov, and Joost Van De Weijer. Class-incremental learning: survey and performance evaluation on image classification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. [41] Sanket Vaibhav Mehta, Darshan Patil, Sarath Chandar, and Emma Strubell. An empirical investigation of the role of pre-training in lifelong learning. J. Mach. Learn. Res., 24:214:1 214:50, 2023. [42] Youngmin Oh, Donghyeon Baek, and Bumsub Ham. Alife: Adaptive logit regularizer and feature replay for incremental semantic segmentation. Neur IPS, 2022. [43] Sylvestre-Alvise Rebuffi, Alexander Kolesnikov, Georg Sperl, and Christoph H Lampert. icarl: Incremental classifier and representation learning. In CVPR, 2017. [44] David Rolnick, Arun Ahuja, Jonathan Schwarz, Timothy Lillicrap, and Gregory Wayne. Experience replay for continual learning. In Neur IPS, volume 32, 2019. [45] Tim GJ Rudner, Freddie Bickford Smith, Qixuan Feng, Yee Whye Teh, and Yarin Gal. Continual learning via sequential function-space variational inference. In ICML, 2022. [46] Gobinda Saha, Isha Garg, and Kaushik Roy. Gradient projection memory for continual learning. In International Conference on Learning Representations, 2020. [47] Ozan Sener and Vladlen Koltun. Multi-task learning as multi-objective optimization. Neur IPS, 2018. [48] Joan Serrà, Didac Suris, Marius Miron, and Alexandros Karatzoglou. Overcoming catastrophic forgetting with hard attention to the task. In ICML, pages 4555 4564, 2018. [49] Guangyuan Shi, Jiaxin Chen, Wenlong Zhang, Li-Ming Zhan, and Xiao-Ming Wu. Overcoming catastrophic forgetting in incremental few-shot learning by finding flat minima. Neur IPS, 2021. [50] Wenju Sun, Qingyong Li, Jing Zhang, Wen Wang, and Yangli-ao Geng. Decoupling learning and remembering: A bilevel memory framework with knowledge projection for task-incremental learning. In CVPR, 2023. [51] Zhicheng Sun, Yadong Mu, and Gang Hua. Regularizing second-order influences for continual learning. In CVPR, 2023. [52] Lam Tran Tung, Viet Nguyen Van, Phi Nguyen Hoang, and Khoat Than. Sharpness and gradient aware minimization for memory-based continual learning. In Proceedings of the 12th International Symposium on Information and Communication Technology, SOICT 2023, Ho Chi Minh, Vietnam, December 7-8, 2023, pages 189 196. ACM, 2023. [53] Gido M van de Ven, Tinne Tuytelaars, and Andreas S Tolias. Three types of incremental learning. Nature Machine Intelligence, pages 1185 1197, 2022. [54] Fu-Yun Wang, Da-Wei Zhou, Han-Jia Ye, and De-Chuan Zhan. Foster: Feature boosting and compression for class-incremental learning. In European conference on computer vision, pages 398 414, 2022. [55] Liyuan Wang, Xingxing Zhang, Hang Su, and Jun Zhu. A comprehensive survey of continual learning: Theory, method and application. ar Xiv preprint ar Xiv:2302.00487, 2023. [56] Zirui Wang and Yulia Tsvetkov. Gradient vaccine: Investigating and improving multi-task optimization in massively multilingual models. In Proceedings of the International Conference on Learning Representations (ICLR), 2021. [57] Shipeng Yan, Jiangwei Xie, and Xuming He. DER: dynamically expandable representation for class incremental learning. In CVPR, pages 3014 3023, 2021. [58] Enneng Yang, Li Shen, Zhenyi Wang, Shiwei Liu, Guibing Guo, and Xingwei Wang. Data augmented flatness-aware gradient projection for continual learning. In IEEE/CVF International Conference on Computer Vision, ICCV 2023, Paris, France, October 1-6, 2023, pages 5607 5616. IEEE, 2023. [59] Zhewei Yao, Amir Gholami, Kurt Keutzer, and Michael W Mahoney. Pyhessian: Neural networks through the lens of the hessian. In 2020 IEEE international conference on big data (Big data), pages 581 590. IEEE, 2020. [60] Jaehong Yoon, Saehoon Kim, Eunho Yang, and Sung Ju Hwang. Scalable and order-robust continual learning with additive parameter decomposition. In International Conference on Learning Representations, 2020. [61] Hangjie Yuan, Jianwen Jiang, Samuel Albanie, Tao Feng, Ziyuan Huang, Dong Ni, and Mingqian Tang. Rlip: Relational language-image pre-training for human-object interaction detection. In Neur IPS, 2022. [62] Hangjie Yuan, Shiwei Zhang, Xiang Wang, Samuel Albanie, Yining Pan, Tao Feng, Jianwen Jiang, Dong Ni, Yingya Zhang, and Deli Zhao. Rlipv2: Fast scaling of relational language-image pre-training. In ICCV, 2023. [63] Xingxuan Zhang, Renzhe Xu, Han Yu, Hao Zou, and Peng Cui. Gradient norm aware minimization seeks first-order flatness and improves generalization. In CVPR 2023, pages 20247 20257, 2023. [64] Bowen Zhao, Xi Xiao, Guojun Gan, Bin Zhang, and Shu-Tao Xia. Maintaining discrimination and fairness in class incremental learning. In CVPR, 2020. [65] Qihuang Zhong, Liang Ding, Li Shen, Peng Mi, Juhua Liu, Bo Du, and Dacheng Tao. Improving sharpness-aware minimization with fisher mask for better generalization on language models. ar Xiv preprint ar Xiv:2210.05497, 2022. [66] Da-Wei Zhou, Fu-Yun Wang, Han-Jia Ye, and De-Chuan Zhan. Pycil: A python toolbox for classincremental learning, 2023. [67] Da-Wei Zhou, Qi-Wei Wang, Zhi-Hong Qi, Han-Jia Ye, De-Chuan Zhan, and Ziwei Liu. Deep classincremental learning: A survey. ar Xiv preprint ar Xiv:2302.03648, 2023. [68] Da-Wei Zhou, Qi-Wei Wang, Han-Jia Ye, and De-Chuan Zhan. A model or 603 exemplars: Towards memory-efficient class-incremental learning. ICLR, 2023. [69] Kai Zhu, Wei Zhai, Yang Cao, Jiebo Luo, and Zheng-Jun Zha. Self-sustaining representation expansion for non-exemplar class-incremental learning. In CVPR, 2022. [70] Juntang Zhuang, Boqing Gong, Liangzhe Yuan, Yin Cui, Hartwig Adam, Nicha Dvornek, Sekhar Tatikonda, James Duncan, and Ting Liu. Surrogate gap minimization improves sharpness-aware training. ar Xiv preprint ar Xiv:2203.08065, 2022. [71] Martin Zinkevich. Online convex programming and generalized infinitesimal gradient ascent. In Machine Learning, Proceedings of the Twentieth International Conference (ICML), 2003. A.1 Overview In this supplementary material, we first present more intuitive visualizations of C-Flat, elucidating the loss landscape from local viewpoint (Appendix A.5.1) and each task during CL (Appendix A.5.2). Next, we provide more details on the accuracy and runtime trade-offs of other CL methods with our C-Flat (Appendix A.6) We summarize the pseudo code of C-Flat in algorithm 1. Algorithm 1 C-Flat Optimization Input: Training phase T, training data ST , model f T 1 with parameter θT 1 from last phase if T > 1, batch size b, oracle loss function l, learning rate η > 0, neighborhood size ρ, trade-off coefficient λ, small constant ϵ. Output: Model trained at the current time T with C-Flat. Initialization: if T=1: then Randomly Initialize parameter θT =1, ηT =1 = η, ρT =1 = ρ. else Reconstruct the model and training set if necessary, Initialize model parameter θT according to the training strategy, like randomly initialization or θT = θT 1 in pre-trained model based approaches, ηT = η, ρT = ρ, Frozen part of the parameter if required. end if Optimization: while θT not converge, do Sample batch BT of b random instances from ST Compute batch s loss gradient g BT = l BT (f T (θT )) Compute R0 ρ perturbation: ϵ0 = ρT |g BT | g BT 2+ϵ Approximate zeroth-order gradient: g0 = l BT (f T (θT + ϵ0)) Compute hessian vector product: h BT = 2l BT (θ) l BT (f T (θT )) l BT (f T (θT )) 2+ϵ Compute R1 ρ perturbation: ϵ1 = ρT h BT h BT 2+ϵ Approximate first-order gradient: g1 = 2l BT (f T (θT + ϵ1)) l BT (f T (θT +ϵ1)) l BT (f T (θT +ϵ1)) 2+ϵ Update: Model parameter: θT = θT ηT (g0 + λg1); Update training parameters ηT , ρT according to a scheduler that the values drop with iterations; end while Post-Processing on Model and Training data if required. return Model f T with parameter θT A.3 C-Flat-GPM We summarize the pseudo code of C-Flat for GPM family in algorithm 2. A.4 Convergency Proof Assumptions 1: the loss function is twice differentiable, bounded by M, with bounded variance σ2, and obeys the triangle inequality. Both the loss function and its second-order gradient are β Lipschitz smooth. η 1/β, ρ 1/4β, and ηT i = η/ i, ρT i = ρ/ 4 i for epoch i in any task T. Algorithm 2 C-Flat for GPM-family at T > 1 Input: Training set ˆ ST , parameter θT = θT 1, loss l, learning rate η1, η2, basis matrix M and significance Λ from replay buffer. while θT not converge, do Sample batch BT Compute perturbation ϵc using C-Flat optimization Update basis significance: Λ = Λ η1 Λl BT (θT + ϵc) Update model parameter: θT = θT η2 (I MΛM) l BT (θT + ϵc) Update M and replay buffer. end while return Model parameter θT Claim 1: with Assumptions 1, the convergency of zeroth-sharpness with batch size b is guaranteed [3] by i=1 E[ l R0 ρ 2] 4β n T [l(θ) l(θ )] + 8σ2 hence, the zeroth-order part of C-Flat is bounded: i=1 E[ l R0 ρ ST (f T (θT )) 2] 4β n T [l ST (f T (θT ))] + 8σ2 Lemma 1: let ξtr(θ) = ltr(f T (θ), f T (θ )), with Assumptions 1, the first-order part is bounded by i=1 E[ l R1 ρ ST (f T (θT )) 2] 1 i=1 E[ ξtr(θT + ϵ1) ξtr(θT )) 2] i=1 E[ ϵ1 2] β2η2 i=1 E[ ρT i 2] ρ2 i=1 E[i 2] 16(2 n T 1) β2n T (15) Theorem 1: with Assumptions 1, by combining the zerothand first-order parts, we can prove C-Flat converges in all tasks that, i=1 E[ l C ST (f T (θT )) 2] 2 i=1 E[ l R0 ρ ST (f T (θT )) 2] i=1 E[ λR1 ρ,ST (f T (θT )) 2] 8Mβ n T + 32λ2(2 n T 1) β2n T . (16) A.5 More Visualizations of C-Flat In this section, we present additional visualization of the loss landscape involving two cases using Py Hessian [59]: (i) Changes in the loss landscape from localized viewpoints; (ii) Changes in the loss landscape across each task during CL. A.5.1 Landscapes in a Local Viewpoint First, we present a more detailed visualization through changes in the local region of the loss landscape. We set a minimal radius threshold. At this threshold, more detailed changes are displayed. Similarly, we choose three typical method (Replay [44], WA [64], MEMO [68]) from each category of CL methods for visualization. As shown in Fig. 9, in a tiny view, C-Flat contributes to a flatter surface, a change that more intuitively reveals the mechanism of C-Flat. Figure 9: The visualizations of loss landscapes in a local viewpoint (Replay, WA and MEMO) A.5.2 Landscapes Across Each Task Second, we further visualize the loss landscape of more tasks using Py Hessian for more intuitive explanations during CL. To simplify, we choose one CL method (Replay [44]) for visualization on task 2, 7, 12 and 17 with 5 task intervals. As shown in Fig. 10 (a) to (d), the loss landscape all becomes much flatter than that of the vanilla method across each task. This trend provides strong empirical support for C-Flat. (c) Task 12 (d) Task 17 Figure 10: The visualizations of loss landscapes during CL. A.6 Overhead of C-Flat To enhance the computing efficiency, we apply C-Flat in a limited number of iterations within each epoch. Remarkably, we observe that without executing C-Flat in every iteration can also significantly boost the performance of CL (All cases derived from C-Flat improves CL performance). As illustrated in Table 4, 10% C-Flat iterations is enough to improve CL performances, and around 50% C-Flat iterations is enough to approach and even exceed the impact of a full C-Flat training. As a consequence, the overhead of 50% C-Flat is at least 30% shorter compared with the full C-Flat training. These observations holds potential for light C-Flat boosted CL applications. Table 4: Accuracy and training speed of training with different ratios of iterations using C-Flat. Superscripts denotes the ratio of iterations in each epoch is trained with 100%, 50%, 20% and 10%. Method C-Flat1 C-Flat0.5 C-Flat0.2 C-Flat0.1 Oracle Replay [44] 61.02 (100%) 60.98 (67%) 60.63 (40%) 60.48 (34%) 60.28 i Ca RL [43] 63.04 (100%) 62.94 (65%) 62.78 (41%) 62.75 (35%) 62.74 WA [64] 68.67 (100%) 68.20 (59%) 67.96 (38%) 68.02 (31%) 67.75 PODNet [11] 64.35 (100%) 63.82 (60%) 63.27 (39%) 63.80 (34%) 63.05 DER [57] 72.25 (100%) 71.82 (59%) 71.82 (39%) 71.44 (31%) 71.52 FOSTER [54] 70.24 (100%) 70.43 (70%) 69.99 (52%) 69.71 (47%) 69.30 MEMO [68] 69.97 (100%) 70.03 (64%) 70.48 (41%) 69.90 (32%) 69.71 Neur IPS Paper Checklist Question: Do the main claims made in the abstract and introduction accurately reflect the paper s contributions and scope? Answer: [Yes] Justification: We have clearly stated the contributions and scope in the abstract and introduction. And our claims match experimental results conducted in various settings. Guidelines: The answer NA means that the abstract and introduction do not include the claims made in the paper. 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