Continual Learning

Machine unlearning aims to eliminate the influence of specific data from trained models to safeguard privacy. However, this presents a significant challenge in the context of continual learning (CL), where models update sequentially on dynamic datasets. A major limitation is that current certified unlearning algorithms fail to account for the complex, cumulative model evolution inherent to CL framework. In this work, we establish the first theoretical foundation bridging CL and machine unlearning. We formulate the CL's unlearning objective as the minimization of post-unlearning excess risk, which decomposes into CL excess risk and unlearning loss, characterizing the fundamental trade-off between preserving historical knowledge and targeted forgetting. Under mild assumptions, we first establish an upper bound for the CL excess risk in non-convex models. We then adapt two certified unlearning approaches, gradient-based and Hessian-based, to the CL framework. Our analysis reveals that while the gradient-based approach is less effective than the Hessian-based method in minimizing unlearning loss, it offers the distinct advantage of nearly zero storage overhead for enabling unlearning. This insight motivates a hybrid strategy that reduces storage costs while maintaining post-unlearning performance. Experimental results further validate our theoretical findings.

While prompt-based parameter-efficient continual learning mitigates catastrophic forgetting by isolating task-specific prompts, this isolation also limits later tasks from improving earlier ones, leaving backward knowledge transfer underexplored. We address this limitation by proposing Selective bAckward refinement for positive Backward knowledge transfER (SABER), a replay-free framework that enables controlled backward transfer in prompt-based continual learning. SABER determines when backward refinement is beneficial using complementary task-correlation criteria based on prompt-gradient geometry and loss-distribution similarity, and how to perform refinement safely by restricting updates to non-interfering directions in the prompt parameter space. Extensive experiments across multiple continual learning benchmarks, and diverse pretrained backbones, including T5-Large, LLaMA, and Qwen, demonstrate that SABER consistently achieves positive backward transfer while maintaining strong overall average performance.

Continual training of deep neural networks under non-stationarity often leads to a progressive loss of plasticity, eventually limiting further learning. We relate plasticity to the empirical Neural Tangent Kernel, and identify dynamical isometry (the condition that layer-wise Jacobian singular values remain close to one) as a key mechanism for preserving plasticity in continual learning. We revisit a class of networks that are almost-everywhere isometric while remaining universal Lipschitz function approximators, demonstrating that near-dynamical isometry is compatible with expressive nonlinear representations. For general architectures, we propose an efficient isometry-promoting regularization scheme and identify a novel mechanism by which it can reactivate dormant ReLU units. Building on this, we introduce AdamO, an Adam-style adaptive optimizer that decouples isometry regularization from gradient updates, analogous to AdamW. We further reinterpret prior plasticity-preserving approaches through the lens of dynamical isometry, showing that they target only a partial measure of isometry. Across supervised and reinforcement-learning continual-learning benchmarks designed to induce plasticity loss, our methods consistently match or outperform existing approaches.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

Recently, vision-language models (e.g., CLIP) have been increasingly adopted for continual learning to mitigate catastrophic forgetting. However, existing CLIP-based methods typically freeze the backbone to preserve pre-trained knowledge, which limits the model's ability to learn discriminative features for downstream tasks. In this paper, we introduce HypCL, a parameter-efficient framework that continually adapts CLIP in hyperbolic space for continual learning. Our key insight is that the exponentially expanding capacity of hyperbolic geometry naturally accommodates the growing class space and promotes stronger inter-class separation. Specifically, HypCL attaches task-specific adapters and composes their updates sequentially in the Poincaré ball. To exploit the enhanced feature separability of hyperbolic geometry, HypCL maintains visual prototypes computed from the adapted features, which serve as stable anchors for calibrating predictions at inference. Extensive experiments on standard class-incremental benchmarks demonstrate that HypCL consistently outperforms existing CLIP-based continual learning methods.

Decentralized class continual learning refers to a paradigm where distributed clients continuously acquire new classes while retaining previously learned information without relying on a central server. With increasing emphasis on privacy preservation, there is a growing need for on-demand unlearning, introducing two key challenges: Historical Class Unlearning and Network-Wide Knowledge Entanglement. In this work, we propose a decentralized continual learning framework with on-demand unlearning (DCU), which is the first attempt at achieving class continual learning and arbitrary-time class unlearning in a distributed setting. Specifically, our proposed DCU comprises three main stages: prototypes extraction, prototype-guided continual learning, and unlearning with disposable prototypes. Firstly, the prototypes extraction mechanism is designed to capture the class-specific concepts as lightweight, disposable embeddings. Then, the synthetic data guided by these prototypes can be combined with real data to achieve incremental learning through distillation. Besides, synthetic samples with noisy label are used to guide the adjustment of the model's decision boundary, effectively erasing the influence of the target class while preserving other classes' knowledge. Extensive experiments conducted on two datasets demonstrate the effectiveness of our DCU in dynamic learning and target class unlearning.

Continual post-training (CPT) is a popular and effective technique for adapting foundation models like multimodal large language models to ever-evolving downstream tasks. While existing research primarily focuses on methods like data replay, model expansion, or parameter regularization, the fundamental role of the learning paradigm remains largely unexplored. This paper presents a comparative analysis of two core post-training paradigms: supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT), investigating their respective impacts on knowledge retention during CPT. Our experiments are conducted across multiple multimodal tasks, utilizing Qwen2.5-VL-7B-Instruct as the base model. The investigation yields two significant findings: (1) When continuously learning on downstream tasks, SFT leads to catastrophic forgetting of previously learned tasks. In contrast, RFT inherently preserves prior knowledge and achieves performance comparable to multi-task training. (2) RFT successfully protects and even enhances the model's general knowledge on standard benchmarks, while SFT degrades general model capabilities severely. Further analysis reveals that this stability is not primarily due to explicit mechanisms like KL penalty or chain-of-thought reasoning. We investigate RFT's learning dynamics and find that its selective update mechanism inherently prevents interference with established knowledge. Based on this insight, we propose a rollout-based instance filtering algorithm (RIF-RFT) that enhances the training efficiency of RFT by focusing on learnable samples. Our comprehensive study demonstrates the superiority of RFT as a robust paradigm for continual post-training.

Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of continual learning in a tractable yet representative setting. Specifically, we analyze one-hidden-layer quadratic neural networks trained by gradient descent on a sequence of XOR-cluster datasets with Gaussian noise, where different tasks correspond to clusters with orthogonal means. Our analysis is based on a tight characterization of gradient descent dynamics for the training loss, which yields explicit bounds on the rate of train-time forgetting as functions of the number of iterations, sample size, number of tasks, and hidden-layer width. We then leverage an algorithmic stability framework to bound the generalization gap, leading to corresponding guarantees on test-time forgetting. Together, our results provide the first closed-form guarantees for forgetting in continual learning with neural networks and show how key problem parameters jointly govern forgetting dynamics. Numerical experiments corroborate our theoretical results.

Catastrophic forgetting remains a fundamental challenge for neural networks when tasks are trained sequentially. In this work, we reformulate continual learning as a control problem where learning and preservation signals compete within neural activity dynamics. We convert regularization penalties into preservation signals that protect prior-task representations. Learning then proceeds by minimizing the control effort required to integrate new tasks while competing with the preservation of prior tasks. At equilibrium, the neural activities produce weight updates that implicitly encode the full prior-task curvature, a property we term the *continual-natural gradient*, requiring no explicit curvature storage. Experiments confirm that our learning framework recovers true prior-task curvature and enables task discrimination, outperforming existing methods on standard benchmarks without replay.

Mixture-of-Experts (MoE) architectures are appealing for continual learning because sparse routing should localize updates and reduce interference, yet MoE Transformers still forget substantially even with sparse, well-balanced expert utilization. We attribute this gap to a pre-routing bottleneck: multi-head attention concatenates head-specific signals into a single post-attention router input, forcing routing to act on co-occurring feature compositions rather than separable head channels. We show that this router input simultaneously encodes multiple separately decodable semantic and structural factors with uneven head support, and that different feature compositions induce weakly aligned parameter-gradient directions; as a result, routing maps many distinct compositions to the same route. We quantify this collision effect via a route-wise effective composition number $N_{\mathrm{eff}}$ and find that higher $N_{\mathrm{eff}}$ is associated with larger old-task loss increases after continual training. Motivated by these findings, we propose MH-MoE, which performs head-wise routing over sub-representations to increase routing granularity and reduce composition collisions. On TRACE across multiple backbones, MH-MoE consistently improves the retention--accuracy trade-off over LoRA-MoE variants.

Existing parameter isolation-based continual learning methods employ diverse designs to accommodate more tasks within limited model capacity, but often incur increasing computational overhead as model capacity expands for growing task streams. To address this efficiency bottleneck, we propose CAGNN, a graph continual learning framework with a biological neuron-inspired architecture that features capacity-agnostic efficiency. CAGNN leverages graph contextual information to construct task-specific subnetworks and decouples them during training and inference, reducing full-network propagation overhead while enabling knowledge transfer across tasks. Extensive experiments demonstrate CAGNN's superior effectiveness and computational efficiency over state-of-the-art methods.

While Object-Centric Learning has shown great promise in modular perception, its extension to Continual Learning remains underexplored. In this work, we observe that Slot Attention exhibits a distinctive behavior: it organizes latent representations into small and separated regions, each of which preserves identical factor states, crucially emerging not only in the current task but also across sequential tasks with novel factors. This *inter-task separation* offers significant advantages in continual learning, which typically suffers from severe object-wise forgetting. We refer to this phenomenon as *Factor-Wise Homogeneity*, and show that this intrinsic inter-task separation is crucial, serving as a key mechanism to prevent catastrophic forgetting in Continual Object-Centric Learning. However, despite its strong robustness, factor-wise homogeneity alone is insufficient due to the bottleneck in exploiting this separation at the decoder. To overcome this limitation and demonstrate the significance of our findings, we show that a minimal strategy *Decoder-only Post-Replay*, which freezes the factor-wise homogeneous representations and employs decoder-only fine-tuning, is sufficient. This work serves as a fundamental basis for understanding and leveraging the intrinsic dynamics of Slot Attention, offering essential insights for advancing object-centric systems.

Hyperbolic geometry has recently emerged as a powerful representation space for multimodal learning, as it naturally captures hierarchical semantic structure across modalities. Despite this progress, how such representations behave under continual learning poses fundamentally different challenges that remain underexplored. This work provides a geometric perspective on this problem and establishes a theoretical foundation for representation preservation in hyperbolic space, showing that preventing forgetting requires cross-modal invariance under a shared hyperbolic isometry. We further show that forgetting in hyperbolic continual learning involves both semantic relation drift and hierarchy-related distortion, motivating preservation of both cross-modal relational structure and hierarchical geometry. Guided by these insights, a principled continual learning framework is derived that preserves essential geometric structure while allowing effective adaptation to new tasks. Experiments on continual multimodal benchmarks corroborate the effectiveness of the proposed approach.

Continual learning (CL) aims to acquire new knowledge from a non-stationary data stream while retaining performance on previously learned tasks. Memory-based replay methods mitigate catastrophic forgetting by storing and revisiting past samples, but their effectiveness is fundamentally constrained by limited memory capacity, as each stored example represents only a single data instance. In this work, we propose data reassembly for CL, a new paradigm that significantly increases memory efficiency by reassembling composite replay samples from existing training data. Instead of storing raw training examples, we partition the current task training data into elementary patches and dynamically reassemble them into coherent replay instances through an energy-based optimization framework. The proposed objective jointly enforces semantic compatibility with target labels and global consistency among assembled patches. To make this optimization tractable, we derive an efficient variational inference algorithm that constructs a compact yet diverse set of reassembled samples for replay. Extensive theoretical analysis and experiments across multiple CL benchmarks demonstrate that data reassembly consistently outperforms existing memory-based approaches, achieving stronger retention of past knowledge while maintaining competitive computational efficiency.

Federated Continual Learning (FCL) aims to empower distributed devices to learn a sequence of tasks over time. However, existing FCL research largely relies on the impractical assumption of synchronous new task arrival. This overlooks the reality of asynchronous user behavior and system latencies, forcing more efficient clients to endure costly inactivity. The practical necessity of an asynchronous method gives rise to Asynchronous Federated Continual Learning (AFCL). The server constantly receives a mixture of updates from clients at different time steps, leading to a catastrophic task drift that corrupts the global model and prevents effective learning. In this paper, we introduce a novel Cross-task Calibration framework called C$^2$-AFCL that is the first to tackle task drift at a semantic level within an Asynchronous FCL setting. Its core is a two-stage orthogonal calibration mechanism. First, intra-client calibration uses task-aware caches to mitigate variance from local client drift. Second, and more critically, inter-task interference calibration dynamically estimates an interference subspace from historical task knowledge. New updates are orthogonally projected to isolate and remove components that conflict with this subspace, preserving previous knowledge while learning new tasks. Extensive experiments show that C$^2$-AFCL significantly outperforms existing methods, demonstrating robust and efficient learning in dynamic federated environments.

Continual learning (CL) seeks models that acquire new knowledge while avoiding catastrophic forgetting. However, many methods that mitigate forgetting constrain parameter updates and thereby reduce model plasticity. We revisit the singular value spectrum of gradients in representative CL methods and show that they commonly exhibit singular value collapse, where only a small subset of gradient directions drive parameter updates. Motivated by this observation, we propose **P**lasticity **A**ctivation via **P**olar **O**perator (PAPO), a plug-in that preserves the dominant directions that mitigate forgetting while activating previously suppressed directions to enhance plasticity. Concretely, PAPO modifies the gradient $\mathbf{G}$ as $\mathbf{G}\leftarrow \mathbf{G}+\lambda \cdot \operatorname{polar}(\mathbf{G})$, which uniformly increases near-zero singular values without changing the singular vectors. To avoid the cost of explicit singular value decomposition, we approximate the polar factor using the iteration-dependent Polar Express scheme, which relies only on matrix multiplications and additions. In our empirical evaluation on both vision and language benchmarks, incorporating PAPO yields consistent improvements. In particular, on MiniImageNet, integrating PAPO into ER, MAS, GPM and TRGP produces substantial accuracy gains of $9.01\%$, $4.76\%$, $8.90\%$ and $9.19\%$, respectively.

Continual Offline Reinforcement Learning (CORL) enables building long-term autonomous agents from static datasets. However, it faces heterogeneity in environment dynamics, reward functions, and behavior policies across tasks. Combined with the inherent distribution shift in offline learning, this requires agents to selectively reuse shared knowledge during transfer while isolating task-specific features. The flat knowledge sharing mechanisms employed by existing methods struggle to capture such distinctions, limiting cross-task generalization. To address this, we propose Hierarchical Task-Aware Composition (HTAC), which balances plasticity and stability through dual-level task encoding and soft composition mechanisms. HTAC comprises four modules: (1) a Hierarchical Semantic Task Representation that decomposes tasks into domain-level and task-level embeddings; (2) a Dual-level Expert Network that creates domain and task experts on demand for parameter-efficient knowledge isolation; (3) an Adaptive Knowledge Composition module that integrates historical expert outputs via attention mechanisms for knowledge reuse; (4) Task Adapters that preserve historical routing weights to prevent forgetting. Experiments on Offline Continual World show that HTAC outperforms existing baselines, demonstrating better knowledge reuse and transfer capabilities.

Continual learning with large pre-trained models offers significant potential for cross-task knowledge accumulation, but faces critical challenges such as catastrophic forgetting and parameter interference, especially when historical data is unavailable. Existing approaches typically rely on sequential fine-tuning or model merging strategies, yet often overlook the impact of loss landscape sharpness and dominant singular value directions, which leads to subspace misalignment and severe knowledge forgetting. In this paper, we propose the Sharpness-Aware Isotropic Merging (SAIM) framework, which introduces targeted optimizations in both the fine-tuning and merging stages to address these issues. Specifically, SAIM consists of two synergistic modules: (1) a Sharpness-Aware Block Coordinate Descent (SA-BCD) optimizer that guides the model toward flatter minima and selectively updates the most task-sensitive parameters, thereby mitigating parameter interference and enhancing robustness; (2) an adaptive isotropic merging algorithm that dynamically balances the singular value spectrum across tasks, effectively preventing the model from overemphasizing any single task direction, maintaining balanced knowledge representation, and improving subspace alignment. Extensive experiments on vision and language benchmarks demonstrate that SAIM achieves 5-10\% higher accuracy than existing methods and maintains robust performance as the number of tasks increases. Our code are available at \url{https://github.com/Yangqun123456/SAIM}.

The Mixture of Experts (MoE) framework is widely used in continual learning to mitigate catastrophic forgetting. MoEs typically combine a small inter-task shared parameter space with largely independent expert parameters. However, as the number of tasks increases, the shared space becomes a bottleneck, reintroducing forgetting, while fully independent experts require explicit task ID predictors (e.g., routers), adding complexity. In this work, we eliminate the inter-task shared parameter space and the need for a task ID predictor by enabling expert communication and allowing knowledge to be shared dynamically, akin to human collaboration. We bridge the inter-expert knowledge sharing by leveraging the open-set learning capabilities of a multimodal foundation model (e.g., CLIP), thereby providing “expert priors” that bolster each expert’s task-specific representations. Guided by these priors, experts learn calibrated inter-task posteriors. Additionally, multivariate Gaussians over the learned posteriors promote complementary specialization among experts. We propose new evaluation benchmarks that simulate realistic continual learning scenarios, and our prior-conditioned strategy consistently outperforms existing methods across diverse settings without relying on reference datasets or replay memory.

Online Continual Learning (OCL) aims to learn from endless non\text{-}stationary data streams, yet most existing methods assume a flat label space and overlook the hierarchical organization of real\text{-}world concepts that evolves both horizontally (sibling classes) and vertically (coarse or fine categories). To better reflect this context, we introduce a new problem setting, DHOCL (Online Continual Learning from Dynamic Hierarchies), where taxonomies evolve across granularities and each sample provides supervision at a single hierarchical level. In this setting, we find two fundamental issues: (i) partial supervision under mixed granularities provides only point-wise signals over an evolving path-wise hierarchy, which constrains plasticity and undermines cross-level semantic consistency, and (ii) the dynamically evolving hierarchies induce granularity-dependent interference, destabilizing popular replay and regularization mechanisms and thereby exacerbating catastrophic forgetting. To tackle these issues, we propose HALO (Hierarchical Adaptive Learning with Organized Prototypes), which adaptively combines complementary classification heads, regularized by organized learnable hierarchical prototypes, enabling rapid adaptation, hierarchical consistency, and structured knowledge consolidation as the taxonomy evolves. Extensive experiments on multiple benchmarks demonstrate that HALO consistently outperforms existing methods across hierarchical accuracy, mistake severity, and continual performance.