Continual Learning Methods

Language agents spend substantial inference time solving individual tasks, yet the experience acquired in one episode is often underutilized in future episodes. Continual learning expects an agent to accumulate reusable experience across a stream of tasks, improve over time, and avoid interference from irrelevant experiences. Unfortunately, existing benchmarks struggle to evaluate continual learning in language agents rigorously. Most efforts focus on retrieval and reasoning over long-context conversations or documents, while recent lifelong-adaptation benchmarks often rely on naive task streams with limited analysis of cross-task relationships, making it difficult to understand what an agent learns and reuses over time. This paper presents an evaluation framework AgentCL for continual learning in agents, centered on controlled task streams and metrics for transfer gains. AgentCL constructs compositional streams where earlier sub-solutions, evidence, or workflows are intentionally reusable in later tasks, and contrasts them with naive streams where such reusability is not guaranteed. We use the benchmark to evaluate non-parametric memory designs for continual learning. To diagnose how memory design choices affect continual learning, we develop MemProbe, a probing method that stores interactions, insights, and skills, while filtering unreliable experiences during consolidation. Empirical analysis across coding, deep research, and language understanding/reasoning tasks shows that naive streams offer limited ability to distinguish memory designs, whereas controlled streams more clearly distinguish their plasticity. Meanwhile, naive and held-out settings often yield limited gains and can expose memory-induced degradation. These results highlight the need for stronger memory designs that balance plasticity and stable reuse.

In dynamic environments, large language models need to keep adapting to new tasks, but continual learning often suffers from forgetting, limited transfer, and vulnerability to adversarial perturbations. To address this, we present AdvCL, which repurposes adversarial perturbations as a geometric control signal for stable continual adaptation. AdvCL combines three plug-in modules: Intra-Smooth promotes local smoothness via small adversarial perturbations; Proto-Clip uses similarity clipping to prevent excessive alignment to current task prototype; and Inter-Align applies directional alignment toward previous task prototype to reduce representational gaps. Experiments show consistent gains in both standard performance and robustness, with lower forgetting and stronger transfer. We further analyze key mechanisms by quantifying the sensitivity of Intra-Smooth to perturbation settings and the effect of Inter-Align on task similarity and geometric distance. In summary, the modules provide complementary gains when combined, and each can also be integrated individually into diverse CL paradigms, including replay, regularization, and dynamic architectures, thereby offering a geometric control mechanism for continual learning.

Continual learning struggles to balance retaining past knowledge with absorbing new tasks. Stefan-CL elegantly resolves this stability-plasticity dilemma through the physics of melting. It frames consolidated knowledge as a protected "solid" and unused capacity as an adaptable "liquid." As the network learns, this boundary expands, governed by a "latent heat" tuning dial. By mathematically freezing the learned interior, Stefan-CL cuts forgetting to near zero, matching memory-heavy baselines without storing raw data, forging a beautiful, physics-grounded path for AI.

Electroencephalography (EEG) is the cornerstone of non-invasive brain-computer interfaces (BCIs), yet conventional decoding relies on fragmented, task-specific architectures that severely limit cross-task scalability. While EEG foundation models pre-trained on massive corpora promise universal brain decoding, current post-training depends on task-isolated fine-tuning. This static paradigm restricts knowledge transfer across heterogeneous tasks, hinders model scalability, and incurs computational and storage overheads that scale linearly with task count. To overcome these bottlenecks, we formulate downstream adaptation as a cross-task continual learning problem and propose EvoBrain, a dynamic, task-aware continual learning framework for unified EEG decoding. EvoBrain addresses the plasticity-stability trade-off via two complementary components: (1) Neuro-Spectral Task Normalization (NSN) aligns incoming tasks with historical statistics while recalibrating spectral responses to handle distributional and neuro-spectral shifts; and (2) Response-Affinity Distillation (RAD), combined with time-dependent replay, preserves old-task response geometry and promotes selective knowledge transfer between spectrally compatible tasks, effectively mitigating forgetting. Extensive evaluations across six distinct BCI tasks demonstrate that EvoBrain consistently surpasses state-of-the-art methods across diverse foundation backbones, optimally balancing plasticity and stability. To our knowledge, this work pioneers cross-task continual learning in the EEG domain, advancing the realization of a unified, one-for-all brain decoding system.

Fine-tuning safety aligned large language models (LLMs) on downstream data improves adaptation but may erode learned safety behavior. Existing methods use fixed safety examples, global constraints, or one-sided task filtering. Our diagnostics show task updates expose different safety constraints, motivating joint selection of relevant references and compatible task samples. We propose DualSelect, a coupled framework for task and reference selection that refreshes task conditioned safety references before filtering whole task samples compatible with the induced reference direction. Under a minimax view, DualSelect selects safety references with high preservation loss and task conflict, together with compatible task samples, through entropy-regularized scoring surrogates, lazy reference refresh, and gradient correction. On 1B-8B LLMs, DualSelect preserves safety without losing task utility; using the REDORCA judge, it improves Safety Avg. over the strongest baseline by at least 5.10 points and remains highest in Safety Avg. across judges with moderate overhead. This view extends to retention focused continual learning.

Federated continual learning (FCL) lets distributed clients adapt language-model heads to evolving NLP tasks without sharing raw text. Under user-level differential privacy (DP), replay-based continual learning faces a structural obstacle: clients can release only small noisy lists of candidate replay summaries, and those lists are unordered across clients. We introduce Canonicalized Stable-List Replay (CSLR), where clients privately produce candidate replay distributions over a shared sentence-embedding space and the server aligns them using signatures induced by public anchor sentences. The anchors provide identifiability for aggregation rather than additional replay data. We prove that, under an observable anchor-signature margin, $O(\log(N/η)/p)$ anchors distinguish $N$ candidate list elements with probability at least $1-η$, and we give a scoped anchorless non-identifiability result for unordered-label oracle models. Across five seeds on continual classification, NER, and dialogue benchmarks, CSLR improves the final average task metric by 3.9--5.6 points over the strongest non-CSLR DP baseline at $\eps=4$ under the reported replay-release budget, while also outperforming Hungarian and optimal-transport matchers. The formal privacy guarantee covers replay release; end-to-end private training additionally requires composition with a private optimizer for task-head updates.

For agents to learn continuously from interaction with the world at test time, they must be able to explore effectively, acquire new world knowledge and skills, retain relevant episodic experiences, and plan over long horizons. To evaluate these key abilities of test-time continual learning agents, we introduce AgentOdyssey, a novel evaluation framework that procedurally generates open-ended text games with rich entities, world dynamics, and long-horizon tasks. Critically, AgentOdyssey goes beyond the conventional machine learning assumption that learning does not occur at test time by placing agents in a continuous, long-horizon setting that interleaves learning and inference throughout deployment. We further propose a multifaceted evaluation methodology that measures not only game progress but also offers diagnostic tests on world knowledge acquisition, episodic memory, object and action exploration, action diversity, and model cost. We evaluate diverse agent paradigms in the generated games. Our experimental results reveal critical limits in agents' key abilities, as well as factors that influence their meaningful horizon. Although performance scales with stronger base models, even the top agent remains far below human performance, leaving substantial headroom for improvement. Among agent mechanisms, we find that short-term memory benefits multiple agent paradigms and is an important component of agent test-time training.

Financial markets are inherently non-stationary, exhibiting frequent regime shifts and structural changes that render traditional Portfolio Management (PM) approaches ineffective. Existing remedies, such as rolling-window retraining and naive online fine-tuning, are hindered by high computational costs and insufficient knowledge utilization, respectively, resulting in low returns and limited adaptability. Continual learning (CL) offers a promising paradigm by enabling trading agents to accumulate and transfer knowledge across sequential tasks. In this paper, we propose \textbf{Re}gime-aware \textbf{C}ontinual \textbf{A}daptive \textbf{P}ortfolio management (\textbf{ReCAP}), a novel framework that integrates CL into PM to address the challenges of dynamic financial environments. ReCAP employs an adaptive regime detection module to segment historical market data into variable-length regimes, enabling regime-specific learning of policy vectors and the construction of a policy library. During continual trading, a regime-gate module adaptively combines policy vectors from the library based on the current market state, facilitating rapid adaptation to newly detected regimes. Only the regime-gate and the current regime's policy vector are continually updated to preserve useful knowledge effectively. Extensive experiments on five real-world datasets demonstrate that ReCAP consistently outperforms popular baselines, achieving superior returns in long-term investment horizons and rapid adaptation to regime shifts.

Evolution Strategies (ES) has recently emerged as a competitive alternative to reinforcement learning (RL) for large language model (LLM) fine-tuning, offering advantages through simplicity, scalability, and inference-only training. However, recent work suggests that ES fine-tuning on new tasks may induce forgetting of prior tasks. First, this paper shows that prior task forgetting (1) is better characterized as performance drift rather than irreversible forgetting, with prior-task performance often recovering during ES training; and (2) is not a specific failure mode of ES, but can also arise for fine-tuning with RL methods. Second, it analyzes when and why such drift arises, highlighting its dependence on ES training dynamics, particularly random walk behavior in weakly constrained directions of the weight space. Third, based on these insights, it introduces Anchored Weight Decay (AWD) as a parameter-space regularization technique that constrains optimization toward the initial model parameters. AWD effectively stabilizes prior-task performance while preserving target-task performance, achieving benefits comparable to large ES population sizes at much lower computational cost. Thus, contrary to previous beliefs, the paper shows that prior-task forgetting under ES is largely avoidable, positioning ES as a promising approach for continual learning in LLMs.

In-context learning (ICL) derives its power from enabling Large Language Models to adapt to new tasks via prompt-based reasoning alone, entirely bypassing the need for parameter updates. Existing theories primarily study ICL in single-task settings, while real-world prompts often contain sequences of heterogeneous tasks, leaving a gap in understanding whether Large Language Models implicitly perform continual learning during inference. To bridge this gap, we propose the first theoretical framework for in-context continual learning, modeling how a pretrained Transformer processes multiple sequential tasks within a single prompt through shared attention mechanisms. Focusing on linear and masked linear self-attention, we derive error expressions for model predictions under sequential task prompts and analyze their generalization and forgetting behavior. Our results reveal that standard attention mechanisms inevitably induce intertask interference by uniformly or causally aggregating historical contexts, leading to systematic bias. We further provide a bias-variance-interference decomposition of prediction error, characterizing when historical in-context information yields positive transfer or provable negative transfer. This analysis exposes fundamental limits of attention-based continual inference and offers theoretical explanations for order sensitivity and performance degradation in long prompts.

Low-Rank Adaptation (LoRA) has emerged as a promising paradigm for Continual Learning. It independently updates its low-rank factors ($A$ and $B$), creating a composite update to the full weight matrix through their interaction. To prevent catastrophic forgetting, this update should remain orthogonal to the task-specific subspace that contains previously learned knowledge. However, we identify that this composite update systematically violates this orthogonality, reintroducing interference and undermining stability. Furthermore, naively enforcing this orthogonality compromises plasticity, disrupting the delicate stability-plasticity trade-off. To resolve these issues, we propose \textbf{Janus-LoRA}, a framework that restores this balance through two novel components. Specifically, we first introduce Gradient Rectification, a closed-form solution that mathematically decouples LoRA's factor updates, enforcing orthogonality against the historical knowledge subspace identified by an efficient Online Estimation. Next, to enhance plasticity, we introduce a Decoupled Margin Loss that promotes feature-level separation by pushing new feature representations away from old ones, thus creating distinct, low-interference regions for new learning. Comprehensive experiments on challenging benchmarks demonstrate that by harmonizing parameter-level orthogonality with feature-level separation, Janus-LoRA achieves a superior balance and establishes new state-of-the-art performance.

Self-supervised online traversability estimation enables robots to continuously learn from unlabeled open-world experiences and adapt their navigation behavior toward safe and efficient trajectories. Existing approaches either rely on handcrafted proprioceptive traversability scores, limiting robot-agnosticism, or cluster prior data, preventing online learning. Moreover, many continual learning methods incur substantial memory and computational costs, hindering onboard deployment. We introduce COTRATE, an online learning framework for continuous traversability estimation from multimodal, unlabeled robot experience. Our method first infers robust traversability scores using a robot-agnostic, learning-based online terrain assessment module operating on proprioceptiveand inertial signals. These scores then supervise a visual traversability network through a novel alignment loss that associates visual embeddings with online terrain assessments. To mitigate forgetting during continual learning with minimal overhead, we propose a diversity-aware feature selection strategythat preserves performance using a compact replay memory. We further show that the learned traversability representation supports knowledge transfer across different robot platforms with different locomotion kinematics. We evaluate COTRATE on a dataset of $\approx$ 50,000 images collected with two robotic platforms across 11 outdoor terrains, and benchmark it on navigation tasks in three representative outdoor environments. We make the dataset, code, and trained models publicly available.

Recognizing and continuously learning novel human actions without forgetting prior classes is a requirement for emerging AR/VR and robotics applications. For these applications, both on-device processing and learning are essential for privacy and low-latency adaptation. Event cameras address the efficiency of visual sensing with sparse, asynchronous output that is naturally compatible with neuromorphic processing. Yet no prior system has deployed a continual on-device learning pipeline for event-based action recognition using neuromorphic hardware. We present CLANE, Continual Learning of Actions on Neuromorphic Hardware from Event Cameras, deployed end-to-end on Intel Loihi 2. CLANE combines a spiking 2D CNN for spatiotemporal feature extraction with CLP-SNN as its on-chip learning head, extended to action clips via a Temporal Aggregation Layer and a fixed-point Normalization Layer, both novel Loihi 2 modules. On THU E-ACT-50, a 50-class dataset captured under real-world conditions, CLANE achieves 70.4% accuracy in a continual learning task while delivering more than 100x energy reduction and 16x lower latency over a sequential CNN+GRU+CLP edge GPU baseline, validated through iso-algorithm cross-platform benchmarking across three evaluation levels.

Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative models remains poorly understood: after a task change, what aspects of the learned distribution are most easily lost, and what replay samples should be prioritized? We address these questions through the modern Hopfield energy. Recent links between modern Hopfield networks (MHNs) and diffusion models allow analyses in MHNs to be transferred to diffusion models. We introduce intrinsic forgetting as an increase in Hopfield energy after the task change. In tractable settings in an MHN, we prove that high-energy, outlier-like samples undergo a larger energy increase than cluster-like samples, implying that samples located in sharp, isolated basins are more forgettable. We further analyze memory replay and show that replay is particularly effective for high-energy samples, enabling an energy-based selection of replay samples. We validate these predictions in experiments on MHNs and two diffusion models under continual-learning settings: Stable Diffusion and a pixel-space DDPM. In these diffusion models, Hopfield energy tracks reconstruction-based forgetting, and replay experiments reveal energy-dependent mitigation of forgetting that is consistent with the MHN analysis.

Language models are becoming the default interface to factual knowledge, yet they often verify outputs more reliably than they generate them. This generation-verification gap (GV-gap) underlies many recent advances in self-improvement and reasoning, but its dynamics on factual knowledge specifically remain poorly understood. We focus on the training mechanisms underlying factual GV-gaps, distinguishing them from their computational and aesthetic counterparts. We trace generation and verification capabilities through three training phases (acquisition, continual learning, and updating) across four open-source model families at two scales each. Three findings recur across models: (i) verification is consistently learned before generation; (ii) verification is more robust to continual learning than generation; and (iii) factual updates can leave models in a "multi-verse" state, simultaneously verifying both old and new answers as correct. Natural experiments on frontier models reproduce these dynamics at scale and reveal residual verification biases on well-covered facts.

Real-time semantic segmentation models offer an excellent balance between accuracy and inference speed. However, deploying these models in dynamic real world environments often requires the ability to learn novel classes incrementally without retraining on the entire dataset. This capability is known as continual learning. In this regard, the standard fine-tuning methods in deep learning often fail due to catastrophic forgetting, where the model learns new information but forgets previously trained and learned classes. Contributing to this crucial domain, the current paper proposes a novel continual learning framework tailored for PIDNet, which is a widely cited state-of-the-art real-time semantic segmentation model. Our method, PILOT(Parallel Incremental Learning Over Time), introduces a real-time and lightweight strategy by implementing a parallel Derivative-branch (D-branch) designed to capture the high frequency boundary information of novel classes while freezing the trained parameters of the original segmentation network. This novel setup allows the model to adapt to new semantic categories while preserving the knowledge of previously learned classes. By using only data associated with the new class, our model significantly reduces training overhead. Experimental results demonstrate that our approach successfully segments new classes while maintaining high mean Intersection over Union (mIoU) on the original base classes, thereby comfortably outperforming all major continual learning approaches in this domain. Overall, PILOT is shown to effectively mitigate catastrophic forgetting with minimal impact on inference latency, thus maintaining real-time performance.

Open-vocabulary object detection (OVD) has made significant progress, enabling detectors to generalize from seen to unseen categories. However, real-world category spaces continually evolve, and existing OVD models still struggle with newly emerging concepts, while repeated full retraining is prohibitively expensive. To this end, we introduce a new task setting, termed Continual OVD with Novel Concept Injection (COVD), where models sequentially learn incoming novel concept groups while preserving prior concepts and original open-vocabulary knowledge, along with a new benchmark, Novel-114. Our key observation is that pretrained visual encoders often already perceive and represent many novel concepts, and the main bottleneck lies in the lack of stable semantic alignment between visual representations and textual concepts. Based on this, we propose NoIn-Det, an efficient continual injection framework without additional parameters. NoIn-Det freezes the visual encoder, preserves the text representation space using only texts of common concepts and previously injected concepts, and injects novel concepts by updating only a small subset of text-branch parameters beneficial to novel concept learning. Extensive experiments show that NoIn-Det effectively learns novel concepts, preserves old knowledge, and consistently outperforms existing continual learning methods for VLMs without introducing additional parameters.Novel-114 and the code will be released.

While orthogonal subspace methods try to mitigate task interference in Continual Learning (CL), they often suffer from energy diffusion across the basis, hindering knowledge compaction and exhausting capacity for future tasks. We observe that output feature drift induced by parameter updates is inherently low-rank, and theoretically prove that preserving parameters along the principal directions of this drift minimizes the output reconstruction error. Motivated by this, we propose \textbf{E}nergy-Concentrated and \textbf{E}nergy-Ordered \textbf{Lo}w-\textbf{R}ank \textbf{A}daptation (E$^2$-LoRA). By explicitly ordering and concentrating knowledge into leading ranks, E$^2$-LoRA frees capacity for subsequent tasks. Furthermore, we design a dynamic rank allocation strategy to balance stability and plasticity by jointly optimizing energy retention and model plasticity. Extensive experiments across multiple benchmarks demonstrate that E$^2$-LoRA achieves state-of-the-art performance. Code is available at https://github.com/kiddo127/E2-LoRA.

Continual Learning (CL) is a practical paradigm to utilize power of deep pre-trained neural networks, but which pre-trained model has a better ability to balance ``Plasticity-Stability", deserving to be chosen? The logit shift serves as a natural proxy because it represents the logit shift in CL scenarios. However, obtaining the logit shift requires huge computational cost, which hinders large-scale model selection. Existing theoretical analyses fail to offer an efficient alternative because of the assumption of uniform hidden layer widths, which ignores the structural heterogeneity (variable width and depth) of real-world architectures. This raises a critical question: what theoretically relationship can be identified between heterogeneous architecture and logit shift on prior tasks (that the model has been trained on)? To answer the question, we decouple logit shift into architecture dependency and data dependency to establish our framework, which reveals that the combination of two dependency, defined as Architecture-driven Shift (ADS), that can capture the logit shift tendency well computable with few data samples. Specifically, for a well-optimized model on prior tasks, higher ADS is associated with a larger logit shift after training on the current task, which derived based on three mechanistic components: (1) spectral norm scaling of weight matrix gradients with layer width, (2) the optimization path length of the new task, and (3) the asymptotic task conflict in wide networks. Extensive empirical results across more than 175 diverse architectures demonstrate a strong monotonic correlation (the weakest Spearman's $r_s=0.731$) between ADS and logit shift. Practically, we demonstrate that ADS can serve as a lightweight proxy of the expected calibration error, which is a widely used metric for reliable CL model selection, on three datasets across six scenarios.

Continual learning enables large language models to adapt to evolving tasks without retraining from scratch, yet catastrophic forgetting remains a central obstacle. Among continual learning methods, regularization-based approaches are widely used to constrain model updates and reduce forgetting, operating in weight space, gradient space, or output space. However, these dense representation spaces suffer from feature superposition, where multiple concepts are encoded in overlapping dimensions, making it difficult to selectively protect previously learned knowledge without impeding new-task learning. To address this issue, we propose \method (Sparse Autoencoder Feature Distillation), which anchors model representations in the sparse feature space of a pre-trained Sparse Autoencoder, where dense activations are decomposed into a sparse overcomplete basis that reduces representational entanglement, enabling more targeted regularization with less interference to new-task learning. Experiments on two continual learning benchmarks across three model architectures show that \method consistently outperforms existing regularization-based methods, achieving up to 52.70% average accuracy with only -0.46 backward transfer.

Training data for olfaction is scattered through disparate, non-standardized datasets that limit the ability to build representative world models. Olfactory navigation is a highly dynamic and non-stationary task that benefits from real-time continual learning. We introduce an adaptive framework called Grow-Prune-Freeze (GPF) networks that enable an agent to continually learn through growing, pruning, and freezing early layers of its policy in response to world complexity. Grounding GPFs in non-linear random matrix theory, we show that the work of Pennington & Worth (2017) can be extended from single hidden layers to n-layer continual-learning models, and that eigenvalue composition of network weights is preserved as successive layers are added. We show that GPFs based on Expected SARSA achieve a 94% success rate on turbulent plume navigation - a partially observable, non-stationary task representative of the "big world" challenges that motivate adaptive learning in robotics - and provide supporting methodology for applying GPFs in other world models. Further experiments amount evidence that GPFs may generalize well to other machine learning tasks such as reinforcement learning in Atari, image classification, and autoregressive language models. We open source all code and data to encourage improvements on and more research in olfactory robotics.

Speech and audio systems operate in inherently non-stationary environments, yet continual learning (CL) research in this domain, especially in the foundation model era, remains fragmented that fail to account for the coupled, geometry-sensitive nature of acoustic representations. Modern speech foundation models operate over highly entangled, continuous representations that jointly encode linguistic, speaker, and paralinguistic factors within a shared latent space. CL is therefore fundamentally about preserving and evolving shared representation structure rather than retaining isolated task knowledge. In this work, we revisit CL for speech from a representation-centered perspective, and introduce a new taxonomy that organizes CL according to how underlying representation geometry evolves under non-stationary acoustic conditions. We further identify key mismatches between current CL assumptions and speech foundation model behavior, and finally outline a set of open challenges and future research directions.

Standard neural network training relies on learning-rate schedules tied to a fixed horizon, leading to strong path dependence and costly re-tuning as data availability changes. Schedule-Free (SF) methods address this by removing explicit schedules, yet SF-AdamW, the current state-of-the-art anytime optimizer, consistently underperforms well-tuned AdamW baselines. We propose SF-NorMuon, a schedule-free spectral optimizer that closes this gap: with a single hyperparameter configuration, SF-NorMuon matches or exceeds tuned AdamW on 125M and 772M parameter language models across $1$--$8\times$ Chinchilla horizons. On the theoretical side, we prove a stationarity guarantee for schedule-free spectral dynamics and identify weight decay at the fast iterate as essential for long-horizon stability. SF-NorMuon enables practitioners to obtain high-quality checkpoints at any point during training without committing to a horizon in advance. By closing the performance gap with tuned baselines, SF-NorMuon makes horizon-free optimization more practical, taking a step towards truly open-ended, continual learning.

Large language models (LLMs) are typically trained on shuffled corpora, yielding models whose knowledge is frozen at train time and whose temporal grounding remains poorly understood. In this work, we study the impact of pre-training dynamics on the acquisition of time-sensitive factual knowledge, focusing specifically on data ordering. Our main contributions are twofold. First, we introduce a comprehensive benchmark of over 7,000 temporally grounded questions and an evaluation protocol that enables analysis of whether models correctly associate facts with their corresponding time periods. Second, we pretrain 6B-parameter models on temporally ordered Common Crawl snapshots and compare them against standard shuffled pre-training. Our results show that sequentially trained models match shuffled baselines on general language understanding and common knowledge while consistently exhibiting more up-to-date and temporally precise knowledge. Temporally ordered pre-training yields improved factual freshness, while shuffled pre-training peaks on older data, possibly due to increased factual repetition. These findings, along with the release of our code at https://github.com/kyutai-labs/kairos , checkpoints, and datasets at https://huggingface.co/collections/kyutai/kairos provide a foundation for future research on continual learning for LLMs.

Parameter-efficient fine-tuning enables fast personalization of text-to-image diffusion models, but composing multiple custom concepts remains challenging due to representation interference. Existing modular methods either rely on expensive post-hoc fusion or freeze adaptation subspaces, which limit expressiveness and concept fidelity. To address this trade-off, we propose Sequential regularized LoRA (SeqLoRA), a constrained continual learning framework that jointly optimizes both LoRA factors via bilevel optimization. Theoretically, we establish strong convergence guarantees for our algorithm and model the residual layer activations as a matrix sub-Gaussian process to derive high-probability bounds on catastrophic forgetting. We further prove that learning the LoRA basis from data minimizes residual interference energy more effectively than frozen-basis methods. Experiments on multi-concept image generation demonstrate that SeqLoRA improves identity preservation and scalability across up to 101 concepts, while avoiding costly fusion and reducing attribute interference in composed generations.

Continual learning (CL) aims to train models sequentially on multiple tasks while mitigating catastrophic forgetting of previously learned knowledge. Recent advances in large pre-trained models (LPMs) and model merging techniques, such as MAGMAX, have demonstrated effective CL performance by combining task-specific parameters. However, existing methods primarily focus on average performance across all tasks and do not adequately address how to construct models accommodating different deployment environments or varying user preferences. This paper proposes a model merging framework, termed Tunable MAGMAX, which enables preference-aware control of task-specific performance in CL. Our method introduces a preference vector that controls the number of elements selected from each task vector during model merging, allowing us to adjust the merged model performance according to their deployment needs. We further propose a method for automatically constructing appropriate preference vectors by leveraging small amounts of target environment data and datasets from model training tasks, thereby eliminating the need for manual specification. The experimental result on CL benchmark tasks demonstrates that Tunable MAGMAX effectively controls task-wise performance and successfully adapts merged models to various target environments. The proposed Tunable MAGMAX achieves superior or comparable performance to baseline methods, making it a practical solution for deploying CL models to various environments where the preferences of each task performance differ.

In the literature, many continual learning (CL) algorithms have been proposed to address the issue of catastrophic forgetting in ML models (i.e., learning new tasks leads to the loss of performance on previously learned tasks). Although all CL approaches use some form of memory to retain information about past tasks, a grounded understanding of what information needs to be stored to minimize catastrophic forgetting remains elusive. Recently, it has been recognized that under the strong assumption of the existence of a common global minimizer over all tasks, catastrophic forgetting can be completely avoided. However, in practice, tasks rarely have a common global minimizer, and a certain amount of forgetting is inevitable. In this paper, we propose a foundational framework for principled and systematic CL of conflicting tasks using a multi-task learning (MTL) perspective. The approach is based on finding Pareto-optimal solutions, i.e., the solutions which, by definition, minimally forget the previous tasks in the Pareto sense. We derive Pareto-minimal-forgetting CL algorithms for linear and basis-function regression, and general loss functions which have a quadratic upper bound, e.g., logistic regression. For quadratic problems, PMF-CL uses memory-efficient iterative updates with a static memory footage of $\mathcal{O}(d^2)$ for models with $d$ parameters.

Catastrophic forgetting remains a major obstacle to continual learning in large language models (LLMs) and vision--language models (VLMs). Although Mixture-of-Experts (MoE) architectures offer an efficient path to scaling, existing LoRA-based MoE continual learning methods still face a fundamental trade-off: they either isolate experts too aggressively, limiting knowledge transfer across tasks, or allow task-specific updates to overwrite important existing parameters, leading to severe forgetting. To address this, we propose CP-MoE, a continual learning framework built around a transient expert that captures early task-specific updates and guides their integration into stable experts. CP-MoE introduces a consistency-preserving routing bias, which uses the transient expert to estimate representation similarity with stable experts and steer routing towards more compatible expert selection, and a transient expert-guided regularisation mechanism, which selectively protects important historical parameters during merging. Together, these components reduce parameter interference and forgetting while preserving cross-task knowledge transfer. We validate CP-MoE on both unimodal and multimodal continual learning benchmarks with LLM-based and VLM-based MoE models. On SuperNI benchmark, spanning diverse sequential language tasks, CP-MoE achieves state-of-the-art performance and stronger zero-shot transfer to unseen tasks. On VQA v2 dataset, it scales effectively to multimodal visual reasoning, consistently reduces forgetting, and outperforms strong MoE baselines.

Vision-Language Models in Continual Learning (VLM-CL) aim to continuously adapt to new multimodal tasks while retaining prior knowledge. The emerging paradigm that couples Multimodal Large Language Models (MLLMs) with Reinforcement Learning with Verifiable Rewards (RLVR) calls for a new pattern to guide continual adaptation. Advances in reasoning capability now make it feasible to impose constraints at the reasoning level. We formalize portability, a sample-level measure of how reusable the previous policy's behavior is on a new task, and empirically show that reasoning-level signals remain reliable on out-of-distribution samples while answer-level signals do not. We instantiate this as Reasoning Portability (RP) and propose Reasoning-based Dynamic Balance Continual Learning (RDB-CL), which modulates the per-sample Kullback-Leibler regularization in RLVR according to RP: a tight anchor preserves reusable reasoning on high-RP samples, while a relaxed anchor on low-RP samples permits exploration of new reasoning pathways. Experiments show that RDB-CL consistently outperforms baselines, improving Last accuracy by +12.0% over the vanilla RLVR baseline.

Continual learning enables neural networks to learn tasks sequentially without forgetting previously acquired knowledge. However, neural networks suffer from catastrophic forgetting, where learning new tasks degrades performance on earlier ones. We address this problem with Shapley Neuron Valuation (SNV), a principled framework that quantifies Neuron importance in continual learning, grounded in cooperative game theory. SNV selectively freezes important Neurons while keeping others plastic, enabling buffer-free continual learning without expanding architecture. Experiments on ImageNet-1k show that SNV consistently outperforms existing buffer-free methods. In particular, SNV improves accuracy by +2.88% in the class incremental learning and +6.46% in the task incremental learning scenarios compared to the second baseline.

Continual learning (CL) aims to train models sequentially over multiple domains without forgetting previously learned knowledge. However, existing CL methods optimize for in-domain performance and are therefore prone to learning spurious, domain-specific cues (``shortcut learning''), which limits generalization to unseen domains after deployment. In this paper, we address this limitation through continual learning of domain-invariant representation. We introduce a broad class of CL methods that sequentially learn representations capturing invariant structures across domains. Our methods are motivated by the observation that such invariant structures often preserve the underlying causal mechanisms, which can reduce the risk of overfitting to domain-specific cues and thus offer better out-of-domain generalization. Our proposed CL methods combine replay-based training with a tailored sequential invariance alignment to learn -- and preserve -- invariant structures over time. We evaluate our methods under a deployment-oriented protocol that measures performance on unseen target domains. Across six benchmark and real-world datasets spanning vision, medicine, manufacturing, and ecology, our methods consistently outperform existing CL baselines in terms of generalization to unseen target domains. As an ablation, we further show that naïve extensions of sequential training with existing domain-invariant representation learning (DIRL) methods provide only limited benefits. To the best of our knowledge, this is the first work to develop domain-invariant representation methods for CL.

State-of-the-art diffusion models often rely on parameter-efficient fine-tuning to perform specialized image editing tasks. However, real-world applications require continual adaptation to new tasks while preserving previously learned knowledge. Despite the practical necessity, continual learning for image editing remains largely underexplored. We propose ACE-LoRA, a dynamic regularization framework for continual image editing that effectively mitigates catastrophic forgetting. ACE-LoRA leverages Adaptive Orthogonal Decoupling to identify and orthogonalize task interference, and introduces a Rank-Invariant Historical Information Compression strategy to address scalability issues in continual updates. To facilitate continual learning in image editing and provide a standardized evaluation protocol, we introduce CIE-Bench, the first comprehensive benchmark in this domain. CIE-Bench encompasses diverse and practically relevant image editing scenarios with a balanced level of difficulty to effectively expose limitations of existing models while remaining compatible with parameter-efficient fine-tuning. Extensive experiments demonstrate that our method consistently outperforms existing baselines in terms of instruction fidelity, visual realism, and robustness to forgetting, establishing a strong foundation for continual learning in image editing.

Continual learning in multimodal large language models (MLLMs) aims to sequentially acquire knowledge while mitigating catastrophic forgetting, yet existing methods face inherent limitations: architecture-based approaches incur additional computational overhead and often generalize poorly to new tasks, rehearsal-based methods rely on storing historical data, raising privacy and storage concerns, and conventional regularization-based strategies alone are insufficient to fully prevent parameter interference. We propose Octopus, a two-stage continual learning framework based on History-Free Gradient Orthogonalization (HiFGO), which enforces gradient-level orthogonality without historical task data. Our proposed two-stage finetuning strategy decouples task adaptation from regularization, achieving a principled balance between plasticity and stability. Experiments on UCIT show that Octopus establishes state-of-the-art performance, surpassing prior SOTA by 2.14% and 6.82% in terms of Avg and Last.

Continual learning requires models to adapt to new data while preserving previously acquired knowledge. At its core, this challenge can be viewed as principled one-step adaptation: incorporating new information with minimal interference to existing representations. Most existing approaches address this challenge by modifying model parameters or architectures in a supervised, task-specific manner. However, the underlying issue is representational: tasks require distinct yet structured representations that can be selectively updated without disrupting representations, while structure should reflect intrinsic organization in the data rather than task boundaries. In sequential data, time-delayed dependencies provide a natural signal for uncovering this organization, revealing how fundamental representations give rise to more specific ones. Inspired by the modular organization of the human brain, we propose MoRe, a framework that identifies modularity in the representation itself rather than allocating it at the architectural level. MoRe decomposes knowledge into a hierarchy of fundamental and specific modules with identifiability guarantees, enabling principled module reuse, alignment, and expansion during adaptation while preserving old modules by construction. Experiments on synthetic benchmarks and real-world LLM activations demonstrate interpretable hierarchical structure, improved plasticity-stability trade-offs, suggesting MoRe as a principled foundation for continual adaptation

This paper presents a multi-stage framework for detecting reclaimed slurs in multilingual social media discourse. It addresses the challenge of identifying reclamatory versus non-reclamatory usage of LGBTQ+-related slurs across English, Spanish, and Italian tweets. The framework handles three intertwined methodological challenges like data scarcity, class imbalance, and cross-linguistic variation in sentiment expression. It integrates data-driven model selection via cross-validation, semantic-preserving augmentation through back-translation, inductive transfer learning with dynamic epoch-level undersampling, and domain-specific knowledge injection via masked language modeling. Eight multilingual embedding models were evaluated systematically, with XLM-RoBERTa selected as the foundation model based on macro-averaged F1 score. Data augmentation via GPT-4o-mini back-translation to alternate languages effectively tripled the training corpus while preserving semantic content and class distribution ratios. The framework produces four final runs for the evaluation purposes where RUN 1 is inductive transfer learning with augmentation and undersampling, RUN 2 with masked language modeling pre-training, RUN 3 and RUN 4 are previous predictions refined via language-specific decision thresholds optimized via ROC analysis. Language-specific threshold refinement reveals that optimal decision boundaries vary significantly across languages. This reflects distributional differences in model confidence scores and linguistic variation in reclamatory language usage. The threshold-based optimization yields 2-5% absolute F1 improvement without requiring model retraining. The methodology is fully reproducible, with all code and experimental setup available at https://github.com/rbg-research/MultiPRIDE-Evalita-2026.

Data mixing decides how to combine different sources or types of data and is a consequential problem throughout language model training. In pretraining, data composition is a key determinant of model quality; in continual learning and adaptation, it governs what is retained and acquired. Yet existing data mixing methods address only one phase of this lifecycle at a time: some require smaller proxy models tied to a single training phase, others assume a fixed domain set, and continual learning lacks principled guidance altogether. We argue that data mixing is fundamentally an online decision making problem -- one that recurs throughout training and demands a single, unified solution. We introduce OP-Mix (On-Policy Mix), a data mixing algorithm that operates across the entire language model training lifecycle. Our main insight is that candidate data mixtures can be cheaply simulated by interpolating between low-rank adapters trained directly on the current model, eliminating separate proxy models and ensuring the search is always grounded in the model's actual learning dynamics. Across pretraining, continual midtraining, and continual instruction tuning, OP-Mix consistently finds near-optimal mixtures while using a fraction of the compute of the baselines. In pretraining, OP-Mix improves upon training without mixing by 6.3% in average perplexity. For continual learning, OP-Mix matches the performance of both retraining and on-policy distillation while using 66% and 95% less overall compute, respectively. OP-Mix suggests a different view of language model training: not a sequence of distinct phases, but a single continuous process of learning from data.

Large language-vision models (LVLMs) such as CLIP, Flamingo, and BLIP have revolutionized AI by enabling understanding across textual and visual modalities. These models excel at tasks like image captioning, visual question answering, and cross-modal retrieval. However, they face catastrophic forgetting when learning new tasks sequentially, particularly challenging in multi-modal settings where preserving cross-modal alignments adds complexity to the learning process. This paper presents a comprehensive continual learning framework for LVLMs that combines enhanced Elastic Weight Consolidation (EWC) with parameter-efficient fine-tuning techniques. We integrate multi-modal Fisher Information Matrix calculation, consistency preservation across modalities, and adaptive regularization that considers dependencies across visual and textual encoders. The framework achieves a 78% reduction in forgetting rates relative to naive sequential training approaches through extensive evaluation testing. The framework also preserves alignment between modalities during sequential learning with only 15% additional computational cost. This work advances the state of the art in lifelong learning for multi-modal AI systems, with direct applications to autonomous driving, intelligent robotic assistants, and adaptive robotic systems that must continuously learn in dynamic real-world environments.

LoRA is widely adopted for continual fine-tuning of Large Language Models due to its parameter efficiency, modularity across tasks, and compatibility with replay strategies. However, LoRA-based continual learning remains vulnerable to catastrophic forgetting, whose severity depends on how successive task gradients interact: when consecutive task gradients conflict, standard adapter initializations channel updates into subspaces that overwrite previously learned directions. We propose SLICE, a gradient-surgery-based initialization for LoRA adapters in continual learning. SLICE accumulates gradients from both the current task and a replay buffer of prior tasks, reconciles them through a projection operator, and decomposes the result via truncated SVD to initialize the adapter weights. We evaluate SLICE on the TRACE benchmark and sequences of Super-NI tasks, including a set of adversarial Super-NI sequences that we construct by mining task pairs with maximally opposing gradients. Compared to vanilla LoRA, LoRA-GA, and LoRAM, SLICE consistently achieves a better stability-plasticity trade-off, improving Average Performance, Final Performance and Forgetting metrics while preserving General Performance and In Context Performance across both standard and adversarial continual learning sequences.

Enabling Large Language Models (LLMs) to continuously improve from environmental interactions is a central challenge in post-training. While on-policy self-distillation offers a promising paradigm, existing methods predominantly treat environmental feedback as a passive conditioning signal. Consequently, they heavily rely on successful demonstrations and struggle to learn in rare-success regimes. To bridge this gap, we introduce Reflection-Enhanced Self-Distillation (RESD), a framework that transforms raw failure feedback into an active source of corrective supervision. Instead of passively appending feedback, RESD interprets failed trajectories by generating retrospective reflections to diagnose local errors, and curates a persistent global playbook to preserve reusable lessons across training steps. The enriched context enables the self-teacher to provide actionable token-level supervision even in the absence of successful rollouts. Empirical evaluations on multiple continual learning tasks demonstrate that RESD substantially outperforms standard self-distillation baselines. Furthermore, RESD achieves significantly faster early-stage improvement than GRPO with $8\times$ samples using only a single rollout per prompt, highlighting its superior interaction efficiency.

Catastrophic forgetting remains the central obstacle in continual learning (CL): parameters shared across tasks interfere with one another, and existing regularization methods such as EWC and SI apply uniform penalties without awareness of which input region a parameter serves. We propose KAN-CL, a continual learning framework that exploits the compact-support spline parameterization of Kolmogorov-Arnold Networks (KANs) to perform importance-weighted anchoring at per-knot granularity. Deployed as a classification head on a convolutional backbone with standard EWC regularization on the backbone (bbEWC) KAN-CL achieves forgetting reductions of 88% and 93% over a head-only KAN baseline on Split-CIFAR-10/5T and Split-CIFAR-100/10T respectively, while matching or exceeding the accuracy of all baselines on both benchmarks. We further provide a Neural Tangent Kernel (NTK) analysis showing that KAN's spline locality induces a structural rank deficit in the cross-task NTK, yielding a forgetting bound that holds even in the feature-learning regime. These results establish that combining an architecture with natural parameter locality (KAN head) with a complementary backbone regularizer (bbEWC) yields a compositional and principled approach to catastrophic forgetting.

Advancements in reinforcement learning have produced a variety of complex and useful intrinsic driving forces; crucially, these drivers operate under a direct conditioning paradigm. This form of conditioning limits our agents' capacity by restricting how they learn from the environment as well as from others. Off-policy or learn-by-example methods can learn from demonstrators' representations, but they require access to the demonstrating agent's policies or their reward functions. Our work overcomes this direct sampling limitation by introducing vicarious conditioning as an intrinsic reward mechanism. We draw from psychological and biological literature to provide a foundation for vicarious conditioning and use memory-based methods to implement its four steps: attention, retention, reproduction, and reinforcement. Crucially, our vicarious conditioning paradigms support low-shot learning and do not require the demonstrator agent's policy nor its reward functions. We evaluate our approach in the MiniWorld Sidewalk environment, one of the few public environments that features a non-descriptive terminal condition (no reward provided upon agent death), and extend it to Box2D's CarRacing environment. Our results across both environments demonstrate that vicarious conditioning enables longer episode lengths by discouraging the agent from non-descriptive terminal conditions and guiding the agent toward desirable states. Overall, this work emulates a cognitively-plausible learning paradigm better suited to problems such as single-life learning or continual learning.

Data-free continual learning (DFCIL) relies on model inversion to synthesize pseudo-samples and mitigate catastrophic forgetting. However, existing inversion methods are fundamentally limited by a simplifying assumption: they model feature distributions using diagonal covariance, effectively ignoring correlations that define the geometry of learned representations. As a result, synthesized samples often lack fidelity, limiting knowledge retention. In this work, we show that modeling feature dependencies is a key ingredient for effective DFCIL. We introduce REMIX, a structured covariance modeling framework that enables scalable full-covariance modeling without the prohibitive cost of dense matrix inversion and log-determinant computation. By leveraging a Laplace kernel parameterization, REMIX captures structured feature dependencies using memory that scales linearly with the feature dimensionality, while requiring only an additional logarithmic factor in computation. Modeling these correlations produces more coherent synthetic samples and consistently improves performance across standard DFCIL benchmarks. Our results demonstrate that moving beyond diagonal assumptions is essential for effective and scalable data-free continual learning. Our code is available at https://github. com/pkrukowski1/REMIX-Model-Inversion-via-Laplace-Kernel.

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.

Object-centric representations promise a key property for few-shot learning: Rather than treating a scene as a single unit, a model can decompose it into individual object-level parts that can be matched and compared across different concepts. In practice, this potential is rarely realized. Continual learners either collapse scenes into global embeddings, or train with part-level matching objectives that tie representations too closely to seen patterns, leaving them unable to generalize to truly novel concepts. In this paper, we identify this fundamental structural conflict and pioneer a new paradigm that strictly decouples representation learning from compositional inference. Leveraging the inherent patch-level semantic geometry of self-supervised Vision Transformers (ViTs), our framework employs a dual-phase strategy. During training, slot representations are optimized entirely toward holistic class identity, preserving highly generalizable, object-level geometries. At inference, preserved slots are dynamically composed to match novel scenes. We demonstrate that this paradigm offers dual structural benefits: The frozen backbone naturally prevents representation drift, while our lightweight, holistic optimization preserves the features' capacity for novel-concept transfer. Extensive experiments validate this approach, achieving state-of-the-art unseen-concept generalization and minimal forgetting across standard continual learning benchmarks.

Split Federated Learning (SplitFed) combines federated and split learning to preserve privacy while reducing client-side computation. However, in medical image segmentation, heterogeneous label quality across clients can significantly degrade performance. We propose SplitFed-CL, a co-learning framework where a global teacher guides local students to detect and refine unreliable annotations. Reliable labels supervise training directly, while unreliable labels are corrected via weighted student--teacher refinement. SplitFed-CL further incorporates consistency regularization for robustness to input perturbations and a trainable weighting module to balance loss terms adaptively. We also introduce a novel difficulty guided strategy to simulate human like boundary centric annotation errors, where the degree of perturbation is governed by shape complexity and the associated annotation difficulty. Experiments on two multiclass segmentation datasets with controlled synthetic noise, together with a binary segmentation dataset containing real-world annotation errors, demonstrate that SplitFed-CL consistently outperforms seven state-of-the-art baselines, yielding improved segmentation quality and robustness.

Continual learning requires new-task adaptation without damaging previously acquired capabilities. Recent forward-pass and zeroth-order (ZO) results show that low-query adaptation may retain better than first-order (FO) descent, but the usual view of ZO as noisy FO estimation does not explain why. We give a local randomized gradient-shaping analysis: finite differences expose a raw shape that is mean-aligned with FO, while the norm-matched comparator fixes the expected squared adaptation norm. Under this controlled comparison, forgetting depends on how the adaptation shape exposes retention curvature. For norm-matched ZO, the expected shaped retention curvature obeys an exact identity that preserves the isotropic retention floor while contracting only the anisotropic component. Projecting this identity onto the incoming gradient yields the observable FO--ZO quadratic forgetting gap: ZO improves mean forgetting precisely when the FO direction has above-average retention curvature, by a query-dependent fraction of that curvature excess. A practical finite-query accounting separates the mean mechanism from one-batch sampling and smoothing perturbations. As an algorithmic transfer, RISE applies the calibrated ZO shape to exact FO gradients inside parameter blocks. Its target is a stability--plasticity tradeoff: randomized shaping may reduce the retention exposure paid by FO, exact gradients remove finite-smoothing bias from finite-difference ZO, and blockwise sampling supplies many local shaping directions after one gradient computation. The blockwise analysis separates mean-step damage from centered random exposure, showing how block-diagonal curvature, cross-block coupling, and local shaping diagnostics specify where this exact-gradient transfer is most likely to be visible.

Most language-model training data shows final artifacts, not the process that produced them. We study a tractable version of this question in tool use: when a model learns a stream of new API domains, does keeping tool-use trajectories help compared with stripping the intermediate API trace? We fine-tune Llama 3.1 8B Instruct with QLoRA on API-Bank using four sequential domain blocks. Condition A strips previous API request/response lines from the prompt and trains the model to predict the next API call. Condition B keeps the trajectory context. In a single-seed pilot, full held-out generation evaluation shows that Condition B reaches 56.9% final exact full-call accuracy compared with 39.2% for Condition A. B also improves final API-name accuracy by 7.7 points. However, B uses 25.1% more training tokens, the run uses one seed, and the task is next-call prediction rather than full dialogue success.

Continual learning studies how models can adapt to new tasks while retaining previously acquired knowledge. Although a broad spectrum of methods has been proposed to mitigate catastrophic forgetting, the field remains predominantly performance-driven, with limited insight into what forgetting actually corresponds to within the vision model's representation space. Prior work has primarily analyzed forgetting through task-level performance or coarse measures of representational drift, without disentangling output-level accessibility from changes in finer-grained internal structure. To this end, we propose a diagnostic framework that leverages Sparse Autoencoders (SAEs) to define a task-anchored latent feature space, enabling analysis of how task-specific information evolves at a finer granularity, where individual SAE latents are treated as concept proxies for recurring and relatively disentangled visual patterns in the model's internal computations. Within this framework, we decompose forgetting into apparent concept deletion, recoverability, and decodability. We show that a large portion of seemingly lost concept-level information can often be recovered under linearity assumption, with concept decodability degrading as more tasks are introduced. Overall, our findings suggest that a significant part of concept-level forgetting can be attributed to changes in the representational accessibility rather than complete information erasure.

As over 200 million new malware samples are identified each year, antivirus systems must continuously adapt to the evolving threat landscape. However, retraining solely on new samples leads to catastrophic forgetting and exploitable blind spots, while retraining on the entire dataset incurs substantial computational cost. We propose FreeMOCA, a memory- and compute-efficient continual learning framework for malicious code analysis that preserves prior knowledge via adaptive layer-wise interpolation between consecutive task updates, leveraging the fact that warm-started task optima are connected by low-loss paths in parameter space. We evaluate FreeMOCA in both class-incremental (Class-IL) and domain-incremental (Domain-IL) settings on large-scale Windows (EMBER) and Android (AZ) malware benchmarks. FreeMOCA achieves substantial gains in Class-IL, outperforming 11 baselines on both EMBER and AZ benchmarks. It also significantly reduces forgetting, achieving the best retention across baselines, and improving accuracy by up to 42% and 37% on EMBER and AZ, respectively. These results demonstrate that warm-started interpolation in parameter space provides a scalable and effective alternative to replay for continual malware detection. Code is available at: https://github.com/IQSeC-Lab/FreeMOCA.

Recent studies suggest that Reinforcement Fine-Tuning (RFT) is inherently more resilient to catastrophic forgetting than Supervised Fine-Tuning (SFT). However, whether RFT (e.g., GRPO) can effectively overcome forgetting in challenging visual continual learning settings, such as class-incremental learning (CIL) and domain-incremental learning (DIL), remains an open problem. Through a pilot study, we confirm that while RFT consistently outperforms SFT, it still suffers from non-negligible forgetting. We empirically trace this bottleneck to Trajectory-level Drift Agnosticism: among candidate rollouts achieving identical task rewards, the KL divergence from the preceding-task policy varies substantially, which strongly correlates with catastrophic forgetting across sequential tasks. Motivated by this insight, we propose Retention-aware Policy Optimization (RaPO), a simple yet effective RFT method that explicitly mitigates forgetting through trajectory-level reward shaping. Specifically, RaPO comprises two core components: (1) Retention Reward that converts trajectory-level distribution drift into a continuous reward signal, preferentially reinforcing knowledge-preserving rollouts within each group; (2) Cross-Task Advantage Normalization (CTAN), which maintains a persistent exponential moving average of reward statistics across task boundaries to stabilize the optimization progress during continual learning. Leveraging the free-form textual generalization of MLLMs, we comprehensively evaluate RaPO across five visual continual learning settings. Extensive experiments demonstrate that RaPO achieves leading performance, substantially reducing catastrophic forgetting while preserving strong plasticity. To the best of our knowledge, this work represents the first systematic exploration of RFT in visual continual learning, offering insights that we hope will inspire future research.

While Large Language Models (LLMs) have catalyzed progress in embodied intelligence, a fundamental gap between their inherent probabilistic uncertainty and the strict determinism and verifiable safety required in the physical world. To mitigate this gap, this paper introduces NEXUS, a modular framework designed for continual learning in embodied agents. Different from prior works that treat symbolic artifacts merely as static interfaces, NEXUS leverages them for symbolic grounding and knowledge evolution. The framework explicitly decouples physical feasibility from safety specifications: capability of agents is improved through closed-loop execution feedback, while probabilistic risk assessments are grounded into deterministic hard constraints to establish a rigorous pre-action defense. Experiments on SafeAgentBench demonstrate that NEXUS achieves superior task success rates while effectively refusing unsafe instructions, exhibiting robust defense against adversarial attacks, and progressively improving planning efficiency through knowledge accumulation.

Deep continual learning requires models to adapt to new tasks without retraining from scratch. However, neural networks can lose their ability to adapt to new tasks after training on previous ones, a phenomenon known as loss of plasticity. There have been several explanations and diagnostics proposed for plasticity loss. Motivated by the philosophy that "all models are wrong, but some are useful", we ask: can existing diagnostics predict a neural network's plasticity? In this work, we take a practical view to interpret plasticity as trainability, i.e., a neural network's future optimization gain on a target task. We first take a theoretical approach, showing, by constructing a few counterexamples, that some widely adopted diagnostics of plasticity, including representation rank and neural tangent kernel rank, can fail to predict the loss of trainability in both regression and classification settings. We instead propose a novel metric, called optimization readiness, which combines gradient strength and gradient reliability. We prove that optimization readiness lower bounds one-step optimization gain under standard smoothness assumptions, providing a theoretical guarantee for its predictive power. Empirically, we show that across commonly used deep continual learning settings, such as Slowly-Changing Regression and Permuted MNIST, optimization readiness more reliably ranks checkpoints by trainability than prior diagnostics, even with substantially fewer samples.

A central challenge in continual learning for large language models (LLMs) is catastrophic forgetting, where adapting to new tasks can substantially degrade performance on previously learned ones. Existing projection-based methods mitigate such interference by restricting parameter updates to subspaces that are orthogonal to directions associated with past tasks. However, these methods are typically formulated under Euclidean parameter geometry, with update magnitudes and projections governed by the Frobenius norm. The recent empirical success of the Muon optimizer, which applies orthogonalized matrix updates and admits a spectral-norm interpretation, suggests that Frobenius geometry may not be the most effective choice for matrix-valued LLM parameters. Motivated by this observation, we propose Muon-OGD, a spectral-norm-aware continual learning framework that integrates Muon-style operator-norm geometry with orthogonal projection constraints. Our method formulates each update as a spectral-norm-constrained optimization problem with linear non-interference constraints, and solves it efficiently through dual iterations and Newton--Schulz matrix-sign approximations. By applying orthogonalized momentum updates that avoid protected directions associated with prior tasks, Muon-OGD aims to improve the stability--plasticity trade-off in sequential LLM adaptation. We evaluate the proposed method on standard continual learning benchmarks, TRACE, and domain-specific Coding--Math--Medical curricula using both encoder--decoder and decoder-only architectures. Empirically, Muon-OGD consistently improves over sequential fine-tuning and competitive orthogonal-gradient baselines, while remaining computationally scalable. These results suggest that spectral-norm-aware update geometry provides a practical and effective alternative to Frobenius-norm projection for continual learning in LLMs.

Online learning from a stream of data is a defining feature of intelligence, yet modern machine learning systems often struggle in this setting, especially under distributional shift. To understand its basic properties, we study the relationship between online and offline learning in the context of kernel regression. We derive a closed-form expression for the function learned by online kernel regression, revealing that online kernel regression is equivalent to offline regression with shifted, inaccurate target outputs. Conversely, we show that by compensating for this effective shift in the teaching signal through target correction, online kernel-based learning can provably learn the same predictor as its offline counterpart. We derive both a closed-form expression for this target correction and an iterative form that can be applied sequentially. Applying this framework to image classification tasks on CIFAR-10 and CORe50, we show that online stochastic gradient descent with iteratively corrected targets outperforms learning with the true targets in continual learning settings. This work therefore provides a basic framework for analyzing and improving online learning in non-stationary environments.

Model merging provides a compelling paradigm for integrating specialized expertise into a unified multi-task model, a goal that aligns naturally with the sequential knowledge acquisition in continual learning (CL). However, the requirement for preserving diverse forms of previous knowledge conflicts with the storage limitations inherent to CL. In this paper, we systematically analyze existing model merging methods under the constraints of CL. We find that current methods prioritize global alignment, which often leads to the accumulation and amplification of task-specific errors within the continuous data stream; and the vanishing gradients at the onset of subsequent tasks frequently cause optimization to stagnate. These leave the merged model in a suboptimal state at the beginning of the next training phase. To address these challenges, we propose Trajectory Regularized Merging (TRM), a framework that reformulates the merging phase as an optimization process within an augmented trajectory subspace. Our framework integrates three synergistic objectives including task alignment, prediction consistency, and gradient responsiveness to concurrently preserve merged model's historical stability and re-activate optimization dynamics. Extensive experimental results demonstrate that our method achieves state-of-the-art performance across multiple benchmarks.

Class-incremental learning aims to continuously acquire new knowledge while preserving previously learned information, thereby mitigating catastrophic forgetting. Existing methods primarily restrict parameter updates but often overlook their structural properties in high-dimensional spaces. From a subspace perspective, updates induced by different tasks tend to lie in multiple overlapping low-rank subspaces, leading to cross-task subspace interference and severe forgetting. To address this issue, we propose HDSD, a Hierarchical Dual-Subspace Decoupling framework for continual learning in vision-language models. Specifically, we introduce a lightweight Feature Modulation Module (FMM) that explicitly decomposes the parameter space into general and task-specific subspaces. Building on this design, we develop two complementary components. First, a General Fusion Module (GFM) evaluates relative parameter changes across tasks and uses an adaptive threshold to capture stable and transferable knowledge. Second, a Hierarchical Learning Module (HLM) performs structured parameter decomposition via Singular Value Decomposition (SVD) and uses a scaling mechanism to constrain updates within distinct subspace scales. Together, these designs reduce subspace interference and parameter drift. Extensive experiments on conventional benchmarks show that HDSD achieves state-of-the-art results.

Continual learning enables vision-language models to accumulate knowledge and adapt to evolving tasks without retraining from scratch. However, in multi-domain task-incremental learning, large domain shifts intensify the stability-plasticity dilemma. Most existing methods rely on fixed architectures with statically allocated parameters, which limits adaptation to new domains and aggravates catastrophic forgetting. To address these challenges, we propose DIMoE-Adapters, a Dynamic Incremental Mixture-of-Experts Adapters framework that introduces a dynamic expert evolution paradigm to balance stability and plasticity. This paradigm is implemented through two collaborative components: Self-Calibrated Expert Evolution (SCEE) and Prototype-Guided Expert Selection (PGES). SCEE constructs and evolves a sparse expert pool through expert optimization dynamics, improving plasticity while reducing redundant capacity. PGES controls expert utilization based on the pool shaped by SCEE, improving stability across both previously encountered and unseen tasks. Extensive experiments show that DIMoE-Adapters outperforms previous state-of-the-art methods across various settings.

Recent extensive research has demonstrated that the enhanced reasoning capabilities acquired by models through Reinforcement Learning with Verifiable Rewards (RLVR) are primarily concentrated within the rank-1 components. Predicated on this observation, we employed Periodic Rank-1 Substitution and identified a counterintuitive phenomenon: RLVR may exhibit implicit reward overfitting to the training dataset. Specifically, the model can achieve satisfactory performance on the test set even when its rewards remain relatively low during the training process. Furthermore, we characterize three distinct properties of RL training: (1) The effective rank-1 component in RLVR don't maintain other model knowledge except mathematical reasoning capability. (2) RLVR fundamentally functions by optimizing a specific singular spectrum. The distribution of singular values of almost all linear layers in RLVR-trained model behaves like heavy-tailed distribution. (3) the left singular vectors associated with rank-1 components demonstrate a stronger alignment tendency during training, which echoes the discovery that RLVR is optimizing sampling efficiency in essence. Taken together, our findings and analysis further reveal how RLVR shapes model parameters and offer potential insights for improving existing RL paradigms or other training paradigms to implement continual learning.

Channel state information (CSI)-based human activity recognition (HAR) is vulnerable to performance degradation under domain shifts across varying physical environments. Continual learning (CL) offers a principled way to learn new domains sequentially while preserving past knowledge, but existing CL solutions for CSI-based HAR scale poorly with accumulating domains, rely on a large replay buffer, or incur linearly growing inference cost. In this letter, we propose Scene-Adaptive Mixture of Experts with Clustered Specialists (SAMoE-C), which formulates cross-domain CSI-based HAR as a mixture-of-experts system that enables scene-specific adaptation, via an attention-based semantic router that activates only selected experts for each input. Moreover, we develop a novel training protocol, which requires only a tiny replay buffer for stabilizing domain discrimination of the router. Experimental results on a four-scene CSI dataset demonstrate that SAMoE-C approaches the state-of-the-art accuracy, while maintaining a significantly lower inference cost. By jointly combining modular experts, selective activation with router and a lightweight training protocol, SAMoE-C enables scalable cross-domain CSI-based HAR deployment with low training overhead and high computational efficiency in real-world settings.

Continual learning (CL) is essential for deploying medical image segmentation models in clinical environments where imaging domains, anatomical targets, and diagnostic tasks evolve over time. However, continual segmentation still faces three main challenges. First, the scenarios for this task remain insufficiently standardized for real-world clinical settings. Second, existing research has been primarily focused on mitigating forgetting, overlooking the other essential properties such as plasticity. Third, a benchmark work with comprehensive evaluation on existing methods is stll desirable. To address these gaps, we present such benchmark study of continual medical image segmentation. We first define three clinically motivated scenarios, namely Domain-CL, Class-CL, and Organ-CL, to respectively capture the cross-center domain shift, the incremental anatomical structure segmentation, and the cross-organ segmentation. We then introduce an evaluation framework that measures not only general performance and forgetting, but also plasticity, forward generalizability, parameter efficiency, and replay burden. The results, from extensive experiments with representative CL methods, showed that it was still challenging to develop a model that could satisfy all the requirements simultaneously. Nevertheless, these studies also suggested that the replay-based methods achieve the best overall balance between stability and plasticity, the parameter-isolation methods should be effective at reducing forgetting, though at the cost of increased model size, and the forward generalizability remain a significantly understudied aspect of this research field. Finally, we discuss related learning paradigms and outline future directions for continual medical image segmentation.