Continual Learning for LLMs

Modern LLMs show mastery over an ever-growing range of skills, as well as the ability to compose them flexibly. However, extending model capabilities to new skills in a scalable manner is an open problem: fine-tuning and parameter-efficient variants risk catastrophic forgetting, while context-based approaches have limited expressiveness and are constrained by the model's effective context. We explore skill neologisms--soft tokens integrated in the model's vocabulary and optimized to improve capabilities over a specific skill--as a way to selectively acquire new skills without weight updates. We first observe that pre-trained LLMs already exhibit tokens associated with procedural knowledge. We then show on a controlled synthetic task that skill neologisms can be learned to improve model capabilities on specific skills while being composable with out-of-distribution skills, and that independently trained skill neologisms can be composed zero-shot. Finally, we validate zero-shot composition of independently learned skill neologisms on the more realistic natural language setting of the Skill-Mix benchmark. These results suggest that skill neologisms may provide a scalable path towards skill-based continual learning.

Post-training large language models (LLMs) often suffers from catastrophic forgetting, where improvements on a target objective degrade previously acquired capabilities. Recent evidence suggests that this phenomenon is primarily driven by excessive distributional drift during optimization. Motivated by this perspective, we propose Anchored Learning, a simple framework that explicitly controls distributional updates during offline fine-tuning via a dynamically evolving moving anchor. Instead of matching a fixed reference distribution, the anchor interpolates between the current model and a frozen reference to construct an intermediate target that the model distills toward, transforming global fine-tuning into a sequence of local trust-region updates in distribution space. Theoretically, we prove this anchor-based update admits a linear KL-divergence upper bound per iteration, ensuring a stable transition between model distributions. Extensive experiments on iGSM, MedCalc, and IFEval show that Anchored Learning consistently lies on the Pareto frontier of gain-stability trade-offs, achieving near-optimal performance improvements while substantially reducing degradation compared to strong baselines. For example, while standard SFT suffers from over 53% performance degradation on iGSM and MedCalc, Anchored Learning slashes this drop to under 5% while maintaining near-optimal gains (e.g., 75.2% on iGSM).

Continual incorporation of new knowledge is essential for the long-term evolution of large language models (LLMs). Existing approaches typically rely on parameter-update algorithms to mitigate catastrophic forgetting, yet they suffer from fundamental limitations: 1) forgetting is unavoidable as the amount of newly injected knowledge grows; and 2) model updates are often irreversible. As modern LLMs become increasingly expressive, it is natural to question whether large-scale weight updates are necessary for acquiring a small amount of new knowledge. In this work, we propose a principled framework that models autoregressive language generation as a Markov process over tokens, where model memory is represented by a Markov transition matrix. Under this formulation, incorporating new knowledge/tokens corresponds to extending the state space, and preserving existing transitions guarantees retention of previously learned knowledge. We then prove a sample complexity bound for incorporating new tokens via a token-to-dictionary mapping strategy. In particular, for learning the transition behavior of each new token, the required number of samples scales linearly with the number of existing tokens it is mapped to. To realize this mapping, we propose an embedding-tuning algorithm that requires minimal parameter updates and induces zero forgetting. Experimental results further demonstrate the effectiveness of our method and validate our theoretical findings.

Large language models (LLMs) have become a central foundation of modern artificial intelligence, yet their lifecycle remains constrained by a rigid separation between training and deployment, after which learning effectively ceases. This limitation contrasts with natural intelligence, which continually adapts through interaction with its environment. In this paper, we formalise deployment-time learning (DTL) as the third stage in the LLM lifecycle that enables LLM agents to improve from experience during deployment without modifying model parameters. We present CASCADE (CASe-based Continual Adaptation during DEployment), a general and principled framework that equips LLM agents with an explicit, evolving episodic memory. CASCADE formulates experience reuse as a contextual bandit problem, enabling principled exploration-exploitation trade-offs and establishing no-regret guarantees over long-term interactions. This design allows agents to accumulate, select, and refine task-relevant cases, transforming past experience into actionable knowledge. Across 16 diverse tasks spanning medical diagnosis, legal analysis, code generation, web search, tool use, and embodied interaction, CASCADE improves macro-averaged success rate by 20.9% over zero-shot prompting while consistently outperforming gradient-based and memory-based baselines. By reframing deployment as an adaptive learning process, this work establishes a foundation for continually improving AI systems.

Vision-language-action (VLA) models have advanced the field of embodied manipulation by harnessing broad world knowledge and strong generalization. However, current VLA models still face several key challenges, including limited reasoning capability, lack of status monitoring, and difficulty in self-correction. In this paper, we introduce \textbf{Sentinel-VLA}, a metacognitive VLA model equipped with an active ``sentinel'' module to monitor real-time execution status. Only when necessary, such as during initial planning or upon detecting an error, the model triggers a dynamic reasoning or formulate error recovery solutions. This on-demand reasoning mechanism ensures robust decision-making while minimizing computational overhead. Notably, all training data (spanning 44 tasks and over 2.6 million transitions) is automatically generated and annotated through our designed pipeline. We also propose the Self-Evolving Continual Learning (SECL) algorithm, which allows Sentinel-VLA to identify its capability boundaries and automatically collect data for expansion, paired with Orthogonal Continual Adapter (OC-Adapter) to constrain parameter updates to an orthogonal space, thereby preventing catastrophic forgetting. Real-world experiments demonstrate that Sentinel-VLA boosts the task success rate by over 30% compared to the SOTA model, PI0. We will open-source all the code, weights, and data generation pipeline.

Continual learning for large language models is typically evaluated through accuracy retention under sequential fine-tuning. We argue that this perspective is incomplete, because uncertainty reliability can degrade earlier and more sharply than top-1 performance. We study this empirically by measuring conformal coverage and calibration error on sequentially fine-tuned models across three model families and eight task sequences drawn primarily from classification and multiple-choice benchmarks. Across the classification-style settings we study, coverage loss exceeds accuracy loss by a factor of roughly $3.4\times \pm 0.5\times$ on average across seeds; in the most pronounced case, coverage drops from $0.92$ to $0.61$, while accuracy remains within three points of baseline. Standard continual-learning methods that preserve accuracy do not automatically preserve coverage, and naive calibration baselines recover only part of the gap. We propose calibration replay, a lightweight post-hoc procedure that maintains a task-specific held-out buffer and refits a task-specific conformal threshold under the current model after each update. It adds no training-time gradient cost, uses less than one percent of the memory of ordinary experience replay, and typically restores coverage to within two points of nominal at buffer size $m = 200$. We accompany the empirical study with a drift decomposition, a finite-sample recovery theorem showing exact conformal validity under exchangeability, and a mixture-validity proposition explaining why pooled thresholds do not suffice. Our guarantees are stated for classification-style tasks with task-specific buffers; extensions to open-ended generation are exploratory.

Recent advances in formal theorem proving have focused on Olympiad-level mathematics, leaving undergraduate domains largely unexplored. Optimization, fundamental to machine learning, operations research, and scientific computing, remains underserved by existing provers. Its reliance on domain-specific formalisms (convexity, optimality conditions, and algorithmic analysis) creates significant distribution shift, making naive domain transfer ineffective. We present OptProver, a trained model that achieves robust transfer from Olympiad to undergraduate optimization. Starting from a strong Olympiad-level prover, our pipeline mitigates distribution shift through two key innovations. First, we employ large-scale optimization-focused data curation via expert iteration. Second, we introduce a specialized preference learning objective that integrates perplexity-weighted optimization with a mechanism to penalize valid but non-progressing proof steps. This not only addresses distribution shifts but also guides the search toward efficient trajectories. To enable rigorous evaluation, we construct a novel benchmark in Lean 4 focused on optimization. On this benchmark, OptProver achieves state-of-the-art Pass@1 and Pass@32 among comparably sized models while maintaining competitive performance on general theorem-proving tasks, demonstrating effective domain transfer without catastrophic forgetting.

Many continual-learning methods modify gradients upstream (e.g., projection, penalty rescaling, replay mixing) while treating Adam as a neutral backend. We show this composition has a hidden failure mode. In a high-overlap, non-adaptive 8-domain continual LM, all shared-routing projection baselines collapse close to vanilla forgetting (12.5--12.8 vs. 13.2). A 0.5% replay buffer is the strongest shared alternative but still reaches 11.6, while fixed-strength decoupling falls below vanilla at 14.1. Only adaptive decoupled routing remains stable at 9.4, improving over vanilla by 3.8 units. On a 16-domain stream, its gain over the strongest shared-routing projection baseline grows to 4.5--4.8 units. The failure is largely invisible on clean benchmarks. We explain this effect through Adam's second-moment pathway: in the tested regime, projection induces a 1/(1-alpha) inflation of the old-direction effective learning rate, matching measurements within 8% across eight alpha values. The same conflict appears with penalty methods, replay mixing, and at 7B scale under LoRA. Our fix routes the modified gradient only to the first moment while preserving magnitude-faithful second-moment statistics, with overlap-aware adaptive strength. This simple change is the only tested configuration that consistently avoids collapse across methods, optimizers, and scale.

Large language models (LLMs) often exhibit performance disparities across languages, with naive multilingual fine-tuning frequently degrading performance due to negative cross-lingual interference. To address this, we introduce COMPASS (COntinual Multilingual PEFT with Adaptive Semantic Sampling), a novel data-centric framework for adapting LLMs to target languages. COMPASS leverages parameter-efficient fine-tuning (PEFT) by training lightweight, language-specific adapters on a judiciously selected subset of auxiliary multilingual data. The core of our method is a distribution-aware sampling strategy that uses multilingual embeddings and clustering to identify semantic gaps between existing training data and a target usage distribution. By prioritizing auxiliary data from under-represented semantic clusters, COMPASS maximizes positive cross-lingual transfer while minimizing interference. We extend this into a continual learning framework, COMPASS-ECDA, which monitors for data distribution shifts in production and dynamically updates adapters to prevent model staleness, balancing adaptation to new data with the preservation of existing knowledge. Across three different model architectures (Phi-4-Mini, Llama-3.1-8B, and Qwen2.5-7B) and multiple challenging multilingual benchmarks (Global-MMLU, MMLU-ProX), including unseen long-context tasks (OneRuler), we demonstrate that COMPASS consistently outperforms baseline methods guided by linguistic similarity, providing an effective, efficient, and sustainable solution for developing and maintaining high-performing multilingual models in dynamic environments.

Large language models (LLMs) require frequent knowledge updates to reflect changing facts and mitigate hallucinations. To meet this demand, lifelong knowledge editing has emerged as a continual approach to modify specific pieces of knowledge without retraining the entire model. Existing parameter editing methods struggle with stability during sequential edits due to catastrophic forgetting. While retrieval-based approaches are proposed to alleviate this issue, their applicability remains limited across various datasets because of high training costs. To address these limitations and enhance scalability in lifelong settings, we propose LightEdit. Our framework first selects relevant knowledge from retrieved information to modify the query effectively. It then incorporates a decoding strategy to suppress the model's original knowledge probabilities, thereby enabling efficient edits based on the selected information. Extensive experiments on ZSRE, Counterfact, and RIPE benchmarks demonstrate that LightEdit outperforms existing lifelong knowledge editing methods. Furthermore, by minimizing training costs, LightEdit achieves cost-effective scalability, enabling easy adaptation to various datasets.

Extending a fully post-trained language model with new domain capabilities is fundamentally limited by monolithic training paradigms: retraining from scratch is expensive and scales poorly, while continued training often degrades existing capabilities. We present BAR (Branch-Adapt-Route), which trains independent domain experts, each through its own mid-training, supervised finetuning, and reinforcement learning pipeline, and composes them via a Mixture-of-Experts architecture with lightweight router training. Unlike retraining approaches that mix all domains and require full reprocessing for any update (with cost scaling quadratically), BAR enables updating individual experts independently with linear cost scaling and no degradation to existing domains. At the 7B scale, with experts for math, code, tool use, and safety, BAR achieves an overall score of 49.1 (averaged across 7 evaluation categories), matching or exceeding re-training baselines (47.8 without mid-training, 50.5 with). We further show that modular training provides a structural advantage: by isolating each domain, it avoids the catastrophic forgetting that occurs when late-stage RL degrades capabilities from earlier training stages, while significantly reducing the cost and complexity of updating or adding a domain. Together, these results suggest that decoupled, expert-based training is a scalable alternative to monolithic retraining for extending language models.

Adapting foundation models under resource budgets relies heavily on Parameter-Efficient Fine-Tuning (PEFT), with LoRA being a standard modular solution. However, LoRA suffers from spectral interference. Low-rank updates often concentrate energy on the leading singular directions of pretrained weights, perturbing general capabilities and causing catastrophic forgetting and fragile multi-adapter merging. To resolve this, we propose HiP-LoRA, a spectrum-aware adaptation framework. Utilizing the cached singular value decomposition (SVD) of pretrained layers, HiP-LoRA decomposes updates into two channels: a principal channel within the dominant singular subspace, and a residual low-rank channel in the orthogonal complement. A singular-value-weighted stability budget on the principal channel continuously balances pretrained behavior preservation with task-specific plasticity. Experiments on Llama-3.1-8B demonstrate that under matched budgets, HiP-LoRA drastically reduces pretraining degradation and multi-adapter MergeFail, robustly outperforming baselines in interference-sensitive tasks like continual tuning and knowledge editing.

Safety alignment in large language models is remarkably shallow: it is concentrated in the first few output tokens and reversible by fine-tuning on as few as 100 adversarial examples. This fragility becomes critical in real-world deployment, where models undergo sequential adaptation across domains such as medicine, law, and code, causing safety guardrails to erode cumulatively. Yet all existing safety-preserving methods target only single-task fine-tuning, leaving the multi-domain sequential setting entirely unaddressed. We introduce SafeAnchor, a framework that anchors safety in place throughout continual adaptation. SafeAnchor first identifies low-rank safety subspaces in LoRA parameter space via Fisher Information eigendecomposition, then constrains domain-specific gradient updates to the orthogonal complement of these subspaces, and finally monitors for residual safety drift with threshold-triggered corrective replay. Evaluated on Llama-2-7B-Chat and Mistral-7B-Instruct across a three-domain pipeline and eight benchmarks, SafeAnchor retains 93.2% of original safety alignment, outperforming all baselines by 18-42 points, while matching unconstrained fine-tuning to within 1.5 points on domain tasks.

Large language models (LLMs) have demonstrated strong reasoning capabilities, and as existing approaches for enhancing LLM reasoning continue to mature, increasing attention has shifted toward meta-reasoning as a promising direction for further improvement. However, most existing meta-reasoning methods remain episodic: they focus on executing complex meta-reasoning routines within individual instances, but ignore the accumulation of reusable meta-reasoning skills across instances, leading to recurring failure modes and repeatedly high metacognitive effort. In this paper, we introduce Metacognitive Consolidation, a novel framework in which a model consolidates metacognitive experience from past reasoning episodes into reusable knowledge that improves future meta-reasoning. We instantiate this framework by structuring instance-level problem solving into distinct roles for reasoning, monitoring, and control to generate rich, attributable meta-level traces. These traces are then consolidated through a hierarchical, multi-timescale update mechanism that gradually forms evolving meta-knowledge. Experimental results demonstrate consistent performance gains across benchmarks and backbone models, and show that performance improves as metacognitive experience accumulates over time.

Large language models require continuous adaptation to new tasks while preserving safety alignment. However, fine-tuning on even benign data often compromises safety behaviors, including refusal of harmful requests, truthfulness, and commonsense reasoning. We investigate which training samples cause alignment drift through a data-centric lens. Our empirical analysis shows samples contribute unequally: high-gradient samples cause greater safety degradation and drive models toward pretrained distributions, while moderate-gradient samples enable task learning with minimal alignment loss. We propose gradient-based sample selection that filters high-gradient samples during fine-tuning. Across multiple model families on continual domain tasks, our method substantially improves alignment preservation while maintaining competitive task performance, without requiring curated safe data or architectural modifications. Our method is robust across selection ratios, task orderings, and diverse attack benchmarks.

Large Language Models (LLMs) have demonstrated excellent performance in general language understanding, generation and other tasks. However, when fine-tuning for specific domain tasks, the general knowledge accumulated in the pre-training phase is often partially overwritten or forgotten due to parameter updates, which severely limits the generalization ability and transferability of LLMs. Traditional fine-tuning strategies mostly train on the entire parameter space, ignoring the heterogeneity of model parameters, that is, some parameters are extremely important for general tasks, while other parameters are more sensitive to specific tasks. To alleviate the above problems, this paper innovatively proposes a parameter element importance evaluation method, which divides parameters into "core parameters" and "non-core parameters" by distinguishing the importance of parameters for general language ability tasks and specific domain tasks, and fixes the core parameters during fine-tuning, and only fine-tunes the non-core parameters. Extensive experiments on scientific, medical and physical tasks using GPT-J and LLaMA-3 show that our method can mitigate catastrophic forgetting while enhancing the adaptability of the model.

Adapter-based methods have become a cost-effective approach to continual learning (CL) for Large Language Models (LLMs), by sequentially learning a low-rank update matrix for each task. To mitigate catastrophic forgetting, state-of-the-art approaches impose constraints on new adapters with respect to the previous ones, by targeting either subspace or coordinate-wise interference. In this paper, we propose JumpLoRA, a novel framework to adaptively induce sparsity in the Low-Rank Adaptation (LoRA) blocks through the use of JumpReLU gating. The method achieves dynamic parameter isolation, which helps prevent task interference. We demonstrate that our method is highly modular and compatible with LoRA-based CL approaches. Specifically, it significantly boosts the performance of IncLoRA and outperforms the leading state-of-the-art CL method, ELLA.

Large language models are prone to hallucinating factually incorrect statements. A key source of these errors is exposure to new factual information through supervised fine-tuning (SFT), which can increase hallucinations w.r.t.~knowledge acquired during pre-training. Since these errors arise as a by-product of knowledge degradation, we explore whether established continual learning tools can mitigate them. We propose a self-distillation-based SFT method that facilitates effective factual learning while minimizing hallucinations w.r.t.~pre-existing knowledge by regularizing output-distribution drift. We also show that when new knowledge acquisition is unnecessary, suppressing factual plasticity by freezing parameter groups preserves task performance while reducing hallucinations. Lastly, we investigate the mechanism, contrasting capacity limitations, behavior cloning, and localized interference. Our experiments show that a main driver is interference among overlapping semantic representations, which self-distillation mitigates and an associative-memory model explains: forgetting grows with the overlap between new and stored facts.

Frontier model developers aim to train models continually to possess emergent, diverse capabilities. To extend capabilities, the current pre-training and post-training paradigm requires manually starting training runs with static datasets or reward functions every time. Addressing this limitation, our work pursues the insight that open-endedness (via the coevolution of models and tasks) can discover models with increasingly novel skills in a single run. We introduce a new model development framework that extends coevolution to large language model (LLM) discovery, open-ended \textit{Assessment Coevolving with Diverse Capabilities} (AC/DC). AC/DC evolves both LLMs via model merging and natural language tasks via synthetic data generation. AC/DC discovers growing archives of LLMs that surpass the capabilities of larger LLMs while taking up less GPU memory. In particular, our LLM populations achieve a broader Coverage of expertise than other curated models or baselines on downstream benchmarks, without \textit{any} explicit benchmark optimization. Furthermore, AC/DC improves Coverage over time, continually innovates on tasks and models, and improves performance in multi-agent best-of-N selection. Our findings highlight the potential of coevolution as a means of discovering broader sets of capabilities from base LLMs. Overall, AC/DC brings us one step closer to a profoundly new paradigm of LLM development, where continual improvements to the diversity of model capabilities can be accelerated by leveraging existing models as stepping stones to increasingly powerful models.

The prevailing paradigm for improving large language models relies on offline training with human annotations or simulated environments, leaving the rich experience accumulated during real-world deployment entirely unexploited. We propose Online Experiential Learning (OEL), a framework that enables language models to continuously improve from their own deployment experience. OEL operates in two stages: first, transferable experiential knowledge is extracted and accumulated from interaction trajectories collected on the user side; second, this knowledge is consolidated into model parameters via on-policy context distillation, requiring no access to the user-side environment. The two stages are iterated to form an online learning loop, where the improved model collects higher-quality trajectories that yield richer experiential knowledge for subsequent rounds. We evaluate OEL on text-based game environments across multiple model scales and both thinking and non-thinking variants. OEL achieves consistent improvements over successive iterations, enhancing both task accuracy and token efficiency while preserving out-of-distribution performance. Our analysis further shows that extracted experiential knowledge is significantly more effective than raw trajectories, and that on-policy consistency between the knowledge source and the policy model is critical for effective learning.

Continuous knowledge updating for pre-trained large language models (LLMs) is increasingly necessary yet remains challenging. Although inference-time methods like In-Context Learning (ICL) and Retrieval-Augmented Generation (RAG) are popular, they face constraints in context budgets, costs, and retrieval fragmentation. Departing from these context-dependent paradigms, this work investigates a parametric approach using Low-Rank Adaptation (LoRA) as a modular knowledge memory. Although few recent works examine this concept, the fundamental mechanics governing its capacity and composability remain largely unexplored. We bridge this gap through the first systematic empirical study mapping the design space of LoRA-based memory, ranging from characterizing storage capacity and optimizing internalization to scaling multi-module systems and evaluating long-context reasoning. Rather than proposing a single architecture, we provide practical guidance on the operational boundaries of LoRA memory. Overall, our findings position LoRA as the complementary axis of memory alongside RAG and ICL, offering distinct advantages.

Personalizing Large Language Models typically relies on static retrieval or one-time adaptation, assuming user preferences remain invariant over time. However, real-world interactions are dynamic, where user interests continuously evolve, posing a challenge for models to adapt to preference drift without catastrophic forgetting. Standard continual learning approaches often struggle in this context, as they indiscriminately update on noisy interaction streams, failing to distinguish genuine preference shifts from transient contexts. To address this, we introduce SPRInG, a novel semi-parametric framework designed for effective continual personalization. During training, SPRInG employs drift-driven selective adaptation, which utilizes a likelihood-based scoring function to identify high-novelty interactions, selectively updating the user-specific adapter on drift signals while preserving hard-to-learn residuals in a replay buffer. During inference, we apply strict relevance gating and fuse parametric knowledge with retrieved history via probability interpolation. Experiments on the long-form personalized generation benchmark demonstrate that SPRInG significantly outperforms existing baselines, validating its robustness for real-world continual personalization.

Catastrophic forgetting poses a fundamental challenge in continual learning, particularly when models are quantized for deployment efficiency. We systematically investigate the interplay between quantization precision (FP16, INT8, INT4) and replay buffer strategies in large language models, revealing unexpected dynamics. While FP16 achieves superior initial task performance (74.44% on NLU), we observe a striking inversion on subsequent tasks: quantized models outperform FP16 by 8-15% on final task forward accuracy, with INT4 achieving nearly double FP16's performance on Code generation (40% vs 20%). Critically, even minimal replay buffers (0.1%) dramatically improve retention - increasing NLU retention after Math training from 45% to 65% across all precision levels - with INT8 consistently achieving the optimal balance between learning plasticity and knowledge retention. We hypothesize that quantization-induced noise acts as implicit regularization, preventing the overfitting to new task gradients that plagues high-precision models. These findings challenge the conventional wisdom that higher precision is always preferable, suggesting instead that INT8 quantization offers both computational efficiency and superior continual learning dynamics. Our results provide practical guidelines for deploying compressed models in continual learning scenarios: small replay buffers (1-2%) suffice for NLU tasks, while Math and Code benefit from moderate buffers (5-10%), with quantized models requiring less replay than FP16 to achieve comparable retention. Code is available at https://github.com/Festyve/LessIsMore.

Large language models (LLMs) often produce incorrect or outdated content after being employed. Efficient and accurate knowledge updates without costly retraining are a major challenge. This problem is particularly challenging in lifelong settings, where complex, unstructured knowledge must coexist without interference. We introduce RILKE (Representation Intervention for Lifelong KnowledgE Control), a robust and scalable method that treats knowledge control as interventions within the model's representation space. Leveraging representation-space expressiveness, we identify two key properties enabling RILKE to achieve fine-grained control over complex, unstructured knowledge while maintaining general utility with frozen base weights. During training, RILKE learns paraphrase-robust and edit-localized modules that limit each update to a low-dimensional subspace to minimize cross-edit interference. At inference, a query-adaptive router selects the appropriate module to guide the model's generation. Across LLaMA and Qwen models, RILKE scales effectively to large-scale benchmarks, demonstrating high edit success and strong paraphrase generalization while preserving general utility with modest memory overhead. These results show RILKE is an effective and scalable solution for lifelong knowledge control in LLMs.

Domain-specific post-training often causes catastrophic forgetting, making foundation models lose their general reasoning ability and limiting their adaptability to dynamic real-world environments. Preserving general capabilities while acquiring downstream domain knowledge is a central challenge for large language and multimodal models. Traditional continual learning methods, such as regularization, replay and architectural isolation, suffer from poor downstream performance, reliance on inaccessible historical data, or additional parameter overhead. While recent parameter-efficient tuning (PET) methods can alleviate forgetting, their effectiveness strongly depends on the choice of parameters and update strategies. In this paper, we introduce PIECE, a Parameter Importance Estimation-based Continual Enhancement method that preserves general ability while efficiently learning domain knowledge without accessing prior training data or increasing model parameters. PIECE selectively updates only 0.1% of core parameters most relevant to new tasks, guided by two importance estimators: PIECE-F based on Fisher Information, and PIECE-S based on a second-order normalization that combines gradient and curvature information. Experiments across three language models and two multimodal models show that PIECE maintains general capabilities and achieves state-of-the-art continual learning performance across diverse downstream tasks. Our results highlight a practical path to scalable, domain-adaptive foundation models without catastrophic forgetting.

Enabling lifelong learning in LLMs demands resolving the stability-plasticity dilemma (i.e., models must incorporate new knowledge without overwriting prior representations) while maintaining scalability under bounded parameter growth. Existing PEFT methods fail to satisfy this triad; shared-parameter approaches suffer from catastrophic interference, while task-isolated expansions preclude knowledge transfer and scale linearly. We propose Mixtures of SubExperts (MoSEs), a modular and sparse framework that factorizes model capacity into reusable, compositional primitives. MoSEs augment transformer layers with lightweight SubExperts and a learned sub-routing function that dynamically selects and composes a sparse subset of modules conditioned on task inputs. This induces a structured decomposition of the parameter space where knowledge is localized yet accessible, mitigating interference while preserving reuse. Specifically, MoSEs balance the dilemma via three pillars: (i) stability by isolating knowledge within sparsely activated modules, (ii) plasticity through routing-driven recombination and selective expansion, and (iii) scalability via sublinear growth in effective capacity. Notably, the routing mechanism enables compositional generalization, allowing new tasks to be represented as combinations of previously acquired sub-functions. We empirically validate MoSEs on TRACE and SuperNI, showing reduced forgetting, improved forward transfer, and better parameter efficiency over strong PEFT baselines. MoSEs establish a new Pareto frontier, achieving state-of-the-art performance while maintaining strict parameter budgets. Our results suggest that modular sparsity and compositional routing are key inductive biases for building foundation models that continually learn without saturation.

Adapting language models (LMs) to new tasks via post-training carries the risk of degrading existing capabilities -- a phenomenon classically known as catastrophic forgetting. In this paper, toward identifying guidelines for mitigating this phenomenon, we systematically compare the forgetting patterns of two widely adopted post-training methods: supervised fine-tuning (SFT) and reinforcement learning (RL). Our experiments reveal a consistent trend across LM families (Llama, Qwen) and tasks (instruction following, general knowledge, and arithmetic reasoning): RL leads to less forgetting than SFT while achieving comparable or higher target task performance. To investigate the cause for this difference, we consider a simplified setting in which the LM is modeled as a mixture of two distributions, one corresponding to prior knowledge and the other to the target task. We identify that the mode-seeking nature of RL, which stems from its use of on-policy data, enables keeping prior knowledge intact when learning the target task. We then verify this insight by demonstrating that the use on-policy data underlies the robustness of RL to forgetting in practical settings, as opposed to other algorithmic choices such as the KL regularization or advantage estimation. Lastly, as a practical implication, our results highlight the potential of mitigating forgetting using approximately on-policy data, which can be substantially more efficient to obtain than fully on-policy data.

On-device deployment of Large Language Models (LLMs) frequently leverages Low-Rank Adapters (LoRAs) to support diverse downstream tasks under tight resource constraints. To address the limited storage capacity of mobile devices, recent works have explored model merging techniques to fuse multiple LoRAs into a single one. In practice, however, LoRAs are often delivered incrementally, as users request support for new tasks (e.g., novel problem types or languages). This scenario introduces a new challenge: on-device online continual merging, where the objective is to incorporate new LoRAs while preserving the performance on previously supported tasks. In this paper, we propose a data-free and computationally efficient strategy for selecting and merging LoRAs when a new one becomes available, assuming the device can store only a limited number of adapters. Extensive experiments across real-world tasks demonstrate the superiority of our approach compared to alternative strategies while adhering to the storage budget and compute limitations of on-device settings. The project page is available at: https://donaldssh.github.io/K-Merge.

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.

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates continual learning (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of large pre-trained models (LPMs), efficiency has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs layer-wise adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ bandit techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both vision transformers (ViTs) and large language models (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.