Catastrophic Forgetting

Catastrophic forgetting is often viewed as the destruction of previously learned knowledge during sequential learning. Building on the Accessibility Collapse framework, we investigate the geometric structure of recoverability in continual learning. Using Split CIFAR-100 and a sequentially trained ResNet-18, we analyze recoverability, representational drift, and recovery complexity across ten tasks. We introduce Recovery Subspace Dimensionality (k_t), a measure of the minimum number of singular directions required to preserve 90 percent of full probe performance. Contrary to our Recoverability Diffusion hypothesis, recovery dimensionality remains stable throughout training (mean k_t = 8.0) despite substantial representational drift. Principal-angle drift strongly predicts recoverability (r = -0.862), and a simple geometric model explains 82.2 percent of recoverability variance. These findings support the Stable Recovery Manifold hypothesis, suggesting that forgotten knowledge remains compactly decodable despite representational reorganization. The results indicate that catastrophic forgetting is primarily an accessibility and manifold-alignment problem rather than information destruction.

Studies on rodents such as mice have shown the capabilities to adapt their behavior when dealing with changing parameters (drift'') of the environment even if no information about change is provided (uncertainty) -- a behavior that can be modeled by forgetting mechanisms. Non-stationary Reinforcement Learning (NSRL) deals with adapting state-of-the-art RL methods to deal with changing environments: these however usually require (partially) perfect information about the drift such as task IDs'' or ``context''. To mitigate the effects of drift, this work develops \emph{Space-sampled Value Decay} as an explicit forgetting mechanism for value-based deep RL architectures as a simple yet effective approach. In particular we demonstrate and discuss positive effects but also limitations in achieved returns for modifications of Deep Q-networks (DQN) and Soft Actor-Critic (SAC) when evaluated on non-stationary environments.

Class-Incremental Learning (CIL) aims to continuously learn new classes without forgetting previously acquired knowledge. While recent CIL advances have spurred significant interest across various modalities, the audio-visual setting remains underexplored. Furthermore, although foundational multimodal models like SAM-Audio encapsulate rich static priors, our empirical analysis reveals that these representations struggle in incremental settings. This work bridges this gap by integrating SAM-Audio's audio-visual priors into the CIL setting. Specifically, we leverage its dense audio and visual representations and employ a novel guided attention strategy where the audio features contextually guide the visual representations. To further mitigate catastrophic forgetting, we introduce dual-level distillation objectives at both the feature and logit levels. Extensive evaluations on audio-visual CIL benchmarks demonstrate that our approach consistently outperforms state-of-the-art methods.

Federated Learning (FL) enables collaborative and privacy-preserving model training across distributed clients, but most existing FL systems implicitly assume data stationarity. In real-world settings-such as healthcare, industrial IoT (IIOT), cybersecurity, and smart cities-data streams are inherently non-stationary, leading classical FL methods to suffer from performance degradation, instability, and catastrophic forgetting. Continual Learning (CL) addresses learning under evolving data distributions but has been largely studied in centralized settings, overlooking key constraints of federated systems, including privacy, limited communication, and client heterogeneity. Federated Continual Learning (FCL) emerges at the intersection of FL and CL, aiming to support lifelong, adaptive, and privacy-aware learning over distributed and non-stationary data. This survey provides a comprehensive and systematic overview of FCL. We first present a formal definition of the FCL problem and clarify its distinctive characteristics. We then analyze the limitations of classical FL under non-stationary conditions, highlighting how CL principles support long-term adaptation. To organize the rapidly growing literature, we propose a multi-dimensional taxonomy of FCL approaches. Furthermore, we review representative application domains and data modalities, summarize commonly used evaluation metrics, and discuss experimental perspectives for assessing long-term performance and forgetting. Finally, we highlight key open challenges, including handling extreme heterogeneity under temporal drift, designing scalable and privacy-preserving memory mechanisms, and establishing standardized benchmarks. This survey aims to serve as a reference and a roadmap for advancing FCL toward robust and deployable real-world systems.

In many real-world settings, data streams are nonstationary and arrive sequentially, requiring learning systems to adapt continuously without retraining from scratch. Continual learning (CL) addresses this challenge by incorporating new tasks while mitigating catastrophic forgetting, where learning new information degrades performance on previously acquired knowledge. We introduce a control-theoretic perspective on CL that explicitly regulates the evolution of forgetting, framing adaptation as a controlled process subject to long-term stability constraints. We focus on replay-based CL, where a finite memory buffer stores representative samples from prior tasks. We propose COntinual Learning with Drift-Plus-Penalty (COLD), a continual learning framework based on the Drift-Plus-Penalty (DPP) principle from stochastic optimization. To facilitate analysis, we also consider an oracle variant, COLD-ORACLE, as a reference benchmark. At each task, both methods minimize the current task loss while maintaining a virtual queue that tracks deviations from long-term stability on previously learned tasks, capturing the stability-plasticity trade-off as a regulated dynamical process. We establish stability and convergence guarantees that characterize this trade-off through a tunable control parameter. Experiments on standard benchmarks demonstrate that COLD consistently outperforms a broad range of state-of-the-art CL methods while providing competitive and controllable forgetting behavior through explicit regulation of stability and plasticity.

One of the critical limitations of artificial neural networks is their lack of ability to continually learn: training on new tasks often leads to interference and forgetting of the previous ones. While several algorithms have been proposed to protect old memories from interference, they are typically applied during or immediately after each new episode of training. In contrast, humans and animals can learn continuously, acquiring multiple new memories during active learning before consolidating all of them into long-term storage. Here we show that multiple new tasks can be trained sequentially before an unsupervised sleep-like replay phase is applied to partially restore performance across all previously learned tasks. Our study further suggests that task-specific information remains resilient to new training but decays gradually as network is trained on new tasks. These findings point to novel principles for developing a broad range of continual learning AI solutions.

Catastrophic forgetting, the abrupt loss of previously acquired knowledge upon learning new information, remains the central challenge in Continual Learning. This project investigates whether the order in which a model learns information affects how well it retains knowledge. Specifically, we ask: does learning general categories first (like "animals" vs "vehicles") before learning specific classes (like "dog" vs "cat") reduce forgetting compared to learning all classes at once? We test three approaches on CIFAR-100: (1) Coarse-to-Fine: train on 2 super-classes, then expand to 10 specific sub-classes, (2) Fine-to-Coarse: train on 10 sub-classes, then group into 2 super-classes, and (3) Flat: train on all 10 classes from the start. We use Elastic Weight Consolidation (EWC) to prevent forgetting during transitions. Our hypothesis is that learning general patterns first creates a stable foundation that helps the model retain knowledge when learning more detailed distinctions. We evaluate using standard metrics (accuracy, precision, recall, F1) plus continual learning metrics like backward transfer and forgetting rates. This work could inform how we design learning sequences for real-world systems that need to learn incrementally.

Unsupervised Continual Learning (UCL) aims to enable neural networks to learn sequential tasks without labels or access to past data. A major challenge in this setting is Catastrophic Forgetting, where models forget previously learned tasks upon learning new ones. This challenge is amplified in UCL due to the absence of labels to guide learning and memory retention. Existing mitigation strategies, such as knowledge distillation and replay buffers, often raise memory and privacy concerns. Moreover, current UCL methods largely overlook clustering-specific objectives. To fill this gap, we introduce Unsupervised Continual Clustering (UCC) and propose Forward-Backward Knowledge Distillation for Continual Clustering (FBCC). FBCC employs a continual teacher network with a clustering projector and lightweight task-specific students. Through a dual-phase forward-backward distillation process, the teacher learns new clusters while preserving previously discovered cluster structure without storing past data. FBCC represents a pioneering approach to UCC, demonstrating improved clustering performance across sequential tasks. Experiments on four benchmark datasets demonstrate that FBCC consistently outperforms existing continual learning baselines in clustering accuracy while significantly reducing catastrophic forgetting.

Catastrophic forgetting is commonly interpreted as the irreversible erasure of previously acquired knowledge during sequential learning. In this work, we investigate an alternative perspective: that forgetting may arise not from complete destruction of task representations but from a loss of accessibility to preserved information. We introduce a three-level framework separating knowledge storage, representation, and accessibility, and evaluate each component through a series of continual-learning experiments on sequential CIFAR-100 classification using ResNet-18. Our analysis combines checkpoint persistence, linear probing, representation geometry, classifier-reset recovery, and layer-wise recoverability experiments. We observe complete behavioral forgetting of earlier tasks, with task accuracy collapsing from 54.8% to 0%, while linear probe performance retains approximately 76% of the original representational information. Furthermore, retraining only the final classifier restores 75.7% of the original task performance without modifying the backbone network. Layer-wise analysis reveals that early and intermediate layers preserve highly recoverable task information despite severe degradation at later stages. Projection-energy and principal-angle analyses indicate that retained knowledge persists as distributed high-dimensional representations rather than through preservation of a small dominant subspace. These findings suggest that catastrophic forgetting is better characterized as an accessibility failure than complete representational erasure, and that substantial task-relevant information remains embedded within neural representations even after functional forgetting has occurred.

Exemplar-free class-incremental learning (EFCIL) aims to acquire new classes over time without storing raw data. Historically, prototype rehearsal, which samples around stored class prototypes and mixes them with current-task data, has been a popular strategy to reduce catastrophic forgetting. However, recent drift-compensation methods that explicitly realign prototypes in the evolving feature space consistently outperform prototype-based rehearsal, raising the question of whether rehearsal itself is fundamentally limited. We argue that the performance gap stems not from the idea of prototype rehearsal per se, but from how it is typically instantiated: existing approaches treat prototypes as isolated class summaries that ignore information from nearby enemy classes, and fail to correct the emerging class imbalance between a handful of synthetic old-class samples and hundreds of real instances from newly introduced classes. Building on this hypothesis, we revisit prototype rehearsal and propose a manifold-aware variant that restores its competitiveness in EFCIL. First, we introduce Constrained Expansive Over-Sampling, which interpolates each old-class prototype toward its nearest enemy features from new classes, generating boundary-aware rehearsal samples that better follow the underlying data manifold while preserving inter-class separation. Second, we design an Adaptive Class-Balanced loss that performs time-based class weighting, amplifying gradients from older prototypes when they are most informative and gradually annealing their influence as richer supervision from later tasks accumulates. Together, these components turn prototype rehearsal into a drift-resilient, imbalance-aware mechanism that closes, and often reverses, the gap to recent drift-compensation methods, achieving state-of-the-art performance across multiple EFCIL benchmarks.

Custom diffusion models (CDMs) have garnered significant interest owing to their remarkable capacity for generating personalized concepts. However, the majority of CDMs unrealistically presume that the user's collection of personalized concepts is static and incapable of incremental growth over time. Furthermore, they exhibit significant catastrophic forgetting and concept neglect of previously learned concepts when incrementally learning a sequence of new ones. To resolve the above challenges, we develop a novel Continually Customizable Diffusion Model (CCDM), enabling users to perform concept-incremental versatile customization. Specifically, we design an attribute-decoupled LoRA (AD-LoRA) module and a relevance-guided AD-LoRA aggregation strategy to mitigate catastrophic forgetting. They can preserve concept-specific attributes of each task and leverage beneficial inter-task correlations to enhance the continual learning of new customization tasks. Additionally, to address the challenge of concept neglect, we propose a controllable regional context synthesis strategy that performs multi-concept composition in alignment with user-provided conditions. This strategy enhances the overall consistency in multi-concept synthesis by guaranteeing semantic independence between user-defined regions and their smooth boundary transitions. Experiments show our CCDM exhibits significant improvements over baseline methods.

Catastrophic forgetting is often framed as a representational problem: after sequential training, a model appears to lose the features that supported performance on earlier tasks. We challenge the stronger form of this view. Across controlled continual-learning settings, we find that a significant portion of apparent forgetting can be attributed to interface drift between internal stages rather than permanent erasure of task-relevant computation. We study this phenomenon through a stitched evaluation protocol that combines early computation from a post-update network with late computation from its predecessor, optionally mediated by a compact, task-specific transport key. We describe transport keys at a systems level as compact interface-alignment operators estimated from a small set of paired anchor activations and evaluated through model stitching. On split CIFAR-100 with a ResNet-style network, transport keys recover most of the original Task A performance after sequential training on Task B. On a compact vision transformer, we observe a similar recovery pattern. These results suggest that continual learning may require better mechanisms for indexing and re-accessing latent computations, not only methods that prevent weight change.

Reinforcement learning (RL) post-training improves large language models (LLMs) on individual domains such as mathematical reasoning, code generation, question answering, and creative writing (CW), but training on one domain often degrades performance on others. Existing explanations based on catastrophic forgetting or global gradient conflict are incomplete: substantial interference can occur even when full-model gradients are nearly orthogonal. We show that single-domain RL produces sparse, small-magnitude parameter edits with weak overlap among top-changed neurons, while different domains still share substantial active computation routes on which update directions determine whether they act synergistically or conflict. Guided by this observation, we prove under a local perturbation model of multi-domain RL that later-domain training harms an earlier domain mainly through a second-order damage term, which under the observed sparse route structure concentrates in a low-dimensional shared conflict subspace. Moreover, a short domain refresh contracts the harmful component on this subspace, enabling selective recovery with limited collateral damage. Consistent with the theory, a brief Re-Math refresh after Code $\rightarrow$ Math $\rightarrow$ QA $\rightarrow$ CW recovers Math from 57.66 to 66.04 while largely preserving performance on the other domains, yielding the best average score of 66.39. Beyond refresh, a training-free rollback on a sparse proxy conflict coordinate set for the Math-QA pair partially restores Math, providing direct proxy-level evidence for localized damage. These results provide a localized mechanistic account of interference and recovery in multi-domain RL.

Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU's superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.

While prompt engineering is instrumental in maximizing the capabilities of Large Language Models (LLMs) during inference, the role of prompts during training remains critically underexplored. Prevailing fine-tuning paradigms typically treat training prompts as mere surface forms, assuming that semantically equivalent instructions yield identical learning outcomes. However, we reveal that this equivalence is deceptive: while paraphrased prompts often lead to comparable in-task performance, they induce drastically different cross-task impacts regarding catastrophic forgetting and generalization. Crucially, these impacts are positively correlated across tasks, indicating the existence of superior prompts that consistently yield better performance. Furthermore, we discover that these superior prompts can be robustly identified by task loss prior to learning. Leveraging these insights, we introduce State-Adaptive Prompt Optimization (SAPO), a lightweight yet effective training strategy that shifts task formulation from a static input to a dynamic, state-adaptive variable. Comprehensive experiments on diverse benchmarks confirm its effectiveness, which significantly mitigates forgetting while improving generalization, achieving substantial performance gains over state-of-the-art methods. These results provide insights into how training prompts shape learning dynamics and offer a practical recipe for robust fine-tuning. Our code is available at https://github.com/Eric8932/SAPO.

Machine unlearning aims to remove the influence of specific training samples while preserving the model's utility. Existing single-objective approaches, such as gradient ascent or random relabeling, often induce catastrophic forgetting due to conflicting optimization dynamics and unbounded forgetting objectives that cause the model to drift from its pre-trained knowledge. We propose Reference-Aligned UnLearning (RAUL), a multi-objective framework that jointly optimizes forgetting and retention by replacing unbounded loss maximization with a bounded KL alignment of predictions on forgotten samples toward a reference distribution representing unseen data, instantiated either as a uniform distribution or an empirical distribution from a held-out reference set, which constrains the forgetting objective and reduces gradient conflict with retention. The resulting multi-objective optimization (MOO) problem is solved via Jacobian descent, which aggregates multiple gradients into a direction that does not conflict. Our results demonstrate that RAUL achieves the closest gap compared to full retraining.

Sequential fine-tuning of large language models forces a choice: let the shared substrate keep learning and accept catastrophic forgetting, or freeze it after task one and foreclose cross-task refinement. Per-task adapter methods (LoRAHub, AdapterFusion, PackNet, Progressive Networks) take the second path. We introduce CRMA (Constrained Residual Mixing Adapter), a residual adapter whose internal mixing matrix M is doubly-stochastic at every forward pass via Sinkhorn normalization, so by Birkhoff's theorem ||M||_2 <= 1 holds by construction -- a structural bound, not a penalty. CRMA's spectrally bounded backbone provides a continuously trained shared substrate that earlier modular methods could not, while preserving their forgetting guarantees. On Mistral-7B across 5 sequential domains and 3 seeds, modular per-task LoRA on a CRMA backbone reduces loss-relative drift from +42.96% +/- 5.5 (naive sequential fine-tuning) to -0.17% +/- 0.17, with disjoint per-seed ranges, and improves prior-task holdout loss by 1.99% +/- 0.54 over a matched frozen-substrate baseline. Three independent experimental setups (Mistral-7B 4-domain controlled ablation, TinyLlama 3-domain contamination-controlled replication, Mistral-7B cross-domain probes at 7B) all show positive backward transfer -- without replay buffers, without growing per-task memory, and without distillation. An inference-time ablation on Gemma-2-9B confirms CRMA mediates access to sequentially trained knowledge: 98/100 vs. 38/100 on the same weights and same questions with only CRMA injection toggled. 867 logged training steps verify ||M||_2 = 1.0 within float32 precision (max deviation 1.2 x 10^-7). The forgetting-prevention effect holds across 1.1B-9.2B parameters and four architecture families.

While continual pretraining~(CPT) is a practical way to extend large language models to new languages, naïve finetuning on targeted data erodes existing capabilities through catastrophic forgetting. Organizing training around language families reduces cross-language interference but cannot alone prevent forgetting of the general knowledge needed for downstream tasks. We link this forgetting to parameter drift in multilingual CPT and present a suite of five layer-aware parameter alignment strategies: hard layer freezing, soft regularization, post-hoc weight reversion, and model merging. We systematically compare our alignment strategies against two unregularized CPT baselines on benchmarks spanning 32 training languages from five language families, plus held-out languages, across four evaluation axes: perplexity, reading comprehension, physical reasoning, and translation. Parameter alignment substantially reduces forgetting at minimal cost to language acquisition: layer freezing and regularization best preserve comprehension, whereas post-hoc reversion yields the strongest translation gains. Together, these results map the acquisition--forgetting frontier for family-expert CPT and offer practical deployment guidelines pairing each strategy to the tasks it best serves.

In real-world deployment, LLMs are often adapted continually across tasks to keep LLMs up-to-date in production, where new fine-tuning should preserve previously learned skills. However, indiscriminately mixing tasks can dilute task specialization, while sequential fine-tuning (full-parameter or low rank adaptation) often causes catastrophic forgetting due to destructive overwriting. Replay-based continual tuning and maintaining separate task-specific adapters can mitigate forgetting, but introduce additional compute, storage, and management overhead. Recognizing the redundancy of LLM parameters for any single task, we reframe continual task adaptation as task-specific parameter discovery via adaptation-aware probing: a short warm-start probe exposes a task's adaptation trace, enabling us to identify and isolate the small subset of parameters essential for each task to mitigate catastrophic forgetting. Building on this view, we introduce TRACE, a novel approach for discovering Task-specific paRameters via Adaptation-aware probing for Continual finE-tuning. We perform a short warm-start fine-tune to derive task-specific core parameters by comparing the warm-started and pre-trained models. Core parameters are identified via two strategies: importance scoring (L$_2$ norm and Fisher Information) and specificity analysis (cosine similarity of parameter updates). In continual fine-tuning settings, only the active task's core parameters are updated while others remain frozen, preserving prior knowledge. We conduct extensive experiments across multiple standard benchmarks to demonstrate the superior performance of our proposed method. Additionally, we validate the generalization of our method through a cross-model and scale transferability study, demonstrating a "small-to-large" paradigm that guides the fine-tuning of large-scale models under resource constraints.

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.

Continual supervised fine-tuning (SFT) is the de facto recipe for adapting large language models (LLMs) to a stream of downstream tasks, but it suffers from catastrophic forgetting of earlier capabilities. Recent work shows that on-policy signals -- training on the model's own outputs -- reduce forgetting more reliably than off-policy supervision. Existing on-policy methods route this signal through a new training objective (e.g., self-distillation losses with a teacher copy), inheriting an extra forward pass, schedule sensitivity, and stylistic drift from the teacher.We instead route the on-policy signal through the training data source. Our method, On-Policy Replay (OPR), rolls out the most recent checkpoint on a small budget of historical prompts, filters the generations by a task reward, and replays the surviving (prompt, model response) pairs as ordinary SFT examples. There is no teacher, no auxiliary loss, and no on-the-fly distillation. Across three 7--8B instruction-tuned backbones (Qwen2.5-7B-Instruct, Qwen3-8B, Llama3.1-8B-Instruct) on the TRACE continual-learning benchmark, OPR consistently reduces forgetting; on the sharpest stress test (Qwen2.5-7B-Instruct, Sequential SFT BWT -13.93), OPR lifts BWT to -0.65 at a 10% replay budget and to -2.29 at a 1% budget -- a 46% reduction in |BWT| over a tuned Vanilla Replay baseline, with 42--46% reductions observed across all three backbones. We give a KL-shrinkage interpretation that places OPR and prior on-policy distillation methods on a single axis, and we present a counterintuitive finding that explains why Vanilla Replay is already a strong baseline: low-score replay is uniformly worse than Vanilla Replay, demonstrating that the active ingredient in OPR is the on-policy distribution, not the response quality alone.Our code is available at https://github.com/Yancey2024/OnPolicyReplay.

Mainstream strategies for finetuning pretrained multimodal models often degrade out-of-distribution (OOD) robustness, a phenomenon known as catastrophic forgetting. In this paper, we develop a theoretical framework for multimodal contrastive finetuning, yielding closed-form solutions and a geometric decomposition for each strategy. This framework shows that self-distillation is more effective than other regularization approaches to retain the knowledge of the pretrained model. Our analysis reveals a largely overlooked limitation: standard Exponential Moving Average (EMA) teachers, widely used in robust finetuning, suffer from collapse. To solve this, we prove that a Weighted Moving Average (WMA) teacher maintains a persistent regularizing force over finite horizons and yields bias-free convergence in the task subspace while preserving orthogonal knowledge. These insights motivate TRACER (Trajectory-Robust Anchoring for Contrastive Encoder Regularization), which combines contrastive learning with WMA-guided multi-perspective distillation. Extensive experiments on CLIP finetuning demonstrate consistent OOD accuracy and calibration gains across three backbone architectures, and comprehensive ablations confirm that TRACER is both principled and robust to hyperparameter choices. Code is available at https://github.com/HesamAsad/TRACER.

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.

Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.

Video world models should maintain evolving states when evidence is unobserved, yet current generators often freeze hidden states upon interruption. This is not simply a capacity problem: pretrained video diffusion transformers already possess KV-cache mechanisms capable of non-local retrieval, but they are rarely trained to use them as dynamic memory. We introduce ReMind, a framework eliciting dynamic memory behavior via memory-oriented data, event-aware training, and cache adaptation. Organized around a taxonomy of 100+ dynamic events, we build a camera-annotated training mixture combining VLM-filtered real videos, generated hard dynamics, synthetic camera loops, and memory-interruption augmentations. Each clip is converted into a frame graph with protected anchors, degraded intervals, and explicit temporal gaps. A node-structured curriculum, including node-drop, noisy memory, frontier continuation, and reference-cache training, forces the model to retrieve relevant past states across interruptions rather than relying solely on local continuity. PM-RoPE, an elegant camera-phase RoPE extension, unlocks spatiotemporal retrieval at a single-attention cost while preserving pretrained pathways. ReMind achieves the best overall scores on STEVO-Bench and recovery tasks. Furthermore, general image-to-video evaluations confirm this curriculum avoids catastrophic forgetting. We will open-source our code, data, and models.

Pre-trained Vision Transformers (ViTs) are increasingly deployed for medical image classification. However, correcting their inevitable failure cases in dynamic clinical scenarios poses a critical challenge. Conventional fine-tuning approaches inherently suffer from catastrophic forgetting, severely degrading previously acquired diagnostic capabilities. Such instability fundamentally compromises clinical safety. Addressing this vulnerability requires an active, controllable, and reliable intervention mechanism that is both theoretically grounded and inherently interpretable. To this end, we propose X-Edit (eXact, eXplicit, and eXplainable Editing), an efficient null-space model editing framework. X-Edit transitions the editing process from iterative gradient-based optimization to a theoretically grounded, closed-form solution. Specifically, we first explicitly localize the influential layers via causal tracing governing the erroneous prediction. Subsequently, we construct an orthogonal null-space projection matrix from a curated anchor set. By geometrically constraining the exact parameter update strictly within this null space, we provide mathematical guarantees that the intervention rectifies targeted errors without perturbing established diagnostic representations. Extensive evaluations on six medical imaging benchmarks demonstrate that X-Edit comprehensively suppresses catastrophic forgetting while achieving superior edit success rates. Our code is available at https://github.com/HenryLau7/X-Edit.

Fine-tuning large language models (LLMs) frequently induces catastrophic forgetting of prior capabilities. Recent work has shown that reinforcement learning (RL) retains prior capabilities more effectively than supervised fine-tuning (SFT), attributing this to policy-gradient updates remaining closer to the base policy \cite{shenfeld2025rl}. We extend this behavioral account to the mechanistic level and ask whether RL's advantage is mirrored by stronger preservation of internal computational circuits. We introduce differential circuit vulnerability, a head-level measure of how much a circuit degrades under fine-tuning, and use it to compare RL and SFT on Qwen2.5-3B-Instruct adapted to scientific question-answering. We find a clear mechanistic trade-off: SFT adapts more rapidly to the target task but produces substantially greater circuit disruption and forgetting of prior capabilities, whereas RL preserves a larger fraction of the base circuit at the cost of slower task adaptation. These findings suggest that circuit preservation may help explain why RL is more robust to catastrophic forgetting. We released our code here: https://github.com/rl-sft-circuit-research/differential-circuit-vulnerability.

Data rehearsal has emerged as a leading approach for mitigating catastrophic forgetting in Continual Reinforcement Learning (CRL). However, existing work remains confined to policy gradient frameworks, regularizing only actors due to the performance degradation incurred by critic regularization. This actor-centric approach overlooks the potential of data rehearsal for value function approximation. Moreover, existing evaluations in CRL rarely consider multi-cyclic environments where task sequences repeat, a critical real-world scenario that exacerbates forgetting and plasticity. We investigate data rehearsal for Deep Q-Networks using Q-value regularization in multi-cyclic settings and propose Qreg+NWLU which introduces two simple modifications: (1) continuous data rehearsal that dynamically collects and updates stored Q-values throughout training, and (2) "No-Wait" regularization that applies immediately rather than after the first task. Together, these modifications yield improvements in learning efficiency, forgetting mitigation, and knowledge transfer over Qreg and conventional CRL methods within value function approximation settings.

Achieving self-evolution in intelligent agents requires the continual accumulation of new knowledge across changing task sequences without forgetting previously acquired abilities. Existing approaches either internalize knowledge by updating model parameters, which induces catastrophic forgetting, or rely on external memory, which fails to genuinely enhance the model's intrinsic capabilities. We propose MoLEM, a generative mixture of latent memory framework based on a dynamic mixture-of-experts (MoE). We treat multiple experts as independent carriers to generate memory. A router selects and weights experts through key-query matching, and the aggregated latent memory is injected into the reasoning process. The base model for reasoning remains entirely frozen, with all experiential knowledge internalized into the additional modules, avoiding catastrophic forgetting. For continual learning, each training stage is paired with a lightweight autoencoder that selects the appropriate routing group at inference, and inputs that match no stage fall back to the pretrained model. Experiments train the framework on continual-learning sequences spanning math, science, and code domains. After training, we evaluate the framework on the corresponding test sets to measure task learning and competence preservation across continual adaptation stages. After the full continual-learning sequence, our method improves the average accuracy by 10.40% over the Vanilla pretrained baseline, while none of the competing methods consistently exceed this baseline across different training orders.

Fine-tuning large language models on new data improves task performance but degrades capabilities learned during pretraining, a phenomenon known as catastrophic forgetting. Existing methods mitigate this by modifying the fine-tuning objective to suppress high-loss tokens or sequences, but these tokens are essential for learning new tasks, especially those with poor pretraining coverage. In such settings, hard tokens should still contribute to learning, so forgetting must be controlled without suppressing them. We identify a simple mechanism for doing so: per-step forgetting is bounded by the product of the learning rate and the square root of the current training loss. This suggests that high-loss batches are especially prone to inducing forgetting. Motivated by this observation, we introduce FINCH, a loss-adaptive learning-rate schedule that reduces the learning rate on high-loss batches and increases it as the model converges, while leaving the fine-tuning objective unchanged. Across knowledge acquisition, science, and low-resource language adaptation benchmarks, FINCH reduces forgetting by 93% on average while matching the task performance of standard fine-tuning. On Qwen3-4B knowledge acquisition, FINCH cuts TruthfulQA degradation by 5x and reverses HaluEval degradation, while better preserving confidence calibration. Overall, our results show that learning-rate schedules are an effective tool to shape model behavior during fine-tuning, beyond just target-task optimization.

Fine-tuning a language model for a target task routinely degrades capabilities the training data never explicitly threatened. We study this phenomenon, known as catastrophic forgetting, and propose a post-hoc repair solution that uses only the pretrained checkpoint $W_{\mathrm{base}}$ and its fine-tuned descendant $W_{\mathrm{ft}}$. The goal is not merely to revert the model toward the base checkpoint, but to recover capabilities damaged by fine-tuning while preserving both the target-task gains and any beneficial held-out improvements. We introduce DG-Hard, a checkpoint-only spectral repair method for the fine-tuning update $Δ= W_{\mathrm{ft}} - W_{\mathrm{base}}$. DG-Hard treats $Δ$ as a low-rank task-aligned signal embedded in an IID-like noise residual that gradient descent has no incentive to remove, and applies the Donoho-Gavish hard singular-value threshold to each weight-delta matrix, keeping the structured high-energy part of the update and removing the spectral bulk. This reduces repair to a closed-form SVD filtering step requiring no data-dependent tuning. A central difficulty is evaluation: average accuracy hides per-benchmark failures, while naive recovery scores reward models that simply revert toward the base. We therefore introduce a partition-conditional metric that separately tracks healing, preservation, non-damage, and target-task retention. Across $14$ (model, task) settings and nine cross-domain held-out benchmarks, DG-Hard achieves the strongest balanced repair among post-hoc baselines. DG-Hard also restores safety alignment degraded by benign fine-tuning on three independent safety axes, despite using no alignment data. These results suggest that part of fine-tuning-induced capability loss is not an unavoidable consequence of specialization, but a removable spectral residue in the weight update itself.

When a data contributor requests removal, model trainers face a practical gap: unlearning algorithms require a forget set, yet no tool can locate which training records belong to a given author. Existing provenance systems operate at file or dataset level, forcing catastrophic over-deletion. We present ob, a record- and token-level data provenance system that propagates author identity through data processing pipelines and resolves revocation requests into precise forget sets via deterministic queries. Evaluation on 219,555 Wikipedia pages demonstrates that record-level provenance eliminates dataset-level over-deletion (from 101x to 1.3x), while integration adds 1.3-4.0% throughput overhead (HuggingFace) and 2.1-19.0% (Datatrove) on wiki data. On a 1.7B model, provenance-based forget sets improve unlearning by 42% over random baselines.

Machine unlearning in Vertical Federated Learning (VFL) has attracted growing interest, yet existing methods certify forgetting solely using output-level metrics. We challenge these works by introducing Mirage, a representation-level auditing framework that comprises four complementary diagnostics: Linear probe recovery (LPR), centered kernel alignment (CKA), feature separability scoring, and layer-wise recovery analysis. Extensive experiments across seven datasets and seven baseline methods following recent VFL unlearning protocols reveal three key findings: (1) Forgetting gap: methods that pass output-level certification still retain substantial class structure in their representations, with LPR exceeding the retrained baseline by up to 15.4 points; CKA shows that these models remain structurally closer to the original than to the retrained reference, while separability scores indicate persistent geometric discrimination. (2) Unlearning trilemma: no existing method simultaneously achieves high utility, output-level forgetting, and representation-level forgetting. (3) Class-sample asymmetry: class-level forgetting leaves strong representational traces (LPR exceeding 96 percent on several datasets), whereas sample-level forgetting is indistinguishable from chance (LPR is approximately 50 percent); layer-wise analysis further shows that residual class information persists across network depths. These findings call for representation-aware evaluation standards in federated unlearning research. Code is publicly available at https://github.com/YuZhenyuLindy/Mirage.

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.

Time Series Foundation Models (TSFMs) have demonstrated notable success in general-purpose forecasting tasks; however, their adaptation to specialized classification problems remains constrained by the computational bottleneck of standard attention and the systematic omission of classical statistical knowledge. This technical report introduces KairosHope, a next-generation TSFM designed to reconcile massive generalization with analytical precision in classification tasks. The core of the proposal is the HOPE block, an architecture that replaces quadratic attention with a dual-memory system: Titans modules for dynamic short-term retention and a Continuum Memory System (CMS) for the abstraction of long-term historical context. To enrich the inductive bias, a Hybrid Decision Head is introduced, which fuses deep latent representations with deterministic statistical features extracted via tsfeatures package. KairosHope undergoes self-supervised pre-training on the massive Monash archive, combining Masked Time Series Modeling (MTSM) and contrastive learning (InfoNCE). Its subsequent adaptation to the UCR benchmark datasets is conducted through a rigorous Linear Probing and Full Fine-Tuning (LP-FT) protocol to prevent catastrophic forgetting. Empirical results demonstrate superior performance in domains characterized by strict temporal causality such as HAR or Sensor data. Consequently, KairosHope establishes a robust and efficient framework for the adaptation of foundation models to time series analysis.

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.

Visual Geometry Grounded Transformers (VGGT) have set new benchmarks in high-fidelity 3D scene reconstruction. However, as the sequence length increases, these models suffer from catastrophic geometric forgetting and accumulation drift, primarily due to the quadratic complexity of global attention which necessitates truncated temporal windows. To overcome the resulting geometric drift, we present Mamba-VGGT, an enhanced VGGT framework capable of persistent long-range reasoning. Our key contribution is a Sliding Window Mamba (SWM) memory module that maintains an explicit external memory token across temporal windows. This module leverages selective state-space modeling to distill and propagate global geometric priors, effectively bypassing the memory constraints of traditional transformers. To integrate these long-term temporal cues without disrupting the highly optimized spatial features of the pre-trained VGGT, we propose a Zero-Init Spatial Memory Injector. Utilizing zero-convolutional layers, this injector adaptively fuses persistent memory into the patch token stream, ensuring structural stability and seamless feature alignment. Extensive experiments demonstrate that our approach significantly outperforms existing VGGT-based methods in maintaining spatial consistency and reducing trajectory accumulation errors. Our work provides a scalable, linear-complexity solution for geometry-grounded world modeling in extensive 3D environments.

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.

Continually pre-training a large language model on heterogeneous text domains, without replay or task labels, has remained an unsolved architectural problem at LLM scale. Existing methods rely on replay buffers, task identifiers, regularization penalties that scale poorly, or sentence-classification-scale evaluation. We introduce TFGN, an architectural overlay for transformer language models that produces input-conditioned, parameter-efficient updates while leaving the rest of the transformer unchanged. On six heterogeneous text domains (Prose, Python, Math, Biomedical, Chinese, JavaScript) at 1B tokens per phase across three model scales (~398M, ~739M, ~9B) and two regimes (From-Scratch and Retrofit), TFGN achieves backward transfer of -0.007 at LLaMA 3.1 8B Retrofit, HellaSwag retention 0.506/0.504/0.510, and >=99.59% L2-orthogonal gradient separation between domain pairs - with no replay, no task IDs, no Fisher penalty. The same matrices show positive cross-domain forward transfer: held-out JavaScript PPL drops 26.8% at LLaMA-8B Retrofit and 62.0% at GPT-2 Medium From-Scratch purely from Python training. Two extensions on the same substrate close further open problems. A closed-loop meta-control layer (Extension A) reduces forgetting by an additional 81% at ~398M, mapping onto the System A and System M roles of Dupoux et al. (arXiv:2603.15381). An operator-level plan vector (Extension B) reshapes forward-pass behavior at 99.96% cosine fidelity over 30 source->target pairs. The architectural insight is a Read/Write decomposition: the forward pass is fully dense, while cross-domain parameter updates are structured so prior-domain subspaces are not written to. To our knowledge, TFGN is the first architecture that simultaneously closes catastrophic forgetting at LLM scale, realizes a closed-loop autonomous-learning meta-controller, and carries an operator-level latent planner.

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.

Neural networks suffer from catastrophic forgetting in class-incremental learning (CIL) settings. Rehearsal$\unicode{x2013}$replaying a subset of past samples$\unicode{x2013}$is a well-established mitigation strategy. However, recent results suggest that, despite balanced rehearsal allocation, some classes are forgotten substantially more than others. Despite its relevance, this imbalanced forgetting phenomenon remains underexplored. This work shows that imbalanced forgetting arises systematically and severely in rehearsal-based CIL and investigates it extensively. Specifically, we construct, from a principled analysis, three last-layer coefficients that capture different gradient-level sources of interference affecting each past class during an incremental step. We then demonstrate that, together, they reliably predict how past classes will rank in terms of forgetting at the end of that step. While predictive performance alone does not establish causality, these results support the interpretation of the coefficients as a plausible mechanistic account linking last-layer gradient-level interactions during training to class-level forgetting outcomes. Notably, one coefficient$\unicode{x2013}$capturing self-induced interference$\unicode{x2013}$emerges as the strongest predictor, with controlled experiments providing evidence consistent with this coefficient being influenced by the new-class interference coefficient. Overall, our findings provide valuable insights and suggest promising directions for mitigating imbalanced forgetting by reducing class-wise disparities in the identified sources of interference.

Parameter-Efficient Fine-Tuning (PEFT), particularly Low-Rank Adaptation (LoRA), has become a standard approach for adapting Large Language Models (LLMs) under limited compute. However, in continual settings where models are updated sequentially with small datasets, conventional LoRA updates struggle to balance rapid adaptation and knowledge retention. Existing methods typically treat the low-rank space as a homogeneous update region, lacking mechanisms to regulate how short-term updates are consolidated over time. We propose a continual LoRA framework with \textbf{Pro}gram memory, inspired by \textbf{C}omplementary \textbf{L}earning Systems in neuroscience. Our approach, dubbed \textbf{ProCL}, organizes LoRA adapters into structured program memory slots that are dynamically retrieved through input-conditioned attention. This enables rapid and localized adaptation, encouraging similar inputs to reuse shared adapter regions while reserving unused capacity for future data. The slots are then combined with the underlying adapter, which maintains a distributed representation that gradually accumulates knowledge across tasks to balance plasticity and stability. Our method operates entirely within the LoRA parameterization and incurs no additional inference cost. Experiments on diverse benchmarks demonstrate improved retention and reduced catastrophic forgetting over other continual LoRA strategies.

Large language models (LLMs) are trained for downstream tasks by updating their parameters (e.g., via RL). However, updating parameters forces them to absorb task-specific information, which can result in catastrophic forgetting and loss of plasticity. In contrast, in-context learning with fixed LLM parameters can cheaply and rapidly adapt to task-specific requirements (e.g., prompt optimization), but cannot by itself typically match the performance gains available through updating LLM parameters. There is no good reason for restricting learning to being in-context or in-weights. Moreover, humans also likely learn at different time scales (e.g., System 1 vs 2). To this end, we introduce a fast-slow learning framework for LLMs, with model parameters as "slow" weights and optimized context as "fast" weights. These fast "weights" can learn from textual feedback to absorb the task-specific information, while allowing slow weights to stay closer to the base model and persist general reasoning behaviors. Fast-Slow Training (FST) is up to 3x more sample-efficient than only slow learning (RL) across reasoning tasks, while consistently reaching a higher performance asymptote. Moreover, FST-trained models remain closer to the base LLM (up to 70% less KL divergence), resulting in less catastrophic forgetting than RL-training. This reduced drift also preserves plasticity: after training on one task, FST trained models adapt more effectively to a subsequent task than parameter-only trained models. In continual learning scenarios, where task domains change on the fly, FST continues to acquire each new task while parameter-only RL stalls.

Despite the rapid advancements in large language model (LLM) development, fine-tuning them for specific tasks often results in the catastrophic forgetting of their general, language-based reasoning abilities. This work investigates and addresses this challenge in the context of the Generative Retrieval (GenRetrieval) task. During GenRetrieval fine-tuning, we find this forgetting occurs rapidly and correlates with the distance between the fine-tuned and original model parameters. Given these observations, we propose ORBIT, a novel approach that actively tracks the distance between fine-tuned and initial model weights, and uses a weight averaging strategy to constrain model drift during GenRetrieval fine-tuning when this inter-model distance exceeds a maximum threshold. Our results show that ORBIT retains substantial text and retrieval performance by outperforming both common continual learning baselines and related regularization methods that also employ weight averaging.

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.

Lifelong Model Editing aims to continuously update evolving facts in Large Language Models while preserving unrelated knowledge and general capabilities, yet it remains plagued by catastrophic forgetting and model collapse. Empirically, we find that recent editors resilient over long horizons share the same core strategy: Lifelong Normalization (LN), which normalizes value gradients using running statistics. Removing LN causes immediate performance collapse, and we observe a counter-intuitive positive cumulative effect where early edits can promote the success of future edits. Yet the mechanism of LN remains a "black box", leaving its precise role in lifelong stability poorly understood. In this work, we provide the first theoretical account of LN in the lifelong regime. Our analysis reveals a self-reinforcing stability loop and proves that, when combined with ridge-regularized regression, LN yields parameter updates with asymptotic orthogonality and bounded norms, directly mitigating forgetting and systemic collapse. Based on these insights, we derive StableEdit, which strengthens this stability loop via an explicit warm-up stage and full whitening, improving long-horizon stability at minimal overhead. Extensive experiments validate our theory and demonstrate competitive performance. Our code is available at https://github.com/MINE-USTC/StableEdit.

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.

Adaptive behavior requires the brain to transition between distinct contexts while maintaining representations of prior experience. The ability to reconfigure neural representations without erasing previously acquired knowledge is central to learning in dynamic environments, yet the neural mechanisms that support this balance remain unclear. Understanding these mechanisms is also critical for addressing catastrophic forgetting in artificial systems designed for lifelong learning. Here, we identify joint sparse coding and temporal dynamics in both the mouse medial prefrontal cortex (mPFC) and computational networks as mechanisms that help preserve prior representations during context transitions. Specifically, sparsity in context-dependent representations reduces cross-context interference, whereas temporal dynamics within the network activity further enhance context separability across time. Strikingly, networks endowed with both properties, such as spiking neural networks, exhibit improved retention during lifelong learning without auxiliary heuristics. These findings establish joint sparse coding and temporal dynamics as a core mechanism supporting flexible context reconfiguration in lifelong learning and, through their activity constraining nature, as an energy-efficient architectural principle for stable adaptation. Together, they provide a mechanistic framework for understanding how the brain preserves prior knowledge while flexibly adapting to new contexts.

Graph learning research has increasingly shifted toward continual graph learning (CGL), which better reflects real-world scenarios where graphs evolve over time. However, existing CGL methods largely assume clean supervision and overlook a critical challenge: the newly arriving portions of the graph are often noisy, due to annotation errors or adversarial corruption. This mismatch limits their applicability in practice. In this work, we study robust continual graph learning, where models must simultaneously handle catastrophic forgetting and noisy supervision in evolving graph data. We show that label noise introduces a new failure mode, catastrophic remembering, where models persistently reinforce corrupted knowledge across tasks. To address these challenges, we propose a Unified Flow-Oriented framework (UFO). First, UFO models conditional feature distributions via flow-based generative modeling and produces replay representations, mitigating forgetting without storing historical data. Second, UFO estimates instance-level reliability scores to distinguish clean from noisy nodes, reducing the impact of corrupted supervision and alleviating catastrophic remembering. Extensive experiments on four benchmark graph datasets under varying noise ratios demonstrate that UFO consistently outperforms existing methods in both accuracy and forgetting metrics. Code is available at: https://anonymous.4open.science/r/UFO.

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.

Continual post-training aims to extend large language models (LLMs) with new knowledge, skills, and behaviors, yet it remains unclear when sequential updates enable capability transfer and when they cause catastrophic forgetting. Existing methods mitigate forgetting through sequential fine-tuning, replay, regularization, or model merging, but offer limited criteria for determining when incorporating new updates is beneficial or harmful. In this work, we study LLM continual post-training through three questions: What drives forgetting? When do sequentially acquired capabilities transfer or interfere? How can compatibility be used to control update integration? We address these questions through task geometry: we represent each post-training task by its parameter update and study the covariance geometry induced by the update. Our central finding is that: forgetting can be considered as a state-relative update-integration failure, it arises when the covariance geometries induced by tasks misalign with the geometry of the evolving model state. Sequential updates transfer when they remain compatible with the model state shaped by previous updates, and interfere when state-relative geometry conflict becomes high. Motivated by this finding, we propose Geometry-Conflict Wasserstein Merging (GCWM), a data-free update-integration method that constructs a shared Wasserstein metric via Gaussian Wasserstein barycenters and uses geometry conflict to gate geometry-aware correction. Across Qwen3 0.6B--14B on domain-continual and capability-continual settings, GCWM consistently outperforms data-free baselines, improving retention and final performance without replay data. These results identify geometry conflict as both an explanatory signal for forgetting and a practical control signal for LLM continual post-training.

Pre-trained models with parameter-efficient fine-tuning (PEFT) have demonstrated promising potential for class-incremental learning (CIL), yet catastrophic forgetting still persists when adapting models to new tasks. In this paper, we present a novel perspective on catastrophic forgetting through the analysis of inter-layer relation drift, i.e., the progressive disruption of relationships among layer-wise representations during the learning of new tasks. We theoretically show that the increase of such drift reduces the classification margins of previously learned tasks, thereby degrading overall model performance. To address this issue, we propose \underline{S}elf-\underline{R}ectifying inter-layer \underline{R}elation Low-Rank Adaptation~(SR$^2$-LoRA), a simple yet effective method that mitigates catastrophic forgetting by constraining inter-layer relation drift. Specifically, SR$^2$-LoRA constructs the relation matrices induced by the previous and current models on current-task samples, and aligns the corresponding singular values. We further theoretically show that this alignment exhibits greater robustness to estimation perturbations than direct entry-wise alignment. Extensive experiments on standard CIL benchmarks demonstrate that SR$^2$-LoRA effectively mitigates catastrophic forgetting, with its advantages becoming more pronounced as the number of tasks increases. Code is available in the \href{https://github.com/FqWan24/SR-2-LoRA}{repository}.

Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.

We address the challenge of knowledge composition in Vision-Language Models (VLMs), where accumulating expertise across multiple domains or tasks typically leads to catastrophic forgetting. We introduce GeoStack (Geometric Stacking), a modular framework that allows independently trained domain experts to be composed into a unified model. By imposing geometric and structural constraints on the adapter manifold, GeoStack ensures the foundational knowledge of the base model is preserved. Furthermore, we mathematically demonstrate a weight-folding property that achieves constant-time inference complexity ($O(1)$), regardless of the number of integrated experts. Experimental results across multi-domain adaptation and class-incremental learning show that GeoStack provides an efficient mechanism for long-term knowledge composition while significantly mitigating catastrophic forgetting. Code is available at https://github.com/QuantitativeImagingLaboratory/GeoStack.

The "Locate-then-Update" paradigm has become a predominant approach in the post-training of large language models (LLMs), identifying critical components via mechanistic interpretability for targeted parameter updates. However, this paradigm rests on a fundamental yet unverified assumption: can mechanisms derived from current static parameters reliably guide future dynamic parameter updates? To investigate this, we systematically track the structural evolution of Transformer circuits throughout the supervised fine-tuning (SFT) process, revealing the underlying dynamics of task mechanisms. We introduce three novel metrics-Circuit Distance, Circuit Stability, and Circuit Conflict-to analyze circuit evolution across three dimensions: neural migration, semantic stability, and cross-task interference. Our empirical results reveal that circuits inherently exhibit "Free Evolution" during parameter updates. Consequently, static mechanisms extracted from current states inevitably suffer from temporal latency, making them fundamentally inadequate for guiding future states. Moreover, by deconstructing the "illusion of effectiveness" in existing methods, this work underscores the necessity of "foresight" in mechanistic localization and proposes a predictive framework for future research.

The core challenge of machine unlearning is to strike a balance between target knowledge removal and non-target knowledge retention. In the context of Multimodal Large Language Models (MLLMs), this challenge becomes even more pronounced, as knowledge is further divided into visual and textual modalities that are tightly intertwined. In this paper, we introduce an MLLM unlearning approach that aims to forget target visual knowledge while preserving non-target visual knowledge and all textual knowledge. Specifically, we freeze the LLM backbone and achieve unlearning by fine-tuning the visual module. First, we propose a Contrastive Visual Forgetting (CVF) mechanism to separate target visual knowledge from retained visual knowledge, guiding the representations of target visual concepts toward appropriate regions in the feature space. Second, we identify the null space associated with retained knowledge and constrain the unlearning process within this space, thereby significantly mitigating degradation in knowledge retention. Third, beyond static unlearning scenarios, we extend our approach to continual unlearning, where forgetting requests arrive sequentially. Extensive experiments across diverse benchmarks demonstrate that our approach achieves a strong balance between effective forgetting and robust knowledge retention.

Machine unlearning seeks to remove the influence of designated training data while preserving performance on the remaining data. Approximate unlearning can be viewed as a local editing problem; in min-max unlearning, the key local object is the surrogate point at which the retain objective is evaluated. When forget and retain gradients are strongly aligned, an unconstrained forget-maximizing perturbation can move to a surrogate point that increases retain loss. We propose Retain-Orthogonal Surrogate Unlearning (ROSU), which constrains the inner surrogate construction by maximizing first-order forget gain subject to zero first-order retain change under a fixed perturbation budget. This yields a closed-form retain-orthogonal perturbation, a lightweight transported outer update, and amplification along the retain-neutral direction. Our analysis establishes (i) a curvature-controlled second-order bound on retain damage, (ii) a positive-alignment regime in which ROSU strictly reduces surrogate retain loss relative to standard min-max perturbations, and (iii) near-equivalence when the two gradients are nearly orthogonal. Across vision and language benchmarks (CIFAR-10/100, Tiny-ImageNet, TOFU, WMDP), the empirical pattern follows this geometry: ROSU gives its clearest gains in high-coupling regimes while remaining competitive elsewhere.

Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is \href{https://github.com/dannis97500/HEDP/}{available here}.