NeurIPS 2026 Papers

Federated continual learning (FCL) evaluates how distributed clients learn from changing data streams while retaining previously learned knowledge. Existing evaluations are difficult to compare because they often change datasets, task splits, client data splits, task orders, backbones, memory assumptions, and reporting rules simultaneously. We introduce \textbf{HERO}, a heterogeneity-aware benchmark library for FCL. HERO builds benchmark streams by separating three choices that are often coupled, namely the task split, the client data split, and the client task sequence. In HERO-Core, the main comparable benchmark, $\alpha$ controls client data skew and $\rho$ controls task-order mismatch. We evaluate representative FCL methods on CIFAR-100 and TinyImageNet using final average accuracy, average forgetting, and bottom-10\% client accuracy. We also include a graph-based Domain-IL portability case study on OGB-MolPCBA, where scaffold-domain granularity changes the input distribution while the prediction task remains fixed. Our results show that method behavior changes across easy and heterogeneous settings, that average accuracy can hide weak bottom-client performance, that task-order mismatch favors different strategies from synchronized evaluation, and that the same HERO interface can expose domain-shift difficulty beyond image-based FCIL. HERO releases benchmark streams, configurations, method implementations, and reporting scripts to support reproducible and setting-aware FCL evaluation.

Online Continual Learning (OCL) requires models to learn from non-stationary data streams under a strict single-pass constraint, making them highly susceptible to catastrophic forgetting. While existing studies have explored various strategies from data, architecture, and optimization perspectives, the optimizer often directly uses generic approaches such as SGD and AdamW. In this work, we reveal a new link between optimization dynamics and OCL needs by recasting Polyak-Ruppert averaging as the engine of "plasticity" and Primal averaging as the anchor of "stability". This inspires our novel optimizer, SPIN (**S**tability-**P**lasticity **IN**terpolation), which explicitly decouples plasticity and stability by interpolating between a fast-moving "plasticity" sequence and an adaptive "stability" sequence. We theoretically demonstrate that SPIN implicitly employs an inverse Hessian approximation, providing crucial Tikhonov regularization to damp noisy, single-sample Hessian estimates and mitigate forgetting. More importantly, SPIN can be seamlessly integrated existing OCL methods by taking resulted gradients as input and replacing standard optimizers. Extensive experiments show that using SPIN instead of standard optimizers yields consistent and significant performance gains across multiple OCL approaches, including the challenging rehearsal-free setting and under strict memory constraints.

Continual Reinforcement Learning (CRL) requires agents to adapt to sequentially arriving tasks while retaining performance on previous ones. Most existing CRL methods rely on model-free frameworks, addressing catastrophic forgetting via regularization, parameter isolation, or experience replay. World models offer a promising alternative by accumulating transferable dynamics knowledge and enabling planning-based decision-making. However, existing world model approaches suffer from slow adaptation at task boundaries: abrupt reward shifts mislead the planner, fixed planning horizons accumulate prediction errors when the dynamics model is unreliable, and quality-agnostic replay dilutes training while exacerbating forgetting. We propose HERD (Horizon-adaptive Elite Replay with reward Disagreement), which addresses these challenges from two complementary perspectives: for $\textbf{\emph{how to learn}}$, Uncertainty-aware Reward Planning leverages ensemble disagreement to accelerate reward calibration and guide exploration, while Adaptive Planning Horizon adjusts rollout depth based on dynamics prediction error to prevent error accumulation; for $\textbf{\emph{what to learn}}$, Elite Experience Replay applies quality-stratified reweighting of historical trajectories to strengthen knowledge retention. Together, these components $\textbf{\emph{accelerate new-task adaptation and mitigate catastrophic forgetting.}}$ Experiments on Continual World, Continual Bench, and DM Control show that HERD consistently outperforms existing methods in overall performance, forgetting mitigation, and new-task adaptation.

The uncertainty of a statistical model is most commonly factorized into an aleatoric and an epistemic part. This factorization changes how predictions are interpreted in downstream decision tasks. Importantly, except for the idealistic scenario with no model mismatch, the quantification is a characteristic of the model and not the data generating process. In this paper, we propose Forgetting to Improve a method that reduces this discrepancy by incorporating the task into the modeling framework. Our key insight is to acknowledge that in scenarios of model mismatch, data can have a detrimental effect on the modeling for a specific task. Based on this insight, we propose an influence function for Gaussian process models that allows for principled removal of detrimental data samples. We showcase the flexibility of this approach by demonstrating significant improvements across a range of tasks, including Bayesian optimization, model-based reinforcement learning, and transductive learning.

Machine unlearning aims to remove the influence of selected training examples without full retraining. Standard evaluations often summarize unlearning quality with aggregate metrics, such as accuracy- and forgetting-based scores, which can hide localized failures. We study this failure mode at the example level by comparing the predictions of an unlearned model to those of the model retrained after deletion. We show that this pointwise discrepancy can be highly non-uniform: for gradient-ascent and random-labeling methods, with and without retain-set fine-tuning, it grows with geometric proximity to the forget set. We call this phenomenon *localized collateral forgetting*. Our analysis identifies a mechanism behind the effect: surrogate targets used during unlearning can be inconsistent with the local prediction structure induced by retraining, and this inconsistency propagates through shared representations to nearby examples. Motivated by this mechanism, we propose *Local Teacher Distillation*, a simple mitigation strategy that replaces random targets with soft labels from a small teacher trained only on retained neighbors of the forget set. On CIFAR-100 partial-class deletion, this local teacher brings the unlearned model substantially closer to retraining, especially near the forget set, while maintaining competitive aggregate unlearning metrics.

Federated Continual Learning (FCL) suffers from spatial-temporal catastrophic forgetting caused by sequential task learning on individual clients and the aggregation of heterogeneous client knowledge. However, most existing methods either overemphasize preserving old knowledge, which restricts model plasticity for new tasks, or rely on training complex generative models for replay, incurring substantial computational overhead. In the human immune system, immune memory is preserved implicitly and can be reactivated through vaccination even after long periods of dormancy. Motivated by this, we propose ***FedVaccine***, a novel framework that explicitly permits forgetting to preserve high plasticity for new tasks, while efficiently recovering past knowledge through re-learning a compact vaccine set. Specifically, the vaccine set for each task is synthesized by compress task gradient information under the guidance of the fine-tuned local model, capturing representative data characteristics and task-specific discriminative patterns. Two novel components are also introduced: ***Priming & Boosting***, which encodes task-specific knowledge in a compact spectral form, priming the model with essential information and enabling efficient memory boosting via vaccine set replay after forgetting; and ***Vaccination Aggregation***, which aggregates vaccine sets from all clients to train a globally generalized model without accessing any raw private data. Extensive experiments on three benchmarks demonstrate that FedVaccine achieves competitive performance, enables rapid knowledge recovery after forgetting, and incurs no additional overhead from training generative models.

As privacy, copyright, and safety requirements evolve, federated learning systems face a growing imperative to accommodate sequential unlearning requests. However, existing federated unlearning methods are designed for single-shot settings and their direct sequential application may lead to uncontrolled parameter-space overlap, causing cross-request interference that undermines prior forgetting. To address this, we propose the Spectral Orthogonality for Federated Continual unlearning (FedSOUL), a framework that reduces direct overlap among sequential unlearning updates. The core idea is to structure model updates in a shared orthonormal spectral basis, where each client is assigned a dedicated subspace in the frequency domain. Under this design, each unlearning request updates only its associated subspace, while all others remain unchanged, ensuring that sequential updates do not overlap in the allocated spectral coefficient space and thereby reducing cross-request interference. Beyond interference control, FedSOUL also improves efficiency by operating on sparse spectral coefficients, using FFT-based transforms for efficient computation and communicating only sparse coefficient updates. From a theoretical perspective, we relate continual unlearning to geometric conditions on update directions and show that our spectral construction satisfies update orthogonality by design, while functional preservation depends on bounded projected gradient leakage. Extensive experiments demonstrate that FedSOUL maintains stable unlearning–utility trade-offs across up to ten sequential requests and consistently outperforms competitive federated baselines. Our code is available at https://anonymous.4open.science/r/fedunlearning-1B92/.

We argue that forgetting is not confined to continual learning but is a general optimization phenomenon: during standard training, dominant mini-batch gradients suppress rare but useful update directions, causing short-term forgetting at every step. When such knowledge is never revisited, these losses compound into long-term forgetting—the classical failure mode of continual learning. We introduce FOGO, a scalable optimizer that continuously detects and resolves gradient interference across both regimes. FOGO spectrally orthogonalizes momentum updates to prevent dominant directions from monopolizing optimization, then stores representative past directions in a compact codebook memory built on random projection, where pairwise distances are provably preserved in low-dimensional space. At each step, conflicts between the current update and stored directions are resolved via lightweight orthogonal correction and lifted back through a proximal step, with minimal overhead and no data storage. Across class-imbalanced classification, continual visual learning under domain and class shifts, continual fine-tuning of LLaVA-7B, and GPT-2 pretraining, FOGO consistently improves convergence and knowledge retention, outperforming Adam and Muon.

Multimodal Large Language Models (MLLMs) achieve strong performance through instruction tuning, yet real-world deployment often requires continual capability expansion across sequential tasks. In such scenarios, Multimodal Continual Instruction Tuning (MCIT) aims to acquire new capabilities while limiting catastrophic forgetting. Existing methods mainly follow a module-composition paradigm: they maintain task-level prompts or LoRA experts and dynamically route or aggregate a subset of them at inference. However, samples within the same task can still differ substantially in visual scenes, question intents, and reasoning demands. This motivates instance-level adaptation to individual query-image pairs rather than only selecting or combining task-level modules. To this end, we propose DRAPE (Dynamic Cross-Modal Prompt Generation), a prompt-learning framework that synthesizes continuous instance-specific soft prompts for MCIT. Instead of selecting prompts from a fixed pool, DRAPE derives prompt queries from the textual instruction and cross-attends to visual patch features, producing query-image conditioned prompts that are prepended to the frozen LLM. To mitigate forgetting during sequential updates, DRAPE applies null-space gradient projection to the shared projector and uses CLIP-based prototype routing for task-label-free generator selection at inference. Extensive experiments on MCIT benchmarks show that DRAPE achieves state-of-the-art performance among representative prompt-based and LoRA-based continual-learning baselines.

Biological circuits learn without catastrophic forgetting, but the structural basis of this ability remains unclear. We investigate whether distance-dependent connectivity (DDC), spatial recurrency found in the mammalian cortex, contributes to continual learning by embedding neurons of a biologically plausible recurrent spiking neural network in a 3D Euclidean substrate, using pairwise distance to set recurrent connection probability, and ablating that distance dependence in silico. We show that DDC shapes a synaptic resource geography: it controls the spatial breadth of the candidate synaptic pool for learning to occur, plasticity further compresses that pool, and the resulting substrate governs how subsequent inputs compete for the same synapses. On challenging 10-way class-incremental MNIST classification, this produces a non-monotonic accuracy curve, with an intermediate DDC range achieving the best performance (71.4%) and outperforming both highly local circuits that collapse into a synaptic-resource bottleneck and random connectivity that produces weakly guided, broader synaptic contention. This pattern was better explained by synaptic competition, resulting in separable neural dynamics, than by neuron assembly separation. These results suggest that appropriate cortical DDC may prevent diffuse random contention. For continual learning problems, this finding highlights the conceptual importance of circuit dynamics more than active neuron ensembles and engrams.

Cold-start exemplar-free class-incremental learning requires learning a growing set of classes without replay, external pretraining, or a large initial task. Existing cold-start methods typically either train the backbone throughout the stream and compensate for semantic drift, or freeze a backbone after the first task, producing features biased toward the initial classes. These choices also create a computational tension: drift-compensation methods require repeated backbone training and increasingly expensive updates as the task horizon grows, while frozen-backbone methods are cheap but weak under cold start. We study a third option: a feature extractor that is never fit to image data at all. We propose CIRCLE, a class-incremental classifier built from fixed bidirectional two-dimensional reservoir features, adapted from BiRC2D for image classification, and streaming linear discriminant analysis heads. CIRCLE groups multiple random reservoir instantiations into feature ensembles and averages the softmax outputs of independent SLDA heads, yielding a tunable bias-variance tradeoff between richer random features and prediction-level ensembling. Because the feature extractor is fixed and the head admits streaming closed-form updates, CIRCLE performs sample-wise training without replay, task-boundary information, or backbone backpropagation. On CIFAR-100, TinyImageNet, ImageNet-Subset, and ImageNet-1k, CIRCLE is competitive at 10-20 task splits and substantially outperforms strong CS-EFCIL baselines at 50, 100, and 500 task splits, while training much faster than trained-backbone drift-compensation methods. Ablations show that the BiRC2D-style extractor, SLDA head, and balanced feature/prediction ensembling each contribute to the final performance.

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.

Multimodal Large Language Models (MLLMs) trained on sequential tasks suffer from catastrophic forgetting. We study this problem in LoRA-based multimodal continual instruction tuning. By analyzing the diagonal Fisher information of LoRA parameters, we find that forgetting is amplified not merely by shared high-sensitivity parameters across tasks, but by the concentration of updates on those shared parameters, \ie, some tasks distribute their change uniformly across parameters, while others pack most of it into a narrow subset, causing disproportionate interference on the parameters that prior tasks depend on. We further observe that this concentration manifests in the dominant directions of recent gradients. Based on this insight, we propose \textbf{D}om\textbf{i}nant-direction \textbf{G}radient \textbf{Pro}jection (\textbf{DiGPro}), which maintains a short buffer of recent gradient directions, extracts their dominant subspace with adaptive rank selection, and attenuates the parallel component for each optimizer step. Crucially, DiGPro requires no prior-task data or stored subspaces, operating on the current gradient history. Experiments on cross-modal and vision-centric continual learning benchmarks show DiGPro consistently reduces forgetting and attains competitive final results. The code is available in the supplementary materials.

Adapting language models to new domains during post-training risks degrading previously acquired capabilities, a phenomenon commonly known as \emph{catastrophic forgetting}. Existing mitigation methods largely treat forgetting as a consequence of excessive model drift. They therefore constrain updates by preserving old outputs, replaying old data, or regularizing changes to parameters and representations so that the updated model remains close to its previous state. We take a \textit{different view}: {Rather than pulling the updated model back toward its old state, we translate the new domain into the model’s pre-existing knowledge space, making unfamiliar knowledge learnable through familiar procedures}. Therefore, we propose \textbf{Skill Schema Transport (SST)}, a post-training framework that transports new knowledge into the model's existing skill space. SST abstracts each example type into a skill schema, preserving its essential operations, dependencies, and verification steps while removing domain-specific surface forms. By recasting new examples as instances of reusable procedures, SST turns knowledge update from trajectory memorization into procedural reuse. In continual domain adaptation settings, SST consistently reduces forgetting while improving generalization to related tasks. Across two 3B instruction-tuned backbones, SST improves average final performance on streamed domains by 2.53-5.75 points over sequential post-training. It also lowers max-drop forgetting in all evaluated settings, with the largest reduction from 42.41 to 7.10 points on the Qwen-3B MATH stream, while substantially recovering the OOD degradation induced by sequential updates.

Replay is a standard strategy for mitigating catastrophic forgetting in continual learning, where a bounded memory buffer stores exemplars from previously seen classes. Existing replay methods have largely focused on instance-level decisions, such as which samples to store, replay, or replace, while the class-wise allocation of memory slots is often treated as a uniform heuristic. Here, we study class-wise memory allocation as a complementary design axis and propose VAMA, a value-aware memory allocation framework. VAMA keeps cross-task budgets balanced, estimates task-local class values from Shapley-inspired sample utility scores, and converts them into class-wise quotas through a regularized allocation rule that conservatively deviates from class-balanced replay. This design changes only the class-wise budgeting rule and leaves within-class exemplar selection unchanged, making VAMA easy to integrate into replay pipelines. Experiments on CIFAR-100 and ImageNet-100 show that VAMA consistently improves ER, iCaRL, and FOSTER across different memory budgets and task protocols. Further analyses show that the improvements are not due to non-uniform allocation alone, and that allocation-relevant class-value rankings stabilize early in training, enabling efficient value-aware allocation. These results suggest that class-wise memory allocation is a consequential design choice in replay-based continual learning.

Personalized federated continual learning (pFCL) alleviates catastrophic forgetting across tasks and data heterogeneity across clients. We view both challenges as interference between knowledge and propose Bayesian frameworks that define knowledge as posterior belief and quantify two types of interference: intra-model interference, measuring task-induced posterior drift, and inter-model interference, measuring aggregation-induced posterior drift. We show that such interference bounds catastrophic forgetting and data heterogeneity-induced loss, respectively. We then develop an interference-regularized local objective to guide personalization under catastrophic forgetting and data heterogeneity. The framework unifies standard FCL and pFL categories. Experiments on synthetic and real-world benchmarks demonstrate improved model performance over state-of-the-art pFCL methods.

Remote photoplethysmography (rPPG) enables non-contact physiological measurement from facial videos, but performance often degrades under unseen environments due to severe domain shifts. Continual learning offers a practical paradigm for updating rPPG models over sequential domains. However, it is challenged by two coupled issues: First, adapting to new domains may overwrite previously acquired physiological representations, resulting in the degradation of physiological consistency across domains. Second, drastic environmental variations induce heterogeneous facial video distributions, making the adaptation process unstable and prone to suboptimal convergence. To address these challenges, we propose ApexPhys, a continual rPPG framework that simultaneously anchors physiological invariance and expands domain plasticity. Specifically, we introduce a Backbone Consistency Representation Preservation (BCRP) mechanism, which leverages the Fisher Information Matrix to identify and preserve parameters critical to physiological consistency. To enhance adaptation flexibility under diverse environmental shifts, we further propose a Hierarchical Expansion Strategy (HES) that autonomously perceives layer-wise distribution discrepancies and dynamically expands hierarchical adaptation branches. Additionally, we develop a Prior-Guided Pathfinding (PGP) strategy, which leverages parameter inheritance to guide the adaptation along a stable trajectory. Experiments on five public datasets demonstrate that ApexPhys achieves strong anti-forgetting performance and robust adaptation under continual learning.

We theoretically and empirically establish a previously unexplored connection between Long-Tailed Recognition (LTR) and Continual Learning (CL). Specifically, we show that training on a long-tailed dataset drives model parameters into an $\mathcal{O}(1/\sqrt{\mathrm{IF}})$ neighborhood of the dominant-class solution, under both uniform and exponentially decaying cardinality distributions. Building on this result, we prove that the CL objective upper-bounds the balanced LTR loss, revealing that LTR can be reformulated as a sequential learning problem. Motivated by this connection, we introduce Continual Learning for Long-Tailed Recognition (CLTR), a principled framework that leverages standard off-the-shelf CL methods to sequentially learn Head and Tail classes while mitigating catastrophic forgetting. Extensive experiments on CIFAR100-LT, CIFAR10-LT, ImageNet-LT, and Caltech256 validate our theoretical predictions and demonstrate strong performance across diverse LTR benchmarks. In the foundation-model regime, CLTR with DualPrompt on a CLIP backbone outperforms standard adaptation baselines and is competitive with specialized methods using external semantic supervision. Our work bridges LTR and CL both theoretically and empirically, providing a principled approach for addressing long-tailed learning using standard CL strategies.