Continual Learning

Differentiable physical networks provide a simple setting in which learning can be studied through the interaction between trainable parameters and physical equilibrium constraints. We investigate sequential learning in differentiable resistor networks governed by Kirchhoff's laws. Although individual input--output mappings can be learned by gradient-based adjustment of edge conductances, sequential training on conflicting tasks produces catastrophic forgetting. We show that forgetting is controlled by task conflict and by the degree of adaptation to the new task. Uniform anchoring and normalised gradient-weighted anchoring reduce forgetting only by increasing the final loss on the new task, giving a clear forgetting--adaptation trade-off. We also show that forgetting is associated with localised conductance changes on high-current edges, giving a physical interpretation as reconfiguration of dominant transport pathways. Broader random-task ensembles show that the strongest forgetting occurs when the second task reverses the output ordering imposed by the first task. Finally, comparisons across Erdős--Rényi, small-world, scale-free, and random-geometric graph ensembles show that topology changes the forgetting--adaptation balance. These results position differentiable resistor networks as compact, physically interpretable testbeds for studying continual learning in tunable matter.

In the pursuit of autonomous learning systems, the foundational assumption of stationarity, the premise that data distributions and model behaviors remain constant, is fundamentally untenable. Historically, the research community has addressed non-stationary environments almost exclusively under the scope of concept drift, focusing primarily on temporal shifts in streams. However, as learning systems become increasingly autonomous and complex, merely adapting to temporal non-stationarity is no longer sufficient. Evolving beyond this traditional perspective, we propose a novel, three-dimensional taxonomy that systematizes the field based on the operational state of the system. First, time stream drift distinguishes between stochastic arbitrary patterns and structural rhythmic dynamics. Second, data stream drift disentangles shifts in feature representations, identified as representation drift, from changes in underlying semantics, recognized as semantic drift. Third, model stream drift characterizes the internal endogenous divergence of learning systems through the lenses of sequential plasticity, decentralized heterogeneity, and policy instability. Based on this framework, we systematically review 193 representative studies and identify key open challenges. By bridging the fragmented paradigms of drift adaptation, continual learning, and temporal generalization, this survey outlines a roadmap for building self-evolving intelligent systems capable of learning autonomously through continuous change.

This paper proposes and evaluates a new performance estimation method that leverages continual learning (CL) algorithms to carry out sequential simulation experiments for a feedback-based molecular communication protocol. As the protocol is sequentially examined in various experimental settings, the proposed CL-based performance estimators incrementally learn a series of unexperienced estimation tasks without compromising those that have been learned in the past. They are designed to work on a standard neural network architecture by customizing regularization and replay strategies in the loss function. Experimental results demonstrate that the proposed estimators can effectively learn on a continuous stream of simulation results and enhance the baseline neural network by improving estimation accuracy at a variety of computational costs. This paper's contribution is to establish the implications of CL in the field of molecular communication.

Current agentic memory systems (vector stores, retrieval-augmented generation, scratchpads, and context-window management) do not implement memory: they implement lookup. We argue that treating lookup as memory is a category error with provable consequences for agent capability, long-term learning, and security. Retrieval generalizes by similarity to stored cases; weight-based memory generalizes by applying abstract rules to inputs never seen before. Conflating the two produces agents that accumulate notes indefinitely without developing expertise, face a provable generalization ceiling on compositionally novel tasks that no increase in context size or retrieval quality can overcome, and are structurally vulnerable to persistent memory poisoning as injected content propagates across all future sessions. Drawing on Complementary Learning Systems theory from neuroscience, we show that biological intelligence solved this problem by pairing fast hippocampal exemplar storage with slow neocortical weight consolidation, and that current AI agents implement only the first half. We formalize these limitations, address four alternative views, and close with a co-existence proposal and a call to action for system builders, benchmark designers, and the memory community.

To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be reused across tasks: shared structure enables transfer when tasks are similar but may also induce interference when new learning disrupts existing representations. However, it remains unclear when and why structural separation influences this trade-off. In this study, we examine how network architecture, task similarity, and representational dimensionality jointly shape learning in a sequential task paradigm inspired by transfer-interference studies. We compare a task-partitioned modular recurrent network with a single-module baseline by systematically varying task similarity (low, medium, high) and the scale of weight initialization, which induces different learning regimes that we empirically characterize through the effective dimensionality of the learned representations. We find that architecture has minimal impact in high-dimensional regimes where representations are sufficiently unconstrained to accommodate multiple tasks without strong interference. In contrast, in lower-dimensional (rich) regimes, architectural separation is decisive: modular networks exhibit graded alignment of task-specific subspaces with overlap for similar tasks, partial orthogonalization for moderately dissimilar tasks, and stronger separation for dissimilar tasks. This graded geometry is absent in the single network baseline. Our findings suggest that representational dimensionality acts as a key organizing variable governing when structural separation becomes functionally relevant, and highlight adaptive geometry as a central principle for designing continual learning systems.

Continual learning agents with finite capacity must balance acquiring new knowledge with retaining the old. This requires controlled forgetting of knowledge that is no longer needed, freeing up capacity to learn. Weight decay, viewed as a mechanism for forgetting, can serve this role by gradually discarding information stored in the weights. However, a fixed scalar weight decay drives this forgetting uniformly over time and uniformly across all parameters, even when some encode stable knowledge while others track rapidly changing targets. We introduce Forgetting through Adaptive Decay (FADE), which adapts per-parameter weight decay rates online via approximate meta-gradient descent. We derive FADE for the online linear setting and apply it to the final layer of neural networks. Our empirical analysis shows that FADE automatically discovers distinct decay rates for different parameters, complements step-size adaptation, and consistently improves over fixed weight decay across online tracking and streaming classification problems.

In a continual learning setting, we require a model to be plastic enough to learn a new task and stable enough to not disturb previously learned capabilities. We argue that this dilemma has an architectural root. A finite network has limited representational and plastic resources, yet the required capacity depends on properties of the future task stream that are unknown: how many tasks will be encountered, and how much they overlap in feature space. Regularization-based methods preserve past knowledge within fixed-capacity architectures and therefore implicitly rely on an oracle architecture sized for this unknown future. When tasks are only weakly related, fixed architectures progressively run out of plastic resources; when tasks are few or strongly overlapping, models are often over-provisioned. Inspired by neurogenesis in biology, we propose NORACL to address the stability-plasticity dilemma by tackling the oracle architecture problem through neuronal growth. Starting from a compact network, NORACL grows only when needed by monitoring two complementary signals for representational and plasticity saturation. We evaluate NORACL against oracle-sized static baselines across varying task counts and geometries. Across all settings, NORACL achieves final average accuracies that are better than or on par with oracle-provisioned static baselines while using fewer parameters. Additionally, NORACL yields architectures with interpretable growth, i.e. dissimilar tasks predominantly expand feature-extraction layers, whereas tasks which rely on common features shift growth toward later feature-combination layers. Our analysis further explains why fixed-capacity networks lose plasticity as tasks accumulate, whereas NORACL creates fresh capacity for new tasks through growth. Together, these results show that adaptive neurogenesis pushes the stability-plasticity Pareto frontier of continual learning.

Continual offline reinforcement learning (CORL) aims to learn a sequence of tasks from datasets collected over time while preserving performance on previously learned tasks. This setting corresponds to domains where new tasks arise over time, but adapting the model in live environment interactions is expensive, risky, or impossible. However, CORL inherits the dual difficulty of offline reinforcement learning and adapting while preventing catastrophic forgetting. Replay-based continual learning approaches remain a strong baseline but incur memory overhead and suffer from a distribution mismatch between replayed samples and newly learned policies. At the same time, architectural continual learning methods have shown strong potential in supervised learning but remain underexplored in CORL. In this work, we propose TSN-Affinity, a novel CORL method based on TinySubNetworks and Decision Transformer. The method enables task-specific parameterization and controlled knowledge sharing through a RL-aware reuse strategy that routes tasks according to action compatibility and latent similarity. We evaluate the approach on benchmarks based on Atari games and simulations of manipulation tasks with the Franka Emika Panda robotic arm, covering both discrete and continuous control. Results show strong retention from sparse SubNetworks, with routing further improving multi-task performance. Our findings suggest that similarity-guided architectural reuse is a strong and viable alternative to replay-based strategies in a CORL setting. Our code is available at: https://github.com/anonymized-for-submission123/tsn-affinity.

Block-sequential continual learning demands that a single model both protect prior solutions from catastrophic forgetting and efficiently infer at inference time which prior solution matches the current input without task labels. We present Functional Task Networks (FTN), a parameter-isolation method inspired by structural and dynamical motifs found in the mammalian neocortex. Similar to mixture-of-experts, this method uses a high dimensional, self-organizing binary mask over a large population of small but deep networks, inspired by dendritic models of pyramidal neurons. The mask is produced by a three-stage procedure: (1) gradient descent on a continuous mask identifies task-relevant neurons, (2) a smoothing kernel biases the result toward spatial contiguity, (3) and k-winner-take-all binarizes the resulting group at a fixed capacity budget. Like mixture-of-experts, each neuron is an independent deep network, so disjoint masks give exactly disjoint gradient updates, providing structural guarantees against catastrophic forgetting. This three-stage procedure recovers the sub-network of a previously-trained task in a single gradient step, providing unsupervised task segmentation at inference time. We test it on three continual-learning benchmarks: (1) a synthetic multi-task classification/regression generator, (2) MNIST with shuffled class labels (pure concept shift), and (3) Permuted MNIST (domain shift). On all three, FTN with fine grained smoothing (FTN-Slow) results in nearly zero forgetting. FTN with a large kernel and only 2 iterations of smoothing (FTN-Fast) trades off some retention for increased speed. We show that the spatial organization mechanism reduces the effective mask search from the combinatorial top-k subset problem in O(C(H,K)) to the complexity of a near-linear scan in O(H) over compact cortical neighborhoods, which is parallelized by the gradient-based update.

Streaming Continual Learning (CL) typically converts a continuous stream into a sequence of discrete tasks through temporal partitioning. We argue that this temporal taskification step is not a neutral preprocessing choice, but a structural component of evaluation: different valid splits of the same stream can induce different CL regimes and therefore different benchmark conclusions. To study this effect, we introduce a taskification-level framework based on plasticity and stability profiles, a profile distance between taskifications, and Boundary-Profile Sensitivity (BPS), which diagnoses how strongly small boundary perturbations alter the induced regime before any CL model is trained. We evaluate continual finetuning, Experience Replay, Elastic Weight Consolidation, and Learning without Forgetting on network traffic forecasting with CESNET-Timeseries24, keeping the stream, model, and training budget fixed while varying only the temporal taskification. Across 9-, 30-, and 44-day splits, we observe substantial changes in forecasting error, forgetting, and backward transfer, showing that taskification alone can materially affect CL evaluation. We further find that shorter taskifications induce noisier distribution-level patterns, larger structural distances, and higher BPS, indicating greater sensitivity to boundary perturbations. These results show that benchmark conclusions in streaming CL depend not only on the learner and the data stream, but also on how that stream is taskified, motivating temporal taskification as a first-class evaluation variable.

Continual learning (CL) examines how models learn a sequence of tasks while retaining previously learned knowledge. Despite substantial progress in benchmarking CL methods, comparative evaluations typically keep the fine-tuning regime fixed. In this paper, we argue that the fine-tuning regime, defined by the trainable parameter subspace, is itself a key evaluation variable. We formalize adaptation regimes as projected optimization over fixed trainable subspaces, showing that changing the trainable depth alters the effective update signal through which both current task fitting and knowledge preservation operate. This analysis motivates the hypothesis that method comparisons need not be invariant across regimes. We test this hypothesis in task incremental CL while considering 5 trainable depth regimes and 5 standard methods: online EWC, LwF, SI, GEM, and DER. We find that the relative ranking of methods is not consistently preserved across regimes when evaluating across 5 benchmark datasets, namely MNIST, Fashion MNIST, KMNIST, QMNIST, and CIFAR-100, and across 11 task orders per dataset. We further show that deeper adaptation regimes are associated with larger update magnitudes, higher forgetting, and a stronger relationship between the two. These results show that comparative conclusions in CL can depend strongly on the chosen fine-tuning regime, motivating regime-aware evaluation protocols that treat trainable depth as an explicit experimental factor.

On-device continual learning (CL) is critical for edge AI systems operating on non-stationary data streams, but most existing methods rely on backpropagation or exemplar-heavy classifiers, incurring substantial compute, memory, and latency overheads. Hyperdimensional computing (HDC) offers a lightweight alternative through fast, non-iterative online updates. Combined with a compact convolutional neural network (CNN) feature extractor, HDC enables efficient on-device adaptation with strong visual representations. However, prior HDC-based CL systems often depend on multi-tier memory hierarchies and complex cluster management, limiting deployability on resource-constrained hardware. We present ImageHD, an FPGA accelerator for on-device continual learning of visual data based on HDC. ImageHD targets streaming CL under strict latency and on-chip memory constraints, avoiding costly iterative optimization. At the algorithmic level, we introduce a hardware-aware CL method that bounds class exemplars through a unified exemplar memory and a hardware-efficient cluster merging strategy, while incorporating a quantized CNN front-end to reduce deployment overhead without sacrificing accuracy. At the system level, ImageHD is implemented as a streaming dataflow architecture on the AMD Zynq ZCU104 FPGA, integrating HDC encoding, similarity search, and bounded cluster management using word-packed binary hypervectors for massively parallel bitwise computation within tight on-chip resource budgets. On CORe50, ImageHD achieves up to 40.4x (4.84x) speedup and 383x (105.1x) energy efficiency over optimized CPU (GPU) baselines, demonstrating the practicality of HDC-enabled continual learning for real-time edge AI.

In continual learning, the primary challenge is to learn new information without forgetting old knowledge. A common solution addresses this trade-off through regularization, penalizing changes to parameters critical for previous tasks. In most cases, this regularization term is directly added to the training loss and optimized with standard gradient descent, which blends learning and retention signals into a single update and does not explicitly separate essential parameters from redundant ones. As task sequences grow, this coupling can over-constrain the model, limiting forward transfer and leading to inefficient use of capacity. We propose a different approach that separates task learning from stability enforcement via operator splitting. The learning step focuses on minimizing the current task loss, while a proximal stability step applies a sparse regularizer to prune unnecessary parameters and preserve task-relevant ones. This turns the stability-plasticity into a negotiated update between two complementary operators, rather than a conflicting gradient. We provide theoretical justification for the splitting method on the continual-learning objective, and demonstrate that our proposed solver achieves state-of-the-art results on standard benchmarks, improving both stability and adaptability without the need for replay buffers, Bayesian sampling, or meta-learning components.

The ability of humans for lifelong learning is an inspiration for deep learning methods and in particular for continual learning. In this work, we apply Hebbian learning, a biologically inspired learning process, to sound classification. We propose a kernel plasticity approach that selectively modulates network kernels during incremental learning, acting on selected kernels to learn new information and on others to retain previous knowledge. Using the ESC-50 dataset, the proposed method achieves 76.3% overall accuracy over five incremental steps, outperforming a baseline without kernel plasticity (68.7%) and demonstrating significantly greater stability across tasks.

As AI generative models evolve at unprecedented speed, image attribution has become a moving target. New diffusion, adversarial and autoregressive generators appear almost monthly, making existing watermark, classifier and inversion methods obsolete upon release. The core problem lies not in model recognition, but in the inability to adapt attribution itself. We introduce IncreFA, a framework that redefines attribution as a structured incremental learning problem, allowing the system to learn continuously as new generative models emerge. IncreFA departs from conventional incremental learning by exploiting the hierarchical relationships among generative architectures and coupling them with continual adaptation. It integrates two mutually reinforcing mechanisms: (1) Hierarchical Constraints, which encode architectural hierarchies through learnable orthogonal priors to disentangle family-level invariants from model-specific idiosyncrasies; and (2) a Latent Memory Bank, which replays compact latent exemplars and mixes them to generate pseudo-unseen samples, stabilising representation drift and enhancing open-set awareness. On the newly constructed Incremental Attribution Benchmark (IABench) covering 28 generative models released between 2022 and 2025, IncreFA achieves state-of-the-art attribution accuracy and 98.93% unseen detection under a temporally ordered open-set protocol. Code will be available at https://github.com/Ant0ny44/IncreFA.

Continual learning (CL) is concerned with learning multiple tasks sequentially without forgetting previously learned tasks. Despite substantial empirical advances over recent years, the theoretical development of CL remains in its infancy. At the heart of developing CL theory lies the challenge that the data distribution varies across tasks, and we argue that properly addressing this challenge requires understanding this variation--dependency among tasks. To explicitly model task dependency, we consider nonlinear regression tasks and propose the assumption that these tasks are dependent in such a way that the data of the current task is a nonlinear transformation of previous data. With this model and under natural assumptions, we prove statistical recovery guarantees (more specifically, bounds on estimation errors) for several CL paradigms in practical use, including experience replay with data-independent regularization and data-independent weights that balance the losses of tasks, replay with data-dependent weights, and continual learning with data-dependent regularization (e.g., knowledge distillation). To the best of our knowledge, our bounds are informative in cases where prior work gives vacuous bounds.

Continual learning aims to update models under distribution shift without forgetting, yet many high-stakes deployments, such as healthcare, also require interpretability. In practice, models that adapt well (e.g., deep networks) are often opaque, while models that are interpretable (e.g., decision trees) are brittle under shift, making it difficult to achieve both properties simultaneously. In response, we propose Tree of Concepts, an interpretable continual learning framework that uses a shallow decision tree to define a fixed, rule-based concept interface and trains a concept bottleneck model to predict these concepts from raw features. Continual updates act on the concept extractor and label head while keeping concept semantics stable over time, yielding explanations that do not drift across sequential updates. On multiple tabular healthcare benchmarks under continual learning protocols, our method achieves a stronger stability-plasticity trade-off than existing baselines, including replay-enhanced variants. Our results suggest that structured concept interfaces can support continual adaptation while preserving a consistent audit interface in non-stationary, high-stakes domains.

Catastrophic forgetting remains a fundamental challenge in continual learning, in which models often forget previous knowledge when fine-tuned on a new task. This issue is especially pronounced in class incremental learning (CIL), which is the most challenging setting in continual learning. Existing methods to address catastrophic forgetting often sacrifice either model interpretability or accuracy. To address this challenge, we introduce ClassIncremental Concept Bottleneck Model (CI-CBM), which leverage effective techniques, including concept regularization and pseudo-concept generation to maintain interpretable decision processes throughout incremental learning phases. Through extensive evaluation on seven datasets, CI-CBM achieves comparable performance to black-box models and outperforms previous interpretable approaches in CIL, with an average 36% accuracy gain. CICBM provides interpretable decisions on individual inputs and understandable global decision rules, as shown in our experiments, thereby demonstrating that human understandable concepts can be maintained during incremental learning without compromising model performance. Our approach is effective in both pretrained and non-pretrained scenarios; in the latter, the backbone is trained from scratch during the first learning phase. Code is publicly available at github.com/importAmir/CI-CBM.

Synaptic plasticity is metabolically expensive, yet animals continuously update their internal models without exhausting energy reserves. However, when artificial neural networks are trained, the network parameters are typically updated on every sample that is presented, even if the sample was classified correctly. Inspired by the human negativity bias and error-related negativity, we propose 'memorized mistake-gated learning' -- a biologically plausible plasticity rule where synaptic updates are strictly gated by current and past classification errors. This reduces the number of updates the network needs to make by $50\%\sim80\%$. Mistake gating is particularly well suited in two cases: 1) For incremental learning where new knowledge is acquired on a background of pre-existing knowledge, 2) For online learning scenarios when data needs to be stored for later replay, as mistake-gating reduces storage buffer requirements. The algorithm can be implemented in a few lines of code, adds no hyper-parameters, and comes at negligible computational overhead. Learning on mistakes is an energy efficient and biologically relevant modification to commonly used learning rules that is well suited for continual learning.

Functional magnetic resonance imaging (fMRI) is widely used for studying and diagnosing brain disorders, with functional connectivity (FC) matrices providing powerful representations of large-scale neural interactions. However, existing diagnostic models are trained either on a single site or under full multi-site access, making them unsuitable for real-world scenarios where clinical data arrive sequentially from different institutions. This results in limited generalization and severe catastrophic forgetting. This paper presents the first continual learning framework specifically designed for fMRI-based diagnosis across heterogeneous clinical sites. Our framework introduces a structure-aware variational autoencoder that synthesizes realistic FC matrices for both patient and control groups. Built on this generative backbone, we develop a multi-level knowledge distillation strategy that aligns predictions and graph representations between new-site data and replayed samples. To further enhance efficiency, we incorporate a hierarchical contextual bandit scheme for adaptive replay sampling. Experiments on multi-site datasets for major depressive disorder (MDD), schizophrenia (SZ), and autism spectrum disorder (ASD) show that the proposed generative model enhances data augmentation quality, and the overall continual learning framework substantially outperforms existing methods in mitigating catastrophic forgetting. Our code is available at https://github.com/4me808/FORGE.

Continual learning enables models to acquire new knowledge over time while retaining previously learned capabilities. However, its application to text-to-3D generation remains unexplored. We present ReConText3D, the first framework for continual text-to-3D generation. We first demonstrate that existing text-to-3D models suffer from catastrophic forgetting under incremental training. ReConText3D enables generative models to incrementally learn new 3D categories from textual descriptions while preserving the ability to synthesize previously seen assets. Our method constructs a compact and diverse replay memory through text-embedding k-Center selection, allowing representative rehearsal of prior knowledge without modifying the underlying architecture. To systematically evaluate continual text-to-3D learning, we introduce Toys4K-CL, a benchmark derived from the Toys4K dataset that provides balanced and semantically diverse class-incremental splits. Extensive experiments on the Toys4K-CL benchmark show that ReConText3D consistently outperforms all baselines across different generative backbones, maintaining high-quality generation for both old and new classes. To the best of our knowledge, this work establishes the first continual learning framework and benchmark for text-to-3D generation, opening a new direction for incremental 3D generative modeling. Project page is available at: https://mauk95.github.io/ReConText3D/.

A central challenge in continual learning is forgetting: the loss of performance on previously learned tasks after learning new ones. Prior theory has analyzed forgetting under random orderings of fixed task collections in overparameterized linear regression. We shift the focus from task order to task distribution, asking how its structure determines forgetting. In the linear setting with a shared solution, i.i.d. task sampling, and sequential exact fitting, we derive an exact operator identity expressing historical forgetting directly in terms of the task distribution. Building on this identity, we establish an exponential decay guarantee for expected historical forgetting under every fixed task distribution in finite dimensions, characterize its asymptotic behavior, and relate decay to the distribution's coverage of observable directions. For an individual learned task, we show that subsequent tasks can collectively support recovery without exact revisits. We derive a lower bound on recovery time and construct a task distribution attaining its inverse-coverage scaling.

Recent advances in deep learning underscore the need for systems that can not only acquire new knowledge through Continual Learning (CL) but also remove outdated, sensitive, or private information through Machine Unlearning (MU). However, while CL methods are well-developed, MU techniques remain in early stages, creating a critical gap for unified frameworks that depend on both capabilities. We find that naively combining existing CL and MU approaches results in knowledge leakage a gradual degradation of foundational knowledge across repeated adaptation cycles. To address this, we formalize Continual Learning Unlearning (CLU) as a unified paradigm with three key goals: (i) precise deletion of unwanted knowledge, (ii) efficient integration of new knowledge while preserving prior information, and (iii) minimizing knowledge leakage across cycles. We propose Bi-Directional Low-Rank Adaptation (BID-LoRA), a novel framework featuring three dedicated adapter pathways-retain, new, and unlearn applied to attention layers, combined with escape unlearning that pushes forget-class embeddings to positions maximally distant from retained knowledge, updating only 5% of parameters. Experiments on CIFAR-100 show that BID-LoRA outperforms CLU baselines across multiple adaptation cycles. We further evaluate on CASIA-Face100, a curated face recognition subset, demonstrating practical applicability to real-world identity management systems where new users must be enrolled and withdrawn users removed.

Lifelong model editing (LME) aims to sequentially rectify outdated or inaccurate knowledge in deployed LLMs while minimizing side effects on unrelated inputs. However, existing approaches typically apply parameter perturbations to a static and dense set of LLM layers for all editing instances. This practice is counter-intuitive, as we hypothesize that different pieces of knowledge are stored in distinct layers of the model. Neglecting this layer-wise specificity can impede adaptability in integrating new knowledge and result in catastrophic forgetting for both general and previously edited knowledge. To address this, we propose HiEdit, a hierarchical reinforcement learning framework that adaptively identifies the most knowledge-relevant layers for each editing instance. By enabling dynamic, instance-aware layer selection and incorporating an intrinsic reward for sparsity, HiEdit achieves precise, localized updates. Experiments on various LLMs show that HiEdit boosts the performance of the competitive RLEdit by an average of 8.48% with perturbing only half of the layers per edit. Our code is available at: https://github.com/yangfanww/hiedit.

Continual Learning (CL) aims to train neural networks on a dynamic stream of tasks without forgetting previously learned knowledge. Among optimization-based approaches, C-Flat has emerged as a promising solution due to its plug-and-play nature and its ability to encourage uniformly low-loss regions for both new and old tasks. However, C-Flat requires three additional gradient computations per iteration, imposing substantial overhead on the optimization process. In this work, we propose C-Flat Turbo, a faster yet stronger optimizer that significantly reduces the training cost. We show that the gradients associated with first-order flatness contain direction-invariant components relative to the proxy-model gradients, enabling us to skip redundant gradient computations in the perturbed ascent steps. Moreover, we observe that these flatness-promoting gradients progressively stabilize across tasks, which motivates a linear scheduling strategy with an adaptive trigger to allocate larger turbo steps for later tasks. Experiments show that C-Flat Turbo is 1.0$\times$ to 1.25$\times$ faster than C-Flat across a wide range of CL methods, while achieving comparable or even improved accuracy.

Catastrophic forgetting is not an engineering failure. It is a mathematical consequence of storing knowledge as global parameter superposition. Existing methods, such as regularization, replay, and frozen subnetworks, add external mechanisms to a shared-parameter substrate. None derives retention from the learning dynamics themselves. This paper introduces the Informational Buildup Framework (IBF), an alternative substrate for continual learning, based on the premise that information is the achievement of structural alignment rather than stored content. In IBF, two equations govern the dynamics: a Law of Motion that drives configuration toward higher coherence, and Modification Dynamics that persistently deform the coherence landscape in response to localized discrepancies. Memory, agency, and self-correction arise from these dynamics rather than being added as separate modules. We first demonstrate the full lifecycle in a transparent two-dimensional toy model, then validate across three domains: a controlled non-stationary world, chess evaluated independently by Stockfish, and Split-CIFAR-100 with a frozen ViT encoder. Across all three, IBF achieves replay-superior retention without storing raw data. We observe near-zero forgetting on CIFAR-100 (BT = -0.004), positive backward transfer in chess (+38.5 cp), and 43% less forgetting than replay in the controlled domain. In chess, the framework achieves a mean behavioral advantage of +88.9 +/- 2.8 cp under independent evaluation, exceeding MLP and replay baselines.

Continual learning (CL) on edge devices requires not only high accuracy but also training-time efficiency to support on-device adaptation under strict memory and computational constraints. While prompt-based continual learning (PCL) is parameter-efficient and achieves competitive accuracy, prior work has focused mainly on accuracy or inference-time performance, often overlooking the memory and computational costs of on-device training. In this paper, we propose CPS-Prompt, a critical patch-aware sparse prompting framework that explicitly targets training-time memory usage and computational cost by integrating critical patch sampling (CPS) for task-aware token reduction and decoupled prompt and classifier training (DPCT) to reduce backpropagation overhead. Experiments on three public benchmarks and real edge hardware show that CPS-Prompt improves peak memory, training time, and energy efficiency by about 1.6x over the balanced CODA-Prompt baseline, while maintaining accuracy within 2% of the state-of-the-art C-Prompt on average and remaining competitive with CODA-Prompt in accuracy. The code is available at https://github.com/laymond1/cps-prompt.

Task-free online continual learning has recently emerged as a realistic paradigm for addressing continual learning in dynamic, real-world environments, where data arrive in a non-stationary stream without clear task boundaries and can only be observed once. To consider such challenging scenarios, many recent approaches have employed prompt selection, an adaptive strategy that selects prompts from a pool based on input signals. However, we observe that such selection strategies often fail to select appropriate prompts, yielding suboptimal results despite additional training of key parameters. Motivated by this observation, we propose a simple yet effective SinglePrompt that eliminates the need for prompt selection and focuses on classifier optimization. Specifically, we simply (i) inject a single prompt into each self-attention block, (ii) employ a cosine similarity-based logit design to alleviate the forgetting effect inherent in the classifier weights, and (iii) mask logits for unexposed classes in the current minibatch. With this simple task-free design, our framework achieves state-of-the-art performance across various online continual learning benchmarks. Source code is available at https://github.com/efficient-learning-lab/SinglePrompt.

Continual learning in artificial neural networks is fundamentally limited by the stability--plasticity dilemma: systems that retain prior knowledge tend to resist acquiring new knowledge, and vice versa. Existing approaches, most notably elastic weight consolidation~(EWC), address this empirically without a physical account of why plasticity eventually collapses as tasks accumulate. Separately, the distinction between sudden insight and gradual skill acquisition through repetitive practice has lacked a unified theoretical description. Here, we show that both problems admit a common resolution within non-equilibrium statistical physics. We model the state of a learning system as a particle evolving under Langevin dynamics on a double-well energy landscape, with the noise amplitude governed by a time-dependent effective temperature $T(t)$. The probability density obeys a Fokker--Planck equation, and transitions between metastable states are governed by the Kramers escape rate $k = (ω_0ω_b/2π)\,e^{-ΔE/T}$. We make two contributions. First, we identify the EWC penalty term as an energy barrier whose height grows linearly with the number of accumulated tasks, yielding an exponential collapse of the transition rate predicted analytically and confirmed numerically. Second, we show that insight and repetitive learning correspond to two qualitatively distinct temperature protocols within the same Fokker--Planck equation: insight events produce transient spikes in $T(t)$ that drive rapid barrier crossing, whereas repetitive practice operates at a modestly elevated but fixed temperature, achieving transitions through sustained stochastic diffusion. These results establish a physically grounded framework for understanding plasticity and its failure in continual learning systems, and suggest principled design criteria for adaptive noise schedules in artificial intelligence.

Real-world multimodal knowledge graphs (MMKGs) are dynamic, with new entities, relations, and multimodal knowledge emerging over time. Existing continual knowledge graph reasoning (CKGR) methods focus on structural triples and cannot fully exploit multimodal signals from new entities. Existing multimodal knowledge graph reasoning (MMKGR) methods, however, usually assume static graphs and suffer catastrophic forgetting as graphs evolve. To address this gap, we present a systematic study of continual multimodal knowledge graph reasoning (CMMKGR). We construct several continual multimodal knowledge graph benchmarks from existing MMKG datasets and propose MRCKG, a new CMMKGR model. Specifically, MRCKG employs a multimodal-structural collaborative curriculum to schedule progressive learning based on the structural connectivity of new triples to the historical graph and their multimodal compatibility. It also introduces a cross-modal knowledge preservation mechanism to mitigate forgetting through entity representation stability, relational semantic consistency, and modality anchoring. In addition, a multimodal contrastive replay scheme with a two-stage optimization strategy reinforces learned knowledge via multimodal importance sampling and representation alignment. Experiments on multiple datasets show that MRCKG preserves previously learned multimodal knowledge while substantially improving the learning of new knowledge.