Catastrophic Forgetting

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.

Federated learning (FL) holds great potential for medical applications. However, statistical heterogeneity across healthcare institutions poses a major challenge for FL, as the global model struggles both to generalize across unseen patient populations and to adapt to the unique data distributions of individual hospitals. This heterogeneity also exacerbates forgetting at both the global and local level, resulting in previous learned patient patterns to be misclassified after model updates. While prior work has largely treated generalization and personalization as separate challenges, we show that a better balance between the two can be achieved through selective alignment with the global model and a modified aggregation scheme, which together mitigate the effects of statistical heterogeneity. Specifically, we introduce FedKPer, which introduces knowledge personalization into the training stage of each local device. Afterwards, generalization is considered via the global model aggregation process, where local updates that are reliable and label-diverse are emphasized. We evaluate the performance of FedKPer, devising additional metrics that relate to common consequences of forgetting. Overall, we demonstrate FedKPer improves the generalization-personalization trade-off without sacrificing retention.

Supervised Fine-Tuning (SFT) is essential for aligning Large Language Models (LLMs) with user intent, yet it is believed to suppress generative diversity. Although this reduction is frequently referenced, formal empirical testing of the phenomenon remains limited. The expressiveness of LLMs by itself was addressed by multiple prior methods. Their varying perspectives suggest that deeper investigation could yield further improvements. In this study, we attribute the decline to two primary drivers: the neglect of low-frequency patterns within fine-tuning datasets and the forgetting of preexisting knowledge. Motivated by our theoretical analysis, we develop Tempered Focal (TOFU) loss, a novel objective that addresses both stated challenges simultaneously. Our extensive evaluation confirms at scale that generation breadth narrows after SFT and strengthens the hypothesis explaining this effect. Across multiple models and benchmarks, we demonstrate that TOFU enhances output diversity while preserving high response quality, offering a principled approach to SFT.

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.

Memory-augmented LLM agents offer an appealing shortcut to continual learning: rather than updating model parameters, they accumulate experience in external memory, seemingly sidestepping the stability-plasticity dilemma of parametric learning. We show that this challenge does not disappear but resurfaces at the memory level. Under a limited context window, old and new experiences compete during retrieval, relocating the continual-learning bottleneck from parameter updates to memory access. To study this phenomenon, we introduce a (k,v) framework that disentangles two fundamental design axes of external memory: how experience is represented and how it is organized for retrieval. Across sequential-task experiments in ALFWorld and BabyAI, we find that abstract procedural memories transfer more reliably than detailed trajectories, while negative transfer disproportionately harms the hard cases. Moreover, finer-grained memory organization is not universally beneficial: designs that yield strong forward transfer can simultaneously induce severe forgetting. Together, these results reveal that external memory does not resolve the continual-learning problem; it reshapes it into a problem of memory representation and retrieval design.

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.

Generative information retrieval (GenIR) consolidates retrieval into a single neural model that decodes document identifiers (docids) directly from queries. While this model-as-index paradigm offers architectural simplicity, it is poorly suited to dynamic document collections. Unlike modular systems, where indexes are easily updated, GenIR's knowledge is parametrically encoded in its weights; consequently, standard adaptation methods such as full and parameter-efficient fine-tuning can induce catastrophic forgetting. We show that sequential adaptation improves retrieval on newly added documents but substantially degrades performance on earlier slices, exposing a pronounced stability-plasticity trade-off. To address this, we propose post-adaptation memory tuning (PAMT), a memory-only stabilization stage that augments an adapted model with a modular parametric memory head (PMH). PAMT freezes the backbone and attaches a product-key memory with fixed addressing. During prefix-trie constrained decoding, decoder hidden states sparsely query PMH to produce residual corrections in hidden space; these corrections are mapped to score adjustments via the frozen output embedding matrix, computed only over trie-valid tokens. This guides docid generation while keeping routing and backbone parameters fixed. To limit cross-slice interference, PAMT updates only a fixed budget of memory values selected using decoding-time access statistics, prioritizing entries frequently activated by the current slice and rarely used in prior sessions. Experiments on MS MARCO and Natural Questions under sequential, disjoint corpus increments show that PAMT substantially improves retention on earlier slices with minimal impact on retrieval performance for newly added documents, while modifying only a sparse subset of memory values per session.

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

Federated continual learning (FCL) allows distributed autonomous fleets to adapt collaboratively to evolving terrain types across extended mission lifecycles. However, current approaches face several key challenges: 1) they use uniform protection strategies that do not account for the varying sensitivities to forgetting on different network layers; 2) they focus primarily on preventing forgetting during training, without addressing the long-term effects of cumulative drift; and 3) they often depend on idealized simulations that fail to capture the real-world heterogeneity present in distributed fleets. In this paper, we propose a lifecycle-aware dual-timescale FCL framework that incorporates training-time (pre-forgetting) prevention and (post-forgetting) recovery. Under this framework, we design a layer-selective rehearsal strategy that mitigates immediate forgetting during local training, and a rapid knowledge recovery strategy that restores degraded models after long-term cumulative drift. We present a theoretical analysis that characterizes heterogeneous forgetting dynamics and establishes the inevitability of long-term degradation. Our experimental results show that this framework achieves up to 8.3% mIoU improvement over the strongest federated baseline and up to 31.7% over conventional fine-tuning. We also deploy the FCL framework on a real-world rover testbed to assess system-level robustness under realistic constraints; the testing results further confirm the effectiveness of our FCL design.

Knowledge Graph Embeddings (KGEs) support a wide range of downstream tasks over Knowledge Graphs (KGs). In practice, KGs evolve as new entities and facts are added, motivating Continual Knowledge Graph Embedding (CKGE) methods that update embeddings over time. Current CKGE approaches address catastrophic forgetting (i.e., the performance degradation on previously learned tasks) primarily by limiting changes to existing embeddings. However, we show that this view is incomplete. When new entities are introduced, their embeddings can interfere with previously learned ones, causing the model to predict them in place of previously correct answers. This phenomenon, which we call entity interference, has been largely overlooked and is not accounted for in current CKGE evaluation protocols. As a result, the assessment of catastrophic forgetting becomes misleading, and CKGE methods performance is systematically overestimated. To address this issue, we introduce a corrected CKGE evaluation protocol that accounts for entity interference. Through experiments on multiple benchmarks, we show that ignoring this effect can lead to performance overestimation of up to 25%, particularly in scenarios with significant entity growth. We further analyze how different CKGE methods and KGE models are affected by the different sources of forgetting, and introduce a catastrophic forgetting metric tailored to CKGE.

With the accumulation of resources in the era of big data and the rise of pre-trained models in deep learning, optimizing neural networks for various tasks often involves different strategies for fine-tuning pre-trained models versus training from scratch. However, existing optimizers primarily focus on reducing the loss function by updating model parameters, without fully addressing the unique demands of these two major paradigms. In this paper, we propose DualOpt, a novel approach that decouples optimization techniques specifically tailored for these distinct training scenarios. For training from scratch, we introduce real-time layer-wise weight decay, designed to enhance both convergence and generalization by aligning with the characteristics of weight updates and network architecture. For more importantly fine-tuning, we integrate weight rollback with the optimizer, incorporating a rollback term into each weight update step. This ensures consistency in the weight distribution between upstream and downstream models, effectively mitigating knowledge forgetting and improving fine-tuning performance. Additionally, we extend the layer-wise weight decay to dynamically adjust the rollback levels across layers, adapting to the varying demands of different downstream tasks. Extensive experiments across diverse tasks, including image classification, object detection, semantic segmentation, and instance segmentation, demonstrate the broad applicability and state-of-the-art performance of DualOpt. Code is available at https://github.com/qklee-lz/OLOR-AAAI-2024.

As a means to balance the growth of the AI industry with the need for privacy protection, machine unlearning plays a crucial role in realizing the ``right to be forgotten'' in artificial intelligence. This technique enables AI systems to remove the influence of specific data while preserving the rest of the learned knowledge. Although it has been actively studied, most existing unlearning methods assume that unlearning is performed only once. In this work, we evaluate existing unlearning algorithms in a more realistic scenario where unlearning is conducted repeatedly, and in this setting, we identify two critical phenomena: (1) Knowledge Erosion, where the accuracy on retain data progressively degrades over unlearning phases, and (2) Forgetting Reversal, where previously forgotten samples become recognizable again in later phases. To address these challenges, we propose SAFER (StAbility-preserving Forgetting with Effective Regularization), a continual unlearning framework that maintains representation stability for retain data while enforcing negative logit margins for forget data. Extensive experiments show that SAFER mitigates not only knowledge erosion but also forgetting reversal, achieving stable performance across multiple unlearning phases.

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.

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

Fine-tuning pre-trained Vision-Language Models (VLMs) for robotic manipulation introduces a fundamental stability-plasticity dilemma: continuous flow-matching action experts backpropagate concentrated, low-rank regression gradients into transformer backbones trained on high-dimensional cross-entropy objectives. This cross-modal gradient asymmetry rapidly degrades pre-trained visual reasoning. Existing solutions either disconnect continuous gradient flow via stop-gradients or constrain updates via LoRA, which restricts update rank but remains directionally blind to semantic corruption; both typically rely on mixed-batch VQA co-training, doubling training compute. We introduce AEGIS (Anchor-Enforced Gradient Isolation System), a buffer-free, layer-wise orthogonal gradient projection framework enabling continuous flow-matching fine-tuning while isolating pre-trained representations from destructive parameter updates. Prior to training, AEGIS estimates per-layer Gaussian activation statistics from pre-training data as a static reference anchor. During fine-tuning, a closed-form Wasserstein-2 transport penalty generates an anchor-restoration gradient through the active computation graph. A sequential dual-backward pass applies layer-wise Gram-Schmidt orthogonalization, projecting task gradients onto the orthogonal complement of the restoration vector during directional conflict. We establish an exact energy preservation bound for layer-wise orthogonal projection, showing that AEGIS sheds only 0.62% of gradient energy empirically while halting cumulative feature drift. On PaliGemma2-3B fine-tuned on the LIBERO manipulation benchmark, AEGIS fully preserves pre-trained Visual Question Answering performance and baseline holdout loss while matching continuous action convergence, without replay buffers, teacher models, or co-training data.

Large Language Models (LLMs) have achieved remarkable success, underpinning diverse AI applications. However, they often suffer from performance degradation due to factors such as catastrophic forgetting during Supervised Fine-Tuning (SFT), quantization, and pruning. In this work, we introduce a performance recovery framework based on Self-Distillation Fine-Tuning (SDFT) that effectively restores model capabilities. Complementing this practical contribution, we provide a rigorous theoretical explanation for the underlying recovery mechanism. We posit that an LLM's generative capability fundamentally relies on the high-dimensional manifold constructed by its hidden layers. To investigate this, we employ Centered Kernel Alignment (CKA) to quantify the alignment between student and teacher activation trajectories, leveraging its invariance to orthogonal transformations and scaling. Our experiments demonstrate a strong correlation between performance recovery and manifold alignment, substantiating the claim that self-distillation effectively aligns the student's high-dimensional manifold with the optimal structure represented by the teacher. This study bridges the gap between practical recovery frameworks and geometric representation theory, offering new insights into the internal mechanisms of self-distillation.

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

In continual visual question answering (VQA), existing Continual Learning (CL) methods are mostly built for symmetric, unimodal architectures. However, modern Vision-Language Models (VLMs) violate this assumption, as their trainable components are inherently asymmetric. This structural mismatch renders VLMs highly prone to catastrophic forgetting when learning from continuous data streams. Specifically, the asymmetry causes standard global regularization to favor the massive language decoder during optimization, leaving the smaller but critical visual projection layers highly vulnerable to interference. Consequently, this localized degradation leads to a severe loss of compositional reasoning capabilities. To address this, we propose Asymmetric Information Masking (AIM), which balances stability and plasticity by applying targeted masks based on modality-specific sensitivity. Experiments on VQA v2 and GQA under continual VQA settings show that AIM achieves state-of-the-art performance in both Average Performance (AP) and Average Forgetting (AF), while better preserving generalization to novel skill-concept compositions.

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.

Multimodal Continual Instruction Tuning (MCIT) is essential for sequential task adaptation of Multimodal Large Language Models (MLLMs) but is severely restricted by catastrophic forgetting. While existing literature focuses on the reasoning language backbone, in this work, we expose a critical yet neglected dual-forgetting phenomenon across both perception drift in Cross-modal Projection Space and reasoning collapse in Low-rank Parameter Space. To resolve this, we present MAny (Merge Anything), a framework that merges task-specific knowledge through Cross-modal Projection Merging (CPM) and Low-rank Parameter Merging (LPM). Specifically, CPM recovers perceptual alignment by adaptively merging cross-modal visual representations via visual-prototype guidance, ensuring accurate feature recovery during inference. Simultaneously, LPM eliminates mutual interference among task-specific low-rank modules by recursively merging low-rank weight matrices. By leveraging recursive least squares, LPM provides a closed-form solution that mathematically guarantees an optimal fusion trajectory for reasoning stability. Notably, MAny operates as a training-free paradigm that achieves knowledge merging via efficient CPU-based algebraic operations, eliminating additional gradient-based optimization beyond initial tuning. Our extensive evaluations confirm the superior performance and robustness of MAny across multiple MLLMs and benchmarks. Specifically, on the UCIT benchmark, MAny achieves significant leads of up to 8.57% and 2.85% in final average accuracy over state-of-the-art methods across two different MLLMs, respectively.

Supervised Fine-Tuning (SFT) of large language models often suffers from task interference and catastrophic forgetting. Recent approaches alleviate this issue by isolating task-critical parameters during training. However, these methods represent a static solution to a dynamic problem, assuming that parameter importance remains fixed once identified. In this work, we empirically demonstrate that parameter importance exhibits temporal drift over the course of training. To address this, we propose Evolving Parameter Isolation (EPI), a fine-tuning framework that adapts isolation decisions based on online estimates of parameter importance. Instead of freezing a fixed subset of parameters, EPI periodically updates isolation masks using gradient-based signals, enabling the model to protect emerging task-critical parameters while releasing outdated ones to recover plasticity. Experiments on diverse multi-task benchmarks demonstrate that EPI consistently reduces interference and forgetting compared to static isolation and standard fine-tuning, while improving overall generalization. Our analysis highlights the necessity of synchronizing isolation mechanisms with the evolving dynamics of learning diverse abilities.

Supervised fine-tuning (SFT) is a common first stage of LLM post-training, teaching the model to follow instructions and shaping its behavior as a helpful assistant. At the same time, SFT may harm the fundamental capabilities of an LLM, particularly after long pretraining: a phenomenon known as catastrophic overtraining (Springer et al., 2025). To understand overtraining, we first investigate catastrophic forgetting in finetuning through the lens of implicit regularization of the learning rate. For models trained to the same SFT loss, we identify how the learning rate mediates optimization: finetuning with large and small steps converges to qualitatively different models. Next, we link forgetting to overtraining: learning rate decay increases the sharpness of the pretrained model, which in turn exacerbates catastrophic forgetting during SFT, leading to overtraining. Our findings paint a picture of the overtraining mechanism in LLMs and broadly contribute to the understanding of the interplay between optimization dynamics during pretraining and finetuning.

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.

Continual learning, the ability to acquire new tasks sequentially without forgetting prior knowledge, is essential for deploying neural networks in dynamic real-world environments, from nuclear digital twin monitoring to grid-edge fault detection. Existing synaptic importance methods, such as Elastic Weight Consolidation (EWC) and Synaptic Intelligence (SI), rely on gradient computation, making them incompatible with neuromorphic hardware that lacks backpropagation support. We propose ISI-CV, the first gradient-free synaptic importance metric for SNN continual learning, derived from the Coefficient of Variation (CV) of Inter-Spike Intervals (ISIs). Neurons that fire regularly (low CV) encode stable, task-relevant features and are protected from overwriting; neurons with irregular firing are permitted to adapt freely. ISI-CV requires only spike time counters and integer arithmetic, all of which are native to every neuromorphic chip. We evaluate on four benchmarks of increasing difficulty: Split-MNIST, Permuted-MNIST, Split-FashionMNIST, and Split-N-MNIST using real Dynamic Vision Sensor (DVS) event data. Across three seeds, ISI-CV achieves zero forgetting (AF = 0.000 +/- 0.000) on Split-MNIST and Split-FashionMNIST, near-zero forgetting on Permuted-MNIST (AF = 0.001 +/- 0.000), and the highest accuracy with the lowest forgetting on real neuromorphic DVS data (AA = 0.820 +/- 0.012, AF = 0.221 +/- 0.014). On N-MNIST, gradient-based methods produce unreliable importance estimates and perform worse than no regularization; ISI-CV avoids this failure by design.

Deep learning models continue to scale, with some requiring more storage than many large-scale datasets. Thus, we introduce a new paradigm: Continual Distillation (CD), where a student learns sequentially from a stream of teacher models without retaining access to earlier teachers. CD faces two challenges: teacher training data is unavailable, and teachers have varying expertise. We show that external unlabeled data enables Unseen Knowledge Transfer (UKT), allowing the student to acquire information from domains not present in the training data, while known to the teacher. We also show that sequential distillation causes Unseen Knowledge Forgetting (UKF) when transferred knowledge is lost after training on later teachers. To better trade off between UKT and UKF, we propose Self External Data Distillation (SE2D), a method that preserves logits on external data to stabilize learning across heterogeneous teachers. Experiments on multiple benchmarks show that SE2D reduces UKF and improves cross-domain generalization. The code and implementation for this work are publicly available at: https://github.com/Nicolas1203/continual_distillation.

Catastrophic forgetting remains a key challenge in Continual Learning (CL). In replay-based CL with severe memory constraints, performance critically depends on the sample selection strategy for the replay buffer. Most existing approaches construct memory buffers using embeddings learned under supervised objectives. However, class-agnostic, self-supervised representations often encode rich, class-relevant semantics that are overlooked. We propose a new method, Multiple Embedding Replay Selection, MERS, which replaces the buffer selection module with a graph-based approach that integrates both supervised and self-supervised embeddings. Empirical results show consistent improvements over SOTA selection strategies across a range of continual learning algorithms, with particularly strong gains in low-memory regimes. On CIFAR-100 and TinyImageNet, MERS outperforms single-embedding baselines without adding model parameters or increasing replay volume, making it a practical, drop-in enhancement for replay-based continual learning.

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.

Large Language Models (LLMs) are typically static after training, yet real-world applications require continual adaptation to new knowledge without degrading existing capabilities. Standard approaches to updating models, like full finetuning or parameter-efficient methods (e.g., LoRA), face a fundamental trade-off: catastrophic forgetting. They modify shared dense representations, causing interference across tasks. Sparse Memory Finetuning (SMF) offers a promising alternative by localizing updates to a small subset of parameters in explicit memory layers. In this work, we present an open-source pipeline to retrofit existing pretrained models (Qwen-2.5-0.5B) with sparse memory modules, enabling effective continual learning on consumer hardware. We extend prior work by introducing a theoretically grounded slot-selection mechanism based on Kullback-Leibler (KL) divergence, which prioritizes memory updates for informationally "surprising" tokens relative to a background distribution. Our experiments demonstrate that our retrofitted models can acquire new factual knowledge with minimal forgetting of held-out capabilities, validating the sparse update hypothesis in a practical setting.

Adapting LLMs to new domains causes forgetting because standard methods (e.g., full fine-tuning, LoRA) inject new directions into the weight space. We show that forgetting is governed by one algebraic property: whether the update preserves the column span of the pretrained weight matrix (Proposition 1). We propose GAIN, the simplest multiplicative alternative (W_new = S * W), which satisfies this by construction and can be absorbed into existing weights for zero inference cost. Across five models (774M to 70B) adapted sequentially over eight domains, GAIN improves earlier-domain perplexity by 7-13%, while LoRA degrades it by 18-36%. GAIN matches replay-augmented LoRA without storing prior data and dominates EWC on the forgetting-adaptation Pareto front. While LoRA can only reduce forgetting by sacrificing in-domain adaptation, GAIN achieves both with no domain boundaries and no regularization. The principle generalises: (IA)^3, an independent multiplicative method, also improves earlier domains.

Autonomous AI agents operating in dynamic environments face a persistent challenge: acquiring new capabilities without erasing prior knowledge. We present Adaptive Memory Crystallization (AMC), a memory architecture for progressive experience consolidation in continual reinforcement learning. AMC is conceptually inspired by the qualitative structure of synaptic tagging and capture (STC) theory, the idea that memories transition through discrete stability phases, but makes no claim to model the underlying molecular or synaptic mechanisms. AMC models memory as a continuous crystallization process in which experiences migrate from plastic to stable states according to a multi-objective utility signal. The framework introduces a three-phase memory hierarchy (Liquid--Glass--Crystal) governed by an Itô stochastic differential equation (SDE) whose population-level behavior is captured by an explicit Fokker--Planck equation admitting a closed-form Beta stationary distribution. We provide proofs of: (i) well-posedness and global convergence of the crystallization SDE to a unique Beta stationary distribution; (ii) exponential convergence of individual crystallization states to their fixed points, with explicit rates and variance bounds; and (iii) end-to-end Q-learning error bounds and matching memory-capacity lower bounds that link SDE parameters directly to agent performance. Empirical evaluation on Meta-World MT50, Atari 20-game sequential learning, and MuJoCo continual locomotion consistently shows improvements in forward transfer (+34--43% over the strongest baseline), reductions in catastrophic forgetting (67--80%), and a 62% decrease in memory footprint.