We characterize weakly regularized continual classification in homogeneous models as sequential projections onto task margin sets. This result generalizes prior analyses restricted to either stationary (single-task) deep models or continual linear models. We show that global convergence generally fails, even for simple models linear in data but nonlinear in parameters. Nevertheless, by leveraging results from nonconvex projection theory, we identify regularity properties of homogeneous deep networks that guarantee local linear convergence under random and cyclic task sequences. Finally, we extend our analysis to continual regression, unifying the framework for homogeneous models.

Recent advancements in Large Language Models (LLMs) have emphasized the critical role of fine-tuning (FT) techniques in adapting LLMs to specific tasks, especially when retraining from scratch is computationally infeasible. Fine-tuning enables LLMs to leverage task-or domain-specific data, producing models that more effectively meet the requirements of targeted applications. However, conventional FT approaches often suffer from catastrophic forgetting and suboptimal data efficiency, limiting their real-world applicability. To address these challenges, this paper proposes DEAL, a novel framework that integrates Low-Rank Adaptation (LoRA) with a continuous fine-tuning strategy.

Multi-domain task incremental learning (MTIL) demands models to master domainspecific expertise while preserving generalization capabilities. Inspired by human lifelong learning [1, 2], which relies on revisiting, aligning, and integrating past experiences, we propose a Learning and Ensembling Bridge Adapters (LEBA) framework. To facilitate cohesive knowledge transfer across domains, specifically, we propose a continuous-domain bridge adaptation module, leveraging the distribution transfer capabilities of Schrödinger bridge for stable progressive learning. To strengthen memory consolidation, we further propose a progressive knowledge ensemble strategy that revisits past task representations via a diffusion model and dynamically integrates historical adapters. For efficiency, LEBA maintains a compact adapter pool through similarity-based selection and employs learnable weights to align replayed samples with current task semantics. Together, these components effectively mitigate catastrophic forgetting and enhance generalization across tasks.

We analyze task orderings in continual learning for linear regression, assuming joint realizability of training data. We focus on orderings that greedily maximize dissimilarity between consecutive tasks, a concept briefly explored in prior work but still surrounded by open questions. Using tools from the Kaczmarz method literature, we formalize such orderings and develop geometric and algebraic intuitions around them. Empirically, we demonstrate that greedy orderings converge faster than random ones in terms of the average loss across tasks, both for linear regression with random data and for linear probing on CIFAR-100classification tasks. Analytically, in a high-rank regression setting, we prove a loss bound for greedy orderings analogous to that of random ones. However, under general rank, we establish a repetition-dependent separation. Specifically, while prior work showed that for random orderings, with or without replacement, the average loss after k iterations is bounded by O(1/ k)--we prove that single-pass greedy orderings may fail catastrophically, whereas those allowing repetition converge at rate O(1/ 3 k). Overall, we reveal nuances within and between greedy and random orderings.

Human brain achieves dynamic stability-plasticity balance through synaptic homeostasis, a self-regulatory mechanism that stabilizes critical memory traces while preserving optimal learning capacities. Inspired by this biological principle, we propose SPICED: a neuromorphic framework that integrates the synaptic homeostasis mechanism for unsupervised continual EEG decoding, particularly addressing practical scenarios where new individuals with inter-individual variability emerge continually. SPICED comprises a novel synaptic network that enables dynamic expansion during continual adaptation through three bio-inspired neural mechanisms: (1) critical memory reactivation, which mimics brain functional specificity, selectively activates task-relevant memories to facilitate adaptation; (2) synaptic consolidation, which strengthens these reactivated critical memory traces and enhances their replay prioritizations for further adaptations and (3) synaptic renormalization, which are periodically triggered to weaken global memory traces to preserve learning capacities. The interplay within synaptic homeostasis dynamically strengthens task-discriminative memory traces and weakens detrimental memories.

Organisms constantly pivot between tasks such as evading predators, foraging, traversing rugged terrain, and socializing, often within milliseconds. Remarkably, they preserve knowledge of once-learned environments sans catastrophic forgetting, a phenomenon neuroscientists hypothesize, is due to a singular neural circuitry dynamically overlayed by neuromodulatory agents such as dopamine and acetylcholine. In parallel, deep learning research addresses analogous challenges via domain generalization (DG) and continual learning (CL), yet these methods remain siloed, despite the brain's ability to perform them seamlessly. In particular, prior work has not explored architectures involving associative memories (AMs), which are an integral part of biological systems, to jointly address these tasks. We propose Memory-Integrated Reconfigurable Adapters (MIRA), a unified framework that integrates Hopfield-style associative memory modules atop a shared backbone. These memory modules store adapter-weight updates as values and retrieve them via learned keys. Associative memory keys are learned post-hoc to index and retrieve an affine combination of stored adapter updates for any given task or domain on a per-sample basis. By varying only the task-specific objectives, we demonstrate that MIRA seamlessly accommodates domain shifts and sequential task exposures under one roof. Empirical evaluations on standard benchmarks confirm that our AM-augmented architecture significantly enhances adaptability and retention: in DG, MIRA achieves SoTA out-of-distribution accuracy, and in incremental learning settings, it outperforms architectures explicitly designed to handle catastrophic forgetting using generic CL algorithms.

However, existing methods face two critical challenges: parameter interference among tasks, which leads to catastrophic forgetting, and limited adaptability to evolving test distributions. To address these issues, we introduce the task of Test-Time Continual Model Merging (TTCMM), which leverages a small set of unlabeled test samples during inference to alleviate parameter conflicts and handle distribution shifts. We propose MINGLE, a novel framework for TTCMM. MINGLE employs a mixture-of-experts architecture with parameter-efficient, low-rank experts, which enhances adaptability to evolving test distributions while dynamically merging models to mitigate conflicts. To further reduce forgetting, we propose Null-Space Constrained Gating, which restricts gating updates to subspaces orthogonal to prior task representations, thereby suppressing activations on old tasks and preserving past knowledge. We further introduce an Adaptive Relaxation Strategy that adjusts constraint strength dynamically based on interference signals observed during test-time adaptation, striking a balance between stability and adaptability. Extensive experiments on standard continual merging benchmarks demonstrate that MINGLE achieves robust generalization, significantly reduces forgetting, and consistently surpasses previous state-of-the-art methods by 7-9% on average across diverse task orders.

We propose a novel online Gaussian process (GP) model that is capable of capturing long-term memory in sequential data in an online learning setting. Our model, Online HiPPO Sparse Variational Gaussian Process (OHSVGP), leverages the HiPPO (High-order Polynomial Projection Operators) framework, which is popularized in the RNN domain due to its long-range memory modeling capabilities. We interpret the HiPPO time-varying orthogonal projections as inducing variables with timedependent orthogonal polynomial basis functions, which allows the SVGP inducing variables to memorize the process history. We show that the HiPPO framework fits naturally into the interdomain GP framework and demonstrate that the kernel matrices can also be updated online in a recurrence form based on the ODE evolution of HiPPO. We evaluate OHSVGP with online prediction for 1D time series, continual learning in discriminative GP model for data with multidimensional inputs, and deep generative modeling with sparse Gaussian process variational autoencoder, showing that it outperforms existing online GP methods in terms of predictive performance, long-term memory preservation, and computational efficiency.

Embodied agents are expected to perform object navigation in dynamic, open-world environments. However, existing approaches typically rely on static trajectories and a fixed set of object categories during training, overlooking the real-world requirement for continual adaptation to evolving scenarios. To facilitate related studies, we introduce the continual object navigation benchmark, which requires agents to acquire navigation skills for new object categories while avoiding catastrophic forgetting of previously learned knowledge. To tackle this challenge, we propose C-Nav, a continual visual navigation framework that integrates two key innovations: (1) A dual-path anti-forgetting mechanism, which comprises feature distillation that aligns multi-modal inputs into a consistent representation space to ensure representation consistency, and feature replay that retains temporal features within the action decoder to ensure policy consistency.

Online Continual Learning (OCL) requires models to learn sequentially from data streams with limited memory. Rehearsal-based methods, particularly Experience Replay (ER), are commonly used in OCL scenarios. This paper revisits ER through the lens of ϵ-constraint optimization, revealing that ER implicitly employs a soft constraint on past task performance, with its weighting parameter post-hoc defining a slack variable. While effective, ER's implicit and fixed slack strategy has limitations: it can inadvertently lead to updates that negatively impact generalization, and its fixed trade-off between plasticity and stability may not optimally balance current streaming with memory retention, potentially overfitting to the memory buffer. To address these shortcomings, we propose the Gradient-Guided Epsilon Constraint (GEC) method for online continual learning. GEC explicitly formulates the OCL update as an ϵ-constraint optimization problem, which minimize the loss on the current task data and transform the stability objective as constraints and propose a gradient-guided method to dynamically adjusts the update direction based on whether the performance on memory samples violates a predefined slack tolerance ε: if forgetting exceeds this tolerance, GEC prioritizes constraint satisfaction; otherwise, it focuses on the current task while controlling the rate of increase in memory loss. Empirical evaluations on standard OCL benchmarks demonstrate GEC's ability to achieve a superior trade-off, leading to improved overall performance.