Curriculum learning has emerged as an effective strategy to enhance the training efficiency and generalization of machine learning models. However, its theoretical underpinnings remain relatively underexplored. In this work, we develop a theoretical framework for curriculum learning based on biased regularized empirical risk minimization (RERM), identifying conditions under which curriculum learning provably improves generalization. We introduce a sufficient condition that characterizes a "good" curriculum and analyze a multi-task curriculum framework, where solving a sequence of convex tasks can facilitate better generalization. We also demonstrate how these theoretical insights translate to practical benefits when using stochastic gradient descent (SGD) as an optimization method. Beyond convex settings, we explore the utility of curriculum learning for non-convex tasks. Empirical evaluations on synthetic datasets and MNIST validate our theoretical findings and highlight the practical efficacy of curriculum-based training.

First,theobtained high-probability regret bounds are data-dependent and could be much smaller thantheworst-case bounds, which resolvesanopenproblem askedbyNeu[31].

Forexample, regularization-based methods (e.g., [12,1,18]) penalize the modification of important weights of oldtasks; parameter-isolation based methods (e.g., [7,26,31,9])fixthemodel learnt foroldtasks; and memory-based methods (e.g., [3, 6, 25]) aim to update the model with minimal interference introduced tooldtasks. More specifically, we first introduce notions of 'sufficient projection' and 'positive correlation' based on the gradient projection onto the subspaces of old tasks to characterize the task correlation.

Indias linguistic diversity poses significant challenges for developing inclusive Automatic Speech Recognition (ASR) systems. Traditional multilingual models, which require simultaneous access to all language data, are impractical due to the sequential arrival of data and privacy constraints. Continual Learning (CL) offers a solution by enabling models to learn new languages sequentially without catastrophically forgetting previously learned knowledge. This paper investigates CL for ASR on Indian languages using a subset of the IndicSUPERB benchmark. We employ a Conformer-based hybrid RNN-T/CTC model, initially pretrained on Hindi, which is then incrementally trained on eight additional Indian languages, for a total sequence of nine languages. We evaluate three prominent regularization- and distillation-based CL strategies: Elastic Weight Consolidation (EWC), Memory Aware Synapses (MAS), and Learning without Forgetting (LwF), selected for their suitability in no-replay, privacy-conscious scenarios. Performance is analyzed using Word Error Rate (WER) for both RNN-T and CTC paths on clean and noisy data, as well as knowledge retention via Backward Transfer. We also explore the impact of varying the number of training epochs (1, 2, 5, and 10) per task. Results, compared against naive fine-tuning, demonstrate CLs effectiveness in mitigating forgetting, making it a promising approach for scalable ASR in diverse Indian languages under realistic constraints. The code is available at: https://github.com/FrozenWolf-Cyber/Indic-CL-ASR

Continual learning, or the ability to progressively integrate new concepts, is fundamental to intelligent beings, enabling adaptability in dynamic environments. In contrast, artificial deep neural networks face the challenge of catastrophic forgetting when learning new tasks sequentially. To alleviate the problem of forgetting, recent approaches aim to preserve essential weight subspaces for previous tasks by limiting updates to orthogonal subspaces via gradient projection. While effective, this approach can lead to suboptimal performance, particularly when tasks are highly correlated. In this work, we introduce COnceptor-based gradient projection for DEep Continual Learning (CODE-CL), a novel method that leverages conceptor matrix representations, a computational model inspired by neuroscience, to more flexibly handle highly correlated tasks. CODE-CL encodes directional importance within the input space of past tasks, allowing new knowledge integration in directions modulated by $1-S$, where $S$ represents the direction's relevance for prior tasks. Additionally, we analyze task overlap using conceptor-based representations to identify highly correlated tasks, facilitating efficient forward knowledge transfer through scaled projection within their intersecting subspace. This strategy enhances flexibility, allowing learning in correlated tasks without significantly disrupting previous knowledge. Extensive experiments on continual learning image classification benchmarks validate CODE-CL's efficacy, showcasing superior performance with minimal forgetting, outperforming most state-of-the-art methods.

Adapting pre-trained large language models to different domains in natural language processing requires two key considerations: high computational demands and model's inability to continual adaptation. To simultaneously address both issues, this paper presents COPAL (COntinual Pruning in Adaptive Language settings), an algorithm developed for pruning large language generative models under a continual model adaptation setting. While avoiding resource-heavy finetuning or retraining, our pruning process is guided by the proposed sensitivity analysis. The sensitivity effectively measures model's ability to withstand perturbations introduced by the new dataset and finds model's weights that are relevant for all encountered datasets. As a result, COPAL allows seamless model adaptation to new domains while enhancing the resource efficiency. Our empirical evaluation on a various size of LLMs show that COPAL outperforms baseline models, demonstrating its efficacy in efficiency and adaptability.

Replay methods are known to be successful at mitigating catastrophic forgetting in continual learning scenarios despite having limited access to historical data. However, storing historical data is cheap in many real-world settings, yet replaying all historical data is often prohibited due to processing time constraints. In such settings, we propose that continual learning systems should learn the time to learn and schedule which tasks to replay at different time steps. We first demonstrate the benefits of our proposal by using Monte Carlo tree search to find a proper replay schedule, and show that the found replay schedules can outperform fixed scheduling policies when combined with various replay methods in different continual learning settings. Additionally, we propose a framework for learning replay scheduling policies with reinforcement learning. We show that the learned policies can generalize better in new continual learning scenarios compared to equally replaying all seen tasks, without added computational cost. Our study reveals the importance of learning the time to learn in continual learning, which brings current research closer to real-world needs.

Continual graph learning (CGL) is purposed to continuously update a graph model with graph data being fed in a streaming manner. Since the model easily forgets previously learned knowledge when training with new-coming data, the catastrophic forgetting problem has been the major focus in CGL. Recent replay-based methods intend to solve this problem by updating the model using both (1) the entire new-coming data and (2) a sampling-based memory bank that stores replayed graphs to approximate the distribution of historical data. After updating the model, a new replayed graph sampled from the incoming graph will be added to the existing memory bank. Despite these methods are intuitive and effective for the CGL, two issues are identified in this paper. Firstly, most sampling-based methods struggle to fully capture the historical distribution when the storage budget is tight. Secondly, a significant data imbalance exists in terms of the scales of the complex new-coming graph data and the lightweight memory bank, resulting in unbalanced training. To solve these issues, a Condense and Train (CaT) framework is proposed in this paper. Prior to each model update, the new-coming graph is condensed to a small yet informative synthesised replayed graph, which is then stored in a Condensed Graph Memory with historical replay graphs. In the continual learning phase, a Training in Memory scheme is used to update the model directly with the Condensed Graph Memory rather than the whole new-coming graph, which alleviates the data imbalance problem. Extensive experiments conducted on four benchmark datasets successfully demonstrate superior performances of the proposed CaT framework in terms of effectiveness and efficiency. The code has been released on https://github.com/superallen13/CaT-CGL.