To cope with real-world dynamics, an intelligent agent needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative strategies address continual learning, and how they are adapted to particular challenges in various applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

pdf/a-comprehensive-survey-of-continual-learning-theory-method-3aewabe3.pdf

A Comprehensive Survey of Continual Learning: Theory, Method and Application

Class-incremental learning (CIL) aims to adapt to emerging new classes without forgetting old ones. Traditional CIL models are trained from scratch to continually acquire knowledge as data evolves. Recently, pre-training has achieved substantial progress, making vast pre-trained models (PTMs) accessible for CIL. Contrary to traditional methods, PTMs possess generalizable embeddings, which can be easily transferred. In this work, we revisit CIL with PTMs and argue that the core factors in CIL are adaptivity for model updating and generalizability for knowledge transferring. 1) We first reveal that frozen PTM can already provide generalizable embeddings for CIL. Surprisingly, a simple baseline (SimpleCIL) which continually sets the classifiers of PTM to prototype features can beat state-of-the-art even without training on the downstream task. 2) Due to the distribution gap between pre-trained and downstream datasets, PTM can be further cultivated with adaptivity via model adapting. We propose ADapt And Merge (ADAM), which aggregates the embeddings of PTM and adapted models for classifier construction. ADAM is a general framework that can be orthogonally combined with any parameter-efficient tuning method, which holds the advantages of PTM's generalizability and adapted model's adaptivity. 3) Additionally, we find previous benchmarks are unsuitable in the era of PTM due to data overlapping and propose four new benchmarks for assessment, namely ImageNet-A, ObjectNet, OmniBenchmark, and VTAB. Extensive experiments validate the effectiveness of ADAM with a unified and concise framework.

pdf/revisiting-class-incremental-learning-with-pre-trained-3nufvtkt.pdf

Revisiting Class-Incremental Learning with Pre-Trained Models: Generalizability and Adaptivity are All You Need

Continual learning (CL) aims to incrementally learn different tasks (such as classification) in a non-stationary data stream without forgetting old ones. Most CL works focus on tackling catastrophic forgetting under a learning-from-scratch paradigm. However, with the increasing prominence of foundation models, pre-trained models equipped with informative representations have become available for various downstream requirements. Several CL methods based on pre-trained models have been explored, either utilizing pre-extracted features directly (which makes bridging distribution gaps challenging) or incorporating adaptors (which may be subject to forgetting). In this paper, we propose a concise and effective approach for CL with pre-trained models. Given that forgetting occurs during parameter updating, we contemplate an alternative approach that exploits training-free random projectors and class-prototype accumulation, which thus bypasses the issue. Specifically, we inject a frozen Random Projection layer with nonlinear activation between the pre-trained model's feature representations and output head, which captures interactions between features with expanded dimensionality, providing enhanced linear separability for class-prototype-based CL. We also demonstrate the importance of decorrelating the class-prototypes to reduce the distribution disparity when using pre-trained representations. These techniques prove to be effective and circumvent the problem of forgetting for both class- and domain-incremental continual learning. Compared to previous methods applied to pre-trained ViT-B/16 models, we reduce final error rates by between 10\% and 62\% on seven class-incremental benchmark datasets, despite not using any rehearsal memory. We conclude that the full potential of pre-trained models for simple, effective, and fast continual learning has not hitherto been fully tapped.

RanPAC: Random Projections and Pre-trained Models for Continual Learning

Prompt-based continual learning is an emerging direction in leveraging pre-trained knowledge for downstream continual learning, and has almost reached the performance pinnacle under supervised pre-training. However, our empirical research reveals that the current strategies fall short of their full potential under the more realistic self-supervised pre-training, which is essential for handling vast quantities of unlabeled data in practice. This is largely due to the difficulty of task-specific knowledge being incorporated into instructed representations via prompt parameters and predicted by uninstructed representations at test time. To overcome the exposed sub-optimality, we conduct a theoretical analysis of the continual learning objective in the context of pre-training, and decompose it into hierarchical components: within-task prediction, task-identity inference, and task-adaptive prediction. Following these empirical and theoretical insights, we propose Hierarchical Decomposition (HiDe-)Prompt, an innovative approach that explicitly optimizes the hierarchical components with an ensemble of task-specific prompts and statistics of both uninstructed and instructed representations, further with the coordination of a contrastive regularization strategy. Our extensive experiments demonstrate the superior performance of HiDe-Prompt and its robustness to pre-training paradigms in continual learning (e.g., up to 15.01% and 9.61% lead on Split CIFAR-100 and Split ImageNet-R, respectively). Our code is available at \url{https://github.com/thu-ml/HiDe-Prompt}.

pdf/hierarchical-decomposition-of-prompt-based-continual-3qfk64ydgg.pdf

Hierarchical Decomposition of Prompt-Based Continual Learning: Rethinking Obscured Sub-optimality

Creating learning models that can exhibit sophisticated reasoning abilities is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this direction. In the past few years there has been an explosion of neural network architectures, datasets, and benchmarks specifically designed to tackle mathematical problems, reporting impressive achievements in disparate fields such as automated theorem proving, numerical integration, and the discovery of new conjectures or matrix multiplication algorithms. However, despite this notable success it is still unclear whether deep learning models possess an elementary understanding of quantities and numbers. This survey critically examines the recent literature, concluding that even state-of-the-art architectures and large language models often fall short when probed with relatively simple tasks designed to test basic numerical and arithmetic knowledge. 

Can Neural Networks Do Arithmetic? A Survey on the Elementary Numerical Skills of State-of-the-Art Deep Learning Models

The goal of continual learning is to improve the performance of recognition models in learning sequentially arrived data. Although most existing works are established on the premise of learning from scratch, growing efforts have been devoted to incorporating the benefits of pre-training. However, how to adaptively exploit the pre-trained knowledge for each incremental task while maintaining its generalizability remains an open question. In this work, we present an extensive analysis for continual learning on a pre-trained model (CLPM), and attribute the key challenge to a progressive overfitting problem. Observing that selectively reducing the learning rate can almost resolve this issue in the representation layer, we propose a simple but extremely effective approach named Slow Learner with Classifier Alignment (SLCA), which further improves the classification layer by modeling the class-wise distributions and aligning the classification layers in a post-hoc fashion. Across a variety of scenarios, our proposal provides substantial improvements for CLPM (e.g., up to 49.76%, 50.05%, 44.69% and 40.16% on Split CIFAR-100, Split ImageNet-R, Split CUB-200 and Split Cars-196, respectively), and thus outperforms state-of-the-art approaches by a large margin. Based on such a strong baseline, critical factors and promising directions are analyzed in-depth to facilitate subsequent research.

SLCA: Slow Learner with Classifier Alignment for Continual Learning on a Pre-trained Model

Acquiring mathematical skills is considered a key challenge for modern Artificial Intelligence systems. Inspired by the way humans discover numerical knowledge, here we introduce a deep reinforcement learning framework that allows to simulate how cognitive agents could gradually learn to solve arithmetic problems by interacting with a virtual abacus. The proposed model successfully learn to perform multi-digit additions and subtractions, achieving an error rate below 1% even when operands are much longer than those observed during training. We also compare the performance of learning agents receiving a different amount of explicit supervision, and we analyze the most common error patterns to better understand the limitations and biases resulting from our design choices.

pdf/learning-to-solve-arithmetic-problems-with-a-virtual-abacus-qhgdlnn9.pdf

Learning to solve arithmetic problems with a virtual abacus

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SLCA: Slow Learner with Classifier Alignment for Continual Learning on a Pre-trained Model

Learning to solve arithmetic problems with a virtual abacus