Continual Learning with Pre-trained Models: Bridging Theory and Practice through Truncated Singular Value Decomposition

Основні поняття

This work proposes ICL-TSVD, a method that bridges the gap between empirical performance and theoretical guarantees in continual learning with pre-trained models. ICL-TSVD integrates the strengths of RanPAC into the Ideal Continual Learner framework and addresses the ill-conditioning of lifted features through continual SVD truncation, achieving both stability and strong performance.

Анотація

The authors identify that the instability of existing continual learning methods with pre-trained models, such as RanPAC and Ideal Continual Learner (ICL), is related to the emergence of extremely small singular values in the spectrum of the pre-trained random ReLU features as more tasks are observed. To address this challenge, the authors propose ICL-TSVD, which truncates the extremely small singular values prior to solving the minimum-norm ICL problem.

Key highlights:

• ICL-TSVD combines the empirically strong RanPAC approach with the principled ICL framework, bridging the gap between theory and practice.
• The authors provide a continual implementation of ICL-TSVD that is numerically stable and more scalable than RanPAC.
• Theoretical guarantees are derived for ICL-TSVD, proving that it maintains small estimation and generalization errors when a suitable fraction of SVD factors are truncated.
• Extensive experiments show that ICL-TSVD uniformly outperforms prior works, including RanPAC, across multiple datasets, especially in the challenging class-incremental learning setting with one class per task.

Статистика

The minimum eigenvalue of H⊤
1:tH1:t drastically drops after a certain number of tasks, leading to instability in solving Min-Norm ICL.
The training MSE loss of the incremental SVD solution to Min-Norm ICL explodes precisely when the extremely small eigenvalues emerge.

Цитати

"The goal of continual learning (CL) is to train a model that can solve multiple tasks presented sequentially."
"Recent CL approaches have achieved strong performance by leveraging large pre-trained models that generalize well to downstream tasks. However, such methods lack theoretical guarantees, making them prone to unexpected failures."
"Conversely, principled CL approaches often fail to achieve competitive performance."

Ключові висновки, отримані з

ICL-TSVD: Bridging Theory and Practice in Continual Learning with Pre-trained Models

by Lian... о arxiv.org 10-02-2024

https://arxiv.org/pdf/2410.00645.pdf

Глибші Запити

How can the proposed ICL-TSVD framework be extended to handle more complex neural network architectures beyond linear classifiers?

The ICL-TSVD framework, which integrates the strengths of the Ideal Continual Learner (ICL) and the empirical performance of RanPAC, is primarily designed for linear classifiers. However, it can be extended to accommodate more complex neural network architectures through several strategies:

Layer-wise Adaptation: Instead of using a single linear classifier, the framework can be adapted to train multi-layer neural networks. This can be achieved by applying the truncated singular value decomposition (SVD) at each layer of the network, ensuring that the ill-conditioning issues are addressed throughout the network's depth. By maintaining stability in the feature representations at each layer, the model can learn more complex mappings while still benefiting from the theoretical guarantees provided by ICL-TSVD.

Non-linear Activation Functions: The current implementation utilizes ReLU activations. To extend ICL-TSVD to handle architectures with different activation functions (e.g., sigmoid, tanh), one could incorporate a generalized form of the random feature mapping that accommodates these non-linearities. This would involve deriving new theoretical guarantees that account for the non-linear transformations applied to the lifted features.

End-to-End Training: The framework can be modified to allow for end-to-end training of the entire neural network, where the ICL-TSVD approach is used to stabilize the training process. This could involve integrating the SVD truncation into the backpropagation algorithm, ensuring that the gradients are computed in a way that respects the stability conditions established by the SVD.

Hybrid Models: Combining ICL-TSVD with other architectures, such as convolutional neural networks (CNNs) or transformers, can enhance its applicability. For instance, one could use ICL-TSVD to stabilize the training of a CNN by applying the SVD truncation to the feature maps generated by the convolutional layers, thereby addressing the potential for catastrophic forgetting while leveraging the representational power of deep networks.

By implementing these strategies, the ICL-TSVD framework can be effectively adapted to handle more complex neural network architectures, thereby broadening its applicability in continual learning scenarios.

What are the potential limitations of the linear regression model assumption used in the theoretical analysis, and how can it be relaxed or generalized?

The linear regression model assumption in the theoretical analysis of ICL-TSVD presents several limitations:

Linearity Assumption: The assumption that the relationship between the features and the target labels is linear may not hold in many real-world scenarios. This can lead to suboptimal performance when the underlying data distribution is inherently non-linear.

Overfitting Risks: In the over-parameterized regime, while linear models can achieve low training error, they may also overfit the noise present in the data, especially in high-dimensional spaces. This can result in poor generalization to unseen tasks.

Noise Sensitivity: The linear regression model assumes that the noise in the observations is additive and independent of the input features. In practice, this may not be the case, particularly in complex datasets where noise can be correlated with certain features.

To relax or generalize the linear regression model assumption, the following approaches can be considered:

Non-linear Models: Extending the theoretical framework to include non-linear models, such as kernel methods or neural networks, would allow for capturing more complex relationships in the data. This could involve deriving new bounds on estimation and generalization errors that account for the non-linear transformations.

Regularization Techniques: Incorporating regularization methods, such as L1 or L2 regularization, can help mitigate overfitting by penalizing complex models. This would allow for a more robust analysis that considers the trade-off between model complexity and generalization performance.

Robust Statistical Methods: Utilizing robust statistical techniques that account for noise and outliers can enhance the model's resilience. This could involve using robust loss functions or incorporating noise modeling directly into the framework.

Probabilistic Frameworks: Adopting a probabilistic approach, such as Bayesian regression, can provide a more flexible framework that accounts for uncertainty in the model parameters and predictions. This would allow for a more comprehensive understanding of the model's behavior under various conditions.

By addressing these limitations, the theoretical analysis of ICL-TSVD can be made more applicable to a wider range of scenarios, enhancing its robustness and effectiveness in continual learning tasks.

Can the insights from ICL-TSVD be applied to other machine learning problems beyond continual learning, such as few-shot learning or domain adaptation?

Yes, the insights from the ICL-TSVD framework can be effectively applied to other machine learning problems beyond continual learning, including few-shot learning and domain adaptation. Here’s how:

Few-Shot Learning: The principles of stability and generalization in ICL-TSVD can be particularly beneficial in few-shot learning scenarios, where models are trained on a limited number of examples per class. The use of truncated SVD can help stabilize the learning process by mitigating the effects of overfitting to the few available samples. By ensuring that the model retains essential features while discarding noise, ICL-TSVD can enhance the model's ability to generalize from few examples.

Domain Adaptation: In domain adaptation, the goal is to transfer knowledge from a source domain to a target domain, which may have different feature distributions. The insights from ICL-TSVD regarding the stability of feature representations can be leveraged to align the feature spaces of the source and target domains. By applying SVD truncation to the features from both domains, one can reduce the impact of domain-specific noise and improve the model's robustness to domain shifts.

Transfer Learning: The framework's ability to handle ill-conditioned features can also be beneficial in transfer learning scenarios, where pre-trained models are fine-tuned on new tasks. The continual SVD truncation can help maintain the stability of the learned representations, ensuring that the model does not forget previously acquired knowledge while adapting to new tasks.

Generalization Across Tasks: The theoretical guarantees provided by ICL-TSVD regarding small training and generalization errors can be applied to any scenario where models need to generalize across different tasks or datasets. This includes multi-task learning, where the model is trained on multiple related tasks simultaneously, benefiting from the stability and robustness of the learned representations.

By applying the insights from ICL-TSVD to these areas, researchers and practitioners can develop more robust and effective machine learning models that are capable of handling the challenges associated with few-shot learning, domain adaptation, and beyond.