Curriculum Learning by Transfer Learning: Theory and Experiments with Deep Networks (1802.03796v4)

Abstract: We provide theoretical investigation of curriculum learning in the context of stochastic gradient descent when optimizing the convex linear regression loss. We prove that the rate of convergence of an ideal curriculum learning method is monotonically increasing with the difficulty of the examples. Moreover, among all equally difficult points, convergence is faster when using points which incur higher loss with respect to the current hypothesis. We then analyze curriculum learning in the context of training a CNN. We describe a method which infers the curriculum by way of transfer learning from another network, pre-trained on a different task. While this approach can only approximate the ideal curriculum, we observe empirically similar behavior to the one predicted by the theory, namely, a significant boost in convergence speed at the beginning of training. When the task is made more difficult, improvement in generalization performance is also observed. Finally, curriculum learning exhibits robustness against unfavorable conditions such as excessive regularization.

• The paper demonstrates that ordering training examples by difficulty through transfer learning significantly accelerates convergence in deep neural networks.
• It employs both rigorous SGD-based theoretical analysis and empirical evaluations on CNNs using datasets like CIFAR-100 and STL-10.
• The study highlights that automated difficulty estimation can improve training efficiency and paves the way for dynamic curriculum design in AI.

Curriculum Learning by Transfer Learning: A Theoretical and Empirical Examination

The paper "Curriculum Learning by Transfer Learning: Theory and Experiments with Deep Networks," authored by Daphna Weinshall, Gad Cohen, and Dan Amir, explores the intersection of curriculum learning and transfer learning within the context of neural networks. The work explores both theoretical analysis and empirical evaluations, offering insights into how ordering training data by difficulty can influence learning dynamics and outcomes.

Theoretical Analysis

The authors commence with a rigorous theoretical exploration of curriculum learning, employing stochastic gradient descent (SGD) to optimize a convex linear regression loss function. A key theoretical finding is that the rate of convergence under an optimal curriculum learning strategy increases with the difficulty of examples. Specifically, among examples of similar difficulty, those that incur higher loss relative to the current hypothesis expedite convergence more efficiently. The implication here is profound: curriculum learning has the potential to accelerate convergence rates, particularly in the early phases of training, by judiciously adjusting the difficulty of samples presented to the learning algorithm.

Furthermore, the authors investigate the relationship between curriculum learning and the loss incurred by samples under the current model. When the difficulty level is fixed, they conclude that convergence tends to be faster for samples that present higher loss, aligning with intuitive notions underlying methods like boosting. However, this relationship is not universally applicable, especially when difficulty is not fixed across samples. This nuanced finding underscores the complexity and context-dependent nature of curriculum learning strategies.

Empirical Studies

To substantiate their theoretical claims, the authors design empirical studies using convolutional neural networks (CNNs) trained on datasets like CIFAR-100 and STL-10. Their experiments assess how curriculum learning, guided by difficulty rankings sourced through transfer learning, impacts model performance across various conditions. The methodology includes a transfer of difficulty rankings from a pre-trained, robust network to the task network, without direct supervision or human assessment of sample difficulty.

Empirical results consistently demonstrate that curriculum learning not only accelerates initial training convergence but can also improve generalization, especially under more challenging conditions such as smaller network architectures or higher task difficulty. Control conditions, such as random-order presentation and anti-curriculum (presenting harder examples first) scheduling, validate that the observed benefits are attributable to the curriculum's structured nature rather than mere scheduling artifacts.

Implications and Future Directions

The dual examination of curriculum learning via theory and practice in this paper offers salient contributions to the machine learning domain. Theoretically, it enhances our understanding of how sample difficulty affects learning trajectories and outcomes. Practically, it embodies a novel approach to curriculum formulation by leveraging transfer learning for automatic difficulty estimation, a process that circumvents the often subjective and labor-intensive human difficulty scoring.

Looking ahead, this work suggests potential pathways for further refinement of curriculum learning paradigms. Future research may explore more sophisticated methods for difficulty estimation, possibly integrating reinforcement learning or dynamic adjustment during training to adapt the curriculum in real-time. Additionally, broader investigations into different model architectures and task types could elucidate the generalizability and limits of curriculum learning strategies. As the field of AI continues to evolve, approaches like these that aim to efficiently harness data complexity hold promise for driving more effective and generalized machine learning systems.