Adaptively Point-weighting Curriculum Learning

TL;DR

APW addresses the limitation of fixed weighting in automatic curriculum learning by adaptively weighting training samples according to per-sample losses and the network's evolving state, enabling a genuine easy-to-hard curriculum. It introduces a difficulty measurer and a phase-aware training scheduler to update sample weights via an AdaBoost-inspired rule, and provides two practical variants, S-APW and M-APW, along with three weighting modes. Theoretical results show APW improves training and test prediction confidence on easy samples and offers generalization guarantees, while experiments across CIFAR-10/100, CIFAR-10N/100N, Mini-WebVision, and WebVision demonstrate robustness to label noise and often superior performance over existing loss-reweighting CL methods. The approach is lightweight, hyperparameter-efficient, and broadly applicable across vision, NLP, and graph domains.

Abstract

Curriculum learning (CL) mimics human learning, in which easy samples are learned first, followed by harder samples, and has become an effective method for training deep networks. However, many existing automatic CL methods maintain a preference for easy samples during the entire training process regardless of the constantly evolving training state. This is just like a human curriculum that fails to provide individualized instruction, which can delay learning progress. To address this issue, we propose an adaptively point-weighting (APW) curriculum learning method that assigns a weight to each training sample based on its training loss. The weighting strategy of APW follows the easy-to-hard training paradigm, guided by the current training state of the network. We present a theoretical analysis of APW, including training effectiveness, training stability, and generalization performance. Experimental results validate these theoretical findings and demonstrate the superiority of the proposed APW method.

Figures (5)

• Figure 1: An illustration of the loss-reweighting CL methods.
• Figure 2: Experimental results on CIFAR-10/100 and CIFAR-10/100 (N-40) trained using Simple-CNN. For APWs and S-APWs, bars denote mean performance over the three weighting approaches (E-weighting, I-weighting, and EI-weighting) and error bars span the minimum and maximum across these strategies.
• Figure 3: Sensitivity of APW to $q$. Experimental results on CIFAR-100 (N-40) trained using Simple-CNN. We report T-ACC and E-Prop$^\dagger$ of APW-E under different $q \in \{K^\dagger/4, K^\dagger/2, K^\dagger, 2K^\dagger, 4K^\dagger\}$. Each curve shows the mean over 5 runs, with shaded regions indicating $\pm$ one standard deviation.
• Figure 4: A diagram illustrating the generalization performance ( cf. Theorem \ref{['theorem:generalization_error']}) of applying the APW method. (a) An unregularized logistic regression (LR) model struggles when trained on a linearly separable dataset because the maximum-likelihood solution is attained only in the limit of an unbounded parameter norm; as a result, the hyperplane reached in finite iterations empirically generalizes poorly on the test set. For a detailed theoretical analysis, see Appendix \ref{['appendix:APW:band']}. (b)-(c) Theorem \ref{['theorem:generalization_error']} indicates that APW can enhance the E-Prop on the test set by improving that on the training set. In this manner, APW enables the LR model to obtain a better hyperplane that improves the generalization performance on the test set.
• Figure 5: Comparison of the hyperplanes of the standard LR model and the LR model trained with APW. The plots in each column are taken at the same training iteration for both methods. In each plot, blue and red markers denote training samples from the two classes; circles indicate easy samples and crosses indicate hard samples. In the second row, the marker size is proportional to the APW-assigned weight of each sample. In the third row, the region between the black dashed lines represents the confidence band, and correctly classified samples that lie outside this confidence band are marked as easy samples.

Theorems & Definitions (16)

• Definition 3.1
• Definition 3.2
• Definition 3.3
• Lemma 3.4
• Theorem 3.5
• Theorem 3.6: Training Effectiveness
• Theorem 3.7: Training Stability
• Lemma 3.8
• Theorem 3.9: Generalization Performance
• proof