Dimensionality-Driven Learning with Noisy Labels

Abstract: Datasets with significant proportions of noisy (incorrect) class labels present challenges for training accurate Deep Neural Networks (DNNs). We propose a new perspective for understanding DNN generalization for such datasets, by investigating the dimensionality of the deep representation subspace of training samples. We show that from a dimensionality perspective, DNNs exhibit quite distinctive learning styles when trained with clean labels versus when trained with a proportion of noisy labels. Based on this finding, we develop a new dimensionality-driven learning strategy, which monitors the dimensionality of subspaces during training and adapts the loss function accordingly. We empirically demonstrate that our approach is highly tolerant to significant proportions of noisy labels, and can effectively learn low-dimensional local subspaces that capture the data distribution.

• The paper presents a novel D2L strategy that leverages local intrinsic dimensionality to mitigate the effects of noisy labels in deep neural networks.
• It identifies a two-stage learning process with an initial dimensionality compression phase followed by a dimensionality expansion linked to overfitting noisy data.
• Empirical results across datasets such as CIFAR-10 with 60% noise demonstrate D2L's superiority over traditional noise correction methods.

Dimensionality-Driven Learning with Noisy Labels: A Technical Overview

This paper presents a nuanced investigation into the behavior of Deep Neural Networks (DNNs) in the presence of noisy labels, introducing a novel approach termed Dimensionality-Driven Learning (D2L). The authors employ the concept of Local Intrinsic Dimensionality (LID) to analyze DNN learning dynamics, focusing on how intrinsic dimensionality impacts generalization under noisy label conditions.

Key Insights

DNNs are renowned for their capacity to generalize remarkably well across numerous domains. However, the presence of noisy labels can significantly hinder their generalization performance. This study contributes to an in-depth understanding of this issue by examining how DNNs adaptively reshape the dimensional structure of data representations throughout the training process.

The findings reveal that DNNs undergo a two-stage learning process when faced with noisy labels:

1. An initial dimensionality compression phase, where the model forms low-dimensional subspaces closely aligned with the underlying data manifold.
2. A subsequent dimensionality expansion phase, which is dominated by overfitting as the model attempts to memorize mislabeled instances, increasing the complexity of the learned subspace.

Dimensionality-Driven Learning (D2L)

Based on these observations, the D2L strategy is proposed as an innovative solution to mitigate the detrimental effects of noisy labels during training. The methodology involves dynamically monitoring the LID of the learned representations and leveraging this information to adjust the training loss function adaptively. Specifically, D2L modifies label assignments based on the dimensionality behavior during training, thereby preventing the model from entering the dimensionality expansion phase prematurely.

Numerical Results and Empirical Evidence

The paper provides compelling empirical evidence supporting the D2L paradigm across multiple datasets, including MNIST, SVHN, CIFAR-10, and CIFAR-100. The results consistently show that D2L outperforms traditional and state-of-the-art label noise handling techniques, such as Forward and Backward loss corrections, especially in high noise regimes. For instance, D2L exhibits superior test accuracy on the CIFAR-10 dataset even with 60% noisy labels, highlighting its robustness and efficacy in complex scenarios.

Implications and Future Directions

Theoretical and practical implications of D2L are substantial. From a theoretical standpoint, this work posits that intrinsic dimensionality analysis can be a potent tool for understanding model behaviors under noisy conditions. Practically, D2L provides an efficient framework to enhance neural network robustness without necessitating additional datasets or complex noise models.

Looking forward, this paper opens avenues for further exploration in several domains:

• Adversarial Robustness: Investigating whether similar dimensionality-driven strategies can be applied to enhance robustness against adversarial attacks.
• Semi-Supervised Learning: Exploring if dimensionality analysis can bolster learning when dealing with partially labeled data.
• Regularization Techniques: Understanding how regularization and different network architectures interact with dimensionality-based learning strategies.

In conclusion, this paper significantly advances the understanding of DNNs under label noise through a dimensionality-centric lens, offering both a powerful theoretical perspective and a practical solution to a pervasive challenge in machine learning.