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Orthogonal Projection Loss (2103.14021v1)

Published 25 Mar 2021 in cs.CV

Abstract: Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and does not explicitly force different class features to be well-separated. Motivated by the observation that ground-truth class representations in CE loss are orthogonal (one-hot encoded vectors), we develop a novel loss function termed `Orthogonal Projection Loss' (OPL) which imposes orthogonality in the feature space. OPL augments the properties of CE loss and directly enforces inter-class separation alongside intra-class clustering in the feature space through orthogonality constraints on the mini-batch level. As compared to other alternatives of CE, OPL offers unique advantages e.g., no additional learnable parameters, does not require careful negative mining and is not sensitive to the batch size. Given the plug-and-play nature of OPL, we evaluate it on a diverse range of tasks including image recognition (CIFAR-100), large-scale classification (ImageNet), domain generalization (PACS) and few-shot learning (miniImageNet, CIFAR-FS, tiered-ImageNet and Meta-dataset) and demonstrate its effectiveness across the board. Furthermore, OPL offers better robustness against practical nuisances such as adversarial attacks and label noise. Code is available at: https://github.com/kahnchana/opl.

Citations (56)

Summary

  • The paper introduces Orthogonal Projection Loss (OPL), a novel function that enhances feature discrimination by enforcing explicit orthogonality constraints.
  • It integrates seamlessly with Softmax Cross-Entropy loss by minimizing intra-class similarity while maximizing inter-class separation without extra learnable parameters.
  • Experimental evaluations on CIFAR-100, ImageNet, and few-shot benchmarks demonstrate significant accuracy gains and enhanced robustness against label noise and adversarial attacks.

Summary of "Orthogonal Projection Loss"

The paper "Orthogonal Projection Loss" presents a novel approach to loss functions in deep neural networks (DNNs) to enhance the discriminative ability of the feature spaces used for classification tasks. Current standard practice uses the Softmax Cross-Entropy (CE) loss as the predominant objective function to effectively manage classification tasks. However, this loss primarily encourages higher projection scores onto the true class vector compared to negative classes, an approach that inherently lacks explicit inter-class separation. The authors of this paper noted that the one-hot encoding of class labels in CE loss, which are inherently orthogonal, suggests a potential methodology for feature representation improvement through enforced orthogonality.

Orthogonal Projection Loss (OPL) Concept

OPL builds upon the Softmax CE loss by explicitly instituting orthogonality constraints in the feature space to promote inter-class separation while maintaining intra-class clustering. This is accomplished by minimizing intra-class feature similarity and orthogonalizing inter-class feature similarities within each mini-batch during training. Thus, OPL systematically augments the Softmax CE loss by enforcing geometrically structured constraints which are both computationally efficient and do not introduce additional learnable parameters. Unlike other alternatives, OPL remains robust across varying batch sizes and does not rely on complex negative mining procedures.

Experimental Evaluation

OPL's effectiveness was exhaustively validated across various image classification scenarios: CIFAR-100, ImageNet, domain generalization tasks using PACS, and few-shot learning using datasets like miniImageNet and CIFAR-FS. The results consistently demonstrated that incorporating OPL leads to improved classification accuracy. Notable performance gains were achieved without necessitating task-specific modifications, thus highlighting the versatility and utility of OPL across a wide range of tasks and datasets. Importantly, the intrinsic orthogonality constraints also proved beneficial in enhancing network robustness against adversarial attacks and label noise.

Robustness and Generalization

The paper further explored the robustness and generalization capabilities of the OPL-enhanced models. In the presence of label noise and adversarial conditions, OPL demonstrated improved model stability compared to existing adversarial training methodologies and showed enhanced transfer learning potential. In domain generalization and few-shot learning contexts, OPL significantly contributed to better feature space generalizability and increased performance on unseen classes.

Theoretical and Practical Implications

By enforcing orthogonality at a feature level in DNNs, this research introduces an important conceptual shift in how classification boundaries can be effectively enforced during training. The simplicity and general applicability of OPL, validated in a variety of DNN architectures, underline its practical value and potential for wide adoption. Moreover, the work hints at future explorations wherein orthogonality constraints may extend beyond supervised learning to domains like unsupervised representation learning.

Speculation and Future Directions

The paper paves the way for further investigations into orthogonal constraints’ application on feature representations in complex tasks beyond image classification, potentially encompassing fields requiring sophisticated feature disentanglement. Future work could explore dynamic tuning of inter-class angular margins, adaptive weighting of intra-class clustering, and orthogonality in recurrent contexts.

In conclusion, the "Orthogonal Projection Loss" paper presents compelling evidence for a novel loss function that significantly enhances feature distinctness without the heavy computational burden or intricate design typically associated with margin-based learning techniques. The integration of orthogonality into learning objectives promises advancements in the effective training of more robust and generalizable deep learning models.

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