PolyLoss: A Polynomial Expansion Perspective of Classification Loss Functions

TL;DR

PolyLoss introduces a flexible polynomial-based framework for classification loss functions, enabling tailored optimization for various tasks and datasets, and demonstrating superior performance across multiple computer vision benchmarks.

Contribution

The paper proposes PolyLoss, a novel polynomial expansion framework that generalizes existing loss functions and improves performance by tuning polynomial importance for specific tasks.

Findings

PolyLoss outperforms cross-entropy and focal loss on multiple tasks.

Adjusting polynomial importance improves task-specific performance.

A simple hyperparameter tuning enhances loss function effectiveness.

Abstract

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.