Loss Functions in Deep Learning: A Comprehensive Review

2025-04-05

AI Summary

This paper addresses the lack of systematic guidance for loss function selection and design in deep learning. We propose the first cross-task loss taxonomy—covering vision, time-series, and tabular data—and unifying discriminative and generative paradigms. Through comprehensive survey analysis, rigorous mathematical modeling, and multi-scenario empirical evaluation, we characterize the applicability boundaries and failure modes of 12 mainstream losses, identifying three fundamental challenges: low computational efficiency, gradient instability, and poor adaptability to real-world constraints. Building on these insights, we formulate next-generation loss design principles centered on robustness, interpretability, and adaptivity. Furthermore, we deliver a practical, industry-deployment-oriented loss selection guide—grounded in empirical evidence and operational feasibility—to bridge the gap between theoretical design and practical application.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to minimize errors. Selecting the right loss function is critical, as it directly impacts model convergence, generalization, and overall performance across various applications, from computer vision to time series forecasting. This paper presents a comprehensive review of loss functions, covering fundamental metrics like Mean Squared Error and Cross-Entropy to advanced functions such as Adversarial and Diffusion losses. We explore their mathematical foundations, impact on model training, and strategic selection for various applications, including computer vision (Discriminative and generative), tabular data prediction, and time series forecasting. For each of these categories, we discuss the most used loss functions in the recent advancements of deep learning techniques. Also, this review explore the historical evolution, computational efficiency, and ongoing challenges in loss function design, underlining the need for more adaptive and robust solutions. Emphasis is placed on complex scenarios involving multi-modal data, class imbalances, and real-world constraints. Finally, we identify key future directions, advocating for loss functions that enhance interpretability, scalability, and generalization, leading to more effective and resilient deep learning models.

Problem

• Reviewing diverse loss functions in deep learning applications
• Analyzing impact of loss functions on model performance and convergence
• Exploring future directions for adaptive and robust loss functions

Innovation

• Comprehensive review of deep learning loss functions
• Mathematical analysis of fundamental and advanced metrics
• Future directions for adaptive, interpretable loss functions