On Loss Functions for Deep Neural Networks in Classification (1702.05659v1)

Abstract: Deep neural networks are currently among the most commonly used classifiers. Despite easily achieving very good performance, one of the best selling points of these models is their modular design - one can conveniently adapt their architecture to specific needs, change connectivity patterns, attach specialised layers, experiment with a large amount of activation functions, normalisation schemes and many others. While one can find impressively wide spread of various configurations of almost every aspect of the deep nets, one element is, in authors' opinion, underrepresented - while solving classification problems, vast majority of papers and applications simply use log loss. In this paper we try to investigate how particular choices of loss functions affect deep models and their learning dynamics, as well as resulting classifiers robustness to various effects. We perform experiments on classical datasets, as well as provide some additional, theoretical insights into the problem. In particular we show that L1 and L2 losses are, quite surprisingly, justified classification objectives for deep nets, by providing probabilistic interpretation in terms of expected misclassification. We also introduce two losses which are not typically used as deep nets objectives and show that they are viable alternatives to the existing ones.

• The paper challenges the conventional reliance on log loss by demonstrating that alternative loss functions can effectively minimize misclassification errors.
• The paper provides rigorous theoretical proofs and extensive experiments on datasets like MNIST and CIFAR10, highlighting faster convergence and improved accuracy with higher-order hinge losses.
• The paper shows that expectation-based losses enhance robustness to both input and label noise, underscoring their potential for real-world applications.

Analysis of "On Loss Functions for Deep Neural Networks in Classification" by Janocha and Czarnecki

The paper "On Loss Functions for Deep Neural Networks in Classification" by Katarzyna Janocha and Wojciech Marian Czarnecki offers a comprehensive investigation into the choice of loss functions for deep neural network classifiers. The authors critically examine the dominant reliance on log loss in classification tasks and propose alternative loss functions that merit consideration.

Key Contributions

The paper presents both theoretical and empirical analyses of various loss functions. The focal point of this investigation is the influence of these functions on learning dynamics and robustness of classifiers. Notably, this paper diverges from common practices by emphasizing alternatives to log loss, and substantiates these alternatives with rigorous proof and empirical validation.

Theoretical Insights

A significant theoretical contribution is the paper’s exploration of the probabilistic interpretations of $\mathcal{L}_1$ and $\mathcal{L}_2$ losses. These losses, often relegated to regression tasks, can validly serve as classification objectives with a proper probabilistic grounding. The authors provide a thorough mathematical exposition showing that these losses can minimize expected misclassification probabilities. This insight challenges the prevailing notion of their inapplicability to classification, positing them as efficient under particular conditions.

Empirical Evaluation

The empirical segment involves extensive experimentation on widely-known datasets such as MNIST and CIFAR10. The experiments delineate the performance of twelve loss functions across various network architectures and complexity levels. The results indicate that higher-order hinge losses often outperform others in terms of both convergence speed and accuracy, emphasizing their potential in training effective classifiers. Contrarily, the expectation losses illustrate a robust performance under noisy conditions, underpinning the theoretical claims.

Robustness to Noise

The analysis extends to the robustness of classifiers against input and label noise, with expectation-based losses demonstrating an enhanced capacity for noise handling. This quality is suggested to derive from the probabilistic misclassification approach inherent in their formulation.

Implications and Future Directions

The authors advocate for a broader acknowledgment and integration of diverse loss functions in deep learning workflows. Such diversity could potentially yield classifiers better suited to specific tasks, especially when dealing with noisy datasets. Moreover, exploring non-traditional loss functions, like the Tanimoto and Cauchy-Schwarz Divergence losses, emerges as a crucial future direction for further fine-tuning model performances.

Conclusion

In sum, Janocha and Czarnecki’s work reflects a pivotal endeavor to expand the toolkit available to deep learning practitioners beyond the conventionally used log loss. Their insights into alternative loss functions offer a nuanced perspective that could drive future research and application, ensuring more versatile and resilient deep learning models. This paper not only lays the groundwork for future theoretical explorations but also encourages empirical adaptations in practical machine learning settings.