# A comprehensive theoretical framework for the optimization of neural networks classification performance with respect to weighted metrics

arXiv: https://arxiv.org/abs/2305.13472 · HTML: https://mlsanity.com/paper/2305.13472/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 14 of 14)

- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series](https://mlsanity.com/paper/1811.10166/) (2018)
- [On Loss Functions for Deep Neural Networks in Classification](https://mlsanity.com/paper/1702.05659/) (2017)
- [Addressing the Loss-Metric Mismatch with Adaptive Loss Alignment](https://mlsanity.com/paper/1905.05895/) (2019)
- [Optimizing Non-decomposable Performance Measures: A Tale of Two Classes](https://mlsanity.com/paper/1505.06812/) (2015)
- [Balanced softmax cross-entropy for incremental learning with and without memory](https://mlsanity.com/paper/2103.12532/) (2021)
- [Score-oriented loss (SOL) functions](https://mlsanity.com/paper/2103.15522/) (2021)
- [Training Over-parameterized Models with Non-decomposable Objectives](https://mlsanity.com/paper/2107.04641/) (2021)
- [A New Loss Function for CNN Classifier Based on Pre-defined Evenly-Distributed Class Centroids](https://mlsanity.com/paper/1904.06008/) (2019)
- [Prediction of severe thunderstorm events with ensemble deep learning and radar data](https://mlsanity.com/paper/2109.09791/) (2021)
- [Bad and good errors: value-weighted skill scores in deep ensemble learning](https://mlsanity.com/paper/2103.02881/) (2021)
- [Operational solar flare forecasting via video-based deep learning](https://mlsanity.com/paper/2209.05128/) (2022)

## Built on by (most cited first, 3 of 3)

- [The Multiclass Score-Oriented Loss (MultiSOL) on the Simplex](https://mlsanity.com/paper/2511.22587/) (2025)
- [Don't stop me now: How Validation Criteria Affect Checkpoint Selection and Early Stopping](https://mlsanity.com/paper/2602.22107/) (2026)
- [Weighted Score-Oriented Losses for Temporally Localized Event Prediction](https://mlsanity.com/paper/2606.23145/) (2026)

## Abstract (arXiv)

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores.