Geometric Insights into Focal Loss: Reducing Curvature for Enhanced Model Calibration

• URL: http://arxiv.org/abs/2405.00442v1
• Date: Wed, 1 May 2024 10:53:54 GMT
• Title: Geometric Insights into Focal Loss: Reducing Curvature for Enhanced Model Calibration
• Authors: Masanari Kimura, Hiroki Naganuma,
• Abstract summary: The confidence level of a model in a classification problem is often given by the output vector of a softmax function for convenience. This problem is called model calibration and has been studied extensively. We show that focal loss reduces the curvature of the loss surface in training the model.
• Score: 1.642094639107215
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The key factor in implementing machine learning algorithms in decision-making situations is not only the accuracy of the model but also its confidence level. The confidence level of a model in a classification problem is often given by the output vector of a softmax function for convenience. However, these values are known to deviate significantly from the actual expected model confidence. This problem is called model calibration and has been studied extensively. One of the simplest techniques to tackle this task is focal loss, a generalization of cross-entropy by introducing one positive parameter. Although many related studies exist because of the simplicity of the idea and its formalization, the theoretical analysis of its behavior is still insufficient. In this study, our objective is to understand the behavior of focal loss by reinterpreting this function geometrically. Our analysis suggests that focal loss reduces the curvature of the loss surface in training the model. This indicates that curvature may be one of the essential factors in achieving model calibration. We design numerical experiments to support this conjecture to reveal the behavior of focal loss and the relationship between calibration performance and curvature.

Related papers

• On the Dynamics Under the Unhinged Loss and Beyond [104.49565602940699]
  We introduce the unhinged loss, a concise loss function, that offers more mathematical opportunities to analyze closed-form dynamics. The unhinged loss allows for considering more practical techniques, such as time-vary learning rates and feature normalization.
  arXiv  Detail & Related papers  (2023-12-13T02:11:07Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Knowledge Distillation Performs Partial Variance Reduction [93.6365393721122]
  Knowledge distillation is a popular approach for enhancing the performance of ''student'' models. The underlying mechanics behind knowledge distillation (KD) are still not fully understood. We show that KD can be interpreted as a novel type of variance reduction mechanism.
  arXiv  Detail & Related papers  (2023-05-27T21:25:55Z)
• Causal Analysis for Robust Interpretability of Neural Networks [0.2519906683279152]
  We develop a robust interventional-based method to capture cause-effect mechanisms in pre-trained neural networks. We apply our method to vision models trained on classification tasks.
  arXiv  Detail & Related papers  (2023-05-15T18:37:24Z)
• An Indirect Rate-Distortion Characterization for Semantic Sources: General Model and the Case of Gaussian Observation [83.93224401261068]
  Source model is motivated by the recent surge of interest in the semantic aspect of information. intrinsic state corresponds to the semantic feature of the source, which in general is not observable. Rate-distortion function is the semantic rate-distortion function of the source.
  arXiv  Detail & Related papers  (2022-01-29T02:14:24Z)
• On the Role of Optimization in Double Descent: A Least Squares Study [30.44215064390409]
  We show an excess risk bound for the descent gradient solution of the least squares objective. We find that in case of noiseless regression, double descent is explained solely by optimization-related quantities. We empirically explore if our predictions hold for neural networks.
  arXiv  Detail & Related papers  (2021-07-27T09:13:11Z)
• Deep learning: a statistical viewpoint [120.94133818355645]
  Deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-perfect solutions to non-optimal training problems. We conjecture that specific principles underlie these phenomena.
  arXiv  Detail & Related papers  (2021-03-16T16:26:36Z)
• Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning [0.0]
  It is shown that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and the bias measured on a specific scale. This new method to correct for bias adds extra local GLM step to the analysis. The convex order appears to be the natural tool to compare competing models.
  arXiv  Detail & Related papers  (2021-03-05T12:40:30Z)
• Calibrating Deep Neural Networks using Focal Loss [77.92765139898906]
  Miscalibration is a mismatch between a model's confidence and its correctness. We show that focal loss allows us to learn models that are already very well calibrated. We show that our approach achieves state-of-the-art calibration without compromising on accuracy in almost all cases.
  arXiv  Detail & Related papers  (2020-02-21T17:35:50Z)
• Considering discrepancy when calibrating a mechanistic electrophysiology model [41.77362715012383]
  Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. In this piece we draw attention to an important and under-addressed source of uncertainty in our predictions -- that of uncertainty in the model structure or the equations themselves.
  arXiv  Detail & Related papers  (2020-01-13T13:26:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.