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

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.

Augmenting NER Datasets with LLMs: Towards Automated and Refined Annotation

In the field of Natural Language Processing (NLP), Named Entity Recognition (NER) is recognized as a critical technology, employed across a wide array of applications. Traditional methodologies for annotating datasets for NER models are challenged by high costs and variations in dataset quality. This research introduces a novel hybrid annotation approach that synergizes human effort with the capabilities of Large Language Models (LLMs). This approach not only aims to ameliorate the noise inherent in manual annotations, such as omissions, thereby enhancing the performance of NER models, but also achieves this in a cost-effective manner. Additionally, by employing a label mixing strategy, it addresses the issue of class imbalance encountered in LLM-based annotations. Through an analysis across multiple datasets, this method has been consistently shown to provide superior performance compared to traditional annotation methods, even under constrained budget conditions. This study illuminates the potential of leveraging LLMs to improve dataset quality, introduces a novel technique to mitigate class imbalances, and demonstrates the feasibility of achieving high-performance NER in a cost-effective way.

Towards Understanding Variants of Invariant Risk Minimization through the Lens of Calibration

Machine learning models traditionally assume that training and test data are independently and identically distributed. However, in real-world applications, the test distribution often differs from training. This problem, known as out-of-distribution generalization, challenges conventional models. Invariant Risk Minimization (IRM) emerges as a solution, aiming to identify features invariant across different environments to enhance out-of-distribution robustness. However, IRM's complexity, particularly its bi-level optimization, has led to the development of various approximate methods. Our study investigates these approximate IRM techniques, employing the Expected Calibration Error (ECE) as a key metric. ECE, which measures the reliability of model prediction, serves as an indicator of whether models effectively capture environment-invariant features. Through a comparative analysis of datasets with distributional shifts, we observe that Information Bottleneck-based IRM, which condenses representational information, achieves a balance in improving ECE while preserving accuracy relatively. This finding is pivotal, as it demonstrates a feasible path to maintaining robustness without compromising accuracy. Nonetheless, our experiments also caution against over-regularization, which can diminish accuracy. This underscores the necessity for a systematic approach in evaluating out-of-distribution generalization metrics, one that beyond mere accuracy to address the nuanced interplay between accuracy and calibration.

An Empirical Investigation of Pre-trained Model Selection for Out-of-Distribution Generalization and Calibration

In the realm of out-of-distribution generalization tasks, finetuning has risen as a key strategy. While the most focus has been on optimizing learning algorithms, our research highlights the influence of pre-trained model selection in finetuning on out-of-distribution performance and inference uncertainty. Balancing model size constraints of a single GPU, we examined the impact of varying pre-trained datasets and model parameters on performance metrics like accuracy and expected calibration error. Our findings underscore the significant influence of pre-trained model selection, showing marked performance improvements over algorithm choice. Larger models outperformed others, though the balance between memorization and true generalization merits further investigation. Ultimately, our research emphasizes the importance of pre-trained model selection for enhancing out-of-distribution generalization.

No Wrong Turns: The Simple Geometry Of Neural Networks Optimization Paths

Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural networks. This efficiency, however, contrasts with the non-convex and seemingly complex structure of neural loss landscapes. In this study, we delve into the fundamental geometric properties of sampled gradients along optimization paths. We focus on two key quantities, which appear in the restricted secant inequality and error bound. Both hold high significance for first-order optimization. Our analysis reveals that these quantities exhibit predictable, consistent behavior throughout training, despite the stochasticity induced by sampling minibatches. Our findings suggest that not only do optimization trajectories never encounter significant obstacles, but they also maintain stable dynamics during the majority of training. These observed properties are sufficiently expressive to theoretically guarantee linear convergence and prescribe learning rate schedules mirroring empirical practices. We conduct our experiments on image classification, semantic segmentation and language modeling across different batch sizes, network architectures, datasets, optimizers, and initialization seeds. We discuss the impact of each factor. Our work provides novel insights into the properties of neural network loss functions, and opens the door to theoretical frameworks more relevant to prevalent practice.

Empirical Study on Optimizer Selection for Out-of-Distribution Generalization

Modern deep learning systems are fragile and do not generalize well under distribution shifts. While much promising work has been accomplished to address these concerns, a systematic study of the role of optimizers and their out-of-distribution generalization performance has not been undertaken. In this study, we examine the performance of popular first-order optimizers for different classes of distributional shift under empirical risk minimization and invariant risk minimization. We address the problem settings for image and text classification using DomainBed, WILDS, and Backgrounds Challenge as out-of-distribution datasets for the exhaustive study. We search over a wide range of hyperparameters and examine the classification accuracy (in-distribution and out-of-distribution) for over 20,000 models. We arrive at the following findings: i) contrary to conventional wisdom, adaptive optimizers (e.g., Adam) perform worse than non-adaptive optimizers (e.g., SGD, momentum-based SGD), ii) in-distribution performance and out-of-distribution performance exhibit three types of behavior depending on the dataset - linear returns, increasing returns, and diminishing returns. We believe these findings can help practitioners choose the right optimizer and know what behavior to expect.

Optimal transport meets noisy label robust loss and MixUp regularization for domain adaptation

It is common in computer vision to be confronted with domain shift: images which have the same class but different acquisition conditions. In domain adaptation (DA), one wants to classify unlabeled target images using source labeled images. Unfortunately, deep neural networks trained on a source training set perform poorly on target images which do not belong to the training domain. One strategy to improve these performances is to align the source and target image distributions in an embedded space using optimal transport (OT). However OT can cause negative transfer, i.e. aligning samples with different labels, which leads to overfitting especially in the presence of label shift between domains. In this work, we mitigate negative alignment by explaining it as a noisy label assignment to target images. We then mitigate its effect by appropriate regularization. We propose to couple the MixUp regularization \citep{zhang2018mixup} with a loss that is robust to noisy labels in order to improve domain adaptation performance. We show in an extensive ablation study that a combination of the two techniques is critical to achieve improved performance. Finally, we evaluate our method, called \textsc{mixunbot}, on several benchmarks and real-world DA problems.

Conjugate Gradient Method for Generative Adversarial Networks

While the generative model has many advantages, it is not feasible to calculate the Jensen-Shannon divergence of the density function of the data and the density function of the model of deep neural networks; for this reason, various alternative approaches have been developed. Generative adversarial networks (GANs) can be used to formulate this problem as a discriminative problem with two models, a generator and a discriminator whose learning can be formulated in the context of game theory and the local Nash equilibrium. Since this optimization is more difficult than minimization of a single objective function, we propose to apply the conjugate gradient method to solve the local Nash equilibrium problem in GANs. We give a proof and convergence analysis under mild assumptions showing that the proposed method converges to a local Nash equilibrium with three different learning-rate schedules including a constant learning rate. Furthermore, we demonstrate the convergence of a simple toy problem to a local Nash equilibrium and compare the proposed method with other optimization methods in experiments using real-world data, finding that the proposed method outperforms stochastic gradient descent (SGD) and momentum SGD.