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. • We reinterpret focal loss and show that it behaves as the curvature reduction. • We provide the conjecture of the connection between curvature and model calibration. • We design the numerical experiments to demonstrate our theoretical hypothesis.

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, the restricted secant inequality and error bound, as well as their ratio γ, which 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.

One of the training strategies of generative models is to minimize the Jensen–Shannon divergence between the model distribution and the data distribution. Since data distribution is unknown, generative adversarial networks (GANs) formulate this problem as a game between two models, a generator and a discriminator. The training can be formulated in the context of game theory and the local Nash equilibrium (LNE). It does not seem feasible to derive guarantees of stability or optimality for the existing methods. This optimization problem is far more challenging than the single objective setting. Here, we use the conjugate gradient method to reliably and efficiently solve the LNE problem in GANs. We give a proof and convergence analysis under mild assumptions showing that the proposed method converges to a LNE with three different learning rate update rules, including a constant learning rate. Finally, we demonstrate that the proposed method outperforms stochastic gradient descent (SGD) and momentum SGD in terms of best Frechet inception distance (FID) score and outperforms Adam on average.

In scenarios such as people-flow analysis and autonomous driving using camera footage, the performance of deep neural networks can be impacted by environmental changes such as the degradation of the camera lenses over time and changes in weather conditions. Understanding the impact of environmental changes on model performance is critical to the safe use of the model but has not been systematically investigated. In this study, we cast environmental changes as distribution shifts in the data and tackle the out-of-distribution generalization problem. In particular, we investigate the impact of performance degradation and uncertainty estimation under more than 30 distribution shifts considered in real-world applications. Our experimental results show that there is a correlation between classification accuracy and uncertainty in out-of-distribution environments. Furthermore, it is suggested that uncertainty calibration is not necessarily effective in environments where severe corruption occurs. We believe these findings will contribute to the safe use of the model in the real world.

Classical learning theory states that when the number of parameters of the model is too large compared to the data, the model will overfit and the generalization performance deteriorates. However, it has been empirically shown that deep neural networks (DNN) can achieve high generalization capability by training with extremely large amount of data and model parameters, which exceeds the predictions of classical learning theory. One drawback of this is that training of DNN requires enormous calculation time. Therefore, it is necessary to reduce the training time through large scale parallelization. Straightforward data-parallelization of DNN degrades convergence and generalization. In the present work, we investigate the possibility of using second order methods to solve this generalization gap in large-batch training. This is motivated by our observation that each mini-batch becomes more statistically stable, and thus the effect of considering the curvature plays a more important role in large-batch training. We have also found that naively adapting the natural gradient method causes the generalization performance to deteriorate further due to the lack of regularization capability. We propose an improved second order method by smoothing the loss function, which allows second-order methods to generalize as well as mini-batch SGD.