Stable Weight Decay Regularization

Weight decay is a popular regularization technique for training of deep neural networks. Modern deep learning libraries mainly use $L_{2}$ regularization as the default implementation of weight decay. \citet{loshchilov2018decoupled} demonstrated that $L_{2}$ regularization is not identical to weight decay for adaptive gradient methods, such as Adaptive Momentum Estimation (Adam), and proposed Adam with Decoupled Weight Decay (AdamW). However, we found that the popular implementations of weight decay, including $L_{2}$ regularization and decoupled weight decay, in modern deep learning libraries usually damage performance. First, the $L_{2}$ regularization is unstable weight decay for all optimizers that use Momentum, such as stochastic gradient descent (SGD). Second, decoupled weight decay is highly unstable for all adaptive gradient methods. We further propose the Stable Weight Decay (SWD) method to fix the unstable weight decay problem from a dynamical perspective. The proposed SWD method makes significant improvements over $L_{2}$ regularization and decoupled weight decay in our experiments. Simply fixing weight decay in Adam by SWD, with no extra hyperparameter, can usually outperform complex Adam variants, which have more hyperparameters.

Artificial Neural Variability for Deep Learning: On Overfitting, Noise Memorization, and Catastrophic Forgetting

Deep learning is often criticized by two serious issues which rarely exist in natural nervous systems: overfitting and catastrophic forgetting. It can even memorize randomly labelled data, which has little knowledge behind the instance-label pairs. When a deep network continually learns over time by accommodating new tasks, it usually quickly overwrites the knowledge learned from previous tasks. Referred to as the neural variability, it is well-known in neuroscience that human brain reactions exhibit substantial variability even in response to the same stimulus. This mechanism balances accuracy and plasticity/flexibility in the motor learning of natural nervous systems. Thus it motivates us to design a similar mechanism named artificial neural variability (ANV), which helps artificial neural networks learn some advantages from "natural" neural networks. We rigorously prove that ANV plays as an implicit regularizer of the mutual information between the training data and the learned model. This result theoretically guarantees ANV a strictly improved generalizability, robustness to label noise, and robustness to catastrophic forgetting. We then devise a neural variable risk minimization (NVRM) framework and neural variable optimizers to achieve ANV for conventional network architectures in practice. The empirical studies demonstrate that NVRM can effectively relieve overfitting, label noise memorization, and catastrophic forgetting at negligible costs.

On Focal Loss for Class-Posterior Probability Estimation: A Theoretical Perspective

The focal loss has demonstrated its effectiveness in many real-world applications such as object detection and image classification, but its theoretical understanding has been limited so far. In this paper, we first prove that the focal loss is classification-calibrated, i.e., its minimizer surely yields the Bayes-optimal classifier and thus the use of the focal loss in classification can be theoretically justified. However, we also prove a negative fact that the focal loss is not strictly proper, i.e., the confidence score of the classifier obtained by focal loss minimization does not match the true class-posterior probability and thus it is not reliable as a class-posterior probability estimator. To mitigate this problem, we next prove that a particular closed-form transformation of the confidence score allows us to recover the true class-posterior probability. Through experiments on benchmark datasets, we demonstrate that our proposed transformation significantly improves the accuracy of class-posterior probability estimation.

A Survey of Label-noise Representation Learning: Past, Present and Future

Classical machine learning implicitly assumes that labels of the training data are sampled from a clean distribution, which can be too restrictive for real-world scenarios. However, statistical learning-based methods may not train deep learning models robustly with these noisy labels. Therefore, it is urgent to design Label-Noise Representation Learning (LNRL) methods for robustly training deep models with noisy labels. To fully understand LNRL, we conduct a survey study. We first clarify a formal definition for LNRL from the perspective of machine learning. Then, via the lens of learning theory and empirical study, we figure out why noisy labels affect deep models' performance. Based on the theoretical guidance, we categorize different LNRL methods into three directions. Under this unified taxonomy, we provide a thorough discussion of the pros and cons of different categories. More importantly, we summarize the essential components of robust LNRL, which can spark new directions. Lastly, we propose possible research directions within LNRL, such as new datasets, instance-dependent LNRL, and adversarial LNRL. Finally, we envision potential directions beyond LNRL, such as learning with feature-noise, preference-noise, domain-noise, similarity-noise, graph-noise, and demonstration-noise.

Binary classification with ambiguous training data

In supervised learning, we often face with ambiguous (A) samples that are difficult to label even by domain experts. In this paper, we consider a binary classification problem in the presence of such A samples. This problem is substantially different from semi-supervised learning since unlabeled samples are not necessarily difficult samples. Also, it is different from 3-class classification with the positive (P), negative (N), and A classes since we do not want to classify test samples into the A class. Our proposed method extends binary classification with reject option, which trains a classifier and a rejector simultaneously using P and N samples based on the 0-1-$c$ loss with rejection cost $c$. More specifically, we propose to train a classifier and a rejector under the 0-1-$c$-$d$ loss using P, N, and A samples, where $d$ is the misclassification penalty for ambiguous samples. In our practical implementation, we use a convex upper bound of the 0-1-$c$-$d$ loss for computational tractability. Numerical experiments demonstrate that our method can successfully utilize the additional information brought by such A training data.

Robust Imitation Learning from Noisy Demonstrations

Learning from noisy demonstrations is a practical but highly challenging problem in imitation learning. In this paper, we first theoretically show that robust imitation learning can be achieved by optimizing a classification risk with a symmetric loss. Based on this theoretical finding, we then propose a new imitation learning method that optimizes the classification risk by effectively combining pseudo-labeling with co-training. Unlike existing methods, our method does not require additional labels or strict assumptions about noise distributions. Experimental results on continuous-control benchmarks show that our method is more robust compared to state-of-the-art methods.

Classification with Rejection Based on Cost-sensitive Classification

The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection and cost-sensitive classification, we propose a novel method of classification with rejection by learning an ensemble of cost-sensitive classifiers, which satisfies all the following properties for the first time: (i) it can avoid estimating class-posterior probabilities, resulting in improved classification accuracy. (ii) it allows a flexible choice of losses including non-convex ones, (iii) it does not require complicated modifications when using different losses, (iv) it is applicable to both binary and multiclass cases, and (v) it is theoretically justifiable for any classification-calibrated loss. Experimental results demonstrate the usefulness of our proposed approach in clean-labeled, noisy-labeled, and positive-unlabeled classification.