Classifiers built with neural networks handle large-scale high dimensional data, such as facial images from computer vision, extremely well while traditional statistical methods often fail miserably. In this paper, we attempt to understand this empirical success in high dimensional classification by deriving the convergence rates of excess risk. In particular, a teacher-student framework is proposed that assumes the Bayes classifier to be expressed as ReLU neural networks. In this setup, we obtain a sharp rate of convergence, i.e., $\tilde{O}_d(n^{-2/3})$, for classifiers trained using either 0-1 loss or hinge loss. This rate can be further improved to $\tilde{O}_d(n^{-1})$ when the data distribution is separable. Here, $n$ denotes the sample size. An interesting observation is that the data dimension only contributes to the $\log(n)$ term in the above rates. This may provide one theoretical explanation for the empirical successes of deep neural networks in high dimensional classification, particularly for structured data.
The University of Tokyo（东京大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
While deep learning has outperformed other methods for various tasks, theoretical frameworks that explain its reason have not been fully established. To address this issue, we investigate the excess risk of two-layer ReLU neural networks in a teacher-student regression model, in which a student network learns an unknown teacher network through its outputs. Especially, we consider the student network that has the same width as the teacher network and is trained in two phases: first by noisy gradient descent and then by the vanilla gradient descent. Our result shows that the student network prov…
In the framework of on-line learning, a learning machine might move around a teacher due to the differences in structures or output functions between the teacher and the learning machine. In this paper we analyze the generalization performance of a new student supervised by a moving machine. A model composed of a fixed true teacher, a moving teacher, and a student is treated theoretically using statistical mechanics, where the true teacher is a nonmonotonic perceptron and the others are simple perceptrons. Calculating the generalization errors numerically, we show that the generalization error…
We propose self-training with noisy student-teacher approach for streaming keyword spotting, that can utilize large-scale unlabeled data and aggressive data augmentation. The proposed method applies aggressive data augmentation (spectral augmentation) on the input of both student and teacher and utilize unlabeled data at scale, which significantly boosts the accuracy of student against challenging conditions. Such aggressive augmentation usually degrades model performance when used with supervised training with hard-labeled data. Experiments show that aggressive spec augmentation on baseline s…
Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on training two-layer ReLU neural networks in a teacher-student regression model, in which a student network learns an unknown teacher network through its outputs. We show that with a specific regularization and sufficient over-parameterization, the student network can identify the parameters of the teacher network with high probability via gradient descent with a norm dependent stepsize even though the o…
Performing knowledge transfer from a large teacher network to a smaller student is a popular task in modern deep learning applications. However, due to growing dataset sizes and stricter privacy regulations, it is increasingly common not to have access to the data that was used to train the teacher. We propose a novel method which trains a student to match the predictions of its teacher without using any data or metadata. We achieve this by training an adversarial generator to search for images on which the student poorly matches the teacher, and then using them to train the student. Our resul…
Knowledge distillation is a popular technique for training a small student network to emulate a larger teacher model, such as an ensemble of networks. We show that while knowledge distillation can improve student generalization, it does not typically work as it is commonly understood: there often remains a surprisingly large discrepancy between the predictive distributions of the teacher and the student, even in cases when the student has the capacity to perfectly match the teacher. We identify difficulties in optimization as a key reason for why the student is unable to match the teacher. We …
School of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程学院）
Feature-based student-teacher learning, a training method that encourages the student's hidden features to mimic those of the teacher network, is empirically successful in transferring the knowledge from a pre-trained teacher network to the student network. Furthermore, recent empirical results demonstrate that, the teacher's features can boost the student network's generalization even when the student's input sample is corrupted by noise. However, there is a lack of theoretical insights into why and when this method of transferring knowledge can be successful between such heterogeneous tasks.…
University of Waikato（怀卡托大学）；Télécom ParisTech（巴黎高科电信学院）；Dalhousie University（达尔豪斯大学）
Concept drift detection is a crucial task in data stream evolving environments. Most of state of the art approaches designed to tackle this problem monitor the loss of predictive models. However, this approach falls short in many real-world scenarios, where the true labels are not readily available to compute the loss. In this context, there is increasing attention to approaches that perform concept drift detection in an unsupervised manner, i.e., without access to the true labels. We propose a novel approach to unsupervised concept drift detection based on a student-teacher learning paradigm.…
More accurate machine learning models often demand more computation and memory at test time, making them difficult to deploy on CPU- or memory-constrained devices. Teacher-student compression (TSC), also known as distillation, alleviates this burden by training a less expensive student model to mimic the expensive teacher model while maintaining most of the original accuracy. However, when fresh data is unavailable for the compression task, the teacher's training data is typically reused, leading to suboptimal compression. In this work, we propose to augment the compression dataset with synthe…
To reduce the overwhelming size of Deep Neural Networks (DNN) teacher-student methodology tries to transfer knowledge from a complex teacher network to a simple student network. We instead propose a novel method called the teacher-class network consisting of a single teacher and multiple student networks (i.e. class of students). Instead of transferring knowledge to one student only, the proposed method transfers a chunk of knowledge to each student. Our students are not trained for problem-specific logits, they are trained to mimic knowledge (dense representation) learned by the teacher netwo…
Peking University（北京大学）；Huawei Technologies Co., Ltd（华为技术有限公司）；The University of Sydney（悉尼大学）
Deep convolutional neural networks have been widely used in numerous applications, but their demanding storage and computational resource requirements prevent their applications on mobile devices. Knowledge distillation aims to optimize a portable student network by taking the knowledge from a well-trained heavy teacher network. Traditional teacher-student based methods used to rely on additional fully-connected layers to bridge intermediate layers of teacher and student networks, which brings in a large number of auxiliary parameters. In contrast, this paper aims to propagate information from…
University of Oxford（牛津大学）；Oxford University Hospitals Trust（牛津大学医院信托）
Accurate and reliable prediction of hospital admission location is important due to resource-constraints and space availability in a clinical setting, particularly when dealing with patients who come from the emergency department. In this work we propose a student-teacher network via reinforcement learning to deal with this specific problem. A representation of the weights of the student network is treated as the state and is fed as an input to the teacher network. The teacher network's action is to select the most appropriate batch of data to train the student network on from a training set s…
Washington State University（华盛顿州立大学）；DeepMind（深度思维）；D.E. Shaw（德劭集团）
Despite the fact that deep neural networks are powerful models and achieve appealing results on many tasks, they are too large to be deployed on edge devices like smartphones or embedded sensor nodes. There have been efforts to compress these networks, and a popular method is knowledge distillation, where a large (teacher) pre-trained network is used to train a smaller (student) network. However, in this paper, we show that the student network performance degrades when the gap between student and teacher is large. Given a fixed student network, one cannot employ an arbitrarily large teacher, o…
Imperial College（帝国理工学院）；International School of Advanced Studies (SISSA)（国际高等研究学院（SISSA））；University of Oxford（牛津大学）；Facebook AI Research（脸书人工智能研究院）
Continual learning-the ability to learn many tasks in sequence-is critical for artificial learning systems. Yet standard training methods for deep networks often suffer from catastrophic forgetting, where learning new tasks erases knowledge of earlier tasks. While catastrophic forgetting labels the problem, the theoretical reasons for interference between tasks remain unclear. Here, we attempt to narrow this gap between theory and practice by studying continual learning in the teacher-student setup. We extend previous analytical work on two-layer networks in the teacher-student setup to multip…
City University of Hong Kong（香港城市大学）；SenseTime Research（商汤科技研究院）
Recently, consistency-based methods have achieved state-of-the-art results in semi-supervised learning (SSL). These methods always involve two roles, an explicit or implicit teacher model and a student model, and penalize predictions under different perturbations by a consistency constraint. However, the weights of these two roles are tightly coupled since the teacher is essentially an exponential moving average (EMA) of the student. In this work, we show that the coupled EMA teacher causes a performance bottleneck. To address this problem, we introduce Dual Student, which replaces the teacher…
Peking University（北京大学）；The University of Sydney（悉尼大学）
Deep neural networks bring in impressive accuracy in various applications, but the success often relies on the heavy network architecture. Taking well-trained heavy networks as teachers, classical teacher-student learning paradigm aims to learn a student network that is lightweight yet accurate. In this way, a portable student network with significantly fewer parameters can achieve a considerable accuracy which is comparable to that of teacher network. However, beyond accuracy, robustness of the learned student network against perturbation is also essential for practical uses. Existing teacher…
The teacher-student (T/S) learning has been shown to be effective for a variety of problems such as domain adaptation and model compression. One shortcoming of the T/S learning is that a teacher model, not always perfect, sporadically produces wrong guidance in form of posterior probabilities that misleads the student model towards a suboptimal performance. To overcome this problem, we propose a conditional T/S learning scheme, in which a "smart" student model selectively chooses to learn from either the teacher model or the ground truth labels conditioned on whether the teacher can correctly …
Brno University of Technology（布尔诺理工大学）；Amazon.com, Inc.（亚马逊公司）
For real-world speech recognition applications, noise robustness is still a challenge. In this work, we adopt the teacher-student (T/S) learning technique using a parallel clean and noisy corpus for improving automatic speech recognition (ASR) performance under multimedia noise. On top of that, we apply a logits selection method which only preserves the k highest values to prevent wrong emphasis of knowledge from the teacher and to reduce bandwidth needed for transferring data. We incorporate up to 8000 hours of untranscribed data for training and present our results on sequence trained models…
