We study generalization in deep learning by appealing to complexity measures originally developed in approximation and information theory. While these concepts are challenged by the high-dimensional and data-defined nature of deep learning, we show that simple vector quantization approaches such as PCA, GMMs, and SVMs capture their spirit when applied layer-wise to deep extracted features giving rise to relatively inexpensive complexity measures that correlate well with generalization performance. We discuss our results in 2020 NeurIPS PGDL challenge.
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Jožef Stefan International Postgraduate School（约瑟夫·斯特凡国际研究生院）
The competition "Predicting Generalization in Deep Learning (PGDL)" aims to provide a platform for rigorous study of generalization of deep learning models and offer insight into the progress of understanding and explaining these models. This report presents the solution that was submitted by the user \emph{smeznar} which achieved the eight place in the competition. In the proposed approach, we create simple metrics and find their best combination with automatic testing on the provided dataset, exploring how combinations of various properties of the input neural network architectures can be us…
The Chinese University of Hong Kong（香港中文大学）；University of Chinese Academy of Sciences（中国科学院大学）；Tsinghua University（清华大学）
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents {\it bounded-distortion metric learning} (BDML), a new metric learning framework which amounts to finding an optimal Mahalanobis metric space with a bounded-distortion constraint. An efficient solver based on the multiplicative weights update method is proposed. Moreover, we generalize BDML to pseudo-metric learning and…
Developing a robust generalization measure for the performance of machine learning models is an important and challenging task. A lot of recent research in the area focuses on the model decision boundary when predicting generalization. In this paper, as part of the "Predicting Generalization in Deep Learning" competition, we analyse the complexity of decision boundaries using the concept of fractal dimension and develop a generalization measure based on that technique.
Paris Research Center, Huawei Technologies France（华为技术法国巴黎研究中心）；Université Paris-Est（巴黎东大学）
In this paper, we use tools from rate-distortion theory to establish new upper bounds on the generalization error of statistical distributed learning algorithms. Specifically, there are $K$ clients whose individually chosen models are aggregated by a central server. The bounds depend on the compressibility of each client's algorithm while keeping other clients' algorithms un-compressed, and leverage the fact that small changes in each local model change the aggregated model by a factor of only $1/K$. Adopting a recently proposed approach by Sefidgaran et al., and extending it suitably to the d…
Google Research（谷歌研究院）；University of Toronto（多伦多大学）；Element AI；Microsoft Research（微软研究院）；University Paris-Saclay（巴黎-萨克雷大学）；ChaLearn
Understanding generalization in deep learning is arguably one of the most important questions in deep learning. Deep learning has been successfully adopted to a large number of problems ranging from pattern recognition to complex decision making, but many recent researchers have raised many concerns about deep learning, among which the most important is generalization. Despite numerous attempts, conventional statistical learning approaches have yet been able to provide a satisfactory explanation on why deep learning works. A recent line of works aims to address the problem by trying to predict…
Tehran Institute for Advanced Studies, Khatam University（哈塔姆大学德黑兰高等研究院）；INRIA（法国国家信息与自动化研究所）；ENS – PSL Research University（PSL研究大学巴黎高等师范学院）
Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting different complexity notions such as the mutual information between the data sample and the algorithm output, compressibility of the hypothesis space, and the fractal dimension of the hypothesis space. While these bounds have illuminated the problem at hand from different angles, their suggested complexity notions might appear seemingly unrelated, thereby res…
As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of generalization. This leads to the crucial question of how generalization gap should be predicted from the training data and network parameters. In this paper, we propose such a measure, and conduct extensive empirical studies on how well it can predict the generalization gap. Our measure is based on the concept of margin distribution, which are the distances of…
Variational autoencoders optimize an objective that combines a reconstruction loss (the distortion) and a KL term (the rate). The rate is an upper bound on the mutual information, which is often interpreted as a regularizer that controls the degree of compression. We here examine whether inclusion of the rate also acts as an inductive bias that improves generalization. We perform rate-distortion analyses that control the strength of the rate term, the network capacity, and the difficulty of the generalization problem. Decreasing the strength of the rate paradoxically improves generalization in…
Predicting Out-of-Domain Generalization with Neighborhood Invariance
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Massachusetts Institute of Technology（麻省理工学院）；New York University（纽约大学）；Prescient Design, Genentech（基因泰克Prescient Design）
The estimation of the generalization error of classifiers often relies on a validation set. Such a set is hardly available in few-shot learning scenarios, a highly disregarded shortcoming in the field. In these scenarios, it is common to rely on features extracted from pre-trained neural networks combined with distance-based classifiers such as nearest class mean. In this work, we introduce a Gaussian model of the feature distribution. By estimating the parameters of this model, we are able to predict the generalization error on new classification tasks with few samples. We observe that accura…
This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective function for training deep neural networks. DILATE aims at accurately predicting sudden changes, and explicitly incorporates two terms supporting precise shape and temporal change detection. We introduce a differentiable loss function suitable for training deep neural nets, and provide a custom back-prop implementation for speeding up optimization. We also int…
IMT Atlantique（大西洋高等电信学校）；Lab-STICC（布列塔尼电子与电信通信科学实验室）；MILA, Université de Montréal（蒙特利尔大学MILA人工智能研究所）；Université Cote d’Azur（蔚蓝海岸大学）；École Normale Supérieure de Lyon（里昂高等师范学院）
In the context of few-shot learning, one cannot measure the generalization ability of a trained classifier using validation sets, due to the small number of labeled samples. In this paper, we are interested in finding alternatives to answer the question: is my classifier generalizing well to previously unseen data? We first analyze the reasons for the variability of generalization performances. We then investigate the case of using transfer-based solutions, and consider three settings: i) supervised where we only have access to a few labeled samples, ii) semi-supervised where we have access to…
Peking University（北京大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Peng Cheng Laboratory（鹏城实验室）；The University of Sydney（悉尼大学）
Deep neural networks often consist of a great number of trainable parameters for extracting powerful features from given datasets. On one hand, massive trainable parameters significantly enhance the performance of these deep networks. On the other hand, they bring the problem of over-fitting. To this end, dropout based methods disable some elements in the output feature maps during the training phase for reducing the co-adaptation of neurons. Although the generalization ability of the resulting models can be enhanced by these approaches, the conventional binary dropout is not the optimal solut…
For a long time, designing neural architectures that exhibit high performance was considered a dark art that required expert hand-tuning. One of the few well-known guidelines for architecture design is the avoidance of exploding gradients, though even this guideline has remained relatively vague and circumstantial. We introduce the nonlinearity coefficient (NLC), a measurement of the complexity of the function computed by a neural network that is based on the magnitude of the gradient. Via an extensive empirical study, we show that the NLC is a powerful predictor of test error and that attaini…
UC Berkeley（加州大学伯克利分校）；KAIST（韩国科学技术院）；Google Brain（谷歌大脑）；University of Michigan Ann Arbor（密歇根大学安娜堡分校）
Model-based reinforcement learning (RL) enjoys several benefits, such as data-efficiency and planning, by learning a model of the environment's dynamics. However, learning a global model that can generalize across different dynamics is a challenging task. To tackle this problem, we decompose the task of learning a global dynamics model into two stages: (a) learning a context latent vector that captures the local dynamics, then (b) predicting the next state conditioned on it. In order to encode dynamics-specific information into the context latent vector, we introduce a novel loss function that…
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
Recent papers have shown that sufficiently overparameterized neural networks can perfectly fit even random labels. Thus, it is crucial to understand the underlying reason behind the generalization performance of a network on real-world data. In this work, we propose several measures to predict the generalization error of a network given the training data and its parameters. Using one of these measures, based on noise resilience of the network, we secured 5th position in the predicting generalization in deep learning (PGDL) competition at NeurIPS 2020.
Pakistan Institute of Engineering and Applied Sciences（巴基斯坦工程与应用科学学院）
Wind energy forecasting helps to manage power production, and hence, reduces energy cost. Deep Neural Networks (DNN) mimics hierarchical learning in the human brain and thus possesses hierarchical, distributed, and multi-task learning capabilities. Based on aforementioned characteristics, we report Deep Belief Network (DBN) based forecast engine for wind power prediction because of its good generalization and unsupervised pre-training attributes. The proposed DBN-WP forecast engine, which exhibits stochastic feature generation capabilities and is composed of multiple Restricted Boltzmann Machi…
AITRICS；KAIST（韩国科学技术院）；BARO AI；Seoul South Korea（首尔（韩国））；Daejeon South Korea（大田（韩国））
While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a meta-learning framework for predicting generalization. Our model learns a scalar complexity measure through interactions with many heterogeneous tasks in a data-driven way. The trained NC model can be added to the standard training loss to regularize any task learner in a standard supervised learning scenario. We contrast NC's approach against existing manually-design…
To meet the standard of differential privacy, noise is usually added into the original data, which inevitably deteriorates the predicting performance of subsequent learning algorithms. In this paper, motivated by the success of improving predicting performance by ensemble learning, we propose to enhance privacy-preserving logistic regression by stacking. We show that this can be done either by sample-based or feature-based partitioning. However, we prove that when privacy-budgets are the same, feature-based partitioning requires fewer samples than sample-based one, and thus likely has better e…
