Frequency Bias in Neural Networks for Input of Non-Uniform Density
Weizmann Institute of Science（魏茨曼科学研究所）；Department of Computer Science and Applied Mathematics, Weizmann Institute of Science（魏茨曼科学研究所计算机科学与应用数学系）；Department of Computer Science, Univeristy of Maryland（马里兰大学计算机科学系）；Department of Computer Science and Applied Mathematics（计算机科学与应用数学系）
Recent works have partly attributed the generalization ability of over-parameterized neural networks to frequency bias -- networks trained with gradient descent on data drawn from a uniform distribution find a low frequency fit before high frequency ones. As realistic training sets are not drawn from a uniform distribution, we here use the Neural Tangent Kernel (NTK) model to explore the effect of variable density on training dynamics. Our results, which combine analytic and empirical observations, show that when learning a pure harmonic function of frequency $κ$, convergence at a point $\x \in \Sphere^{d-1}$ occurs in time $O(κ^d/p(\x))$ where $p(\x)$ denotes the local density at $\x$. Specifically, for data in $\Sphere^1$ we analytically derive the eigenfunctions of the kernel associated with the NTK for two-layer networks. We further prove convergence results for deep, fully connected networks with respect to the spectral decomposition of the NTK. Our empirical study highlights similarities and differences between deep and shallow networks in this model.
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；International Computer Science Institute（国际计算机科学研究所）；Center for Applied Mathematics, Cornell University（康奈尔大学应用数学中心）；Data Science Institute, University of Chicago（芝加哥大学数据科学研究所）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Nordita, KTH Royal Institute of Technology and Stockholm University（北欧理论物理研究所）；University of California at Berkeley（加利福尼亚大学伯克利分校）
Baylor College of Medicine（贝勒医学院）；Rice University（莱斯大学）；Manifold AI（Manifold人工智能公司）；University of Tübingen（图宾根大学）
Adversarial Attacks are still a significant challenge for neural networks. Recent work has shown that adversarial perturbations typically contain high-frequency features, but the root cause of this phenomenon remains unknown. Inspired by theoretical work on linear full-width convolutional models, we hypothesize that the local (i.e. bounded-width) convolutional operations commonly used in current neural networks are implicitly biased to learn high frequency features, and that this is one of the root causes of high frequency adversarial examples. To test this hypothesis, we analyzed the impact o…
Small generalization errors of over-parameterized neural networks (NNs) can be partially explained by the frequency biasing phenomenon, where gradient-based algorithms minimize the low-frequency misfit before reducing the high-frequency residuals. Using the Neural Tangent Kernel (NTK), one can provide a theoretically rigorous analysis for training where data are drawn from constant or piecewise-constant probability densities. Since most training data sets are not drawn from such distributions, we use the NTK model and a data-dependent quadrature rule to theoretically quantify the frequency bia…
As the success of Generative Adversarial Networks (GANs) on natural images quickly propels them into various real-life applications across different domains, it becomes more and more important to clearly understand their limitations. Specifically, understanding GANs' capability across the full spectrum of spatial frequencies, i.e. beyond the low-frequency dominant spectrum of natural images, is critical for assessing the reliability of GAN generated data in any detail-sensitive application (e.g. denoising, filling and super-resolution in medical and satellite images). In this paper, we show th…
The inherent autocorrelation of time series data presents an ongoing challenge to multivariate time series prediction. Recently, a widely adopted approach has been the incorporation of frequency domain information to assist in long-term prediction tasks. Many researchers have independently observed the spectral bias phenomenon in neural networks, where models tend to fit low-frequency signals before high-frequency ones. However, these observations have often been attributed to the specific architectures designed by the researchers, rather than recognizing the phenomenon as a universal characte…
CNNs exhibit many behaviors different from humans, one of which is the capability of employing high-frequency components. This paper discusses the frequency bias phenomenon in image classification tasks: the high-frequency components are actually much less exploited than the low- and mid-frequency components. We first investigate the frequency bias phenomenon by presenting two observations on feature discrimination and learning priority. Furthermore, we hypothesize that (i) the spectral density, (ii) class consistency directly affect the frequency bias. Specifically, our investigations verify …
New York University Abu Dhabi（纽约大学阿布扎比分校）；Courant Institute of Mathematical Sciences（库朗数学科学研究所）；Purdue University（普渡大学）
It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well. An attempt of understanding this puzzle is to discover implicit biases underlying the training process of DNNs, such as the Frequency Principle (F-Principle), i.e., DNNs often fit target functions from low to high frequencies. Inspired by the F-Principle, we propose an effective model of linear F-Principle (LFP) dynamics which accurately predicts the learning results of two-layer ReLU neural networks (NNs) of large widths. This LFP dynamics is rationalized by a linearized mean fi…
Nanyang Technological University（南洋理工大学）；Agency for Science, Technology and Research（新加坡科技研究局）
Model robustness is vital for the reliable deployment of machine learning models in real-world applications. Recent studies have shown that data augmentation can result in model over-relying on features in the low-frequency domain, sacrificing performance against low-frequency corruptions, highlighting a connection between frequency and robustness. Here, we take one step further to more directly study the frequency bias of a model through the lens of its Jacobians and its implication to model robustness. To achieve this, we propose Jacobian frequency regularization for models' Jacobians to hav…
University of California, Berkeley（加州大学伯克利分校）；Google Brain（谷歌大脑）
Despite their ability to represent highly expressive functions, deep learning models seem to find simple solutions that generalize surprisingly well. Spectral bias -- the tendency of neural networks to prioritize learning low frequency functions -- is one possible explanation for this phenomenon, but so far spectral bias has primarily been observed in theoretical models and simplified experiments. In this work, we propose methodologies for measuring spectral bias in modern image classification networks on CIFAR-10 and ImageNet. We find that these networks indeed exhibit spectral bias, and that…
Walmart Global Tech（沃尔玛全球科技）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Indeed
Recent studies on Next-basket Recommendation (NBR) have achieved much progress by leveraging Personalized Item Frequency (PIF) as one of the main features, which measures the frequency of the user's interactions with the item. However, taking the PIF as an explicit feature incurs bias towards frequent items. Items that a user purchases frequently are assigned higher weights in the PIF-based recommender system and appear more frequently in the personalized recommendation list. As a result, the system will lose the fairness and balance between items that the user frequently purchases and items t…
Neural network applications generally benefit from larger-sized models, but for current speech enhancement models, larger scale networks often suffer from decreased robustness to the variety of real-world use cases beyond what is encountered in training data. We introduce several innovations that lead to better large neural networks for speech enhancement. The novel PoCoNet architecture is a convolutional neural network that, with the use of frequency-positional embeddings, is able to more efficiently build frequency-dependent features in the early layers. A semi-supervised method helps increa…
Dropout as regularization has been used extensively to prevent overfitting for training neural networks. During training, units and their connections are randomly dropped, which could be considered as sampling many different submodels from the original model. At test time, weight scaling and Monte Carlo approximation are two widely applied approaches to approximate the outputs. Both approaches work well practically when all submodels are low-bias complex learners. However, in this work, we demonstrate scenarios where some submodels behave closer to high-bias models and a non-uniform weight sca…
We use a dataset of U.S. first names with labels based on predominant gender and racial group to examine the effect of training corpus frequency on tokenization, contextualization, similarity to initial representation, and bias in BERT, GPT-2, T5, and XLNet. We show that predominantly female and non-white names are less frequent in the training corpora of these four language models. We find that infrequent names are more self-similar across contexts, with Spearman's r between frequency and self-similarity as low as -.763. Infrequent names are also less similar to initial representation, with S…
ReFLEX: Length-Generalizable CSI Denoising for MIMO-OFDM via Relative-Frequency Bias
Moscow Institute of Physics and Technology (State University)（莫斯科物理技术学院（国家大学））；Yangtze Delta Region Academy（长江三角洲地区研究院）；Beijing Institute of Technology（北京理工大学）；School of Interdisciplinary Science（交叉科学学院）
Towards Combating Frequency Simplicity-biased Learning for Domain Generalization
Computer Vision Institute（计算机视觉研究所）；School of Computer Science & Software Engineering（计算机科学与软件工程学院）；Shenzhen University（深圳大学）；Shenzhen Institute of Artificial Intelligence Robotics for Society（深圳人工智能与机器人社会研究院）；Guangdong Provincial Key Laboratory of Intelligent Information Processing（广东省智能信息处理重点实验室）；University of Exeter（埃克塞特大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Washington University in St. Louis（圣路易斯华盛顿大学）；NVIDIA（英伟达）
Data-driven models, such as FourCastNet (FCN), have shown exemplary performance in high-resolution global weather forecasting. This performance, however, is based on supervision on mesh-gridded weather data without the utilization of raw climate observational data, the gold standard ground truth. In this work we develop a methodology to correct, remap, and fine-tune gridded uniform forecasts of FCN so it can be directly compared against observational ground truth, which is sparse and non-uniform in space and time. This is akin to bias correction and post-processing of numerical weather predict…
Deep Reinforcement Learning (RL) methods rely on experience replay to approximate the minibatched supervised learning setting; however, unlike supervised learning where access to lots of training data is crucial to generalization, replay-based deep RL appears to struggle in the presence of extraneous data. Recent works have shown that the performance of Deep Q-Network (DQN) degrades when its replay memory becomes too large. This suggests that outdated experiences somehow impact the performance of deep RL, which should not be the case for off-policy methods like DQN. Consequently, we re-examine…
Stanford University（斯坦福大学）；University of Pennsylvania（宾夕法尼亚大学）
The word embedding association test (WEAT) is an important method for measuring linguistic biases against social groups such as ethnic minorities in large text corpora. It does so by comparing the semantic relatedness of words prototypical of the groups (e.g., names unique to those groups) and attribute words (e.g., 'pleasant' and 'unpleasant' words). We show that anti-black WEAT estimates from geo-tagged social media data at the level of metropolitan statistical areas strongly correlate with several measures of racial animus--even when controlling for sociodemographic covariates. However, we …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；EPFL（洛桑联邦理工学院）；Univ. Grenoble-Alpes（格勒诺布尔-阿尔卑斯大学）；Inria（法国国家信息与自动化研究所）
Polynomial neural networks (PNNs) have been recently shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural networks demonstrate a $\textit{spectral bias}$ towards low-frequency functions, which yields faster learning of low-frequency components during training. Inspired by such studies, we conduct a spectral analysis of the Neural Tangent Kernel (NTK) of PNNs. We find that the $Π$-Net family, i.e., a recently proposed parametrization of PNNs, speeds up the learning of the higher freq…
