Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges.
Provable Separations between Memorization and Generalization in Diffusion Models
Department of Industrial Engineering and Management Sciences, Northwestern University（工业工程与管理科学系，西北大学）；Department of Statistics and Data Science, Northwestern University（统计与数据科学系，西北大学）；School of Mathematics, Georgia Institute of Technology（数学系，佐治亚理工学院）
On the Memorization of Consistency Distillation for Diffusion Models
School of Computing & Data Science, The University of Hong Kong（计算与数据科学学院，香港大学）；School of Computing & Data Science and Institute of Data Science, The University of Hong Kong（计算与数据科学学院和数据科学研究所，香港大学）
Two Calm Ends and the Wild Middle: A Geometric Picture of Memorization in Diffusion Models
Department of Mathematics, University of Missouri（数学系，密苏里大学）；Halıcıoğlu Data Science Institute, University of California San Diego（哈利奇奥数据科学研究所，加州大学圣地亚哥分校）
Losing dimensions: Geometric memorization in generative diffusion
Computing Sciences Department, Bocconi University（博科尼大学计算科学系）；Bocconi Institute for Data Science and Analytics (BIDSA)（博科尼数据科学与分析研究所）；Donders Institute, Radboud University（拉德堡德大学多纳尔斯研究所）；OnePlanet Research Center, Wageningen（瓦赫宁根大学OnePlanet研究中心）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Jheronimus Academy of Data Science (JADS)（杰霍尼穆斯数据科学学院）；IBM Research, Cambridge（IBM研究院，剑桥）
Memorization to Generalization: Emergence of Diffusion Models from Associative Memory
Department of Computer Science, Rensselaer Polytechnic Institute ( RPI )（计算机科学系，罗切斯特理工学院（RPI））；Jheronimus Academy of Data Science, Tilburg University（数据科学学院，蒂尔堡大学）；Department of Physics, University of Rome Sapienza（物理系，罗马萨皮恩扎大学）；Donders Institute for Brain, Cognition, and Behaviour, Radboud University（大脑、认知与行为研究所，拉德堡德大学）；IBM Research（IBM研究院）
Memorization Control in Diffusion Models from Denoising-centric Perspective
Department of Computer Science（计算机科学系）；Brunel University of London（布鲁内尔大学）；Hanoi University of Science and Technology（河内科学技术大学）；Faculty of Electrical and Electronic Engineering School of Engineering（电气电子工程系工程学院）；Phenikaa University（Phenikaa大学）；Greenwich Vietnam FPT University（格林威治越南FPT大学）；College of Engineering（工程学院）；Shibaura Institute of Technology（Shibaura技术学院）
Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Study
Université Claude Bernard Lyon 1（克莱尔-伯纳德里昂1大学）；Laboratoire SAF, ISFA, France（SAF实验室，ISFA，法国）；Department of Mathematics University of Vienna, Austria（数学系，维也纳大学，奥地利）；The Ohio State University, USA（俄亥俄州立大学，美国）
Understanding how large neural networks avoid memorizing training data is key to explaining their high generalization performance. To examine the structure of when and where memorization occurs in a deep network, we use a recently developed replica-based mean field theoretic geometric analysis method. We find that all layers preferentially learn from examples which share features, and link this behavior to generalization performance. Memorization predominately occurs in the deeper layers, due to decreasing object manifolds' radius and dimension, whereas early layers are minimally affected. Thi…
Google Research（谷歌研究院）；University of California, Berkeley（加州大学伯克利分校）；Princeton University（普林斯顿大学）
We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN), both linear and nonlinear, initialized randomly and then trained to minimize the reconstruction error. The trained networks stereotypically take one of two forms: the constant function (memorization) and the identity function (generalization). We formally characterize generalization in single-layer FCNs and CNNs. We show empirically that different architect…
Montréal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）；Jagiellonian University（雅盖隆大学）；McGill University（麦吉尔大学）；University of California, Berkeley（加州大学伯克利分校）；Polytechnique Montréal（蒙特利尔理工学院）；University of Bonn（波恩大学）
We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize learning simple patterns first. In our experiments, we expose qualitative differences in gradient-based optimization of deep neural networks (DNNs) on noise vs. real data. We also demonstrate that for appropriately tuned explicit regularization (e.g., dropout) we can degrade DNN training performance on noise datasets without compromising generalization on real…
Huazhong University of Science and Technology（华中科技大学）；Baidu Research（百度研究院）
Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed that DNNs first learn simple patterns and then memorize noise; some other works showed a phenomenon that DNNs have a spectral bias to learn target functions from low to high frequencies during training. However, we show that the monotonicity of the learning bias does not always hold: under the experimental setup of deep double descent, the high-frequency com…
Undetected overfitting can occur when there are significant redundancies between training and validation data. We describe AVE, a new measure of training-validation redundancy for ligand-based classification problems that accounts for the similarity amongst inactive molecules as well as active. We investigated seven widely-used benchmarks for virtual screening and classification, and show that the amount of AVE bias strongly correlates with the performance of ligand-based predictive methods irrespective of the predicted property, chemical fingerprint, similarity measure, or previously-applied …
Deep learning models have a propensity for fitting the entire training set even with random labels, which requires memorization of every training sample. In this paper, we explore the memorization effect in adversarial training (AT) for promoting a deeper understanding of model capacity, convergence, generalization, and especially robust overfitting of the adversarially trained models. We first demonstrate that deep networks have sufficient capacity to memorize adversarial examples of training data with completely random labels, but not all AT algorithms can converge under the extreme circumst…
Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise
Taylor Lab, Huawei Technologies Co., Ltd.（华为技术有限公司泰勒实验室）；Key Laboratory of Interdisciplinary Research of Computation and Economics, Shanghai University of Finance and Economics（上海财经大学计算与经济交叉研究重点实验室）
Google Research（谷歌研究院）；Boston University（波士顿大学）；Blueshift, Alphabet（Alphabet 旗下 Blueshift）
We construct an experimental setup in which changing the scale of initialization strongly impacts the implicit regularization induced by SGD, interpolating from good generalization performance to completely memorizing the training set while making little progress on the test set. Moreover, we find that the extent and manner in which generalization ability is affected depends on the activation and loss function used, with $\sin$ activation demonstrating extreme memorization. In the case of the homogeneous ReLU activation, we show that this behavior can be attributed to the loss function. Our em…
Coherent Gradients (CGH) is a recently proposed hypothesis to explain why over-parameterized neural networks trained with gradient descent generalize well even though they have sufficient capacity to memorize the training set. The key insight of CGH is that, since the overall gradient for a single step of SGD is the sum of the per-example gradients, it is strongest in directions that reduce the loss on multiple examples if such directions exist. In this paper, we validate CGH on ResNet, Inception, and VGG models on ImageNet. Since the techniques presented in the original paper do not scale bey…
Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they achieve good prediction error on unseen data: interpolating the training set does not lead to a large generalization error. Further, overparametrization appears to be beneficial in that it simplifies the optimization landscape. Here we study these phenomena in the context of two-layers neural networks in the neural tangent (NT) regime. We consider a simple data m…
Wasserstein proximal operators describe score-based generative models and resolve memorization
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of South Carolina, Columbia（南卡罗来纳大学哥伦比亚分校）
