We first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained as a noise averaging effect over the labels of similar input examples. This effect theoretically grows with the number of similar examples; the question is then to define and estimate the similarity of examples.
We express a proper definition of similarity, from the neural network perspective, i.e. we quantify how undissociable two inputs $A$ and $B$ are, taking a machine learning viewpoint: how much a parameter variation designed to change the output for $A$ would impact the output for $B$ as well?
We study the mathematical properties of this similarity measure, and show how to use it on a trained network to estimate sample density, in low complexity, enabling new types of statistical analysis for neural networks. We analyze data by retrieving samples perceived as similar by the network, and are able to quantify the denoising effect without requiring true labels. We also propose, during training, to enforce that examples known to be similar should also be seen as similar by the network, and notice speed-up training effects for certain datasets.
Northwestern Polytechnical University（西北工业大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Shanghai United Imaging Intelligence Co., Ltd（上海联影智能有限公司）；Shanghai Jiao Tong University（上海交通大学）
Non-rigid inter-modality registration can facilitate accurate information fusion from different modalities, but it is challenging due to the very different image appearances across modalities. In this paper, we propose to train a non-rigid inter-modality image registration network, which can directly predict the transformation field from the input multimodal images, such as CT and MR images. In particular, the training of our inter-modality registration network is supervised by intra-modality similarity metric based on the available paired data, which is derived from a pre-aligned CT and MR da…
Noiseless Imaging Oy（无噪声成像有限公司）；Tampere University of Technology（坦佩雷理工大学）；United Technology Research Centre Ireland（联合技术研究中心爱尔兰分部）
Single image super resolution (SISR) is an ill-posed problem aiming at estimating a plausible high resolution (HR) image from a single low resolution (LR) image. Current state-of-the-art SISR methods are patch-based. They use either external data or internal self-similarity to learn a prior for a HR image. External data based methods utilize large number of patches from the training data, while self-similarity based approaches leverage one or more similar patches from the input image. In this paper we propose a self-similarity based approach that is able to use large groups of similar patches …
Indian Institute of Technology, Kharagpur（印度理工学院克勒格布尔分校）
A pivotal step in image super-resolution techniques is interpolation, which aims at generating high resolution images without introducing artifacts such as blurring and ringing. In this paper, we propose a technique that performs interpolation through an infusion of high frequency signal components computed by exploiting `process similarity'. By `process similarity', we refer to the resemblance between a decomposition of the image at a resolution to the decomposition of the image at another resolution. In our approach, the decompositions generating image details and approximations are obtained…
When Does Closeness in Distribution Imply Representational Similarity? An Identifiability Perspective
Technical University of Denmark（丹麦技术大学）；University of Trento, Italy（意大利特伦托大学）；Helmholtz AI, Munich（慕尼黑海德堡人工智能研究所）；Technical University of Munich（慕尼黑技术大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Copenhagen（哥本哈根大学）
National Institute of Technology, Silchar（锡尔查尔国家技术学院）
Online Social Networks have embarked on the importance of connection strength measures which has a broad array of applications such as, analyzing diffusion behaviors, community detection, link predictions, recommender systems. Though there are some existing connection strength measures, the density that a connection shares with it's neighbors and the directionality aspect has not received much attention. In this paper, we have proposed an asymmetric edge similarity measure namely, Neighborhood Density-based Edge Similarity (NDES) which provides a fundamental support to derive the strength of c…
Microsoft Research（微软研究院）；Johns Hopkins University（约翰斯·霍普金斯大学）；Square
Herein we define a measure of similarity between classification distributions that is both principled from the perspective of statistical pattern recognition and useful from the perspective of machine learning practitioners. In particular, we propose a novel similarity on classification distributions, dubbed task similarity, that quantifies how an optimally-transformed optimal representation for a source distribution performs when applied to inference related to a target distribution. The definition of task similarity allows for natural definitions of adversarial and orthogonal distributions. …
Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives
Digital Data and Information for Society, Science, and Culture, Zuse Institute Berlin（数字数据与信息用于社会、科学和文化，柏林Zuse研究所）；Institute of Mathematics, Vietnam Academy of Science and Technology（越南科学与技术科学院数学研究所）；Technische Universität Berlin（柏林技术大学）；Applied Algorithmic Intelligence Methods, Zuse Institute Berlin（应用算法智能方法，柏林Zuse研究所）
Out-of-Distribution (OoD) inputs are examples that do not belong to the true underlying distribution of the dataset. Research has shown that deep neural nets make confident mispredictions on OoD inputs. Therefore, it is critical to identify OoD inputs for safe and reliable deployment of deep neural nets. Often a threshold is applied on a similarity score to detect OoD inputs. One such similarity is angular similarity which is the dot product of latent representation with the mean class representation. Angular similarity encodes uncertainty, for example, if the angular similarity is less, it is…
Similarity/Distance measures play a key role in many machine learning, pattern recognition, and data mining algorithms, which leads to the emergence of metric learning field. Many metric learning algorithms learn a global distance function from data that satisfy the constraints of the problem. However, in many real-world datasets that the discrimination power of features varies in the different regions of input space, a global metric is often unable to capture the complexity of the task. To address this challenge, local metric learning methods are proposed that learn multiple metrics across th…
Intel Labs, Intel Corporation（英特尔公司英特尔实验室）；Department of Computer Science, University of Illinois at Chicago（伊利诺伊大学芝加哥分校计算机科学系）
In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search. Recently, there has been an increasing interest in deep graph similarity learning, where the key idea is to learn a deep learning model that maps input graphs to a target space such that the distance in the target space approximates the structural distance in the input space. Here, we provide a comprehensive review of the existing literature of deep graph simil…
The performance of many machine learning techniques depends on the choice of an appropriate similarity or distance measure on the input space. Similarity learning (or metric learning) aims at building such a measure from training data so that observations with the same (resp. different) label are as close (resp. far) as possible. In this paper, similarity learning is investigated from the perspective of pairwise bipartite ranking, where the goal is to rank the elements of a database by decreasing order of the probability that they share the same label with some query data point, based on the s…
Autodesk AI Lab（欧特克人工智能实验室）；Stanford University（斯坦福大学）；Mila（米拉人工智能研究所）；Université de Montréal（蒙特利尔大学）
A fundamental challenge in artificial intelligence is learning useful representations of data that yield good performance on a downstream task, without overfitting to spurious input features. Extracting such task-relevant predictive information is particularly difficult for real-world datasets. In this work, we propose Contrastive Input Morphing (CIM), a representation learning framework that learns input-space transformations of the data to mitigate the effect of irrelevant input features on downstream performance. Our method leverages a perceptual similarity metric via a triplet loss to ensu…
Decoupling Semantic Similarity from Spatial Alignment for Neural Networks
German Cancer Research Center (DKFZ)（德国癌症研究中心）；Helmholtz Imaging（亥姆霍兹成像）；University of Heidelberg（海德堡大学）；National Center for Tumor Diseases (NCT) Heidelberg（海德堡国家肿瘤疾病中心）
The University of Sydney（悉尼大学）；Hong Kong Baptist University（香港浸会大学）；The University of Melbourne（墨尔本大学）；Xidian University（西安电子科技大学）；Brain-Inspired Technology Co., Ltd.（脑启发技术有限公司）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Learning with noisy labels has attracted a lot of attention in recent years, where the mainstream approaches are in pointwise manners. Meanwhile, pairwise manners have shown great potential in supervised metric learning and unsupervised contrastive learning. Thus, a natural question is raised: does learning in a pairwise manner mitigate label noise? To give an affirmative answer, in this paper, we propose a framework called Class2Simi: it transforms data points with noisy class labels to data pairs with noisy similarity labels, where a similarity label denotes whether a pair shares the class l…
To address the limitations of existing magnitude-based pruning algorithms in cases where model weights or activations are of large and similar magnitude, we propose a novel perspective to discover parameter redundancy among channels and accelerate deep CNNs via channel pruning. Precisely, we argue that channels revealing similar feature information have functional overlap and that most channels within each such similarity group can be removed without compromising model's representational power. After deriving an effective metric for evaluating channel similarity through probabilistic modeling,…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
One popular generative model that has high-quality results is the Generative Adversarial Networks(GAN). This type of architecture consists of two separate networks that play against each other. The generator creates an output from the input noise that is given to it. The discriminator has the task of determining if the input to it is real or fake. This takes place constantly eventually leads to the generator modeling the target distribution. This paper includes a study into the actual weights learned by the network and a study into the similarity of the discriminator and generator networks. Th…
In this paper, we propose a novel approach for implicit data representation to evaluate similarity of input data using a trained neural network. In contrast to the previous approach, which uses gradients for representation, we utilize only the outputs from the last hidden layer of a neural network and do not use a backward step. The proposed technique explicitly takes into account the initial task and significantly reduces the size of the vector representation, as well as the computation time. The key point is minimization of information loss between layers. Generally, a neural network discard…
The Pennsylvania State University（宾夕法尼亚州立大学）；Tsinghua University（清华大学）；Google Brain（谷歌大脑）；Facebook（脸书）
In many applications of computer graphics, art and design, it is desirable for a user to provide intuitive non-image input, such as text, sketch, stroke, graph or layout, and have a computer system automatically generate photo-realistic images that adhere to the input content. While classic works that allow such automatic image content generation have followed a framework of image retrieval and composition, recent advances in deep generative models such as generative adversarial networks (GANs), variational autoencoders (VAEs), and flow-based methods have enabled more powerful and versatile im…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic approaches. Since the most of clustering methods depend on their input parameters, it is important to evaluate the result of a clustering algorithm with its different input parameters, to choose the most appropriate one. There are several clustering validity techniques based on inner density and outer density of clusters that represent different metrics to choose t…
Berlin Institute of Technology（柏林工业大学）；Max Planck Institute for the History of Science（马克斯·普朗克科学史研究所）；Korea University（高丽大学）；Max Planck Institut für Informatik（马克斯·普朗克信息学研究所）
Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation in terms of input features. We develop BiLRP, a scalable and theoretically founded method to systematically decompose similarity scores on pairs of input features. Our method can be exp…
Pattern similarity-based methods are widely used in classification and regression problems. Repeated, similar-shaped cycles observed in seasonal time series encourage to apply these methods for forecasting. In this paper we use the pattern similarity-based methods for forecasting monthly electricity demand expressing annual seasonality. An integral part of the models is the time series representation using patterns of time series sequences. Pattern representation ensures the input and output data unification through trend filtering and variance equalization. Consequently, pattern representatio…
Deep neural networks are susceptible to small-but-specific adversarial perturbations capable of deceiving the network. This vulnerability can lead to potentially harmful consequences in security-critical applications. To address this vulnerability, we propose a novel metric called \emph{Gradient Similarity} that allows us to capture the influence of training data on test inputs. We show that \emph{Gradient Similarity} behaves differently for normal and adversarial inputs, and enables us to detect a variety of adversarial attacks with a near perfect ROC-AUC of 95-100\%. Even white-box adversari…
Modeling place functions from a computational perspective is a prevalent research topic. Trajectory embedding, as a neural-network-backed dimension reduction technology, allows the possibility to put places with similar social functions at close locations in the embedding space if the places share similar chronological context as part of a trajectory. The embedding similarity was previously proposed as a new metric for measuring the similarity of place functions. This study explores if this approach is meaningful for geographical units at a much smaller geographical granularity compared to pre…
KTH Royal Institute of Technology（瑞典皇家理工学院）；RaySearch Laboratories（瑞镭实验室）；Silo AI（Silo AI（西洛人工智能公司））
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is…
IBM Research（IBM研究院）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Post-hoc explanations for black box models have been studied extensively in classification and regression settings. However, explanations for models that output similarity between two inputs have received comparatively lesser attention. In this paper, we provide model agnostic local explanations for similarity learners applicable to tabular and text data. We first propose a method that provides feature attributions to explain the similarity between a pair of inputs as determined by a black box similarity learner. We then propose analogies as a new form of explanation in machine learning. Here …
Criteo AI Lab（Criteo人工智能实验室）；Amazon（亚马逊）；Meta AI Research（Meta人工智能研究院）
In this paper, we investigate the impact of neural networks (NNs) topology on adversarial robustness. Specifically, we study the graph produced when an input traverses all the layers of a NN, and show that such graphs are different for clean and adversarial inputs. We find that graphs from clean inputs are more centralized around highway edges, whereas those from adversaries are more diffuse, leveraging under-optimized edges. Through experiments on a variety of datasets and architectures, we show that these under-optimized edges are a source of adversarial vulnerability and that they can be us…
Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider NTK regime wide neural networks as a possible model of biological neural networks. Leveraging NTK theory, we show theoretically that gradient descent drives layerwise weight updates that are aligned with their input activity correlations weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment res…
Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to …
Lakehead University（湖首大学）；University of Calgary（卡尔加里大学）
Objective: This paper presents an Alzheimer's disease (AD) detection method based on learning structural similarity between Magnetic Resonance Images (MRIs) and representing this similarity as a graph. Methods: We construct the similarity graph using embedded features of the input image (i.e., Non-Demented (ND), Very Mild Demented (VMD), Mild Demented (MD), and Moderated Demented (MDTD)). We experiment and compare different dimension-reduction and clustering algorithms to construct the best similarity graph to capture the similarity between the same class images using the cosine distance as a …
Aalto University（阿尔托大学）；University of Manchester（曼彻斯特大学）
Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population structure of data items in the input space, leading to spuriously high similarity for even completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which retains the intuitive invariance properties of the orig…
There is increasing realization in neuroscience that information is represented in the brain, e.g., neocortex, hippocampus, in the form sparse distributed codes (SDCs), a kind of cell assembly. Two essential questions are: a) how are such codes formed on the basis of single trials, and how is similarity preserved during learning, i.e., how do more similar inputs get mapped to more similar SDCs. I describe a novel Modular Sparse Distributed Code (MSDC) that provides simple, neurally plausible answers to both questions. An MSDC coding field (CF) consists of Q WTA competitive modules (CMs), each …
Recent works have derived neural networks with online correlation-based learning rules to perform \textit{kernel similarity matching}. These works applied existing linear similarity matching algorithms to nonlinear features generated with random Fourier methods. In this paper attempt to perform kernel similarity matching by directly learning the nonlinear features. Our algorithm proceeds by deriving and then minimizing an upper bound for the sum of squared errors between output and input kernel similarities. The construction of our upper bound leads to online correlation-based learning rules w…
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Center for Data Science, New York University（纽约大学数据科学中心）
Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in many practical applications, including point clouds and particle physics, a relevant notion of generalization should include varying the input size. In this work we treat symmetric functions (of any size) as functions over probability measures, and study the learning and representation of neural networks defined on measures. By focusing on shallow architectu…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Beijing Academy of Frontier Science and Technology（北京前沿科学技术研究院）
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change of input distribution, thus results in poor generalization, and aggravates the internal covariate shift which slows down the training. To bound dot product and decrease the variance, we propose to use cosine similarity or centered cosine similarity (Pearson Correlation Coefficient…
We present a novel method for reliably explaining the predictions of neural networks. We consider an explanation reliable if it identifies input features relevant to the model output by considering the input and the neighboring data points. Our method is built on top of the assumption of smooth landscape in a loss function of the model prediction: locally consistent loss and gradient profile. A theoretical analysis established in this study suggests that those locally smooth model explanations are learned using a batch of noisy copies of the input with the L1 regularization for a saliency map.…
Similarity of Neural Network Models: A Survey of Functional and Representational Measures
University of Passau（帕绍大学）；University of Mannheim（曼海姆大学）；RWTH Aachen University（亚琛工业大学）；GESIS - Leibniz Institute for the Social Sciences（GESIS莱布尼茨社会科学研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）
We employ a toolset -- dubbed Dr. Frankenstein -- to analyse the similarity of representations in deep neural networks. With this toolset, we aim to match the activations on given layers of two trained neural networks by joining them with a stitching layer. We demonstrate that the inner representations emerging in deep convolutional neural networks with the same architecture but different initializations can be matched with a surprisingly high degree of accuracy even with a single, affine stitching layer. We choose the stitching layer from several possible classes of linear transformations and…
Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿罗森多夫研究中心）；University Hospital Carl Gustav Carus（卡尔·古斯塔夫·卡鲁斯大学医院）
Multimodal medical image fusion helps in combining contrasting features from two or more input imaging modalities to represent fused information in a single image. One of the pivotal clinical applications of medical image fusion is the merging of anatomical and functional modalities for fast diagnosis of malignant tissues. In this paper, we present a novel end-to-end unsupervised learning-based Convolutional Neural Network (CNN) for fusing the high and low frequency components of MRI-PET grayscale image pairs, publicly available at ADNI, by exploiting Structural Similarity Index (SSIM) as the …
CSIRO Data61（联邦科学与工业研究组织 Data61）；The Australian National University（澳大利亚国立大学）；Data to Decisions CRC（数据决策合作研究中心）
We present a neural sequence model designed specifically for symbolic music. The model is based on a learned edit distance mechanism which generalises a classic recursion from computer sci- ence, leading to a neural dynamic program. Re- peated motifs are detected by learning the transfor- mations between them. We represent the arising computational dependencies using a novel data structure, the edit tree; this perspective suggests natural approximations which afford the scaling up of our otherwise cubic time algorithm. We demonstrate our model on real and synthetic data; in all cases it out-pe…
Technical University of Catalonia（加泰罗尼亚理工大学）；University of the Basque Country（巴斯克大学）
This paper develops a two-layer neural network in which the neuron model computes a user-defined similarity function between inputs and weights. The neuron transfer function is formed by composition of an adapted logistic function with the mean of the partial input-weight similarities. The resulting neuron model is capable of dealing directly with variables of potentially different nature (continuous, fuzzy, ordinal, categorical). There is also provision for missing values. The network is trained using a two-stage procedure very similar to that used to train a radial basis function (RBF) neura…
The George Washington University（乔治华盛顿大学）；The Hong Kong Polytechnic University（香港理工大学）；Harvard University（哈佛大学）
Patient similarity analysis is important in health care applications. It takes patient information such as their electronic medical records and genetic data as input and computes the pairwise similarity between patients. Procedures of typical a patient similarity study can be divided into several steps including data integration, similarity measurement, and neighborhood identification. And according to an analysis of patient similarity, doctors can easily find the most suitable treatments. There are many methods to analyze the similarity such as cluster analysis. And during machine learning be…
In this paper, we show that structures similar to self-attention are natural to learn many sequence-to-sequence problems from the perspective of symmetry. Inspired by language processing applications, we study the orthogonal equivariance of seq2seq functions with knowledge, which are functions taking two inputs -- an input sequence and a ``knowledge'' -- and outputting another sequence. The knowledge consists of a set of vectors in the same embedding space as the input sequence, containing the information of the language used to process the input sequence. We show that orthogonal equivariance …
Rethinking Client Drift in Federated Learning: A Logit Perspective
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Institute of High Performance Computing, A*STAR（新加坡科技研究局高性能计算研究院）；Hubei Luojia Laboratory（湖北珞珈实验室）；Wuhan University（武汉大学）；Harbin Institute of Technology（哈尔滨工业大学）；The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong Polytechnic University（香港理工大学）；South China University of Technology（华南理工大学）；Pazhou Lab（琶洲实验室）
Explaining Graph Neural Networks for Node Similarity on Graphs
Vrije Universiteit Amsterdam（瓦赫宁根大学阿姆斯特丹）；Bosch Center for Artificial Intelligence（博世人工智能中心）；Abo Akademi University（阿博阿卡迪米大学）；Elsevier discovery lab（埃斯勒弗发现实验室）；University of Amsterdam（阿姆斯特丹大学）
