Attacks in Adversarial Machine Learning: A Systematic Survey from the Life-cycle Perspective
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Beijing University of Posts and Telecommunications（北京邮电大学）；University at Buffalo, State University of New York（纽约州立大学布法罗分校）
Adversarial machine learning (AML) studies the adversarial phenomenon of machine learning, which may make inconsistent or unexpected predictions with humans. Some paradigms have been recently developed to explore this adversarial phenomenon occurring at different stages of a machine learning system, such as backdoor attack occurring at the pre-training, in-training and inference stage; weight attack occurring at the post-training, deployment and inference stage; adversarial attack occurring at the inference stage. However, although these adversarial paradigms share a common goal, their developments are almost independent, and there is still no big picture of AML. In this work, we aim to provide a unified perspective to the AML community to systematically review the overall progress of this field. We firstly provide a general definition about AML, and then propose a unified mathematical framework to covering existing attack paradigms. According to the proposed unified framework, we build a full taxonomy to systematically categorize and review existing representative methods for each paradigm. Besides, using this unified framework, it is easy to figure out the connections and differences among different attack paradigms, which may inspire future researchers to develop more advanced attack paradigms. Finally, to facilitate the viewing of the built taxonomy and the related literature in adversarial machine learning, we further provide a website, \ie, \url{http://adversarial-ml.com}, where the taxonomies and literature will be continuously updated.
Adversarial attack is aimed at fooling the target classifier with imperceptible perturbation. Adversarial examples, which are carefully crafted with a malicious purpose, can lead to erroneous predictions, resulting in catastrophic accidents. To mitigate the effects of adversarial attacks, we propose a novel purification model called CAP-GAN. CAP-GAN takes account of the idea of pixel-level and feature-level consistency to achieve reasonable purification under cycle-consistent learning. Specifically, we utilize the guided attention module and knowledge distillation to convey meaningful informat…
Nanyang Technological University（南洋理工大学）；Salesforce Research Asia（赛富时亚洲研究院）
Adversarial training has shown impressive success in learning bilingual dictionary without any parallel data by mapping monolingual embeddings to a shared space. However, recent work has shown superior performance for non-adversarial methods in more challenging language pairs. In this work, we revisit adversarial autoencoder for unsupervised word translation and propose two novel extensions to it that yield more stable training and improved results. Our method includes regularization terms to enforce cycle consistency and input reconstruction, and puts the target encoders as an adversary again…
National Yang Ming Chiao Tung University（国立阳明交通大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Deep neural networks have developed rapidly and have achieved outstanding performance in several tasks, such as image classification and natural language processing. However, recent studies have indicated that both digital and physical adversarial examples can fool neural networks. Face-recognition systems are used in various applications that involve security threats from physical adversarial examples. Herein, we propose a physical adversarial attack with the use of full-face makeup. The presence of makeup on the human face is a reasonable possibility, which possibly increases the imperceptib…
CycleGAN (Zhu et al. 2017) is one recent successful approach to learn a transformation between two image distributions. In a series of experiments, we demonstrate an intriguing property of the model: CycleGAN learns to "hide" information about a source image into the images it generates in a nearly imperceptible, high-frequency signal. This trick ensures that the generator can recover the original sample and thus satisfy the cyclic consistency requirement, while the generated image remains realistic. We connect this phenomenon with adversarial attacks by viewing CycleGAN's training procedure a…
Cycle Life Prediction for Lithium-ion Batteries: Machine Learning and More
Technische Universität Darmstadt（达姆施塔特工业大学）；University of Pavia（帕维亚大学）；Massachusetts Institute of Technology（麻省理工学院）；Technische Universität München（慕尼黑工业大学）
University of California, San Diego（加利福尼亚大学圣地亚哥分校）；Google Brain（谷歌大脑）
There has been an ongoing cycle where stronger defenses against adversarial attacks are subsequently broken by a more advanced defense-aware attack. We present a new approach towards ending this cycle where we "deflect'' adversarial attacks by causing the attacker to produce an input that semantically resembles the attack's target class. To this end, we first propose a stronger defense based on Capsule Networks that combines three detection mechanisms to achieve state-of-the-art detection performance on both standard and defense-aware attacks. We then show that undetected attacks against our d…
Adversarial transferability, namely the ability of adversarial perturbations to simultaneously fool multiple learning models, has long been the "big bad wolf" of adversarial machine learning. Successful transferability-based attacks requiring no prior knowledge of the attacked model's parameters or training data have been demonstrated numerous times in the past, implying that machine learning models pose an inherent security threat to real-life systems. However, all of the research performed in this area regarded transferability as a probabilistic property and attempted to estimate the percent…
University of California Irvine（加利福尼亚大学尔湾分校）；Department of Electrical Engineering and Computer Science, University of California Irvine（加利福尼亚大学尔湾分校电气工程与计算机科学系）；Department of Computer Science, University of California, Irvine（加利福尼亚大学尔湾分校计算机科学系）；Institute for Future Health, University of California, Irvine（加利福尼亚大学尔湾分校未来健康研究所）
Continuous monitoring of blood pressure (BP)can help individuals manage their chronic diseases such as hypertension, requiring non-invasive measurement methods in free-living conditions. Recent approaches fuse Photoplethysmograph (PPG) and electrocardiographic (ECG) signals using different machine and deep learning approaches to non-invasively estimate BP; however, they fail to reconstruct the complete signal, leading to less accurate models. In this paper, we propose a cycle generative adversarial network (CycleGAN) based approach to extract a BP signal known as ambulatory blood pressure (ABP…
Intelligence and Space Research Division（情报与空间研究部）；Descartes Labs, Inc.（笛卡尔实验室公司）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
This paper introduces a new method of generating realistic pervasive changes in the context of evaluating the effectiveness of change detection algorithms in controlled settings. The method, a cycle-consistent adversarial network (CycleGAN), requires low quantities of training data to generate realistic changes. Here we show an application of CycleGAN in creating realistic snow-covered scenes of multispectral Sentinel-2 imagery, and demonstrate how these images can be used as a test bed for anomalous change detection algorithms.
Efficient and accurate remaining useful life prediction is a key factor for reliable and safe usage of lithium-ion batteries. This work trains a long short-term memory recurrent neural network model to learn from sequential data of discharge capacities at various cycles and voltages and to work as a cycle life predictor for battery cells cycled under different conditions. Using experimental data of first 60 - 80 cycles, our model achieves promising prediction accuracy on test sets of around 80 samples.
Voice conversion (VC) refers to transforming the speaker characteristics of an utterance without altering its linguistic contents. Many works on voice conversion require to have parallel training data that is highly expensive to acquire. Recently, the cycle-consistent adversarial network (CycleGAN), which does not require parallel training data, has been applied to voice conversion, showing the state-of-the-art performance. The CycleGAN based voice conversion, however, can be used only for a pair of speakers, i.e., one-to-one voice conversion between two speakers. In this paper, we extend the …
University of Trento（特伦托大学）；University of Oxford（牛津大学）；Texas State University（得克萨斯州立大学）；EPFL（洛桑联邦理工学院）
In this work, we propose a novel Cycle In Cycle Generative Adversarial Network (C$^2$GAN) for the task of keypoint-guided image generation. The proposed C$^2$GAN is a cross-modal framework exploring a joint exploitation of the keypoint and the image data in an interactive manner. C$^2$GAN contains two different types of generators, i.e., keypoint-oriented generator and image-oriented generator. Both of them are mutually connected in an end-to-end learnable fashion and explicitly form three cycled sub-networks, i.e., one image generation cycle and two keypoint generation cycles. Each cycle not …
University of Sydney（悉尼大学）；University of New South Wales（新南威尔士大学）
We formalize the problem of learning interdomain correspondences in the absence of paired data as Bayesian inference in a latent variable model (LVM), where one seeks the underlying hidden representations of entities from one domain as entities from the other domain. First, we introduce implicit latent variable models, where the prior over hidden representations can be specified flexibly as an implicit distribution. Next, we develop a new variational inference (VI) algorithm for this model based on minimization of the symmetric Kullback-Leibler (KL) divergence between a variational joint and t…
Lenovo Research AI Lab（联想研究院人工智能实验室）；Kwai Inc.（快手公司）；Tianjin University（天津大学）；Cornell University（康奈尔大学）
Unsupervised text style transfer is full of challenges due to the lack of parallel data and difficulties in content preservation. In this paper, we propose a novel neural approach to unsupervised text style transfer, which we refer to as Cycle-consistent Adversarial autoEncoders (CAE) trained from non-parallel data. CAE consists of three essential components: (1) LSTM autoencoders that encode a text in one style into its latent representation and decode an encoded representation into its original text or a transferred representation into a style-transferred text, (2) adversarial style transfer…
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this paper, we propose an end-to-end approach for large-scale optimal transport, which directly solves the transport map and is compatible with general cost function. It models the transport map via stochastic neural networks and enforces the constraint on the marginal distributions via adversarial training. The proposed framework can be further extended towards l…
In this paper, we investigate algorithms for anomaly detection. Previous anomaly detection methods focus on modeling the distribution of non-anomalous data provided during training. However, this does not necessarily ensure the correct detection of anomalous data. We propose a new Regularized Cycle Consistent Generative Adversarial Network (RCGAN) in which deep neural networks are adversarially trained to better recognize anomalous samples. This approach is based on leveraging a penalty distribution with a new definition of the loss function and novel use of discriminator networks. It is based…
University of Washington（华盛顿大学）；University of Buffalo（布法罗大学）；Microsoft Research（微软研究院）
Current multi-reference style transfer models for Text-to-Speech (TTS) perform sub-optimally on disjoints datasets, where one dataset contains only a single style class for one of the style dimensions. These models generally fail to produce style transfer for the dimension that is underrepresented in the dataset. In this paper, we propose an adversarial cycle consistency training scheme with paired and unpaired triplets to ensure the use of information from all style dimensions. During training, we incorporate unpaired triplets with randomly selected reference audio samples and encourage the s…
This paper tackles GAN optimization and stability issues in the context of voice conversion. First, to simplify the conversion task, we propose to use spectral envelopes as inputs. Second we propose two adversarial weight training paradigms, the generalized weighted GAN and the generator impact GAN, both aim at reducing the impact of the generator on the discriminator, so both can learn more gradually and efficiently during training. Applying an energy constraint to the cycleGAN paradigm considerably improved conversion quality. A subjective experiment conducted on a voice conversion task on t…
Interpretable Battery Cycle Life Range Prediction Using Early Degradation Data at Cell Level
Volvo Group Trucks Technology（沃尔沃集团卡车技术公司）；Chalmers University of Technology（查尔姆斯理工大学）；INRAE（法国国家农业食品与环境研究院）；UVSQ（凡尔赛大学）；Université Paris-Saclay（巴黎萨克雷大学）；NTNU（挪威科技大学）
A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Zhejiang University（浙江大学）；AntGroup（蚂蚁集团）；Ulsan National Institute of Science and Technology（蔚山国立科学技术院）；The University of Hong Kong（香港大学）
Fundus images are very useful in identifying various ophthalmic disorders. However, due to the presence of artifacts, the visibility of the retina is severely affected. This may result in misdiagnosis of the disorder which may lead to more complicated problems. Since deep learning is a powerful tool to extract patterns from data without much human intervention, they can be applied to image-to-image translation problems. An attempt has been made in this paper to automatically rectify such artifacts present in the images of the fundus. We use a CycleGAN based model which consists of residual blo…
As machine learning (ML) increasingly affects people and society, awareness of its potential unwanted consequences has also grown. To anticipate, prevent, and mitigate undesirable downstream consequences, it is critical that we understand when and how harm might be introduced throughout the ML life cycle. In this paper, we provide a framework that identifies seven distinct potential sources of downstream harm in machine learning, spanning data collection, development, and deployment. In doing so, we aim to facilitate more productive and precise communication around these issues, as well as mor…
Ubiquitous use of lithium-ion batteries across multiple industries presents an opportunity to explore cost saving initiatives as the price to performance ratio continually decreases in a competitive environment. Manufacturers using lithium-ion batteries ranging in applications from mobile phones to electric vehicles need to know how long batteries will last for a given service life. To understand this, expensive testing is required. This paper utilizes the data and methods implemented by Kristen A. Severson, et al, to explore the methodologies that the research team used and presents another m…
Text-to-Image translation has been an active area of research in the recent past. The ability for a network to learn the meaning of a sentence and generate an accurate image that depicts the sentence shows ability of the model to think more like humans. Popular methods on text to image translation make use of Generative Adversarial Networks (GANs) to generate high quality images based on text input, but the generated images don't always reflect the meaning of the sentence given to the model as input. We address this issue by using a captioning network to caption on generated images and exploit…
School of Electrical Information and Communication Engineering, Huazhong University of Science & Technology（华中科技大学电子信息与通信学院）；Microsoft AI & Research（微软人工智能与研究）；Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）
Recent techniques built on Generative Adversarial Networks (GANs), such as Cycle-Consistent GANs, are able to learn mappings among different domains built from unpaired datasets, through min-max optimization games between generators and discriminators. However, it remains challenging to stabilize the training process and thus cyclic models fall into mode collapse accompanied by the success of discriminator. To address this problem, we propose an novel Bayesian cyclic model and an integrated cyclic framework for inter-domain mappings. The proposed method motivated by Bayesian GAN explores the f…
University of California Irvine（加州大学欧文分校）；University of California, Irvine（加州大学欧文分校）；Institute for Future Health, University of California, Irvine（加州大学欧文分校未来健康研究所）
Respiratory rate (RR) is a clinical sign representing ventilation. An abnormal change in RR is often the first sign of health deterioration as the body attempts to maintain oxygen delivery to its tissues. There has been a growing interest in remotely monitoring of RR in everyday settings which has made photoplethysmography (PPG) monitoring wearable devices an attractive choice. PPG signals are useful sources for RR extraction due to the presence of respiration-induced modulations in them. The existing PPG-based RR estimation methods mainly rely on hand-crafted rules and manual parameters tunin…
KIST Europe（韩国科学技术研究院欧洲分院）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Korea Institute of Science and Technology Europe Forschungsgesellschaft mbH（韩国科学技术研究院欧洲研究有限公司）
Bearing is a key component in industrial machinery and its failure may lead to unwanted downtime and economic loss. Hence, it is necessary to predict the remaining useful life (RUL) of bearings. Conventional data-driven approaches of RUL prediction require expert domain knowledge for manual feature extraction and may suffer from data distribution discrepancy between training and test data. In this study, we propose a novel generalized multiscale feature extraction method with generative adversarial networks. The adversarial training learns the distribution of training data from different beari…
Guangdong Cardiovascular Institute（广东省心血管病研究所）；Guangdong Academy of Medical Sciences（广东省医学科学院）；University of Notre Dame（圣母大学）
As one of the most commonly ordered imaging tests, computed tomography (CT) scan comes with inevitable radiation exposure that increases the cancer risk to patients. However, CT image quality is directly related to radiation dose, thus it is desirable to obtain high-quality CT images with as little dose as possible. CT image denoising tries to obtain high dose like high-quality CT images (domain X) from low dose low-quality CTimages (domain Y), which can be treated as an image-to-image translation task where the goal is to learn the transform between a source domain X (noisy images) and a targ…
The biggest challenge faced by a Machine Learning Engineer is the lack of data they have, especially for 2-dimensional images. The image is processed to be trained into a Machine Learning model so that it can recognize patterns in the data and provide predictions. This research is intended to create a solution using the Cycle Generative Adversarial Networks (GANs) algorithm in overcoming the problem of lack of data. Then use Style Transfer to be able to generate a new image based on the given style. Based on the results of testing the resulting model has been carried out several improvements, …
Univ. Grenoble Alpes, CNRS, Inria, LIG（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、法国国家信息与自动化研究所、格勒诺布尔信息实验室）；UC Berkeley（加州大学伯克利分校）；Singapore University of Technology and Design（新加坡科技设计大学）
Regularized learning is a fundamental technique in online optimization, machine learning and many other fields of computer science. A natural question that arises in these settings is how regularized learning algorithms behave when faced against each other. We study a natural formulation of this problem by coupling regularized learning dynamics in zero-sum games. We show that the system's behavior is Poincaré recurrent, implying that almost every trajectory revisits any (arbitrarily small) neighborhood of its starting point infinitely often. This cycling behavior is robust to the agents' choic…
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）
Infrared (IR) images are essential to improve the visibility of dark or camouflaged objects. Object recognition and segmentation based on a neural network using IR images provide more accuracy and insight than color visible images. But the bottleneck is the amount of relevant IR images for training. It is difficult to collect real-world IR images for special purposes, including space exploration, military and fire-fighting applications. To solve this problem, we created color visible and IR images using a Unity-based 3D game editor. These synthetically generated color visible and IR images wer…
Nokia Bell Labs（诺基亚贝尔实验室）；University College London（伦敦大学学院）；University of Oxford（牛津大学）
Mobile and embedded devices are increasingly using microphones and audio-based computational models to infer user context. A major challenge in building systems that combine audio models with commodity microphones is to guarantee their accuracy and robustness in the real-world. Besides many environmental dynamics, a primary factor that impacts the robustness of audio models is microphone variability. In this work, we propose Mic2Mic -- a machine-learned system component -- which resides in the inference pipeline of audio models and at real-time reduces the variability in audio data caused by m…
Lakehead University（湖首大学）；Western University（韦仕敦大学）；Harbin Institute of Technology（哈尔滨工业大学）；Nanjing University of Information Science and Technology（南京信息工程大学）；Tianjin University（天津大学）；Okanagan College（奥肯那根学院）；The University of British Columbia Okanagan（不列颠哥伦比亚大学奥肯那根分校）
Deep Convolutional Neural Networks (DCNNs) have exhibited impressive performance on image super-resolution tasks. However, these deep learning-based super-resolution methods perform poorly in real-world super-resolution tasks, where the paired high-resolution and low-resolution images are unavailable and the low-resolution images are degraded by complicated and unknown kernels. To break these limitations, we propose the Unsupervised Bi-directional Cycle Domain Transfer Learning-based Generative Adversarial Network (UBCDTL-GAN), which consists of an Unsupervised Bi-directional Cycle Domain Tran…
In a recent paper, we have presented a generative adversarial network (GAN)-based model for unconditional generation of the mel-spectrograms of singing voices. As the generator of the model is designed to take a variable-length sequence of noise vectors as input, it can generate mel-spectrograms of variable length. However, our previous listening test shows that the quality of the generated audio leaves room for improvement. The present paper extends and expands that previous work in the following aspects. First, we employ a hierarchical architecture in the generator to induce some structure i…
Cold-Start Forecasting of New Product Life-Cycles via Conditional Diffusion Models
Guanghua School of Management, Peking University（北京大学光华管理学院）；Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）
Systematic Feature Design for Cycle Life Prediction of Lithium-Ion Batteries During Formation
Department of Chemical Engineering, Massachusetts Institute of Technology（化学工程系，麻省理工学院）；Technical University of Darmstadt（德累斯顿技术大学）；Department of Materials Science and Engineering, Stanford University（材料科学与工程系，斯坦福大学）；Applied Energy Division, SLAC National Accelerator Laboratory（应用能源部，SLAC国家加速器实验室）；Department of Mathematics, Massachusetts Institute of Technology（数学系，麻省理工学院）
A major problem of structural health monitoring (SHM) has been the prognosis of damage and the definition of the remaining useful life of a structure. Both tasks depend on many parameters, many of which are often uncertain. Many models have been developed for the aforementioned tasks but they have been either deterministic or stochastic with the ability to take into account only a restricted amount of past states of the structure. In the current work, a generative model is proposed in order to make predictions about the damage evolution of structures. The model is able to perform in a populati…
BACE-RUL: A Bi-directional Adversarial Network with Covariate Encoding for Machine Remaining Useful Life Prediction
School of Software Engineering, Sun Yat-Sen University（中山大学软件学院）；School of Computer Science and Technology, China University of Mining and Technology（中国矿业大学计算机科学与技术学院）；National University of Singapore（新加坡国立大学）
NTT Communication Science Laboratories, NTT Corporation（NTT公司NTT通信科学实验室）
We propose a learning-based filter that allows us to directly modify a synthetic speech waveform into a natural speech waveform. Speech-processing systems using a vocoder framework such as statistical parametric speech synthesis and voice conversion are convenient especially for a limited number of data because it is possible to represent and process interpretable acoustic features over a compact space, such as the fundamental frequency (F0) and mel-cepstrum. However, a well-known problem that leads to the quality degradation of generated speech is an over-smoothing effect that eliminates some…
Many researchers assume that, for software analytics, "more data is better." We write to show that, at least for learning defect predictors, this may not be true. To demonstrate this, we analyzed hundreds of popular GitHub projects. These projects ran for 84 months and contained 3,728 commits (median values). Across these projects, most of the defects occur very early in their life cycle. Hence, defect predictors learned from the first 150 commits and four months perform just as well as anything else. This means that, at least for the projects studied here, after the first few months, we need …
Early Cycle Charge Trajectory Generative Prediction and Full Life Cycle Health Management of Iron-Chromium Flow Batteries Based on FlowBD-E1
State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing)（中国石油大学（北京）重质油国家重点实验室）；Zhonghai Energy Storage Technology (Beijing) Co., Ltd.（中海储能科技（北京）有限公司）
École de Technologie Supérieure, Université du Québec（魁北克大学高等技术学院）
In this paper we propose a novel environmental sound classification approach incorporating unsupervised feature learning from codebook via spherical $K$-Means++ algorithm and a new architecture for high-level data augmentation. The audio signal is transformed into a 2D representation using a discrete wavelet transform (DWT). The DWT spectrograms are then augmented by a novel architecture for cycle-consistent generative adversarial network. This high-level augmentation bootstraps generated spectrograms in both intra and inter class manners by translating structural features from sample to sampl…
We provide a machine learning solution that replaces the traditional methods for deciding the pesticide application time of Sunn Pest. We correlate climate data with phases of Sunn Pest in its life-cycle and decide whether the fields should be sprayed. Our solution includes two groups of prediction models. The first group contains decision trees that predict migration time of Sunn Pest from winter quarters to wheat fields. The second group contains random forest models that predict the nymphal stage percentages of Sunn Pest which is a criterion for pesticide application. We trained our models …
KAIST（韩国科学技术院）；University of Ulsan College of Medicine（蔚山大学医学院）
In coronary CT angiography, a series of CT images are taken at different levels of radiation dose during the examination. Although this reduces the total radiation dose, the image quality during the low-dose phases is significantly degraded. To address this problem, here we propose a novel semi-supervised learning technique that can remove the noises of the CT images obtained in the low-dose phases by learning from the CT images in the routine dose phases. Although a supervised learning approach is not possible due to the differences in the underlying heart structure in two phases, the images …
Università degli Studi di Milano（米兰大学）；INFN（意大利国家核物理研究所）；University of Oxford（牛津大学）
We introduce a generative model to simulate radiation patterns within a jet using the Lund jet plane. We show that using an appropriate neural network architecture with a stochastic generation of images, it is possible to construct a generative model which retrieves the underlying two-dimensional distribution to within a few percent. We compare our model with several alternative state-of-the-art generative techniques. Finally, we show how a mapping can be created between different categories of jets, and use this method to retroactively change simulation settings or the underlying process on a…
School of Electronic Engineering and Computer Science（电子工程与计算机科学学院）；Queen Mary University of London（伦敦玛丽女王大学）；School of Mathematical Sciences（数学科学学院）
This research project investigates the application of deep learning to timbre transfer, where the timbre of a source audio can be converted to the timbre of a target audio with minimal loss in quality. The adopted approach combines Variational Autoencoders with Generative Adversarial Networks to construct meaningful representations of the source audio and produce realistic generations of the target audio and is applied to the Flickr 8k Audio dataset for transferring the vocal timbre between speakers and the URMP dataset for transferring the musical timbre between instruments. Furthermore, vari…
