Domain adaptation considers the problem of generalising a model learnt using data from a particular source domain to a different target domain. Often it is difficult to find a suitable single source to adapt from, and one must consider multiple sources. Using an unrelated source can result in sub-optimal performance, known as the \emph{negative transfer}. However, it is challenging to select the appropriate source(s) for classifying a given target instance in multi-source unsupervised domain adaptation (UDA). We model source-selection as an attention-learning problem, where we learn attention over sources for a given target instance. For this purpose, we first independently learn source-specific classification models, and a relatedness map between sources and target domains using pseudo-labelled target domain instances. Next, we learn attention-weights over the sources for aggregating the predictions of the source-specific models. Experimental results on cross-domain sentiment classification benchmarks show that the proposed method outperforms prior proposals in multi-source UDA.
School of Interactive Computing(交互计算学院);Georgia Institute of Technology(佐治亚理工学院)
Representation learning is the dominant technique for unsupervised domain adaptation, but existing approaches often require the specification of "pivot features" that generalize across domains, which are selected by task-specific heuristics. We show that a novel but simple feature embedding approach provides better performance, by exploiting the feature template structure common in NLP problems.
In this work, we study Unsupervised Domain Adaptation (UDA) in a challenging self-supervised approach. One of the difficulties is how to learn task discrimination in the absence of target labels. Unlike previous literature which directly aligns cross-domain distributions or leverages reverse gradient, we propose Domain Confused Contrastive Learning (DCCL) to bridge the source and the target domains via domain puzzles, and retain discriminative representations after adaptation. Technically, DCCL searches for a most domain-challenging direction and exquisitely crafts domain confused augmentation…
Answering questions is a primary goal of many conversational systems or search products. While most current systems have focused on answering questions against structured databases or curated knowledge graphs, on-line community forums or frequently asked questions (FAQ) lists offer an alternative source of information for question answering systems. Automatic duplicate question detection (DQD) is the key technology need for question answering systems to utilize existing online forums like StackExchange. Existing annotations of duplicate questions in such forums are community-driven, making the…
Domain adaptation plays an important role for speech recognition models, in particular, for domains that have low resources. We propose a novel generative model based on cyclic-consistent generative adversarial network (CycleGAN) for unsupervised non-parallel speech domain adaptation. The proposed model employs multiple independent discriminators on the power spectrogram, each in charge of different frequency bands. As a result we have 1) better discriminators that focus on fine-grained details of the frequency features, and 2) a generator that is capable of generating more realistic domain-ad…
Implicit discourse relations are not only more challenging to classify, but also to annotate, than their explicit counterparts. We tackle situations where training data for implicit relations are lacking, and exploit domain adaptation from explicit relations (Ji et al., 2015). We present an unsupervised adversarial domain adaptive network equipped with a reconstruction component. Our system outperforms prior works and other adversarial benchmarks for unsupervised domain adaptation. Additionally, we extend our system to take advantage of labeled data if some are available.
Hanyang University(汉阳大学);Vision AI Labs(视觉人工智能实验室);SK Telecom(SK电讯)
A pre-trained language model, BERT, has brought significant performance improvements across a range of natural language processing tasks. Since the model is trained on a large corpus of diverse topics, it shows robust performance for domain shift problems in which data distributions at training (source data) and testing (target data) differ while sharing similarities. Despite its great improvements compared to previous models, it still suffers from performance degradation due to domain shifts. To mitigate such problems, we propose a simple but effective unsupervised domain adaptation method, a…
We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages. Our approach formulates the alignment learning problem as a domain adaptation problem over the manifold of doubly stochastic matrices. This viewpoint arises from the aim to align the second order information of the two language spaces. The rich geometry of the doubly stochastic manifold allows to employ efficient Riemannian conjugate gradient algorithm for the proposed formulation. Empirically, the proposed approach outperforms state-of-the-ar…
Unsupervised domain adaptation leverages rich information from a labeled source domain to model an unlabeled target domain. Existing methods attempt to align the cross-domain distributions. However, the statistical representations of the alignment of the two domains are not well addressed. In this paper, we propose deep least squares alignment (DLSA) to estimate the distribution of the two domains in a latent space by parameterizing a linear model. We further develop marginal and conditional adaptation loss to reduce the domain discrepancy by minimizing the angle between fitting lines and inte…
Rutgers University(罗格斯大学);Toutiao AI Lab(今日头条AI实验室);Snap Research(Snap研究)
In this paper, we propose Factorized Adversarial Networks (FAN) to solve unsupervised domain adaptation problems for image classification tasks. Our networks map the data distribution into a latent feature space, which is factorized into a domain-specific subspace that contains domain-specific characteristics and a task-specific subspace that retains category information, for both source and target domains, respectively. Unsupervised domain adaptation is achieved by adversarial training to minimize the discrepancy between the distributions of two task-specific subspaces from source and target …
School of Computer and Software, Nanjing University of Information Science and Technology(南京信息工程大学计算机与软件学院);Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing University of Information Science and Technology(南京信息工程大学教育部数字取证工程研究中心);College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautic(南京航空航天大学计算机科学与技术学院)
Unsupervised domain adaptation (UDA) is an emerging research topic in the field of machine learning and pattern recognition, which aims to help the learning of unlabeled target domain by transferring knowledge from the source domain.
The primary goal of this work is to study the effectiveness of an unsupervised domain adaptation approach for various applications such as binary classification and anomaly detection in the context of Alzheimer's disease (AD) detection for the OASIS datasets. We also explore image reconstruction and image synthesis for analyzing and generating 3D structural MRI data to establish performance benchmarks for anomaly detection. We successfully demonstrate that domain adaptation improves the performance of AD detection when implemented in both supervised and unsupervised settings. Additionally, the…
Unsupervised domain adaptation (UDA) with pre-trained language models (PrLM) has achieved promising results since these pre-trained models embed generic knowledge learned from various domains. However, fine-tuning all the parameters of the PrLM on a small domain-specific corpus distort the learned generic knowledge, and it is also expensive to deployment a whole fine-tuned PrLM for each domain. This paper explores an adapter-based fine-tuning approach for unsupervised domain adaptation. Specifically, several trainable adapter modules are inserted in a PrLM, and the embedded generic knowledge i…
Nanyang Technological University(南洋理工大学);Singapore Institute of Manufacturing Technology(新加坡制造技术研究院)
We consider the problem of online unsupervised cross-domain adaptation, where two independent but related data streams with different feature spaces -- a fully labeled source stream and an unlabeled target stream -- are learned together. Unique characteristics and challenges such as covariate shift, asynchronous concept drifts, and contrasting data throughput arises. We propose ACDC, an adversarial unsupervised domain adaptation framework that handles multiple data streams with a complete self-evolving neural network structure that reacts to these defiances. ACDC encapsulates three modules int…
Domain adaptation aims to exploit a label-rich source domain for learning classifiers in a different label-scarce target domain. It is particularly challenging when there are significant divergences between the two domains. In the paper, we propose a novel unsupervised domain adaptation method based on progressive domain augmentation. The proposed method generates virtual intermediate domains via domain interpolation, progressively augments the source domain and bridges the source-target domain divergence by conducting multiple subspace alignment on the Grassmann manifold. We conduct experimen…
Recent work has shown the importance of adaptation of broad-coverage contextualised embedding models on the domain of the target task of interest. Current self-supervised adaptation methods are simplistic, as the training signal comes from a small percentage of \emph{randomly} masked-out tokens. In this paper, we show that careful masking strategies can bridge the knowledge gap of masked language models (MLMs) about the domains more effectively by allocating self-supervision where it is needed. Furthermore, we propose an effective training strategy by adversarially masking out those tokens whi…
This paper uses information-theoretic tools to analyze the generalization error in unsupervised domain adaptation (UDA). We present novel upper bounds for two notions of generalization errors. The first notion measures the gap between the population risk in the target domain and that in the source domain, and the second measures the gap between the population risk in the target domain and the empirical risk in the source domain. While our bounds for the first kind of error are in line with the traditional analysis and give similar insights, our bounds on the second kind of error are algorithm-…
Microsoft(微软);IIT Kanpur(印度理工学院坎普尔分校);Oracle(甲骨文公司);University of Bath(巴斯大学)
Understanding unsupervised domain adaptation has been an important task that has been well explored. However, the wide variety of methods have not analyzed the role of a classifier's performance in detail. In this paper, we thoroughly examine the role of a classifier in terms of matching source and target distributions. We specifically investigate the classifier ability by matching a) the distribution of features, b) probabilistic uncertainty for samples and c) certainty activation mappings. Our analysis suggests that using these three distributions does result in a consistently improved perfo…
Unsupervised domain adaptation seeks to learn an invariant and discriminative representation for an unlabeled target domain by leveraging the information of a labeled source dataset. We propose to improve the discriminative ability of the target domain representation by simultaneously learning tightly clustered target representations while encouraging that each cluster is assigned to a unique and different class from the source. This strategy alleviates the effects of negative transfer when combined with adversarial domain matching between source and target representations. Our approach is rob…
South China University of Technology(华南理工大学);Tencent AI Lab(腾讯人工智能实验室)
Deep learning based medical image diagnosis has shown great potential in clinical medicine. However, it often suffers two major difficulties in practice: 1) only limited labeled samples are available due to expensive annotation costs over medical images; 2) labeled images may contain considerable label noises (e.g., mislabeling labels) due to diagnostic difficulties. In this paper, we seek to exploit rich labeled data from relevant domains to help the learning in the target task with unsupervised domain adaptation (UDA). Unlike most existing UDA methods which rely on clean labeled data or assu…
Current unsupervised domain adaptation methods can address many types of distribution shift, but they assume data from the source domain is freely available. As the use of pre-trained models becomes more prevalent, it is reasonable to assume that source data is unavailable. We propose an unsupervised method for adapting a source classifier to a target domain that varies from the source domain along natural axes, such as brightness and contrast. Our method only requires access to unlabeled target instances and the source classifier. We validate our method in scenarios where the distribution shi…
Tianjin University(天津大学);Chinese University of Hong Kong, Shenzhen(香港中文大学(深圳))
With the supervision from source domain only in class-level, existing unsupervised domain adaptation (UDA) methods mainly learn the domain-invariant representations from a shared feature extractor, which causes the source-bias problem. This paper proposes an unsupervised domain adaptation approach with Teacher-Student Competition (TSC). In particular, a student network is introduced to learn the target-specific feature space, and we design a novel competition mechanism to select more credible pseudo-labels for the training of student network. We introduce a teacher network with the structure o…
Deep learning has produced state-of-the-art results for a variety of tasks. While such approaches for supervised learning have performed well, they assume that training and testing data are drawn from the same distribution, which may not always be the case. As a complement to this challenge, single-source unsupervised domain adaptation can handle situations where a network is trained on labeled data from a source domain and unlabeled data from a related but different target domain with the goal of performing well at test-time on the target domain. Many single-source and typically homogeneous u…
Qiushi Academy for Advanced Studies, Zhejiang University(浙江大学求是高等研究院);International School of Information Science & Engineering, Dalian University of Technology(大连理工大学国际信息与软件学院);Zhejiang University School of Medicine(浙江大学医学院);State University of New York at Buffalo(纽约州立大学布法罗分校)
Unsupervised domain adaptation methods aim to alleviate performance degradation caused by domain-shift by learning domain-invariant representations. Existing deep domain adaptation methods focus on holistic feature alignment by matching source and target holistic feature distributions, without considering local features and their multi-mode statistics. We show that the learned local feature patterns are more generic and transferable and a further local feature distribution matching enables fine-grained feature alignment. In this paper, we present a method for learning domain-invariant local fe…
The primary objective of domain adaptation methods is to transfer knowledge from a source domain to a target domain that has similar but different data distributions. Thus, in order to correctly classify the unlabeled target domain samples, the standard approach is to learn a common representation for both source and target domain, thereby indirectly addressing the problem of learning a classifier in the target domain. However, such an approach does not address the task of classification in the target domain directly. In contrast, we propose an approach that directly addresses the problem of l…
Unsupervised domain adaptation (UDA) deals with the problem of classifying unlabeled target domain data while labeled data is only available for a different source domain. Unfortunately, commonly used classification methods cannot fulfill this task adequately due to the domain gap between the source and target data. In this paper, we propose a novel uncertainty-aware domain adaptation setup that models uncertainty as a multivariate Gaussian distribution in feature space. We show that our proposed uncertainty measure correlates with other common uncertainty quantifications and relates to smooth…
Unsupervised domain adaptation studies how to transfer a learner from a labeled source domain to an unlabeled target domain with different distributions. Existing methods mainly focus on matching the marginal distributions of the source and target domains, which probably lead a misalignment of samples from the same class but different domains. In this paper, we deal with this misalignment by achieving the class-conditioned transferring from a new perspective. We aim to maximize the conditional independence of feature and domain given class in the reproducing kernel Hilbert space. The optimizat…
We propose a method for unsupervised domain adaptation that trains a shared embedding to align the joint distributions of inputs (domain) and outputs (classes), making any classifier agnostic to the domain. Joint alignment ensures that not only the marginal distributions of the domain are aligned, but the labels as well. We propose a novel objective function that encourages the class-conditional distributions to have disjoint support in feature space. We further exploit adversarial regularization to improve the performance of the classifier on the domain for which no annotated data is availabl…
University of Trento(特伦托大学);ITU Copenhagen(哥本哈根信息技术大学)
Deep neural networks excel at learning from labeled data and achieve state-of-the-art resultson a wide array of Natural Language Processing tasks. In contrast, learning from unlabeled data, especially under domain shift, remains a challenge. Motivated by the latest advances, in this survey we review neural unsupervised domain adaptation techniques which do not require labeled target domain data. This is a more challenging yet a more widely applicable setup. We outline methods, from early traditional non-neural methods to pre-trained model transfer. We also revisit the notion of domain, and we …
We address the problem of severe class imbalance in unsupervised domain adaptation, when the class spaces in source and target domains diverge considerably. Till recently, domain adaptation methods assumed the aligned class spaces, such that reducing distribution divergence makes the transfer between domains easier. Such an alignment assumption is invalidated in real world scenarios where some source classes are often under-represented or simply absent in the target domain. We revise the current approaches to class imbalance and propose a new one that uses latent codes in the adversarial domai…
Insightful findings in political science often require researchers to analyze documents of a certain subject or type, yet these documents are usually contained in large corpora that do not distinguish between pertinent and non-pertinent documents. In contrast, we can find corpora that label relevant documents but have limitations (e.g., from a single source or era), preventing their use for political science research. To bridge this gap, we present \textit{adaptive ensembling}, an unsupervised domain adaptation framework, equipped with a novel text classification model and time-aware training …
The transcription quality of automatic speech recognition (ASR) systems degrades significantly when transcribing audios coming from unseen domains. We propose an unsupervised error correction method for unsupervised ASR domain adaption, aiming to recover transcription errors caused by domain mismatch. Unlike existing correction methods that rely on transcribed audios for training, our approach requires only unlabeled data of the target domains in which a pseudo-labeling technique is applied to generate correction training samples. To reduce over-fitting to the pseudo data, we also propose an e…
School of Applied and Engineering Physics, Cornell University(康奈尔大学应用与工程物理学院);Center for Neuroprosthetics, EPFL(洛桑联邦理工学院神经假肢中心)
Modern machine learning tools have shown promise in detecting symptoms of neurological disorders. However, current approaches typically train a unique classifier for each subject. This subject-specific training scheme requires long labeled recordings from each patient, thus failing to detect symptoms in new patients with limited recordings. This paper introduces an unsupervised domain adaptation approach based on adversarial networks to enable few-shot, cross-subject epileptic seizure detection. Using adversarial learning, features from multiple patients were encoded into a subject-invariant s…
JD AI Research(京东人工智能研究院);University of Science and Technology of China(中国科学技术大学);Nanjing University(南京大学)
Unsupervised domain adaptation aims to transfer the classifier learned from the source domain to the target domain in an unsupervised manner. With the help of target pseudo-labels, aligning class-level distributions and learning the classifier in the target domain are two widely used objectives. Existing methods often separately optimize these two individual objectives, which makes them suffer from the neglect of the other. However, optimizing these two aspects together is not trivial. To alleviate the above issues, we propose a novel method that jointly optimizes semantic domain alignment and…
Automatic speech recognition is a difficult problem in pattern recognition because several sources of variability exist in the speech input like the channel variations, the input might be clean or noisy, the speakers may have different accent and variations in the gender, etc. As a result, domain adaptation is important in speech recognition where we train the model for a particular source domain and test it on a different target domain. In this paper, we propose a technique to perform unsupervised gender-based domain adaptation in speech recognition using phonetic features. The experiments ar…
When Unsupervised Domain Adaptation meets One-class Anomaly Detection: Addressing the Two-fold Unsupervised Curse by Leveraging Anomaly Scarcity
Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg(安全、可靠性与信任跨学科研究中心(SnT),卢森堡大学);Cristal Laboratory, National School of Computer Sciences, University of Manouba(晶体实验室,国家计算机科学学校,曼努巴大学)
Unsupervised domain adaptation is the problem setting where data generating distributions in the source and target domains are different, and labels in the target domain are unavailable. One important question in unsupervised domain adaptation is how to measure the difference between the source and target domains. A previously proposed discrepancy that does not use the source domain labels requires high computational cost to estimate and may lead to a loose generalization error bound in the target domain. To mitigate these problems, we propose a novel discrepancy called source-guided discrepan…
Domain adaptation addresses the problem created when training data is generated by a so-called source distribution, but test data is generated by a significantly different target distribution. In this work, we present approximate label matching (ALM), a new unsupervised domain adaptation technique that creates and leverages a rough labeling on the test samples, then uses these noisy labels to learn a transformation that aligns the source and target samples. We show that the transformation estimated by ALM has favorable properties compared to transformations estimated by other methods, which do…
Appropriately evaluating the discrepancy between domains is essential for the success of unsupervised domain adaptation. In this paper, we first point out that existing discrepancy measures are less informative when complex models such as deep neural networks are used, in addition to the facts that they can be computationally highly demanding and their range of applications is limited only to binary classification. We then propose a novel domain discrepancy measure, called the paired hypotheses discrepancy (PHD), to overcome these shortcomings. PHD is computationally efficient and applicable t…
Recently proposed DNN-based stereo matching methods that learn priors directly from data are known to suffer a drastic drop in accuracy in new environments. Although supervised approaches with ground truth disparity maps often work well, collecting them in each deployment environment is cumbersome and costly. For this reason, many unsupervised domain adaptation methods based on image-to-image translation have been proposed, but these methods do not preserve the geometric structure of a stereo image pair because the image-to-image translation is applied to each view separately. To address this …
Unsupervised representation learning for speech audios attained impressive performances for speech recognition tasks, particularly when annotated speech is limited. However, the unsupervised paradigm needs to be carefully designed and little is known about what properties these representations acquire. There is no guarantee that the model learns meaningful representations for valuable information for recognition. Moreover, the adaptation ability of the learned representations to other domains still needs to be estimated. In this work, we explore learning domain-invariant representations via a …
In this work, we connect two distinct concepts for unsupervised domain adaptation: feature distribution alignment between domains by utilizing the task-specific decision boundary and the Wasserstein metric. Our proposed sliced Wasserstein discrepancy (SWD) is designed to capture the natural notion of dissimilarity between the outputs of task-specific classifiers. It provides a geometrically meaningful guidance to detect target samples that are far from the support of the source and enables efficient distribution alignment in an end-to-end trainable fashion. In the experiments, we validate the …
Huazhong University of Science & Technology(华中科技大学);University of Technology Sydney(悉尼科技大学);Farsee2 Tech. Co.(Farsee2科技公司);Baidu Research(百度研究院)
We aim at the problem named One-Shot Unsupervised Domain Adaptation. Unlike traditional Unsupervised Domain Adaptation, it assumes that only one unlabeled target sample can be available when learning to adapt. This setting is realistic but more challenging, in which conventional adaptation approaches are prone to failure due to the scarce of unlabeled target data. To this end, we propose a novel Adversarial Style Mining approach, which combines the style transfer module and task-specific module into an adversarial manner. Specifically, the style transfer module iteratively searches for harder …
Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows
Advanced Material Engineering Division, Toyota Motor Corporation(丰田汽车公司先进材料工程部);Quantum Computing Center, Keio University(庆应义塾大学量子计算中心);Department of Applied Physics and Physico-Informatics, Keio University(庆应义塾大学应用物理与物理信息学系)
The University of Texas at Austin(德克萨斯大学奥斯汀分校);Cornell University(康奈尔大学);Xidian University(西安电子科技大学)
Existing methods for unsupervised domain adaptation often rely on minimizing some statistical distance between the source and target samples in the latent space. To avoid the sampling variability, class imbalance, and data-privacy concerns that often plague these methods, we instead provide a memory and computation-efficient probabilistic framework to extract class prototypes and align the target features with them. We demonstrate the general applicability of our method on a wide range of scenarios, including single-source, multi-source, class-imbalance, and source-private domain adaptation. R…
Istituto Italiano di Tecnologia (IIT)(意大利技术研究院);Università degli Studi di Genova(热那亚大学);Politecnico di Torino(都灵理工大学)
Fine-tuning and Domain Adaptation emerged as effective strategies for efficiently transferring deep learning models to new target tasks. However, target domain labels are not accessible in many real-world scenarios. This led to the development of Unsupervised Domain Adaptation (UDA) methods, which only employ unlabeled target samples. Furthermore, efficiency and privacy requirements may also prevent the use of source domain data during the adaptation stage. This challenging setting, known as Source-Free Unsupervised Domain Adaptation (SF-UDA), is gaining interest among researchers and practiti…
University for Applied Sciences Würzburg-Schweinfurt(维尔茨堡-施韦因富特应用科学大学)
Current supervised learning models cannot generalize well across domain boundaries, which is a known problem in many applications, such as robotics or visual classification. Domain adaptation methods are used to improve these generalization properties. However, these techniques suffer either from being restricted to a particular task, such as visual adaptation, require a lot of computational time and data, which is not always guaranteed, have complex parameterization, or expensive optimization procedures. In this work, we present an approach that requires only a well-chosen snapshot of data to…
This paper addresses unsupervised domain adaptation, the setting where labeled training data is available on a source domain, but the goal is to have good performance on a target domain with only unlabeled data. Like much of previous work, we seek to align the learned representations of the source and target domains while preserving discriminability. The way we accomplish alignment is by learning to perform auxiliary self-supervised task(s) on both domains simultaneously. Each self-supervised task brings the two domains closer together along the direction relevant to that task. Training this j…
We propose a novel unsupervised domain adaptation framework based on domain-specific batch normalization in deep neural networks. We aim to adapt to both domains by specializing batch normalization layers in convolutional neural networks while allowing them to share all other model parameters, which is realized by a two-stage algorithm. In the first stage, we estimate pseudo-labels for the examples in the target domain using an external unsupervised domain adaptation algorithm---for example, MSTN or CPUA---integrating the proposed domain-specific batch normalization. The second stage learns th…
Nanjing University of Aeronautics & Astronautics(南京航空航天大学)
Unsupervised Domain Adaptation (UDA) aims to classify unlabeled target domain by transferring knowledge from labeled source domain with domain shift. Most of the existing UDA methods try to mitigate the adverse impact induced by the shift via reducing domain discrepancy. However, such approaches easily suffer a notorious mode collapse issue due to the lack of labels in target domain. Naturally, one of the effective ways to mitigate this issue is to reliably estimate the pseudo labels for target domain, which itself is hard. To overcome this, we propose a novel UDA method named Progressive Adap…
Unsupervised domain adaptation (UDA) aims to leverage the knowledge learned from a labeled source dataset to solve similar tasks in a new unlabeled domain. Prior UDA methods typically require to access the source data when learning to adapt the model, making them risky and inefficient for decentralized private data. This work tackles a practical setting where only a trained source model is available and investigates how we can effectively utilize such a model without source data to solve UDA problems. We propose a simple yet generic representation learning framework, named \emph{Source HypOthe…
Rutgers University(罗格斯大学);Carnegie Mellon University(卡内基梅隆大学);The University of Texas at Austin(德克萨斯大学奥斯汀分校)
Unsupervised domain adaptation (UDA) aims at inferring class labels for unlabeled target domain given a related labeled source dataset. Intuitively, a model trained on source domain normally produces higher uncertainties for unseen data. In this work, we build on this assumption and propose to adapt from source to target domain via calibrating their predictive uncertainties. The uncertainty is quantified as the Renyi entropy, from which we propose a general Renyi entropy regularization (RER) framework. We further employ variational Bayes learning for reliable uncertainty estimation. In additio…