Incremental few-shot learning via vector quantization in deep embedded space

The capability of incrementally learning new tasks without forgetting old ones is a challenging problem due to catastrophic forgetting . This challenge becomes greater when novel tasks contain very few labelled training samples . Currently , most methods are dedicated to class-incremental learning and rely on sufficient training data to learn additional weights for newly added classes . Those methods can not be easily extended to incremental regression tasks and could suffer from severe overfitting when learning few-shot novel tasks . In this study , we propose a nonparametric method in deep embedded space to tackle incremental few-shot learning problems . The knowledge about the learned tasks is compressed into a small number of quantized reference vectors . The proposed method learns new tasks sequentially by adding more reference vectors to the model using few-shot samples in each novel task . For classification problems , we employ the nearest neighbor scheme to make classification on sparsely available data and incorporate intra-class variation , less forgetting regularization and calibration of reference vectors to mitigate catastrophic forgetting . In addition , the proposed learning vector quantization ( LVQ ) in deep embedded space can be customized as a kernel smoother to handle incremental few-shot regression tasks . Experimental results demonstrate that the proposed method outperforms other state-of-the-art methods in incremental learning . 1 INTRODUCTION . Incremental learning is a learning paradigm that allows the model to continually learn new tasks on novel data , without forgetting how to perform previously learned tasks ( Cauwenberghs & Poggio , 2001 ; Kuzborskij et al. , 2013 ; Mensink et al. , 2013 ) . The capability of incremental learning becomes more important in real-world applications , in which the deployed models are exposed to possible out-of-sample data . Typically , hundreds of thousands of labelled samples in new tasks are required to re-train or fine-tune the model ( Rebuffi et al. , 2017 ) . Unfortunately , it is impractical to gather sufficient samples of new tasks in real applications . In contrast , humans can learn new concepts from just one or a few examples , without losing old knowledge . Therefore , it is desirable to develop algorithms to support incremental learning from very few samples . While a natural approach for incremental few-shot learning is to fine-tune part of the base model using novel training data ( Donahue et al. , 2014 ; Girshick et al. , 2014 ) , the model could suffer from severe over-fitting on new tasks due to a limited number of training samples . Moreover , simple fine-tuning also leads to significant performance drop on previously learned tasks , termed as catastrophic forgetting ( Goodfellow et al. , 2014 ) . Recent attempts to mitigate the catastrophic forgetting are generally categorized into two streams : memory relay of old training samples ( Rebuffi et al. , 2017 ; Shin et al. , 2017 ; Kemker & Kanan , 2018 ) and regularization on important model parameters ( Kirkpatrick et al. , 2017 ; Zenke et al. , 2017 ) . However , those incremental learning approaches are developed and tested on unrealistic scenarios where sufficient training samples are available in novel tasks . They may not work well when the training samples in novel tasks are few ( Tao et al. , 2020b ) . To the best of our knowledge , the majority of incremental learning methodologies focus on classification problems and they can not be extended to regression problems easily . In class-incremental learning , the model has to expand output dimensions to learn N ′ novel classes while keeping the knowledge of existing N classes . Parametric models estimate additional classification weights for novel classes , while nonparametric methods compute the class centroids for novel classes . In comparison , output dimensions in regression problems do not change in incremental learning as neither additional weights nor class centroids are applicable to regression problems . Besides , we find that catastrophic forgetting in incremental few-shot classification can be attributed to three reasons . First , the model is biased towards new classes and forgets old classes because the model is fine-tuned on new data only ( Hou et al. , 2019 ; Zhao et al. , 2020 ) . Meanwhile , the prediction accuracy on novel classes is not good due to over-fitting on few-shot training samples . Second , features of novel samples could overlap with those of old classes in the feature space , leading to ambiguity among classes in the feature space . Finally , features of old classes and classification weights are no longer compatible after the model is fine-tuned with new data . In this paper , we investigate the problem of incremental few-shot learning , where only a few training samples are available in new tasks . A unified model is learned sequentially to jointly recognize all classes or regression targets that have been encountered in previous tasks ( Rebuffi et al. , 2017 ; Wu et al. , 2019 ) . To tackle aforementioned problems , we propose a nonparametric method to handle incremental few-shot learning based on learning vector quantization ( LVQ ) ( Sato & Yamada , 1996 ) in deep embedded space . As such , the adverse effects of imbalanced weights in a parametric classifier can be completely avoided ( Mensink et al. , 2013 ; Snell et al. , 2017 ; Yu et al. , 2020 ) . Our contributions are three fold . First , a unified framework is developed , termed as incremental deep learning vector quantization ( IDLVQ ) , to handle both incremental classification ( IDLVQ-C ) and regression ( IDLVQ-R ) problems . Second , we develop intra-class variance regularization , less forgetting constraints and calibration factors to mitigate catastrophic forgetting in class-incremental learning . Finally , the proposed methods achieve state-of-the-art performance on incremental fewshot classification and regression datasets . 2 RELATED WORK . Incremental learning : Some incremental learning approaches rely on memory replay of old exemplars to prevent forgetting previously learned knowledge . Old exemplars can be saved in memory ( Rebuffi et al. , 2017 ; Castro et al. , 2018 ; Prabhu et al. , 2020 ) or sampled from generative models ( Shin et al. , 2017 ; Kemker & Kanan , 2018 ; van de Ven et al. , 2020 ) . However , explicit storage of training samples is not scalable if the number of classes is large . Furthermore , it is difficult to train a reliable generative model for all classes from very few training samples . In parallel , regularization approaches do not require old exemplars and impose regularization on network weights or outputs to minimize the change of parameters that are important to old tasks ( Kirkpatrick et al. , 2017 ; Zenke et al. , 2017 ) . To avoid quick performance deterioration after learning a sequence of novel tasks in regularization approaches , semantic drift compensation ( SDC ) is developed by learning an embedding network via triplet loss ( Schroff et al. , 2015 ) and compensates the drift of class centroids using novel data only ( Yu et al. , 2020 ) . In comparison , IDLVQ-C saves only one exemplar per class and uses saved exemplars to regularize the change in feature extractor and calibrate the change in reference vectors . Few-shot learning : Few-shot learning attempts to obtain models for classification or regression tasks with only a few labelled samples . Few-shot models are trained on widely-varying episodes of fake few-shot tasks with labelled samples drawn from a large-scale meta-training dataset ( Vinyals et al. , 2016 ; Finn et al. , 2017 ; Ravi & Larochelle , 2017 ; Snell et al. , 2017 ; Sung et al. , 2018 ) . Meanwhile , recent works attempt to handle novel few-shot tasks while retraining the knowledge of the base task . These methods are referred to as dynamic few-shot learning ( Gidaris & Komodakis , 2018 ; Ren et al. , 2019a ; Gidaris & Komodakis , 2019 ) . However , dynamic few-shot learning is different from incremental few-shot learning , because they rely on the entire base training dataset and an extra meta-training dataset during meta-training . In addition , dynamic few-shot learning does not accumulate knowledge for multiple novel tasks sequentially . Incremental few-shot learning : Prior works on incremental few-shot learning focus on classification problems by computing the weights for novel classes in parametric classifiers , without iterative gradient descent . For instance , the weights of novel classes can be imprinted by normalized prototypes of novel classes , while keeping the feature extractor fixed ( Qi et al. , 2018 ) . Since novel weights are computed only with the samples of novel classes , the fixed feature extractor may not be compatible with novel classification weights . More recently , neural gas network is employed to construct an undirected graph to represent knowledge of old classes ( Tao et al. , 2020b ; a ) . The vertices in the graph are constructed in an unsupervised manner using competitive Hebbian learning ( Fritzke , 1995 ) , while the feature embedding is fixed . In contrast , IDLVQ learns both feature extractor and reference vectors concurrently in a supervised manner . 3 BACKGROUND . 3.1 INCREMENTAL FEW-SHOT LEARNING . In this paper , incremental few-shot learning is studied for both classification and regression tasks . For classification tasks , we consider the standard class-incremental setup in literature . After the model is trained on a base task ( t = 1 ) with sufficient data , the model learns novel tasks sequentially . Each novel task contains a number of novel classes with only a few training samples per class . Learning a novel task ( t > 1 ) is referred to as an incremental learning session . In task t , we have access only to training data Dt in the current task and previously saved exemplars ( one exemplar per class in this study ) . Each task has a set of classes Ct = { ct1 , ... , ctnt } , where nt is the number of classes in task t. In addition , it is assumed that there is no overlap between classes in different tasks Ct ⋂ Cs = ∅ for t 6= s. After an incremental learning session , the performance of the model is evaluated on a test set that contains all previously seen classes C = ⋂ i C i . Note that our focus is not multi-task scenario , where a task ID is exposed to the model during test phase and the model is only required to perform a given task one time ( van de Ven & Tolias , 2019 ) . Our model is evaluated in a task-agnostic setting , where task ID is not exposed to the model at test time . For regression tasks , we follow a similar setting with a notable difference that the target is realvalued y ∈ R. In addition , the target values in different tasks do not have to be mutually exclusive , unlike the class-incremental setup . 3.2 LEARNING VECTOR QUANTIZATION . Traditional nonparametric methods , such as nearest neighbors , represent knowledge and make predictions by storing the entire training set . Despite the simplicity and effectiveness , they are not scalable to a large-scale base dataset . Typically , incremental learning methods are only allowed to store a small number of exemplars to preserve the knowledge of previously learned tasks . However , randomly selected exemplars may not well present the knowledge in old tasks . LVQ is a classical data compression method that represents the knowledge through a few learned reference vectors ( Sato & Yamada , 1996 ; Seo & Obermayer , 2003 ; Biehl et al. , 2007 ) . A new sample is classified to the same label as the nearest reference vector in the input space . LVQ has been combined with deep feature extractors as an alternative to standard neural networks for better interpretability ( De Vries et al. , 2016 ; Villmann et al. , 2017 ; Saralajew et al. , 2018 ) . The combinations of LVQ and deep feature extractors have been applied to natural language processing ( NLP ) , facial recognition and biometrics ( Variani et al. , 2015 ; Wang et al. , 2016 ; Ren et al. , 2019b ; Leng et al. , 2015 ) . We notice that LVQ is a nonparametric method which is well suited for incremental few-shot learning because the model capacity grows by incorporating more reference vectors to learn new knowledge . For example , incremental learning vector quantization ( ILVQ ) has been developed to learn classification models adaptively from raw features ( Xu et al. , 2012 ) . In this study , we present the knowledge by learning reference vectors in the feature space through LVQ and adapt them in incremental few-shot learning . Compared with ILVQ by Xu et al . ( 2012 ) , our method does not rely on predefined rules to update reference vectors and can be learned along with deep neural networks in an end-to-end fashion . Besides , our method uses a single reference vector for each class , while ILVQ automatically assigns different numbers of prototypes for different classes .

Summary: This paper suggests to use a generative model to address the problem of 'few shot' incremental learning. The idea is to classify input data by maintaining a population of prototypes and measuring the distance of the examples to be classified from these prototypes. As, each prototype represents a class, an example to be classified is assigned to the class of the closest prototype.  The learning of the neural network transforming input data to the prototype space is learned using 2 loss functions: the first one maximizes the margin between the distance to the prototype of the correct class and the other prototypes, the second one makes the clusters as compact as possible.