Evaluating Online Continual Learning with CALM

1 INTRODUCTION . Machines , like humans , can learn to perform multiple different tasks from feedback alone ( Caruana , 1997 ) . On the other hand , humans , but not machines , can benefit from settings in which tasks are presented repeatedly for multiple trials before switching to the next one ( Flesch et al. , 2018 ) , whereas machines require examples to be presented in a shuffled ( i.i.d ) order to learn effectively . Otherwise , they suffer from an effect known as “ catastrophic forgetting ” or “ catastrophic interference ” ( McCloskey & Cohen , 1989 ; Ratcliff , 1990 ) . While there has been a considerable amount of work focused on solving this problem , an endeavour that also goes by the name of ‘ Continual ’ , ‘ Incremental ’ or ‘ Life-long ’ Learning , a large part of it is evaluated on settings in which there is an explicit delimitation signal for every new task presented to the model ( Kirkpatrick et al. , 2017 ; Zenke et al. , 2017 ; Sodhani et al. , 2018 ; Serra et al. , 2018 ; Lopez-Paz & Ranzato , 2017 ; Fernando et al. , 2017 ; Lee et al. , 2017 ; Rusu et al. , 2016 ; Li & Hoiem , 2018 ; Aljundi et al. , 2017 ; Adel et al. , 2020 ; Titsias et al. , 2020 ; Ebrahimi et al. , 2020 ; von Oswald et al. , 2020 ; Li et al. , 2020 ; Yoon et al. , 2020 ) . However , humans do not need any such signalling at all . Consider , for example , the case of a child growing up in a multi-lingual environment . Even though it is not entirely clear whether the child would rely on environmental cues ( for instance , the identity of the speaker ) to distinguish different input languages or not ( De Houwer , 2017 ) , any mechanism must be necessarily inferred from the context . Moreover , even the concept of “ task ” could be vacuous , as it could be represented by shifting data distributions ( Lesort et al. , 2020 ) . Even though the emerging field of Online Continual Learning ( Parisi & Lomonaco , 2020 ; Aljundi et al. , 2019a ) or Task-Free Continual Learning ( Aljundi et al. , 2019b ; Lee et al. , 2020 ) has started to propose solutions to these problems , commonly available benchmarks make assumptions that are far from the real world conditions , such as lacking latent similarity structure on the data stream ( e.g . orthogonal permutations of an image pixels ) or assuming temporal independence between different examples ( e.g . an image of a chair can be classified as “ chair ” independently of any previous examples ) . Consider , instead , the challenge of natural language learning which requires making sense of a highly correlated and temporally interdependent data stream . We argue that the notable scarcity of benchmarks featuring temporally correlated sequences of examples , with short and long-term dependencies , latent similarities between different classes of examples , and no explicit delimitation when transitioning between different classes has left a blind spot in the Online Continual Learning community , which we address here . Moreover , almost none of the commonly used benchmarks deals with language , further limiting the amount of research that extends to this modality . Here , we make a two-fold contribution towards studying online continual learning in neural networks in a linguistic setting . First , we bring CALM ( Class-Agnostic Continual Language Modelling ) to the community , a continual language modelling evaluation framework containing text that alternates between different classes of input ( e.g . different languages or domains ) with latent similarities to which the models could adapt . We introduce two variants . The first is a characterbased language modelling benchmark featuring five different languages that randomly switch between one another . The second one is a word-based language modelling task , where the text alternates between four different domains . No segmentation signal is given when a switch happens , thus requiring models to learn to adapt to these changes . We also propose novel metrics that capture the impact of catastrophic forgetting in an online learning setting by measuring how efficiently can models adapt to class switches . In line with Aljundi et al . ( 2019b ) , we note that when a distribution shift occurs , a neural network that suffers from catastrophic forgetting will display a spike in the loss signal , even when the distribution had been observed in the past ( see Figure 1a ) . Thus , we propose catastrophic forgetting metrics based on characterizing the size of these peaks . The benchmark is provided as a Python library that can be easily imported into a PyTorch project.1 Second , we evaluate multiple baselines based on expert architectures and propose a novel albeit simple mechanism that we call plastic gates , which we show to improve the performance of Products of Experts . Our post-hoc analysis shows that this mechanism is effective in producing a gating strategy that helps to circumvent catastrophic interference while also uncovering latent similarities in the input classes . 2 RELATED WORK . The field of Continual Learning , Incremental Learning or Lifelong Learning has grown to encompass a large body of work , which is better summarized in respective reviews ( Parisi et al. , 2019 ; Lesort et al. , 2020 ) . An overwhelming majority of this work concerns image classification problems or object recognition . Some evaluation datasets are derived from traditional machine learning datasets by manipulating the input examples in more or less artificial ways –like Permuted MNIST ( Kirkpatrick et al. , 2017 ) or Rotated MNIST ( Lopez-Paz & Ranzato , 2017 ) – while others keep examples unchanged but present them in a specific non-i.i.d . order , like for instance , iCIFAR100 ( Rebuffi et al. , 2017 ) or split-MNIST ( Zenke et al. , 2017 ) . All of these datasets comprise single-input classification problems in which there are no temporal dependencies nor correlations between two consecutive examples . To better approximate the conditions of real-world experiences , Fanello et al . ( 2013 ) , Lomonaco & Maltoni ( 2017 ) and Roady et al . ( 2020 ) introduced iCubWorld , CORe50 , and Stream-51 respectively , which comprise short videos of objects from different angles ( further including naturalistic scenes in the latter case ) . These datasets address the problem of correlated examples , but not of temporal dependencies , which we do address in this work . Li et al . ( 2020 ) and de Masson d ’ Autume et al . ( 2019 ) proposed the only benchmarks dealing with language that we know of , in which the former adopts a sequence to sequence paradigm to study incremental learning of new vocabulary items on simplified or artificial datasets , while the latter adapted existing text classification and QA benchmarks analogously to above-mentioned work in image classification . Our work instead uses naturalistic textual data containing natural latent similarities between distributions that can drive information transfer or forgetting . By and large , work directed to address catastrophic forgetting in neural networks presumes the existence of a task identifier to signal different learning units . However , recent work has aimed at tackling catastrophic forgetting even in conditions in which no task boundaries are provided ( Aljundi et al. , 2019b ; Lee et al. , 2020 ) , going under the name of “ Task-Free Continual Learning ” or “ Online Continual Learning ” ( Parisi & Lomonaco , 2020 ; Aljundi et al. , 2019a ) . Of these works , only Aljundi et al . ( 2019b ) uses naturalistic data to classify actors appearing in soap-opera episodes ( Aljundi et al. , 2016 ) , while others resort to artificially modified datasets like split or permuted MNIST . Here , we complement this resource with a text-based benchmark for Task-Free Continual Learning , while arguing for more work on more naturalistic non-i.i.d . datasets . Another aspect of Continual Learning deals with how models are evaluated . Most often , this is done by measuring accuracy on a dedicated test set ( Lopez-Paz & Ranzato , 2017 ; Díaz-Rodríguez et al. , 2018 ; Hayes et al. , 2018 ; Chaudhry et al. , 2018 ; de Masson d ’ Autume et al. , 2019 ) . However this 1Code and materials included in the supplementary materials will be made publicly available upon acceptance . evaluation protocol is tailored for batch learning conditions , in which a model is fit to a training dataset , and then stops learning . Here , instead , we argue in favour of situated evaluation protocols adapted to far-from-equilibrium learning conditions ( Holland , 1992 ) by adopting an Online Learning framework ( Hoi et al. , 2018 ) , which is also known as the prequential approach ( Dawid , 1984 ; Gama et al. , 2013 ) . On the modelling side , this work explores Mixture of Experts ( Jacobs et al. , 1991 ) and Product of Experts ( Hinton , 1999 ) architectures . Variations thereof are at the base of many architectural proposals for addressing catastrophic forgetting ( Rusu et al. , 2016 ; Li & Hoiem , 2018 ; Aljundi et al. , 2017 ; Lee et al. , 2020 ) . However , often they are accompanied by other mechanisms , such as the growth of new modules , freezing of weights or generative modelling of the input . Here we examine the simplest enactments of these architectures and propose an easy-to-implement gating mechanism which can be learned online and provides a strong baseline for more complex architectures . Finally , our study falls within the line of language modelling using neural network models ( Bengio et al. , 2003 ; Mikolov et al. , 2010 ) . In this context , adaptation to the recent past has been studied in the context of cache models ( Grave et al. , 2017 ; Merity et al. , 2017 ) . There , a non-parametric model deals with capturing high-frequency recent statistics while a parametric model captures the more stable aspects of the distribution . These solutions , however , are not well-adapted for cases in which the whole distribution changes over time . Moreover , language modelling is generally studied in a train-test split , where a model is fitted to the training data and asked to generalize over the unseen test data . Here , instead , we study how a model can adapt to incoming data in an online fashion . 3 THE CALM BENCHMARK . We designed a benchmark for evaluating Online Continual Learning algorithms having in mind the following three desiderata : 1 ) naturally correlated sequential data , 2 ) task agnosticism and 3 ) temporally situated evaluation . Parisi & Lomonaco ( 2020 ) discusses the first two . The first requires that on the one hand , data is observed in a potentially infinite data stream with high-dimensional , non-stationary , and temporally correlated examples . The second , that learning systems should not be fed external task boundaries to help them learn in these conditions . Furthermore , we also introduce a third desideratum , by which we ask models to be evaluated in-situ on each example presented to the model , following the classical Online Learning setting ( Hoi et al. , 2018 ; Sahoo et al. , 2018 ) . We thus propose an Online Continual Learning benchmark featuring a language modelling objective where the data stream can switch between different distributions . Because switches are not announced to the model , this is a “ Single-Incremental-Task “ or “ No task label ” scenario under the framework proposed by Lesort et al . ( 2020 ) . More precisely , consider a sequence of observations xt ∈ X that are fed to a model M parametrized by Θt , which makes the prediction ŷt ∈ Y . Then , the true target yt ∈ Y will be revealed and the loss Lt = L ( ŷt , yt ) is observed and later used to compute the model ’ s performance from a given time S until time T as the average loss in that span L̄TS = 1 T−S ∑T t=S Lt for evaluation purposes . Only after reporting the loss can the model be trained based on the received feedback , preventing data leakage . In practice , these examples are presented as mini-batches ( Xt , Yt ) ∈ X b×w × Yb×w containing b parallel streams , and chunked into small windows of length w for efficiency considerations related to the training of neural networks ( Parisi & Lomonaco , 2020 ) . The data stream is composed of N sequences of consecutive mini-batches of length T1 , T2 , . . . , TN , and starting at positions Si = ∑i−1 j=1 Tj . In turn , each of these sequences belong to one of n different classes [ D1 , . . . , Dn ] , presented in random order . To characterize the effect of forgetting we note that a model that becomes disadapted to a given distribution will display a spike in the loss after the stream switches to this distribution , even if it has been observed before ( see Figure 1a ) . For a model to be resilient to catastrophic forgetting , it must adapt quickly to every new distribution , which can be characterized by the height and width of these peaks . We thus propose the following metrics to complement the standard online performance : • Loss after switch : Tracks the loss for the first k times-steps after a switch occurs to quantify the height of the peak . Formally , L @ sw = 1N ∑N i=1 L̄ Si+k Si • Recovery time after switch : Counts the number of time-steps that it takes the model to reach the mean loss observed for the last seen sequence of the current class . In this way , we can quantify the length of the peak .

Summary: This paper’s main contributions are (i) to propose two new benchmarks for online continual learning in the context of language modelling and (ii) evaluate the performance of a number of composition-of-experts-based models on the new datasets using a number of metrics. The multilingual benchmark, derived from an existing multilingual news corpus, consists of sequences of characters where the language is periodically switched, and the MultiDomain benchmark consists of sequences of English words where the corpus is periodically switched. The comparative performances of the various baselines on the two datasets, as well as an analysis of the mixture weights in one of the models during training, are used to provide insights into the qualitative differences between the datasets.