Mutual Exclusivity as a Challenge for Deep Neural Networks

1 INTRODUCTION . Children are remarkable learners , and thus their inductive biases should interest machine learning researchers . To help learn the meaning of new words efficiently , children use the “ mutual exclusivity ” ( ME ) bias – the assumption that once an object has one name , it does not need another ( Markman & Wachtel , 1988 ) ( Figure 1 ) . In this paper , we examine whether or not standard neural networks demonstrate the mutual exclusivity bias , either as a built-in assumption or as a bias that develops through training . Moreover , we examine common benchmarks in machine translation and object recognition to determine whether or not a maximally efficient learner should use mutual exclusivity . When children endeavour to learn a new word , they rely on inductive biases to narrow the space of possible meanings . Children learn an average of about 10 new words per day from the age of one until the end of high school ( Bloom , 2000 ) , a feat that requires managing a tractable set of candidate meanings . A typical word learning scenario has many sources of ambiguity and uncertainty , including ambiguity in the mapping between words and referents . Children hear multiple words and see multiple objects within a single scene , often without clear supervisory signals to indicate which word goes with which object ( Smith & Yu , 2008 ) . The mutual exclusivity assumption helps to resolve ambiguity in how words maps to their referents . Markman & Wachtel ( 1988 ) examined scenarios like Figure 1 that required children to determine the referent of a novel word . For instance , children who know the meaning of “ cup ” are presented with two objects , one which is familiar ( a cup ) and another which is novel ( an unusual object ) . Given these two objects , children are asked to “ Show me a dax , ” where “ dax ” is a novel nonsense word . Mark- man and Wachtel found that children tend to pick the novel object rather than the familiar object . Although it is possible that the word “ dax ” could be another word for referring to cups , children predict that the novel word refers to the novel object – demonstrating a “ mutual exclusivity ” bias that familiar objects do not need another name . This is only a preference ; with enough evidence , children must eventually override this bias to learn hierarchical categories : a Dalmatian can be called a “ Dalmatian , ” a “ dog ” , or a “ mammal ” ( Markman & Wachtel , 1988 ; Markman , 1989 ) . As an often useful but sometimes misleading cue , the ME bias guides children when learning the words of their native language . It is instructive to compare word learning in children and machines , since word learning is also a widely studied problem in machine learning and artificial intelligence . There has been substantial recent progress in object recognition , much of which is attributed to the success of deep neural networks and the availability of very large datasets ( LeCun et al. , 2015 ) . But when only one or a few examples of a novel word are available , deep learning algorithms lack human-like sample efficiency and flexibility ( Lake et al. , 2017 ) . Insights from cognitive science and cognitive development can help bridge this gap , and ME has been suggested as a psychologically-informed assumption relevant to machine learning ( Lake et al. , 2019 ) . In this paper , we examine standard neural networks to understand if they have an ME bias . Moreover , we analyze whether or not ME is a good assumption in lifelong variants of common translation and object recognition tasks . 2 RELATED WORK . Children utilize a variety of inductive biases like mutual exclusivity when learning the meaning of words ( Bloom , 2000 ) . Previous work comparing children and neural networks has focused on the shape bias – an assumption that objects with the same name tend to have the same shape , as opposed to color or texture ( Landau et al. , 1988 ) . Children acquire a shape bias over the course of language development ( Smith et al. , 2002 ) , and neural networks can do so too , as shown in synthetic learning scenarios ( Colunga & Smith , 2005 ; Feinman & Lake , 2018 ) and large-scale object recognition tasks ( Ritter et al. , 2017 ) ( see also Id et al . ( 2018 ) and Brendel & Bethge ( 2019 ) for alternative findings ) . This bias is related to how quickly children learn the meaning of new words ( Smith et al. , 2002 ) , and recent findings also show that guiding neural networks towards the shape bias improves their performance ( Geirhos et al. , 2019 ) . In this work , we take initial steps towards a similar investigation of the ME bias in neural networks . Compared to the shape bias , ME has broader implications for machine learning systems ; as we show in our analyses , the bias is relevant beyond object recognition . Closer to the present research , Cohn-Gordon & Goodman ( 2019 ) analyzed an ME-like effect in neural machine translation systems at the sentence level , rather than the word level considered in developmental studies and our analyses here . Cohn-Gordon & Goodman ( 2019 ) showed that neural machine translation systems often learn many-to-one sentence mappings that result in meaning loss , such that two different sentences ( meanings ) in the source language are mapped to the same sentence ( meaning ) in the target language . Using a trained network , they show how a probabilistic pragmatics model ( Frank & Goodman , 2012 ) can be used as a post-processor to preserve meaning and encourage one-to-one mappings . These sentence-level biases do not necessarily indicate how models behave at the word level , and we are interested in the role of ME during learning rather than as a postprocessing step . Nevertheless , Cohn-Gordon and Goodman ’ s results are important and encouraging , raising the possibility that ME could aid in training deep learning systems . 3 DO NEURAL NETWORKS REASON BY MUTUAL EXCLUSIVITY ? . In this section , we investigate whether or not standard neural network models have a mutual exclusivity bias . Paralleling the developmental paradigm ( Markman & Wachtel , 1988 ) , ME is analyzed by presenting a novel stimulus ( “ Show me the dax ” ) and asking models to predict which outputs ( meanings ) are most likely . The strength of the bias is operationalized as the aggregate probability mass placed on the novel rather than the familiar meanings . Our analyses relate to classic experiments by Marcus on whether neural networks can generalize outside their training space ( Marcus , 1998 ; 2003 ) . Marcus showed that a feedforward autoencoder trained on arbitrary binary patterns fails to generalize to an output unit that was never activated during training . Our aim is to study whether standard architectures can recognize and learn a more abstract pattern – a perfect one-to-one mapping between input symbols and output symbols . Specifically , we are interested in model predictions regarding unseen meanings given a novel input . We also test for ME using modern neural networks in two settings using synthetic data : classification ( feedforward classifiers ) and translation ( sequence-to-sequence models ; as reported in Appendix A ) . 3.1 CLASSIFICATION . Synthetic data . We consider a simple one-to-one mapping task inspired by Markman & Wachtel ( 1988 ) . Translating this into a synthetic experiment , input units denote words and output units denote objects . Thus , the dataset consists of 100 pairs of input and output patterns , each of which is a one-hot vector of length 100 . Each input vector represents a label ( e.g. , ‘ hat ’ , ‘ cup ’ , ‘ dax ’ ) and each output vector represents a possible referent object ( meaning ) . Figure 2a shows the input and output patterns for the ‘ dax ’ case , and similar patterns are defined for the other 99 input and output symbols . A one-to-one correspondence between each input symbol and each output symbol is generated through a random permutation , and there is no structure to the data beyond the arbitrary one-to-one relationship . Models are trained on 90 name-referent pairs and evaluated on the remaining 10 test pairs . No model can be expected to know the correct meaning of each test name – there is no way to know from the training data – but several salient patterns are discoverable . First , there is a precise one-toone relationship exemplified by the 90 training items ; the 10 test items can be reasonably assumed to follow the same one-to-one pattern , especially if the network architecture has exactly 10 unused input symbols and 10 unused output symbols . Second , the perfect one-to-one relationship ensures a perfect ME bias in the structure of the data . Although the learner does not know precisely which new output symbol a new input symbol refers to , it should predict that the novel input symbol will correspond to one of the novel output symbols . An ideal learner should discover that an output unit with a known label does not need another – in other words , it should utilize ME to make predictions . Mutual exclusivity . We ask the neural network to “ Show me the dax ” by activating the “ dax ” input unit and asking it to select amongst possible referents ( similar to Figure 1 ) . The network produces a probability distribution over candidate referents ( see Figure 2a ) , and can make relative ( two object ) comparisons by isolating the two relevant scores . To quantify the overall propensity toward ME , we define an “ ME score ” that measures the aggregate probability assigned to all of the novel output symbols as opposed to familiar outputs , corresponding to better performance on the classic forced choice ME task . Let us denote the training symbol by Y , drawn from the data distribution ( X , Y ) ∼ D and the held out symbols Y ′ drawn from ( X ′ , Y ′ ) ∼ D′ . The mutual exclusivity score is the sum probability assigned to unseen output symbols Y ′ when shown a novel input symbol x ∈ X ′ ME Score = 1 |D′| ∑ ( xi , yi ) ∈D′ ∑ y∈Y ′ P ( fnet ( x ) = y|xi ) , ( 1 ) averaged over each of the test items . An ideal learner that has discovered the one-to-one relationship in the synthetic data should have a perfect ME score of 1.0 . In Figure 2a , the probability assigned to the novel output symbol is 0.01 and thus the corresponding ME Score is 0.01 . The challenge is to get a high ME score for novel ( test ) items while also correctly classifying known ( training ) items . Neural network architectures . A wide range of standard neural networks are evaluated on the mutual exclusivity test . We use an embedding layer to map the input symbols to vectors of size 20 or 100 , followed optionally by a hidden layer , and then by a 100-way softmax output layer . The networks are trained with different activation functions ( ReLUs ( Nair & Hinton , 2010 ) , TanH , Sigmoid ) , optimizers ( Adam ( Kingma & Ba , 2015 ) , Momentum , SGD ) , learning rates ( 0.1 , 0.01 , 0.001 ) and regularizers ( weight decay , batch-normalisation ( Ioffe & Szegedy , 2015 ) , dropout ( Srivastava et al. , 2014b ) , and entropy regularization ( see Appendix B.1 ) ) . The models are trained to maximize log-likelihood . All together , we evaluated over 400 different models on the synthetic ME task . Results . Several representative training runs with different architectures are shown in Figure 3 . An ideal learner that has discovered the one-to-one pattern should have a mutual exclusivity of 1 ; for a novel input , the network would assign all the probability mass to the unseen output symbols . In contrast , none of the configurations and architectures tested behave in this way . As training progresses , the mutual exclusivity score ( solid blue line ; Figure 3 ) tends to fall along with the training loss ( red line ) . In fact , almost all of the networks acquire a strong anti-mutual exclusivity bias , transitioning from a initial neutral bias to placing most or all of the probability mass on familiar outputs ( seen in Figure 4 ) . An exception to this pattern is the entropy regularized model , which maintains a score equivalent to an untrained network . In general , trained models strongly predict that a novel input symbol will correspond to a known rather than unknown output symbol , in contradiction to ME and the organizing structure of the synthetic data . Further informal experiments suggest our results can not be reduced to simply not enough data : these architectures do not learn this one-to-one regularity regardless of how many input/output symbols are provided in the training set . Even with thousands of training examples demonstrating a one-toone pattern , the networks do not learn this abstract principle and fail to capture this defining pattern in the data . Other tweaks were tried in an attempt to induce ME , including eliminating the bias units or normalizing the weights , yet we were unable to find an architecture that reliably demonstrated the ME effect .

Summary: This paper makes an observation that most of the neural network architectures do not learn the mutual exclusivity (ME) bias: if an object has one label, then it does not need another. Authors demonstrate this in both synthetic tasks and real-world tasks like object recognition and machine translation. Authors argue that ME bias could help the model to handle new classes and rare events better.