Mutual Exclusivity as a Challenge for Deep Neural Networks
Authors: Kanishk Gandhi
Brenden Lake
Venue:  (2020)
Keywords: Cognitive Science
Deep Learning
Word Learning
Lifelong Learning

Abstract: Strong inductive biases allow children to learn in fast and adaptable ways. Children use the mutual exclusivity (ME) bias to help disambiguate how words map to referents, assuming that if an object has one label then it does not need another. In this paper, we investigate whether or not standard neural architectures have a ME bias, demonstrating that they lack this learning assumption. Moreover, we show that their inductive biases are poorly matched to lifelong learning formulations of classification and translation. We demonstrate that there is a compelling case for designing neural networks that reason by mutual exclusivity, which remains an open challenge.

Under review as a conference paper at ICLR 2019
MUTUAL EXCLUSIVITY AS A CHALLENGE FOR DEEP NEURAL NETWORKS
Anonymous authors Paper under double-blind review
ABSTRACT
Strong inductive biases allow children to learn in fast and adaptable ways. Chil- dren use the mutual exclusivity (ME) bias to help disambiguate how words map to referents, assuming that if object has one label then it does not need another. In this paper, we investigate whether or not standard neural architectures have an ME bias, demonstrating that they lack this learning assumption. Moreover, we show that their inductive biases are poorly matched to lifelong learning formulations of classification and translation. We demonstrate that there is a compelling case for designing neural networks that reason by mutual exclusivity, which remains an open challenge.
INTRODUCTION
Children remarkable learners, and thus their inductive biases should interest machine learning searchers. To help learn the meaning of new words efficiently, children use the "mutual exclusivity" (ME) bias the assumption that once object has name, it does not need another (Markman & Wachtel 1988) (Figure [T. In this paper, we examine whether or not standard neural networks demonstrate the mutual exclusivity bias, either as a built-in assumption or as 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 new word, they rely on inductive bi- ases 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 can- didate 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 ob- jects within a single scene, often without clear supervisory signals to indi- cate which word goes with which object (Smith & Yu 2008).
Show me the "dax"
The mutual exclusivity task used in cognitive development research (Markman & Wachtel 1988). Children tend to associate the novel word ("dax") with the novel object (right).
Figure 1:
The mutual exclusivity assumption helps to resolve ambiguity in how words maps to their referents. Markman & Wachtel (1988) examined scenarios like Figure T that required children to determine the referent of 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 the novel object demonstrating "mutual exclusivity" bias that familiar objects do not need another name. This is only preference; with enough evidence, children must eventually override this bias to learn hierarchical categories: Dalmatian can be called "Dalmatian," a "dog". a "mammal" (Markman & Wachtel 1988 Markman 1989). As often useful but sometimes misleading cue, the ME bias guides children when learning the words of their native language.
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

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Novel
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embedding
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@RU
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apple
dax
chair
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Figure 2: Evaluating mutual exclusivity in feedforward (a) and seq2seq (b) neural network. (a) After training set of known objects, novel label ("dax") is presented one-hot input vector. The network maps this vector a one-hot output vector representing the predicted referent, through intermediate embedding layer and an optional hidden layer (not shown). A representative oulput vector produced by a trained network is shown, placing almost all of the probability mass on known outputs. (b) A similar setup for mapping sequences of labels their referents. During the test phase novel label "dax" presented and the ME Score at that output position computed.
recent progress in object recognition, much of which attributed to the success of deep neural networks and the availability of very large datasets (LeCun al. 2015). But when only examples of novel word are available, deep learning algorithms lack human-like sample efficiency and flexibility (Lake al. 2017). Insights from cognitive science and cognitive development can assumption relevant machine learning (Lake et al.) 2019). In this paper, 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.
few
help bridge this gap, and ME has been suggested as paychologically-inoonne
RELATED WORK
Children utilize 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 shape bias over the course of language development (Smith al.. 2002), and neural networks can do so too, as shown synthetic learning scenarios (Colunga & Smith 2005 Feinman & Lake 2018) and large-scale object recognition tasks (Ritter et al.) | 2017) (see also ld et al. (2018) and Brendel & Bethge (2019) for alternative findings). This bias related how quickly children learn the meaning of words (Smith et al.) 2002), and recent findings also show that guiding neural networks towards the shape bias improves their performance (Geirhos al. 2019). In this work, we take initial steps towards 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 (019)) analyzed an ME-like effect in neural machine translation systems 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) the target language, Using a trained network, they show how a probabilistic pragmatics model (Frank& & Goodman 2012) can be used as post-processor to preserve meaning and encourage one-to-one mappings. These sentence-lewe biases do not necessarily indicate how models behave at the word level, and
interested in the role of ME during learning rather than post- processing step. Nevertheless, Mordon and Goodman's 's results are important and encouraging, raising the possibility that ME could aid in training deep learning systems.
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3 DO NEURAL NETWORKS REASON BY MUTUAL EXCLUSIVITY?
In this section, we investigate whether or not standard neural network models have a mutual exclu- sivity 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 feedforward autoencoder trained on arbitrary binary patterns fails to generalize to an output unit that was never activated dur- ing 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. Specif- ically, we are interested in model predictions regarding unseen meanings given novel input. We also test for ME using modern neural networks in two settings using synthetic data: classification (feedforward classifiers) and translation secqueece-to-sequeee models; as reported in Appendix AA)
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 one-hot vector of length 100. Each input vector represents label (e.g., 'hat', 'cup'. 'dax') and each output vector represents a possible referent object (meaning). Figure 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-to- one relationship exemplified by the 90 training items; the 10 test items 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 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 - 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 []. 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 denote the training symbol by V, drawn from the data distribution (X)))) ~ DD and the held out symbols )" drawn from exclusivity score is the sum probability assigned to unseen output symbols )" when shown novel input symbol æ E X²
~ DD. The mutual
ME Score
Σ
E P(fne(()) y/
D
(Z..).) YEY
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 embedding layer map the input symbols vectors of size 20
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ME
3090
3000
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Figure 3: Evaluating mutual exclusivity synthetic categorization tasks. ME Score (solid blue) and the cross- entropy loss (solid red) are plotted against the epochs of training. The configurations in the settings shown were: (a) Results for model with embedding, hidden, and classification layers, (b) Results for model with embedding and classification layers trained with a weight decay factor 0.001, and (c) Results model with an embedding and classification layer trained with an entropy regularizer.
or 100, followed optionally by hidden layer, and then by 100-way softmax output layer. The networks are trained with different activation functions (ReLUs (Nair & Hinton 2010). TanH, Sig- moid), optimizers (Adam (Kingma & Ba, 2013), Momentum, SGD), learning rates (0.1, 0.01, 0.001) and regularizers (weight decay. natch-normalisation (loffe & Szegedy 2015), dropout (Srivastaval al. 2014b), and entropy regularization (see Appendix B. Ip). The models are trained maximize loo-likkliilee likelihood. All together, we evaluated over 400 different models on the synthetic ME task.
Results. Several representative training runs with different ar- chitectures are shown in Figure 3] An ideal learner that has discovered the one-to-one pattern should have a mutual exclu- sivity of I; for 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 fall along with the training loss (red line). In fact, almost all of the networks acquire a strong anti-mutual exclusivity bias, transitioning from initial neutral bias to placing most or all of the probability mass on familiar outputs (seen in Figure 4 An exception this pat- tern is the entropy regularized model, which maintains a score equivalent to an untrained network. In general, trained models strongly predict that novel input symbol will correspond to known rather than unknown output symbol, in contradiction to ME and the organizing structure of the synthetic data.
Decay :3a-31
Crnrpy
Reguletin
Inttll Score
0.0 0.1
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Figure 4: Ideal and untrained ME scores compared with the ME scores of few learned models.
Further informal experiments suggest our results cannot be reduced to simply not enough data: these architectures do not learn this one-to-on regularity regardless of how many input/output symbols are provided in the training set. Even with thousands training examples demonstrating one-to- one pattem, 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 normalizing the weights, yet ME effect.
unable to find architecture that reliably demonstrated the
3.2 DISCUSSION
The results show that standard neural networks fail to reason by mutual exclusivity when trained in variety of typical settings. The models fail to capture the perfect one-to-one mapping (ME bias) seen in the synthetic data, predicting that new symbols map to familiar outputs in a many-to-man fashion.
Although our focus is on neural networks, this characteristic is not unique to this model class. We posit it more generally affects flexible models trained to maximize log- lieeliiid.ood. In trained network, the optimal activation value for an unused output node is zero: for any given training example, increasing value of unused output simply reduces the available probability mass for the
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Name
Languages
Sentence Pairs
Vocabulary Size
IWSLT'14 (Freiagg et al. WMT 14 Luong et 2015)
2014
Eng. Vietnamese
133K
17K(en), 7K(vi)
Bng.-German
~4.5M
50Kíen); 50K(de)
1M Luong & Manning 2016
Eng--Czech
155.M
50K(en), 50K(es)
Table 1: Datasets used to analyze ME machine translation.
target output. Using other loss functions could result in different outcomes, but we also did not find that weight decay and entropy regularization of reasonable values could fundamentally alter the use of novel outputs. In the next section, we investigate if the lack of ME could hurt performance on common learning tasks such as machine translation and image classification.
4 SHOULD NEURAL NETWORKS REASON BY MUTUAL EXCLUSIVITY?
Mutual exclusivity has implications for variety of common learning settings. Mutual exclusivity arises naturally in lifelong learning settings, which more realistically reflect the "open world" char- acteristics human cognitive development. Unlike epoch- learning, lifelong learning agent does not assume fixed set of concepts and categories. Instead, concepts can be introduced at any point during learning. An intelligent learner should be sensitive to this possibility, and ME is means of intelligently reasoning about the meaning of novel stimuli.
Children and adults learn in an open world with some probability of encountering a new class at any point, resembling the first epoch of training neural net only. Moreover, the distribution of categories neither uniformly distributed nor randomly shuffled (Smith & Slone, (017).. To sim- ulate these characteristics, construct lifelong learning scenarios using standard benchmarks as described below.
4.1 MACHINE TRANSLATION
In this section, investigate if mutual exclusivity could be helpful bias when training machine translation models in lifelong learning paradigm. From the previous experiments, we know that the type of sequence- requence-to-sequenee io-sequence (seq2seq) models used for translation acquire an anti-ME bias over the course of training (see Appendix A). Would translation system benefit from assuming that single word the source sentence maps to single word the target sentence, and vice-versa? This assumption is not always correct since synonymy and polysemy are prevalent in natural languages, and thus the answer to whether or not ME holds is not absolute. Instead, we seek to measure the degree to which this bias holds in lifelong learning real datasets, and compare this bias to the inductive biases of models trained on these datasets. The data for translation provides a somewhat natural distribution over the frequency which different words are observed (there are words that appear much more frequently than the others). This allows us to use a single pass through the dataset proxy for lifelong translation learning.
Datasets. We analyze three common datasets for machine translation, each consisting of pairs of sentences in two languages (Table []. The vocabularies are truncated based on word frequency in accordance with the standard practices for training neural machine translation models (Freitag et al.
2014
Luong et al. 2015 Luong & Manning, 2016).
Mutual exclusivity. There are several ways to operationalize mutual exclusivity in a machine trans- lation setting. Mutual exclusivity could be interpreted as whether new word in the source sentence ("Xylophone" in English) is likely to be translated to new word in the target sentence ("Xylophon" German), as opposed to familiar word. Since the word alignments are difficult to determine and not provided with the datasets, we instead measure reasonable proxy: if new word is encoun- tered in the source sequence, is a new word also encountered in the target sentence? For a source sentence S and arbitrary novel word Ns. and target sentence T and a novel word Ny, we measure a dataset's ME Score as the conditional probability P(Nr E T|Ns E S). hypothetical translation model could compute whether not N₂ E S Sb checking if the present word is ab- sent from the vocabulary-soc casily-computable cue for determining whether not model should expect novel output word.
during the training process. Thus this conditional probability is an
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For the three datasets, consider both forward and backward translation to get six scenarios for analysis. The probability P(Nr E Ty E S) is estimated for a sample of 100 randomly shuffled sequences of the dataset sentence pairs. See Appendix [B3] for details on calculating the base rate P(Nr E TT).
1.0
English to Vietnamese trenslation
P(new in target de new source
Engliihh to German translation
P(ee in target cs new in source-en an)
Figllish C2erh translation
Base Rate Rinew target-vv
Base Rate Pinew targetide
Base Firew targetics)
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0.6
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Pinwe targetoii
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C
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1900
varn vien
1991
varn
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2006
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Senterice Poirs
Pinew target en new in source de)
Pinzw in tar getgge--oe en new in source- (3)
Pinew targge--en new in spurce-vi)
Vietnamese English transiation
German English trans eaannetiion
English trerelation
1.0
Base Rate target-an)
Pinew target on!
Fincw target on!
Sentence Polns Seen
Sentence Pairs Seen
Sentence Pairs Seen
Figure 5: Analysis of mutual exclusivity in machine translation datasets. The plots show the conditional proba- bility of encountering a new word in the target sentence, if a new word is present in the source sentence (y-axis; red line). Also plotted is the base rate of encountering new target word (blue line). These quantities are measured different points during training (x-axis). Errors hars standard deviations.
Results and Discussion. The mea- sures of conditional probability in the six scenarios are shown in Ta- ble [ There is a consistent pat- tern through the trajectory of early learning: the conditional probability P(NT E Ns S) is high initially for thousands of initial sentence pre- sentations, but then wanes as the net- work encounters more samples from the dataset. For a large part of the initial training, seq2seq model would benefit from predicting that previously unseen words in the source language are more likely to map to unseen words in the target language. Moreover, this conditional probability is always higher than the base rate of en- countering new word, indicating that conditioning the novelty of the input provides substantial additional signal for predicting novelty in the output. Nevertheless, even the base rate suggests that model should expect novel words with some regularity in our settings. This is in stark contrast to the synthetic results showing that seq2seq models quickly acquire an anti-ME assumption (see Ap- pendix (A), and their expectation of mapping novel inputs novel outputs decays rapidly as training progresses (Appendix Figure
Score
En- Vi
Vi-En
En-De
De-En
En-Cs
Cs-Ei
0.9
0.3K
2K
4K
3K
4K
3K
0.5
3K
40K
37K
30K
40K
30K
0.1
90K
120K
120K
140K
130
150K
Table 2: Number of sentences after which the ME Score P(Nr
Ti 5) falls below threshold.
4.2 IMAGE CLASSIFICATION
Similar to translation, we examine if object classifiers would benefit from reasoning by mutual exclusivity during training processes that mirror lifelong learning. To study this, when selecting an image for training. we sample the class from power law distribution (see Appendix [B2) such that the model is more likely to see certain classes (Smith & Slone 2017).

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Ideally, would model the probability that an object belongs to novel class based on its similarity to previous samples seen by the model (e.g., outlier detection). Identifying that an image belongs to novel class is non-trivial, and instead we calculate the base rate for classifying an image as "new" while a learner progresses through the dataset. The set of classes not seen by the model are referred to "new" here. This measure the standard training process, since this calculation assumes a blind learner that is unaware of any novelty signal present in the raw image.
be seen as lower bound on the usefulness of ME through
Datasets. This section examines the Omniglot dataset (Lake et al. 2015) and the ImageNet dataset (Deng et al. 2009). The Omniglot dataset has been widely used to study few-shot learning, con- sisting of 1623 classes of handwritten characters with 20 images per class. The ImageNet dataset consists of about 1.2 million images from 1000 different classes.
Mutual exclusivity. To measure ME throughout the training process, we examine if an image encountered for the first time while training belongs class that has not been seen before. This is operationalized as the probability of encountering the number of images seen so far P(N]() (see Appendix B.5 This analysis is agnostic to the content of the image and whether or not it is repeated item; it only matters whether or not the class is novel. As before, the analysis is performed using ten random runs through the dataset.
image from new class N function of
We contrast the statistics of the datasets by comparing them to the ME Score (Equation D of neural network classifiers trained on the datasets. See Appendix [B44 for details about the models and their training procedures. The probability mass assigned to the unseen classes by the network is recorded after each optimizer step, as computed using Equation]
(B.44
Results and Discussion. The results are summarized in aad Table 3 The probability that new image belongs to an unseen class P(N it) higher than the ME score of the classifier through most of the learning phase. Comparing the statistics of the datasets to the inductive biases in the classifiers, the ME score for the clas- sifiers is substantially lower than the baseline ME measure in the dataset, P(N[t) (T).le For instance, the ImageNet classifier drops its ME score below 0.05 after about 8,960 images, while the approximate ME measure for the dataset shows that new classes are en- countered at above this rate until at least 1 110,000 images. We found that higher learning rates can force the probabilities assigned to unseen classes to zero on ImageNet after just a single gradient step.
Score
Omniglot
Omniglot Classifier
Imagenet
Imagenet Classifier
0.2
24,304
2,144
2,048 8,448
1,280
0.1
99,248
22,912
3,072
0.05
160,608
43,328
111,872
8,960
Table 3: Number of images after which the ME Score falls below threshold.
These results suggest that neural classifiers, with their bias favoring frequent rather than infrequent outputs for novel stimuli, are not well-suited lifelong learning challenges where such inferences are critical. Although we examined classifiers trained in an online fashion, we would expect similar results when we train them using replay or epoch-based training setups, where repeated presentation of past examples would only strengthen the anti-ME bias. These classifiers are hurt by their lack of ME and their failure to consider that new stimuli likely map to new classes. Ideally, a learning algo- rithm should be capable of leveraging the image content, combined with its own learning maturity, to decide how strongly it should reason by ME. Instead, standard models and training procedures do not provide these capabilities and do not utilize this important inductive bias observed in cognitive development.
5 GENERAL DISCUSSION
Children use the mutual exclusivity (ME) bias to learn the meaning of new words efficiently, yet standard neural networks learn very differently. Our results show that standard deep learning algo- rithms lack the ability to reason with ME, including feedforward networks and recurrent sequence- to-sequence models trained to maximize log- likelihood with common regularizers. Beyond simply lacking this bias, these networks learn an anti-ME bias, preferring to map novel inputs to familiar and frequent (rather than unfamiliar) output classes. Our results also show that these characteristics
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(new clasaree data point)
2.40
Clessifer 1ate
classjnww data point)
0.14
Chassitte
Figure 6: Analysis of mu- tual exclusivity classification datasets. The plots show the probability that a new input im- age belongs to unseen class P(N[t), as function of the number of images seen so far during training (blue), with its standard deviation. This mea- sure is contrasted with the ME score of a neural network classi- fier trained through a similar run of the dataset (orange).
0.22
Dara
0:25
0.20-
0.08
0:15
0.06
0.10-
0.04
0.25
0.02
Number of samples seen
Number of samples seen
(a) Omniglot
(b) Imagenet
are poorly matched to more realistic lifelong learning scenarios where novel classes can appear at any point, demonstrated in the translation and classification experiments presented here. Neural nets may be currently stymied by their lack of ME bias, ignoring a powerful assumption about the structure of learning tasks.
Mutual exclusivity is relevant elsewhere in machine learning. Recent work has contrasted the ability of humans and neural networks to learn compositional instructions from just one or few examples, finding that neural networks lack the ability to generalize systematically (Lake & Baroni] 2018 Lake ct al. 2019). The authors suggest that people rely on ME in these learning situations (Lake et al., 2019
and thus few-shot learning approaches could be improved by utilizing this bias as well.
In our analyses, we show that neural networks tend to learn the opposite bias, preferring to map novel imputs to familiar outputs. More generally, ME can be generalized from applying to "novel versus familiar" stimuli to instead handling 'rare versus frequent" stimuli (c.g., in translation, rare source words may map to rare target words). The utility of reasoning by ME could be extended to early stages of epoch based learning too. For example, during epoch- based learning, neural networks take longer to acquire rare stimuli and patterns of exceptions (McClelland & Rogers) 2003),, often mishandling these items for many epochs by mapping them to familiar responses. Another direction for future work is studying how the ME bias should interact with hierarchical categorization tasks. We posit that the ME assumption will be increasingly important as learners tackle more continual, lifelong. and acgelsccale&a learning challenges (Mitchell et al.) 2018))
Mutual exclusivity is an open challenge for deep neural networks, but there are promising avenues for progress. The ME bias will not be helpful for every problem, but it is equally clear that the status quo is sub-optimal: models should not have a strong anti-ME bias regardless of the task and dataset demands. Ideally, model would decide autonomously how strongly to use ME (or not) based on the demands of the task. For instance, in our synthetic example, the one-to-one correspondence and use this perfect ME bias as a meta-strategy. If the dataset has more many-to-one correspondences, it would adopt another meta- stratssra This meta-strateyy could even change depending on the stage of learning. yet such an approach is not currently available for training models. Previous cognitive models of word learning have found ways incorporate the ME bias (Kachergis et al., 2012] McMurray et al., [012)] Frank et al.) 22099 Lambert et al.) (005). although in ways that do not generalize to training deep neural networks. While successful some domains, these models are highly simplified or require built-in mechanisms for implementing ME, making them so far impractical for use in realistic settings. As outlined above, it would be ideal to acquire ME bias via meta learning or learning to learn (Allen et al. 2019; Snell et al. 2017), with the advantage of calibrating the bias to the dataset itself rather than assuming its strength a priori. For example, the meta learning model of (Santoro et al.) (2016) seems capable of learning an ME bias, although it was not specifically probed in this way. Recent work by Lake (2 demonstrated that neural nets can learn reason by ME if trained explicitly to do so, showing these abilities are within the repertoire of modern tools. However acquiring ME is just one step toward the goal proposed here: using ME to facilitate efficient lifelong learning or large-scale classification and translation.
ideal learner would discover
In conclusion, standard deep neural networks do not naturally reason by mutual exclusivity, but designing them to do so could lead to faster and more flexible learners. There is a compelling case for building models that learn through mutual exclusivity.
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APPENDIX
A DO SEQUENCE- TO-SUURNCH MODELS REASON BY MUTUAL EXCLUSIVITY?
Synthetic data. We evaluate if different class of models, sequence-to-sequeee (seq2seq) neural networks (Sutskever et al.) 2014), take better advantage of ME structure in the data. This popular class of models is used in machine translation and other natural language processing tasks, and thus the nature of their inductive biases is critical for many applications. As in the previous section, we create synthetic dataset that has perfect ME bias: each symbol in the source maps exactly one symbol in the target. We also have perfect alignment in the dataset, so that each token in the source corresponds to the token at the same position in the target. The task illustrated in Figure 2b] We consider translation from sequences of words to sequences of referent symbols.
The dataset consists of 20 label-referent pairings. Ten pairs are used to train the model and famil- iarize the learning algorithm with the task. The remaining ten pairs were used in the test phase. To train the model, we generate 1000 sequences of words whose lengths range from to 5. To generate sequences for the test phase, words in the training sequences are replaced with new words with probability of 0.2. Thus, 1000 sequences are used to test for ME. The ME score evaluated using T at positions in the output sequence where the corresponding input is new. As shown in Figure [b] the ME score is evaluated in the second position which corresponds to the novel word "dax," " using the probability mass assigned to the unseen output symbols.
Equation
Neural network architectures. We probe a seq2seq model that has a recurrent encoder using Gated Recurrent Units (GRUs) (Cho al. 2014) and a GRU decoder. Both the encoder and decoder had embedding and hidden sizes of 256. Dropout (Srivastava et 2014a) with a probability of 0.5 was used during training. The networks are trained using an Adam (Kingma & Ba 2015) optimizer with a learning rate of 0.001 and a log-likelihode loss. Two versions of the network were trained with and without attention (Luong et al. 2015).
Results. Results are shown in Figure 7 and confirm our findings from the feedforward network. The ME score falls zero within a few training iterations, and the networks fail to assign any substantial probability to the unseen classes. The networks achieve a perfect score on the training set, but cannot extrapolate the one-to-one mappings to unseen symbols. Again, not only do seq2seq models fail to show mutual exclusivity bias, they acquire anti-mulual exclusivity bias that goes against the structure the dataset.
Results for the syn- thetic seq2seq task. The config- urations shown in the setting are (a) Results for a seq2seq GRU without attention (b) Results for a seq2seq GRU with attention.
Figure 7:
1.5
Ideal ME Score Inibal Score
Idea) ME Score Initial Score
Score
LoSS
ME
Epochs
Epochs
(a)
(b)
ADDITIONAL DETAILS
B. ENTROPY REGULARIZER
The entropy regularizer operationalized by subtracting the entropy of prediction from the loss. Thus, the model is penalized for being overly confident about its prediction. We found that the entropy regularizer produces an ME score that stays constant across training, at the cost of the model being less confident about predictions made for seen classes.
B.2 SAMPLING USING A POWER LAW TO SIMULATE LIFELONG LEARNING
To simulate a naturalistic lifelong learning scenario, we try to sample a few classes more frequently than the others. To do this, sample the classes for training using power law distribution. Weights
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assigned to the classes using the following formula,
((c)
c1.5
where e the index of the class. After the class for training is chosen, we uniformly sample from the images of that class for training.
B.3 BASE RATE FOR MACHINE TRANSLATION
The base rate for machine translation is defined as the probability of observing new word in the target at particular time training. We go through the unseen sentences in the corpus from the target language at time / to compute the probability of sampling sentence with at least one new word. Thus, the base rate at time t training defined as:
# of unseen sentences in target with new words of unseen sentences
P(new in target at
B.4 EXPERIMENT DETAILS FOR CLASSIFICATION
For Omniglot, a convolutional neural network trained 1623-way classification. The architec- ture consists of convolutional layers (each consisting of 5 x 5 kernels and 64 feature maps), fully connected layer (576 x 128) and softmax classification layer. was trained with a batch size of 16 using an Adam optimizer and learning rate of 0)001. For Imagenet, a Resnet18 8 model (He et al., 2016) was trained on 1000 way classification with a batch size of 256, using an Adam optimizer and a learning rate of 0.001.
B.5 CALCULATION OF PtN IN CLASSIFICATION
For classification, we calculate the score P(N for the model by adding the probabilities the model assigns to all the "new" (unseen) classes when iterating through the remaining corpus (similar to Equation b. For the dataset, we compute P(N by sampling all unseen images in the corpus and compute the proportion from "new" classes given their ground truth labels.
12


Reviews:
[{"review_id": "SkedBT5ntB", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "*** Increased to weak accept after discussion of merits of ME bias was improved in the paper *** \n\nThis paper investigates whether neural networks exhibit a ‘mutual exclusivity (ME) bias’, whereby novel inputs tend to be associated with previously unseen outputs, an inductive bias that is cited to be present in children when learning to associate new words and objects. Via three different sets of experiments, the authors conclude that, under standard training procedures, neural networks in fact display an anti-ME bias: when faced with a novel input, they tend to assign less probability mass to unobserved outputs than is justified by the incoming data. The authors go on to argue that explicitly designing neural networks to reason by mutual exclusivity could lead to faster and more flexible learning. While the experiments across several domains convincingly show the presence of an anti-ME bias in neural network training, I recommend that the paper be rejected because it falls short in demonstrating to what extent performance could be improved by correcting or reversing this bias. The authors pose an interesting hypothesis, but it would gain a lot of credibility if they could provide an empirical analysis of an algorithm that uses ME reasoning to improve learning in a realistic setting or if they could at least perform some quantitative analysis of the effects of ME bias on task performance for a toy example.\n\nComments / questions:\n* The authors duly acknowledge that ME bias is not necessarily desirable in all circumstances, namely in tasks that feature many-to-one mappings, citing polysemy and synonymy in machine translation as examples. Without an empirical example in a realistic setting, it is hard to judge whether the benefits of introducing an ME bias for better classification of new inputs belonging to new classes can outweigh the negatives via a potential increase in misclassification of those belonging to old classes.\n* For the synthetic dataset one-to-one mapping of one-hot vectors it is clear that an ME bias would incur an advantage for classification on a zero-shot basis, i.e. an increased an accuracy for the first time a new input is observed. Is ME bias considered to be useful here because (i) we care directly about improving this type of zero-shot classification, or is it (ii) because it's implicitly assumed that a better initial prediction will lead to faster learning on these examples?\n    * If it is (i) we care about, then it would be useful to quantify the advantage gained either empirically or analytically. It’s not obvious to me how useful the ME bias would be when there is a large number of classes since the probability assigned to the true novel class with a perfect ME bias would be 1 / (# unseen classes). So at the beginning of training, while there are lots of new classes to benefit from the ME bias, the maximum advantage per example is small, and vice versa at the end of training - how do these conflicting effects balance each other out over the course of training and how do the benefits of ME bias scale with the number of classes? Presumably, whether the benefit scales well will depend on the loss function - in any case, this warrants some analysis/discussion especially given that there are no experiments to test it.\n    * The authors say that “ME can be generalized from applying to 'novel versus familiar’ stimuli to instead handling ‘rare versus frequent’ stimuli” and they cite the fact that neural networks take longer to learn from rare stimuli, suggesting that ME could help for reason (ii) above. It’s not obvious to me that ME bias will provide a significant advantage in a one-shot or few-shot learning setting - i.e. how useful is having made a better initial guess (which is random amongst the unseen classes) after you gain some specific information about the target class? Perhaps the benefit is small relative to that of the one-shot or few-shot information gained - I think this needs to be quantified empirically.\n* It would be interesting to see a more detailed analysis of the predictions of the image classifiers in section 4.2. When a new image is presented, how is the probability mass distributed across previously seen classes versus across unseen ones? From a strategic standpoint, in a scenario where it is difficult to determine whether a new image belongs to a new class or not, could it plausibly be more sensible for the network to make a strong prediction on its best guess out of previously seen classes (that it knows more about) rather than a scattered prediction on the unseen classes? Admittedly this is a difficult question to quantify, but my point is to question whether the anti-ME bias shown in Figure 6 is necessarily suboptimal, given the difficulty of classifying a new image as a new class or not.\n\nMinor comments /questions not affecting review:\n* Is the acronym ME pronounced like the word “me” or is it spelled out “M-E”? If the latter, then all cases of “a ME bias” should be corrected to “an ME bias”.\n* Section 4.2 line 3: “sample the class [for the] from a power law distribution\"", "extra_scores": {"experience_assessment": "I do not know much about this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "S1xAWnjRFH", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Summary:\n\nThis 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.\n\nMy comments:\n\nI very much enjoyed reading this paper. I support accepting this paper. It highlights one of the missing inductive biases in ML and proposes it as a challenge. As the authors also agree, ME bias is missing not just in DNNs. It is the issue of MLE. It would be good to have some non-NN results too. I see this is a challenge for MLE than DNNs.\n\n1. In figure-4 you mention that entropy regularizer helps to keep the initial ME score. Can you elaborate more about the way in which entropy regularizer is used with regular MLE training?\n2. It is not very clear how is the base rate computed in Figure 5. I have a guess. But it is better to explain it in detail.\n3. Section 4.2 need more clarity. For example, what do you mean by classifying the image as “new”? Is “new” a class name? Also, how is P(N|t) computed? Please explain.\n4. Are the authors willing to release the code and data to reproduce the results?\n\nMinor comments:\n\n\n1. Page 3: second para, line 4: “our aim is to study”\n2. Page 5: last line: estimate for -> estimated for\n3. Section 4.2: 3rd line: “the class for the from”\n\n=====================================================\n\nAfter rebuttal: I have read the authors' response and  I stand by my decision.\n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "BklyWIdlcS", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper targets at studying the mutual exclusive bias which existed in children learning, to help understand whether there exists similar bias in deep networks. \n\nIn general, the whole paper tries to tell a very interesting, and good story. The paper is very well organized and written. However, I have the following concerns.\n\n1, the ME problem is quite similar to the concept ontology, e.g. , a “Dalmatian,” a “dog”, or a “mammal”.  So what’s the key difference? Hierarchical learners can avoid this problem.\n\n2, I would say, the SOTA neural networks fundamentally are just representation learned, i.e., feature representation learning. The learned features could in principle be employed to construct advanced learners, .e.g., hierarchical Bayesian. It’s probably a bit unfair or misleading to claim neural networks suffering from ME bias. \n\n3, In Sec. 3, the first and section paragraph, I can not quite understand how the ME bias theory guide the following synthetic experiments. Please give more explanations.\n\n4, in Sec. 3.1, considering the small number of training instances, whether it is large enough to train the NN/ not overfitting issues?\n\n5. Whether the ME bias mostly attributed to the one-hot representation? If one uses word2vec as the representation in NN, the ME bias will be solved. Actually, this is the standard practice in some learning tasks, e.g., zero-shot learning. \n\n6, the experimental design of Sec. 4.2 is also a bit unfair. It seems to me that the tasks are organized as unbalanced instances of each classes, and asking the common NNs to learn this  task. Of course, this common NNs can not address it.\n\n----\nI read the rebuttal. the authors clarified and answered the questions. I would like to raise the score.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper presents an understudied bias known to exist in the learning patterns of children, but not present in trained NN models.  This bias is the mutual exclusivity bias: if the child already knows the word for an object, they can recognize that the object is likely not the referent when a new word is introduced.  So that is, the names of objects are mutually exclusive. 

The authors and reviewers had a healthy discussion. In particular, Reviewer 3 would have liked to have seen a new algorithm or model proposed, as well as an analysis of when ME would help or hurt.  I hope these ideas can be incorporated into a future submission of this paper.
Decision: Reject