Rare Words: A Major Problem for Contextualized Embeddings And How to Fix it by Attentive Mimicking

TL;DR

This paper addresses the challenge of rare words in deep language models like BERT by adapting Attentive Mimicking with a new one-token approximation, significantly improving their understanding of rare words without task-specific fine-tuning.

Contribution

The authors adapt Attentive Mimicking for deep language models with subword tokenization using a novel one-token approximation, enhancing rare word understanding.

Findings

Adding the method improves BERT's rare word comprehension

The approach outperforms baseline models on the new dataset

Rare word semantic properties are better captured after adaptation

Abstract

Pretraining deep neural network architectures with a language modeling objective has brought large improvements for many natural language processing tasks. Exemplified by BERT, a recently proposed such architecture, we demonstrate that despite being trained on huge amounts of data, deep language models still struggle to understand rare words. To fix this problem, we adapt Attentive Mimicking, a method that was designed to explicitly learn embeddings for rare words, to deep language models. In order to make this possible, we introduce one-token approximation, a procedure that enables us to use Attentive Mimicking even when the underlying language model uses subword-based tokenization, i.e., it does not assign embeddings to all words. To evaluate our method, we create a novel dataset that tests the ability of language models to capture semantic properties of words without any task-specific fine-tuning. Using this dataset, we show that adding our adapted version of Attentive Mimicking to BERT does indeed substantially improve its understanding of rare words.

Tables

Table 1. Table 1: Example queries and most probable outputs of BERT for frequent (top) and rare words (bottom)

Q: A lime is a     .	A: lime, lemon, fruit
Q: A bicycle is a     .	A: bicycle, motorcycle, bike
Q: A kumquat is a     .	A: noun, horse, dog
Q: A unicycle is a     .	A: structure, unit, chain

Table 2. Table 2: Example entries from WNLaMPro

Key	Rel.	Targets
new	ant	old
general	ant	specific
local	ant	global
book	hyp	product, publication, …
basketball	hyp	game, ball, sport, …
lingonberry	hyp	fruit, bush, berry, …
samosa	coh+	pizza, sandwich, salad, …
harmonium	coh+	brass, flute, sax, …
immorality	coh+	crime, evil, sin, fraud, …
simluation	cor	simulation
chepmistry	cor	chemistry
pinacle	cor	pinnacle

Table 3. Table 3: Patterns for all relations of WNLaMPro. The indefinite article “a” used in the hyp patterns is replaced with “an” as appropriate.

antonym	hypernym
<W> is the opposite of     .	<W> is a     .
<W> is not     .	a <W> is a     .
someone who is <W> is not     .	“<W>” refers to a     .
something that is <W> is not     .	<W> is a kind of     .
“<W>” is the opposite of “   ” .	a <W> is a kind of     .
corruption	cohyponym+
“<W>” is a misspelling of “   ” .	<W> and     .
“<W>” . did you mean “   ” ?	“<W>” and “   ” .

Table 4. Table 4: The number of entries and mean number of target words for the rare ( r ), medium ( m ), and frequent ( f ) subsets of WNLaMPro

	Subset Size			Mean Targets
Rel.	r	m	f	r	m	f
ant	41	59	266	1.0	1.0	1.0
hyp	1191	1785	4750	4.0	3.9	4.2
coh+	1960	2740	6126	26.0	26.0	25.0
cor	2880	–	–	1.0	–	–

Equations

$$v_{(w,\mathcal{C})}=\alpha \cdot A{v}_{(w,\mathcal{C})}^{\text{context}}+(1-\alpha )\cdot v_{(w,\mathcal{C})}^{\text{form}}$$

$$s(C_1,C_2)=\frac{(M{v}_{C_1})\cdot (M{v}_{C_2}{)}^{\top }}{\sqrt{d}}$$

$$\rho (C)\propto \sum _{C^{\prime }\in \mathcal{C}}s(C,C^{\prime }).$$

$$v_{(w,\mathcal{C})}^{\text{context}}=\sum _{C\in \mathcal{C}}\rho (C)\cdot v_C$$

$${\tilde{h}}_i^l(\mathbf{\ell },\mathbf{e},\mathbf{r})=\{\begin{array}{ll}{h}_i^l(\mathbf{\ell };\mathbf{e};\mathbf{r})& \text{if }i\le |\mathbf{\ell }|\\ h_{i+|\mathbf{e}|}^l(\mathbf{\ell };\mathbf{e};\mathbf{r})& \text{if }i>|\mathbf{\ell }|\end{array}$$

$$\text{OTA}(w)=$$

$$\arg \underset{v\in {\mathbb{R}}^n}{\min }\sum _{({\mathbf{t}}_{\ell },{\mathbf{t}}_r)\in \mathcal{C}}d(e(t(w)),[v]\mid e({\mathbf{t}}_{\ell }),e({\mathbf{t}}_r))$$

$$d(\mathbf{e},\tilde{\mathbf{e}}\mid \mathbf{\ell },\mathbf{r})$$

$$d_i^l(\mathbf{e},\tilde{\mathbf{e}}\mid \mathbf{\ell },\mathbf{r})$$

$$({\mathbf{t}}_{\ell },{\mathbf{t}}_r)=(\text{[CLS]},.\text{[SEP]})$$

$$({\mathbf{t}}_{\ell },{\mathbf{t}}_r)=(\text{[CLS]}{t}_{\ell },t_r.\text{[SEP]})$$

$$\text{rank}(p[k],w)$$

$${\text{precision}}_i(p[k],T)$$

$$\text{rank}(x)$$

$${\text{precision}}_i(x)$$

Full text

1 Introduction

Distributed representations of words are a key component of natural language processing (NLP) systems. In particular, deep contextualized representations learned using an unsupervised language modeling objective (?) have led to large performance gains for a variety of NLP tasks. Recently, several authors have proposed to not only use language modeling for feature extraction, but to fine-tune entire language models for specific tasks (?; ?). Taking up this idea, ? (?) introduced BERT, a bidirectional language model based on the Transformer (?) that has achieved a new state-of-the-art for several NLP tasks.

As demonstrated by ? (?), it is possible for language models to solve a diverse set of tasks to some extent without any form of task-specific fine-tuning. This can be achieved by simply presenting the tasks in form of natural language sentences that are to be completed by the model. The very same idea can also be used to test how well a language model understands a given word: we can “ask” it for properties of that word using natural language. For example, a language model that understands the concept of “guilt” should be able to correctly complete the sentence “Guilt is the opposite of    .” with the word “innocence”.

The examples in Table 1 show that, according to this measure, BERT is indeed able to understand frequent words such as “lime” and “bicycle”: it predicts, among others, that the former is a fruit and the latter is the same as a bike. However, it fails terribly for both “kumquat” and “unicycle”, two less frequent words from the same domains. This poor performance raises the question whether deep language models generally struggle to understand rare words and, if so, how this weakness can be overcome.

To answer this question, we create a novel dataset containing queries like the ones shown in Table 1. This dataset consists of (i) natural language patterns such as

[TABLE]

where <W> is a placeholder for a word to be investigated, and (ii) corresponding pairs of keywords (<W>) and targets (fillers for    ) obtained using semantic relations extracted from WordNet (?).

Using this dataset, we show that BERT indeed fails to understand many rare words. To overcome this limitation, we propose to apply Attentive Mimicking (?), a method that allows us to explicitly learn high-quality representations for rare words. A prerequisite for using this method is to have high-quality embeddings for as many words as possible, because it is trained to reproduce known word embeddings. However, many deep language models including BERT make use of byte-pair encoding (?), WordPiece (?) or similar subword tokenization algorithms. Thus, many words are not represented by a single token but by a sequence of subword tokens and do not have their own embeddings.

To solve this problem, we introduce one-token approximation (OTA), a method that approximately infers what the embedding of an arbitrary word would look like if it were represented by a single token. While we apply this method only to BERT, it can easily be adapted for other language modeling architectures.

In summary, our contributions are as follows:

• •

We introduce WordNet Language Model Probing (WNLaMPro), a novel dataset for evaluating the ability of language models to understand specific words.

• •

Using this dataset, we show that the ability of BERT to understand words depends highly on their frequency.

• •

We present one-token approximation (OTA), a method that obtains an embedding for a multi-token word that has behavior similar to the sequence of its subword embeddings.

• •

We apply OTA and Attentive Mimicking (?) to BERT and show that this substantially improves BERT’s understanding of rare words.

Our work is the first to successfully apply mimicking techniques to contextualized word embeddings.

2 Related Work

Using language modeling as a task to obtain contextualized representations of words was first proposed by ? (?), who train a bidirectional LSTM (?) language model for this task and then feed the so-obtained embeddings into task-specific architectures. Several authors extend this idea by transferring not only word embeddings, but entire language modeling architectures to specific tasks (?; ?; ?). Whereas the GPT model proposed by ? (?) is strictly unidirectional (i.e., it looks only at the left context to predict the next word) and the ULMFiT method of ? (?) uses a shallow concatenation of two unidirectional models, ? (?) design BERT as a deep bidirectional model using a Transformer architecture and a masked language modeling task.

There are roughly two types of approaches for explicitly learning high-quality embeddings of rare words: surface-form-based approaches and context-based approaches. The former use subword information to infer a word’s meaning; this includes $n$-grams (?; ?; ?), morphemes (?; ?) and characters (?). On the other hand, context-based approaches take a look at the words surrounding a given rare word to obtain a representation for it (e.g., ? ?; ? ?). Recently, ? (?) introduced the form-context model, combining both approaches by jointly using surface-form and context information. The form-context model and its Attentive Mimicking variant (?) achieve a new state-of-the-art for high-quality representations of rare words.

Presenting tasks in the form of natural language sentences was recently proposed by ? (?) as part of their Natural Language Decathlon, for which they frame ten different tasks as pairs of natural language questions and answers. They train models on triples of questions, contexts and answers in a supervised fashion. An alternative, completely unsupervised approach proposed by ? (?) is to train a language model on a large corpus, present text specialized for a particular task and then let the model complete this text. They achieve good performance on tasks such as reading comprehension, machine translation and question answering – without any form of task-specific fine-tuning. We use this paradigm for constructing WNLaMPro.

Several existing datasets were designed to analyze the ability of word embeddings to capture semantic relations between words. For example, ? (?) compile the BLESS dataset that covers five different semantic relations (e.g., hyponymy) from multiple sources. ? (?) also create a dataset for semantic relations based on hypernyms and hyponyms using WordNet (?). However, these datasets differ from WNLaMPro in two important respects. (i) They focus on frequent words by filtering out infrequent ones whereas we explicitly want to analyze rare words. (ii) They do not provide natural language patterns: they either directly evaluate (uncontextualized) word embeddings using a similarity measure such as cosine distance or they frame the task of identifying the relationship between two words as a supervised task.

3 Attentive Mimicking

3.1 Original Model

Attentive Mimicking (AM) (?) is a method that, given a set of $d$-dimensional high-quality embeddings for frequent words, can be used to infer embeddings for infrequent words that are appropriate for the given embedding space. AM is an extension of the form-context model (?).

The key idea of the form-context model is to compute two distinct embeddings per word, where the first one exclusively uses the word’s surface-form and the other the word’s contexts, i.e., sentences in which the word was observed. Given a word $w$ and a set of contexts $\mathcal{C}$, the surface-form embedding $v_{(w,\mathcal{C})}^{\text{form}}\in\mathbb{R}^{d}$ is obtained by averaging over learned embeddings of all $n$-grams in $w$; the context embedding $v_{(w,\mathcal{C})}^{\text{context}}\in\mathbb{R}^{d}$ is the average over the known embeddings of all context words.

The final representation $v_{(w,\mathcal{C})}$ of $w$ is then a weighted sum of form embeddings and transformed context embeddings:

[TABLE]

where $A$ is a $d\times d$ matrix and $\alpha$ is a function of both embeddings, allowing the model to decide when to rely on the word’s surface form and when on its contexts (see ? (?) for further details).

While the form-context model treats all contexts equally, AM extends it with a self-attention mechanism that is applied to all contexts, allowing the model to distinguish informative from uninformative contexts. The attention weight of each context is determined based on the idea that given a word $w$, two informative contexts $C_{1}$ and $C_{2}$ (i.e., contexts from which the meaning of $w$ can be inferred) resemble each other more than two randomly chosen contexts in which $w$ occurs. In other words, if many contexts for a word $w$ are similar to each other, then it is reasonable to assume that they are more informative with respect to $w$ than other contexts. ? (?) define the similarity between two contexts as

[TABLE]

with $M\in\mathbb{R}^{d\times d}$ a learnable parameter and $v_{C}$ denotes the average of embeddings for all words in a context $C$. The weight of a context is then defined as

[TABLE]

with $\sum_{C\in\mathcal{C}}\rho(C)=1$. This results in the final context embedding

[TABLE]

where again, $v_{C}$ denotes the average of the embeddings of all words in a context $C$.

Similar to earlier models (e.g., ? ?), the model is trained through mimicking. That is, we randomly sample words $w$ and corresponding contexts $\mathcal{C}$ from a large corpus and, given $w$ and $\mathcal{C}$, ask the model to mimic the original embedding of $w$, i.e., to minimize the squared Euclidean distance between the original embedding and $v_{(w,\mathcal{C})}$.

3.2 AM+context

As we found in preliminary experiments that AM focuses heavily on the word’s surface form – an observation that is in line with results reported by ? (?) –, in addition to the default AM configuration of ? (?), we investigate another configuration AM+context, which pushes the model to put more emphasis on a word’s contexts. This is achieved by (i) increasing the minimum number of sampled contexts for each training instance from $1$ to $8$ and (ii) introducing $n$-gram dropout: during training, we randomly remove $10\%$ of all surface-form $n$-grams for each training instance.

4 One-Token Approximation

As AM is trained through mimicking, it must be given high-quality embeddings of many words to learn how to make appropriate use of form and context information. Unfortunately, as many deep language models make use of subword-based tokenization, they assign embeddings to comparably few words. To overcome this limitation, we introduce one-token approximation (OTA). OTA finds an embedding for a multi-token word or phrase $w$ that is similar to the embedding that $w$ would have received if it had been a single token. This allows us to train AM in the usual way by simply mimicking the OTA-based embeddings of multi-token words.

Let $\Sigma$ denote the set of all characters and $\mathcal{T}\subset\Sigma^{*}$ the set of all tokens used by the language model. Furthermore, let ${t:\Sigma^{*}\rightarrow\mathcal{T}^{*}}$ be the tokenization function that splits each word into a sequence of tokens and $e:\mathcal{T}\rightarrow\mathbb{R}^{d}$ the model’s token embedding function, which we extend to sequences of tokens in the natural way as $e([t_{1},\ldots,t_{n}])=[e(t_{1}),\ldots,e(t_{n})]$.

We assume that the language model internally consists of $l_{\text{max}}$ hidden layers and given a sequence of token embeddings $\boldsymbol{e}=[e_{1},\ldots,e_{n}]$, we denote by $h_{i}^{l}(\boldsymbol{e})$ the contextualized representation of the $i$-th input embedding $e_{i}$ at layer $l$. Given two additional sequences of left and right embeddings $\boldsymbol{\ell}$ and $\boldsymbol{r}$, we define

[TABLE]

where $a;b$ denotes the concatenation of sequences $a$ and $b$. That is, we “cut out” the sequence $\boldsymbol{e}$ and $\tilde{h}_{i}^{l}(\boldsymbol{\ell},\boldsymbol{e},\boldsymbol{r})$ is then the embedding of the $i$-th input at layer $l$, either from $\boldsymbol{\ell}$ (if position $i$ is before $\boldsymbol{e}$) or from $\boldsymbol{r}$ (if position $i$ is after $\boldsymbol{e}$).

To obtain an OTA embedding for an arbitrary word $w\in\Sigma^{*}$, we require a set of left and right contexts $\mathcal{C}\subset\mathcal{T}^{*}\times\mathcal{T}^{*}$. Given one such context $c=(\mathbf{t}_{\ell},\mathbf{t}_{r})$, the key idea of OTA is to search for the embedding $v\in\mathbb{R}^{d}$ whose influence on the contextualized representations of $\mathbf{t}_{\ell}$ and $\mathbf{t}_{r}$ is as similar as possible to the influence of $w$’s original, multi-token representation on both sequences. That is, when we apply the language model to the sequences ${s_{1}=[e(\mathbf{t}_{\ell});e(t(w));e(\mathbf{t}_{r})]}$ and ${s_{2}=[e(\mathbf{t}_{\ell});[v];e(\mathbf{t}_{r})]}$, we want the contextualized representations of $\mathbf{t}_{\ell}$ and $\mathbf{t}_{r}$ in $s_{1}$ to be as similar as possible to those in $s_{2}$.

Formally, we define the one-token approximation of $w$ as

[TABLE]

where

[TABLE]

That is, given an input sequence $[\boldsymbol{\ell};\boldsymbol{e};\boldsymbol{r}]$, $d_{i}^{l}(\boldsymbol{e},\tilde{\boldsymbol{e}}\mid\boldsymbol{\ell},\boldsymbol{r})$ measures the influence of replacing $\boldsymbol{e}$ with $\tilde{\boldsymbol{e}}$ on the contextualized representation of the $i$-th word in the $l$-th layer.

As $d(\boldsymbol{e},\tilde{\boldsymbol{e}}\mid\boldsymbol{\ell},\boldsymbol{r})$ is differentiable with respect to $\tilde{\boldsymbol{e}}$, we can use gradient-based optimization to estimate $\text{OTA}(w)$. This idea resembles the approach of ? (?) to infer paragraph vectors for sequences of arbitrary length.

With regards to the choice of contexts $\mathcal{C}$, we define two variants, both of which do not require any additional information: static and random. For the static variant, $\mathcal{C}$ consists of a single context

[TABLE]

with [CLS] and [SEP] being BERT’s classification and separation token, respectively. We use this particular context because in pretraining, BERT is exposed exclusively to sequences starting with [CLS] and ending with [SEP].

As the meaning of a word can often better be understood by looking at its interaction with other words, we surmise that OTA works better when we provide variable contexts in which different words occur. For this reason, we also investigate the random variant. In this variant, each pair $(\mathbf{t}_{\ell},\mathbf{t}_{r})\in\mathcal{C}$ is of the form

[TABLE]

where $t_{\ell}$ and $t_{r}$ are uniformly sampled tokens from $\mathcal{T}$, under the constraint that each of them represent an actual word.

5 WordNet Language Model Probing

In order to assess the ability of language models to understand words as a function of their frequency, we introduce the WordNet Language Model Probing (WNLaMPro) dataset.111The WNLaMPro dataset is publicly available at https://github.com/timoschick/am-for-bert This dataset consists of two parts:

• •

a set of triples $(k,r,T)$ where $k$ is a keyword, $r$ is a relation and $T$ is a set of target words;

• •

a set of patterns $P(r)$ for each relation $r$, where each pattern is a sequence of tokens that contains exactly one keyword placeholder <W> and one target placeholder    .

The dataset contains four different kinds of relations: antonym (ant), hypernym (hyp), cohyponym+ (coh+) and corruption (cor). Examples of dataset entries for all relations are shown in Table 2; the set of patterns for each relation can be seen in Table 3.

We split the dataset into a development and a test set. For each relation, we randomly select $10\%$ of all entries to be included in the development set; the remaining $90\%$ form the test set. We purposefully do not provide a training set as WNLaMPro  is meant to be used without task-specific fine-tuning. We also define three subsets based on keyword counts in WWC: WNLaMPro-rare, containing all words that occur less than 10 times, WNLaMPro-medium, containing all words that occur 10 or more times, but less than 100 times, and WNLaMPro-frequent, containing all remaining words. Statistics about the sizes of these subsets and the mean number of target words per relation are listed in Table 4.

For creating WNLaMPro, we use WordNet (?) to obtain triples $(k,r,T)$. To this end, we denote by $\mathcal{V}$ the vocabulary of all words that occur at least once in the Westbury Wikipedia Corpus (WWC) (?) and match the regular expression [a–z.-]*. The set of all tokens in the BERT vocabulary is denoted by $\mathcal{T}$. For all triplets, we restrict the set of target words to single-token words from $\mathcal{T}$. This allows us to measure BERT’s performance for each keyword $k$ without the conflating influence of rare or multi-subword words on the target side.

5.1 Antonyms

For each adjective $w\in\mathcal{V}$, we collect all antonyms for its most frequent WordNet sense in a set $A$ and, if $A\cap\mathcal{T}\neq\emptyset$, add $(w,\textsc{antonym},A\cap\mathcal{T})$ to the dataset.

5.2 Hypernyms

For each noun $w\in\mathcal{V}$, let $H$ be the set of all hypernyms for its two most frequent senses. As direct hypernyms are sometimes highly specific (e.g., the hypernym of “dog” is “canine”), we include all hypernyms whose path distance to $w$ is at most 3. To avoid the inclusion of very general terms such as “object” or “unit”, we restrict $H$ to hypernyms that have a minimum depth of 6 in the WordNet hierarchy. If $|H\cap\mathcal{T}|\geq 3$, we add $(w,\textsc{hypernym},H\cap\mathcal{T})$ to the dataset. However, if $|H\cap\mathcal{T}|>20$, we keep only the $20$ most frequent target words.

5.3 Cohyponyms+

For each noun $w\in\mathcal{V}$, we compute its set of hypernyms $H$ as described above (but with a maximum path distance of 2), and denote by $C$ the union of all hyponyms for each hypernym in $H$ with a maximum path distance of 4.222Cohyponyms are defined to have a common parent. Our more general definition (having a common ancestor) gives us a test that has more coverage than a restriction to cohyponyms in a strict sense would have. We call our generalization “cohyponym+”. Let $C^{\prime}=(C\setminus\{w\})\cap\mathcal{T}$. If ${|C^{\prime}|\geq 10}$, we add the corresponding tuple $(w,\textsc{cohyponym+},C^{\prime})$ to the dataset. If $|C^{\prime}|>50$, we keep only the $50$ most frequent target words.

5.4 Corruptions

We include this relation to investigate a model’s ability to deal with corruptions of the input that may, for example, be the result of typing errors or errors in optical character recognition. To obtain corrupted words, we take frequent words from $\mathcal{V}\cap\mathcal{T}$ and randomly apply corruptions similar to the ones used by ? (?) and ? (?), but we apply them on the character level. Specifically, given a word $w=c_{1}\ldots c_{n}$, we create a corrupted version $\tilde{w}$ by either (i) inserting a random character $c$ after a random position $i\in[0,n]$, (ii) removing a character at a random position $i\in[1,n]$ or (iii) switching the characters $c_{i}$ and $c_{i+1}$ for a random position $i\in[1,n-1]$. We then add $(\tilde{w},\textsc{corruption},w)$ to the dataset.

6 Experiments

For our evaluation of BERT on WNLaMPro, we use the Transformers library of ? (?). Our implementation of OTA is based on PyTorch (?).333Our implementation of OTA is publicly available at https://github.com/timoschick/one-token-approximation For all of our experiments involving AM, we use the original implementation of ? (?). As WNLaMPro is based on WordNet, all of our experiments are confined to the English language.

6.1 One-Token Approximation

We first compare the static and random context variants of OTA and determine the optimal number of training iterations. To this end, we form a development set by randomly selecting 1000 one-token words from the BERT vocabulary. For each word $w$ in this set, we measure the quality of its approximation $\text{OTA}(w)$ by comparing it to its BERT embedding $e(w)$, using cosine distance. We initialize the OTA vector of each word as a zero vector and optimize it using Adam (?) with an initial learning rate of $10^{-3}$. For both context variants, we search for the ideal number of iterations in the range $\{100\cdot i\mid 1\leq i\leq 50\}$.

Results can be seen in Figure 1. While for both variants, the average cosine distance between BERT’s embeddings and their OTA equivalents is relatively high in the beginning – which is simply due to the fact that all OTA embeddings are initialized randomly – after only a few iterations random consistently outperforms static.444The difference between the best results achieved using random and static is statistically significant in a two-sided binomial test ($p<0.05$). For the random variant, the average cosine distance reaches its minimum at 4000 iterations. We therefore use random contexts with 4000 iterations in our following experiments.

6.2 Evaluation on WNLaMPro

To measure the performance of a language model on WNLaMPro, we proceed as follows. Let $x=(k,r,T)$ be a dataset entry, $w\in T$ a target word, $p\in P(r)$ a pattern and $p[k]$ the same pattern where the keyword placeholder <W> is replaced by $k$. Furthermore, let $(a_{1},\ldots,a_{n})$ be the model’s responses (sorted in descending order by their probability) when it is asked to predict a replacement word for the target placeholder in $p[k]$. Then there is some $j$ such that $a_{j}=w$. We denote with

[TABLE]

the rank of $w$ and precision at $i$ when the model is queried with $p[k]$.555We only look at the first $100$ system responses and set $\text{rank}(p[k],w)=\infty$ if $w\notin\{a_{1},\ldots,a_{100}\}$. We may then define:

[TABLE]

That is, for each triplet $x$, we compute the best rank and precision that can be achieved using any pattern. We do so because our interest is not in testing the model’s ability to understand a given pattern, but its ability to understand a given word: by letting the model choose the best pattern for each word, we minimize the probability that its response is of poor quality simply because it did not understand a given pattern.

We evaluate the uncased version of $\text{BERT}_{\textsc{base}}$ (?) on WNLaMPro to get an impression of (i) the model’s general ability to understand the presented phrases and (ii) the difference in performance for rare and frequent words. To investigate how well OTA does at obtaining single embeddings for multi-token words, we also try a variant of BERT where all multi-token keywords are replaced with their one-token approximations. Furthermore, we compare OTA against the following baseline strategies for obtaining single embeddings for multi-token words $w=t_{1},\ldots,t_{n}$:

• •

first: We use the embedding of the first token, $e(t_{1})$.

• •

last: We use the embedding of the last token, $e(t_{n})$.

• •

avg: We use the average over the embeddings of all tokens, $\frac{1}{n}\sum_{i=1}^{n}e(t_{i})$.

We choose these particular baselines because they are natural choices for obtaining a word embedding from a sequence of subword embeddings without any advanced computation.

The mean reciprocal rank (MRR) over WNLaMPro can be seen in Figure 2 for $\text{BERT}_{\textsc{base}}$, OTA and all baselines. We can see that for all models, the score depends heavily on the word frequency. Notably, OTA performs much better than all of the above baselines, regardless of word frequency. Furthermore, the difference in performance between OTA’s single embeddings and BERT’s original, multi-token embeddings is only marginal, allowing us to conclude that OTA is indeed able to infer single-token embeddings of decent quality for multi-token words.