Introduction
Despite the rapid progress of deep learning techniques on diverse supervised learning tasks, these models remain brittle to subtle shifts in the data distribution. Even when the permissible changes are confined to barely-perceptible perturbations, training robust models remains an open challenge. Following the discovery that imperceptible attacks could cause image recognition models to misclassify examples BIBREF0 , a veritable sub-field has emerged in which authors iteratively propose attacks and countermeasures.
For all the interest in adversarial computer vision, these attacks are rarely encountered outside of academic research. However, adversarial misspellings constitute a longstanding real-world problem. Spammers continually bombard email servers, subtly misspelling words in efforts to evade spam detection while preserving the emails' intended meaning BIBREF1 , BIBREF2 . As another example, programmatic censorship on the Internet has spurred communities to adopt similar methods to communicate surreptitiously BIBREF3 .
In this paper, we focus on adversarially-chosen spelling mistakes in the context of text classification, addressing the following attack types: dropping, adding, and swapping internal characters within words. These perturbations are inspired by psycholinguistic studies BIBREF4 , BIBREF5 which demonstrated that humans can comprehend text altered by jumbling internal characters, provided that the first and last characters of each word remain unperturbed.
First, in experiments addressing both BiLSTM and fine-tuned BERT models, comprising four different input formats: word-only, char-only, word+char, and word-piece BIBREF6 , we demonstrate that an adversary can degrade a classifier's performance to that achieved by random guessing. This requires altering just two characters per sentence. Such modifications might flip words either to a different word in the vocabulary or, more often, to the out-of-vocabulary token UNK. Consequently, adversarial edits can degrade a word-level model by transforming the informative words to UNK. Intuitively, one might suspect that word-piece and character-level models would be less susceptible to spelling attacks as they can make use of the residual word context. However, our experiments demonstrate that character and word-piece models are in fact more vulnerable. We show that this is due to the adversary's effective capacity for finer grained manipulations on these models. While against a word-level model, the adversary is mostly limited to UNK-ing words, against a word-piece or character-level model, each character-level add, drop, or swap produces a distinct input, providing the adversary with a greater set of options.
Second, we evaluate first-line techniques including data augmentation and adversarial training, demonstrating that they offer only marginal benefits here, e.g., a BERT model achieving $90.3$ accuracy on a sentiment classification task, is degraded to $64.1$ by an adversarially-chosen 1-character swap in the sentence, which can only be restored to $69.2$ by adversarial training.
Third (our primary contribution), we propose a task-agnostic defense, attaching a word recognition model that predicts each word in a sentence given a full sequence of (possibly misspelled) inputs. The word recognition model's outputs form the input to a downstream classification model. Our word recognition models build upon the RNN-based semi-character word recognition model due to BIBREF7 . While our word recognizers are trained on domain-specific text from the task at hand, they often predict UNK at test time, owing to the small domain-specific vocabulary. To handle unobserved and rare words, we propose several backoff strategies including falling back on a generic word recognizer trained on a larger corpus. Incorporating our defenses, BERT models subject to 1-character attacks are restored to $88.3$ , $81.1$ , $78.0$ accuracy for swap, drop, add attacks respectively, as compared to $69.2$ , $63.6$ , and $50.0$ for adversarial training
Fourth, we offer a detailed qualitative analysis, demonstrating that a low word error rate alone is insufficient for a word recognizer to confer robustness on the downstream task. Additionally, we find that it is important that the recognition model supply few degrees of freedom to an attacker. We provide a metric to quantify this notion of sensitivity in word recognition models and study its relation to robustness empirically. Models with low sensitivity and word error rate are most robust.
Related Work
Several papers address adversarial attacks on NLP systems. Changes to text, whether word- or character-level, are all perceptible, raising some questions about what should rightly be considered an adversarial example BIBREF8 , BIBREF9 . BIBREF10 address the reading comprehension task, showing that by appending distractor sentences to the end of stories from the SQuAD dataset BIBREF11 , they could cause models to output incorrect answers. Inspired by this work, BIBREF12 demonstrate an attack that breaks entailment systems by replacing a single word with either a synonym or its hypernym. Recently, BIBREF13 investigated the problem of producing natural-seeming adversarial examples, noting that adversarial examples in NLP are often ungrammatical BIBREF14 .
In related work on character-level attacks, BIBREF8 , BIBREF15 explored gradient-based methods to generate string edits to fool classification and translation systems, respectively. While their focus is on efficient methods for generating adversaries, ours is on improving the worst case adversarial performance. Similarly, BIBREF9 studied how synthetic and natural noise affects character-level machine translation. They considered structure invariant representations and adversarial training as defenses against such noise. Here, we show that an auxiliary word recognition model, which can be trained on unlabeled data, provides a strong defense.
Spelling correction BIBREF16 is often viewed as a sub-task of grammatical error correction BIBREF17 , BIBREF18 . Classic methods rely on a source language model and a noisy channel model to find the most likely correction for a given word BIBREF19 , BIBREF20 . Recently, neural techniques have been applied to the task BIBREF7 , BIBREF21 , which model the context and orthography of the input together. Our work extends the ScRNN model of BIBREF7 .
Robust Word Recognition
To tackle character-level adversarial attacks, we introduce a simple two-stage solution, placing a word recognition model ( $W$ ) before the downstream classifier ( $C$ ). Under this scheme, all inputs are classified by the composed model $C \circ W$ . This modular approach, with $W$ and $C$ trained separately, offers several benefits: (i) we can deploy the same word recognition model for multiple downstream classification tasks/models; and (ii) we can train the word recognition model with larger unlabeled corpora.
Against adversarial mistakes, two important factors govern the robustness of this combined model: $W$ 's accuracy in recognizing misspelled words and $W$ 's sensitivity to adversarial perturbations on the same input. We discuss these aspects in detail below.
ScRNN with Backoff
We now describe semi-character RNNs for word recognition, explain their limitations, and suggest techniques to improve them.
Inspired by the psycholinguistic studies BIBREF5 , BIBREF4 , BIBREF7 proposed a semi-character based RNN (ScRNN) that processes a sentence of words with misspelled characters, predicting the correct words at each step. Let $s = \lbrace w_1, w_2, \dots , w_n\rbrace $ denote the input sentence, a sequence of constituent words $w_i$ . Each input word ( $w_i$ ) is represented by concatenating (i) a one hot vector of the first character ( $\mathbf {w_{i1}}$ ); (ii) a one hot representation of the last character ( $\mathbf {w_{il}}$ , where $l$ is the length of word $w_i$ ); and (iii) a bag of characters representation of the internal characters ( $\sum _{j=2}^{l-1}\mathbf {w_{ij}})$ . ScRNN treats the first and the last characters individually, and is agnostic to the ordering of the internal characters. Each word, represented accordingly, is then fed into a BiLSTM cell. At each sequence step, the training target is the correct corresponding word (output dimension equal to vocabulary size), and the model is optimized with cross-entropy loss.
While BIBREF7 demonstrate strong word recognition performance, a drawback of their evaluation setup is that they only attack and evaluate on the subset of words that are a part of their training vocabulary. In such a setting, the word recognition performance is unreasonably dependent on the chosen vocabulary size. In principle, one can design models to predict (correctly) only a few chosen words, and ignore the remaining majority and still reach 100% accuracy. For the adversarial setting, rare and unseen words in the wild are particularly critical, as they provide opportunities for the attackers. A reliable word-recognizer should handle these cases gracefully. Below, we explore different ways to back off when the ScRNN predicts UNK (a frequent outcome for rare and unseen words):
Pass-through: word-recognizer passes on the (possibly misspelled) word as is.
Backoff to neutral word: Alternatively, noting that passing $\colorbox {gray!20}{\texttt {UNK}}$ -predicted words through unchanged exposes the downstream model to potentially corrupted text, we consider backing off to a neutral word like `a', which has a similar distribution across classes.
Backoff to background model: We also consider falling back upon a more generic word recognition model trained upon a larger, less-specialized corpus whenever the foreground word recognition model predicts UNK. Figure 1 depicts this scenario pictorially.
Empirically, we find that the background model (by itself) is less accurate, because of the large number of words it is trained to predict. Thus, it is best to train a precise foreground model on an in-domain corpus and focus on frequent words, and then to resort to a general-purpose background model for rare and unobserved words. Next, we delineate our second consideration for building robust word-recognizers.
Model Sensitivity
In computer vision, an important factor determining the success of an adversary is the norm constraint on the perturbations allowed to an image ( $|| \bf x - \bf x^{\prime }||_{\infty } < \epsilon $ ). Higher values of $\epsilon $ lead to a higher chance of mis-classification for at least one $\bf x^{\prime }$ . Defense methods such as quantization BIBREF22 and thermometer encoding BIBREF23 try to reduce the space of perturbations available to the adversary by making the model invariant to small changes in the input.
In NLP, we often get such invariance for free, e.g., for a word-level model, most of the perturbations produced by our character-level adversary lead to an UNK at its input. If the model is robust to the presence of these UNK tokens, there is little room for an adversary to manipulate it. Character-level models, on the other hand, despite their superior performance in many tasks, do not enjoy such invariance. This characteristic invariance could be exploited by an attacker. Thus, to limit the number of different inputs to the classifier, we wish to reduce the number of distinct word recognition outputs that an attacker can induce, not just the number of words on which the model is “fooled”. We denote this property of a model as its sensitivity.
We can quantify this notion for a word recognition system $W$ as the expected number of unique outputs it assigns to a set of adversarial perturbations. Given a sentence $s$ from the set of sentences $\mathcal {S}$ , let $A(s) = {s_1}^{\prime } , {s_2}^{\prime }, \dots , {s_n}^{\prime }$ denote the set of $n$ perturbations to it under attack type $A$ , and let $V$ be the function that maps strings to an input representation for the downstream classifier. For a word level model, $V$ would transform sentences to a sequence of word ids, mapping OOV words to the same UNK ID. Whereas, for a char (or word+char, word-piece) model, $V$ would map inputs to a sequence of character IDs. Formally, sensitivity is defined as
$$S_{W,V}^A=\mathbb {E}_{s}\left[\frac{\#_{u}(V \circ W({s_1}^{\prime }), \dots , V \circ W({s_n}^{\prime }))}{n}\right] ,$$   (Eq. 12)
where $V \circ W (s_i)$ returns the input representation (of the downstream classifier) for the output string produced by the word-recognizer $W$ using $s_i$ and $\#_{u}(\cdot )$ counts the number of unique arguments.
Intuitively, we expect a high value of $S_{W, V}^A$ to lead to a lower robustness of the downstream classifier, since the adversary has more degrees of freedom to attack the classifier. Thus, when using word recognition as a defense, it is prudent to design a low sensitivity system with a low error rate. However, as we will demonstrate, there is often a trade-off between sensitivity and error rate.
Synthesizing Adversarial Attacks
Suppose we are given a classifier $C: \mathcal {S} \rightarrow \mathcal {Y}$ which maps natural language sentences $s \in \mathcal {S}$ to a label from a predefined set $y \in \mathcal {Y}$ . An adversary for this classifier is a function $A$ which maps a sentence $s$ to its perturbed versions $\lbrace s^{\prime }_1, s^{\prime }_2, \ldots , s^{\prime }_{n}\rbrace $ such that each $s^{\prime }_i$ is close to $s$ under some notion of distance between sentences. We define the robustness of classifier $C$ to the adversary $A$ as:
$$R_{C,A} = \mathbb {E}_s \left[\min _{s^{\prime } \in A(s)} \mathbb {1}[C(s^{\prime }) = y]\right],$$   (Eq. 14)
where $y$ represents the ground truth label for $s$ . In practice, a real-world adversary may only be able to query the classifier a few times, hence $R_{C,A}$ represents the worst-case adversarial performance of $C$ . Methods for generating adversarial examples, such as HotFlip BIBREF8 , focus on efficient algorithms for searching the $\min $ above. Improving $R_{C,A}$ would imply better robustness against all these methods.
We explore adversaries which perturb sentences with four types of character-level edits:
(1) Swap: swapping two adjacent internal characters of a word. (2) Drop: removing an internal character of a word. (3) Keyboard: substituting an internal character with adjacent characters of QWERTY keyboard (4) Add: inserting a new character internally in a word. In line with the psycholinguistic studies BIBREF5 , BIBREF4 , to ensure that the perturbations do not affect human ability to comprehend the sentence, we only allow the adversary to edit the internal characters of a word, and not edit stopwords or words shorter than 4 characters.
For 1-character attacks, we try all possible perturbations listed above until we find an adversary that flips the model prediction. For 2-character attacks, we greedily fix the edit which had the least confidence among 1-character attacks, and then try all the allowed perturbations on the remaining words. Higher order attacks can be performed in a similar manner. The greedy strategy reduces the computation required to obtain higher order attacks, but also means that the robustness score is an upper bound on the true robustness of the classifier.
Experiments and Results
In this section, we first discuss our experiments on the word recognition systems.
Word Error Correction
Data: We evaluate the spell correctors from § "Robust Word Recognition" on movie reviews from the Stanford Sentiment Treebank (SST) BIBREF24 . The SST dataset consists of 8544 movie reviews, with a vocabulary of over 16K words. As a background corpus, we use the IMDB movie reviews BIBREF25 , which contain 54K movie reviews, and a vocabulary of over 78K words. The two datasets do not share any reviews in common. The spell-correction models are evaluated on their ability to correct misspellings. The test setting consists of reviews where each word (with length $\ge 4$ , barring stopwords) is attacked by one of the attack types (from swap, add, drop and keyboard attacks). In the all attack setting, we mix all attacks by randomly choosing one for each word. This most closely resembles a real world attack setting.
In addition to our word recognition models, we also compare to After The Deadline (ATD), an open-source spell corrector. We found ATD to be the best freely-available corrector. We refer the reader to BIBREF7 for comparisons of ScRNN to other anonymized commercial spell checkers.
For the ScRNN model, we use a single-layer Bi-LSTM with a hidden dimension size of 50. The input representation consists of 198 dimensions, which is thrice the number of unique characters (66) in the vocabulary. We cap the vocabulary size to 10K words, whereas we use the entire vocabulary of 78470 words when we backoff to the background model. For training these networks, we corrupt the movie reviews according to all attack types, i.e., applying one of the 4 attack types to each word, and trying to reconstruct the original words via cross entropy loss.
We calculate the word error rates (WER) of each of the models for different attacks and present our findings in Table 2 . Note that ATD incorrectly predicts $11.2$ words for every 100 words (in the `all' setting), whereas, all of the backoff variations of the ScRNN reconstruct better. The most accurate variant involves backing off to the background model, resulting in a low error rate of $6.9\%$ , leading to the best performance on word recognition. This is a $32\%$ relative error reduction compared to the vanilla ScRNN model with a pass-through backoff strategy. We can attribute the improved performance to the fact that there are $5.25\%$ words in the test corpus that are unseen in the training corpus, and are thus only recoverable by backing off to a larger corpus. Notably, only training on the larger background corpus does worse, at $8.7\%$ , since the distribution of word frequencies is different in the background corpus compared to the foreground corpus.
Robustness to adversarial attacks
We use sentiment analysis and paraphrase detection as downstream tasks, as for these two tasks, 1-2 character edits do not change the output labels.
For sentiment classification, we systematically study the effect of character-level adversarial attacks on two architectures and four different input formats. The first architecture encodes the input sentence into a sequence of embeddings, which are then sequentially processed by a BiLSTM. The first and last states of the BiLSTM are then used by the softmax layer to predict the sentiment of the input. We consider three input formats for this architecture: (1) Word-only: where the input words are encoded using a lookup table; (2) Char-only: where the input words are encoded using a separate single-layered BiLSTM over their characters; and (3) Word $+$ Char: where the input words are encoded using a concatenation of (1) and (2) .
The second architecture uses the fine-tuned BERT model BIBREF26 , with an input format of word-piece tokenization. This model has recently set a new state-of-the-art on several NLP benchmarks, including the sentiment analysis task we consider here. All models are trained and evaluated on the binary version of the sentence-level Stanford Sentiment Treebank BIBREF24 dataset with only positive and negative reviews.
We also consider the task of paraphrase detection. Here too, we make use of the fine-tuned BERT BIBREF26 , which is trained and evaluated on the Microsoft Research Paraphrase Corpus (MRPC) BIBREF27 .
Two common methods for dealing with adversarial examples include: (1) data augmentation (DA) BIBREF28 ; and (2) adversarial training (Adv) BIBREF29 . In DA, the trained model is fine-tuned after augmenting the training set with an equal number of examples randomly attacked with a 1-character edit. In Adv, the trained model is fine-tuned with additional adversarial examples (selected at random) that produce incorrect predictions from the current-state classifier. The process is repeated iteratively, generating and adding newer adversarial examples from the updated classifier model, until the adversarial accuracy on dev set stops improving.
In Table 3 , we examine the robustness of the sentiment models under each attack and defense method. In the absence of any attack or defense, BERT (a word-piece model) performs the best ( $90.3\%$ ) followed by word+char models ( $80.5\%$ ), word-only models ( $79.2\%$ ) and then char-only models ( $70.3\%$ ). However, even single-character attacks (chosen adversarially) can be catastrophic, resulting in a significantly degraded performance of $46\%$ , $57\%$ , $59\%$ and $33\%$ , respectively under the `all' setting.
Intuitively, one might suppose that word-piece and character-level models would be more robust to such attacks given they can make use of the remaining context. However, we find that they are the more susceptible. To see why, note that the word `beautiful' can only be altered in a few ways for word-only models, either leading to an UNK or an existing vocabulary word, whereas, word-piece and character-only models treat each unique character combination differently. This provides more variations that an attacker can exploit. Following similar reasoning, add and key attacks pose a greater threat than swap and drop attacks. The robustness of different models can be ordered as word-only $>$ word+char $>$ char-only $\sim $ word-piece, and the efficacy of different attacks as add $>$ key $>$ drop $>$ swap.
Next, we scrutinize the effectiveness of defense methods when faced against adversarially chosen attacks. Clearly from table 3 , DA and Adv are not effective in this case. We observed that despite a low training error, these models were not able to generalize to attacks on newer words at test time. ATD spell corrector is the most effective on keyboard attacks, but performs poorly on other attack types, particularly the add attack strategy.
The ScRNN model with pass-through backoff offers better protection, bringing back the adversarial accuracy within $5\%$ range for the swap attack. It is also effective under other attack classes, and can mitigate the adversarial effect in word-piece models by $21\%$ , character-only models by $19\%$ , and in word, and word+char models by over $4.5\%$ . This suggests that the direct training signal of word error correction is more effective than the indirect signal of sentiment classification available to DA and Adv for model robustness.
We observe additional gains by using background models as a backoff alternative, because of its lower word error rate (WER), especially, under the swap and drop attacks. However, these gains do not consistently translate in all other settings, as lower WER is necessary but not sufficient. Besides lower error rate, we find that a solid defense should furnish the attacker the fewest options to attack, i.e. it should have a low sensitivity.
As we shall see in section § "Understanding Model Sensitivity" , the backoff neutral variation has the lowest sensitivity due to mapping UNK predictions to a fixed neutral word. Thus, it results in the highest robustness on most of the attack types for all four model classes.
Table 4 shows the accuracy of BERT on 200 examples from the dev set of the MRPC paraphrase detection task under various attack and defense settings. We re-trained the ScRNN model variants on the MRPC training set for these experiments. Again, we find that simple 1-2 character attacks can bring down the accuracy of BERT significantly ( $89\%$ to $31\%$ ). Word recognition models can provide an effective defense, with both our pass-through and neutral variants recovering most of the accuracy. While the neutral backoff model is effective on 2-char attacks, it hurts performance in the no attack setting, since it incorrectly modifies certain correctly spelled entity names. Since the two variants are already effective, we did not train a background model for this task.
Understanding Model Sensitivity
To study model sensitivity, for each sentence, we perturb one randomly-chosen word and replace it with all possible perturbations under a given attack type. The resulting set of perturbed sentences is then fed to the word recognizer (whose sensitivity is to be estimated). As described in equation 12 , we count the number of unique predictions from the output sentences. Two corrections are considered unique if they are mapped differently by the downstream classifier.
The neutral backoff variant has the lowest sensitivity (Table 5 ). This is expected, as it returns a fixed neutral word whenever the ScRNN predicts an UNK, therefore reducing the number of unique outputs it predicts. Open vocabulary (i.e. char-only, word+char, word-piece) downstream classifiers consider every unique combination of characters differently, whereas word-only classifiers internally treat all out of vocabulary (OOV) words alike. Hence, for char-only, word+char, and word-piece models, the pass-through version is more sensitive than the background variant, as it passes words as is (and each combination is considered uniquely). However, for word-only models, pass-through is less sensitive as all the OOV character combinations are rendered identical.
Ideally, a preferred defense is one with low sensitivity and word error rate. In practice, however, we see that a low error rate often comes at the cost of sensitivity. We see this trade-off in Figure 2 , where we plot WER and sensitivity on the two axes, and depict the robustness when using different backoff variants. Generally, sensitivity is the more dominant factor out of the two, as the error rates of the considered variants are reasonably low.
We verify if the sentiment (of the reviews) is preserved with char-level attacks. In a human study with 50 attacked (and subsequently misclassified), and 50 unchanged reviews, it was noted that 48 and 49, respectively, preserved the sentiment.
Conclusion
As character and word-piece inputs become commonplace in modern NLP pipelines, it is worth highlighting the vulnerability they add. We show that minimally-doctored attacks can bring down accuracy of classifiers to random guessing. We recommend word recognition as a safeguard against this and build upon RNN-based semi-character word recognizers. We discover that when used as a defense mechanism, the most accurate word recognition models are not always the most robust against adversarial attacks. Additionally, we highlight the need to control the sensitivity of these models to achieve high robustness.
Acknowledgements
The authors are grateful to Graham Neubig, Eduard Hovy, Paul Michel, Mansi Gupta, and Antonios Anastasopoulos for suggestions and feedback.

Question: What does the "sensitivity" quantity denote?
Answer: the number of distinct word recognition outputs that an attacker can induce

The expected number of unique outputs a word recognition system assigns to a set of adversarial perturbations 

the number of distinct word recognition outputs that an attacker can induce, not just the number of words on which the model is “fooled”

Question: What end tasks do they evaluate on?
Answer: Sentiment analysis and paraphrase detection under adversarial attacks

Question: What is a semicharacter architecture?
Answer: A semi-character based RNN (ScRNN) treats the first and last characters individually, and is agnostic to the ordering of the internal characters

processes a sentence of words with misspelled characters, predicting the correct words at each step

Question: Do they experiment with offering multiple candidate corrections and voting on the model output, since this seems highly likely to outperform a one-best correction?
Answer: No

Question: Why is the adversarial setting appropriate for misspelling recognition?
Answer: Adversarial misspellings are a real-world problem

Question: Why do they experiment with RNNs instead of transformers for this task?
Answer: Unanswerable

Question: How do the backoff strategies work?
Answer: In pass-through, the recognizer passes on the possibly misspelled word, backoff to neutral word backs off to a word with similar distribution across classes and backoff to background model backs off to a more generic word recognition model trained with larger and less specialized corpus.

Pass-through passes the possibly misspelled word as is, backoff to neutral word backs off to a word with similar distribution across classes and backoff to background model backs off to a more generic word recognition model trained with larger and less specialized corpus.

Backoff to "a" when an UNK-predicted word is encountered, backoff to a more generic word recognition model when the model predicts UNK