Recent studies have shown that language models pretrained and/or fine-tuned on randomly permuted sentences exhibit competitive performance on GLUE, putting into question the importance of word order information. Somewhat counter-intuitively, some of these studies also report that position embeddings appear to be crucial for models' good performance with shuffled text. We probe these language models for word order information and investigate what position embeddings learned from shuffled text encode, showing that these models retain information pertaining to the original, naturalistic word order. We show this is in part due to a subtlety in how shuffling is implemented in previous work  before rather than after subword segmentation. Surprisingly, we find even Language models trained on text shuffled after subword segmentation retain some semblance of information about word order because of the statistical dependencies between sentence length and unigram probabilities. Finally, we show that beyond GLUE, a variety of language understanding tasks do require word order information, often to an extent that cannot be learned through fine-tuning. Transformers (Vaswani et al., 2017), when used in the context of masked language modelling (Devlin et al., 2018), consume their inputs concurrently. There is no notion of inherent order, unlike in autoregressive setups, where the input is consumed token by token. To compensate for this absence of linear order, the transformer architecture originally proposed in Vaswani et al. (2017) includes a fixed, sinusoidal position embedding added to each token embedding; each token carries a different position embedding, corresponding to its position in the sentence. The transformer-based BERT (De-vlin et al., 2018) replaces these fixed sinusoidal  Equal contribution. embeddings with unique, learned embeddings per position; RoBERTa (Liu et al., 2019), the model investigated in this work, does the same. Position embeddings are the only source of order information in these models; in their absence, contextual representations generated for tokens are independent of the actual position of the tokens in a sentence, and the models thus resemble heavily overparameterised bags-of-words. Sinha et al. (2021) pre-trained RoBERTa models on shuffled corpora to demonstrate that the performance gap between these shuffled' language models and models trained on unshuffled corpora is minor (when fine-tuned and evaluated downstream on the GLUE (Wang et al., 2018) benchmark). They further show that this gap is considerably wider when a model is pre-trained without position embeddings. In this paper, we attempt to shed some light on why these models behave the way they do, and in doing so, seek to answer a set of pertinent questions:  Do shuffled language models still have traces of word order information? Why is there a gap in performance between models without position embeddings and models trained on shuffled tokens, with the latter 6907 Figure 2: Correlations between position embeddings when shuffling training data before segmentation (left), i.e, at the word level, and after segmentation (middle), i.e., at the subword level, as well as when replacing all subwords with random subwords based on their corpus-level frequencies (right). Are there NLU benchmarks, other than GLUE, on which shuffled language models perform poorly? Contributions We first demonstrate, in Section 3, that shuffled language models do contain word order information, and are quite responsive to simple tests for word order information, particularly when compared to models trained without position representations. In Section 4, we demonstrate that pre-training is sufficient to learn this: position embeddings provide the appropriate inductive bias, and performing BPE segmentation after shuffling results in sensible n-grams appearing in the pre-training corpus; this gives models the capacity to learn word order within smaller local windows. Other minor cues like correlations between sentence lengths and token distributions also play a role. We further corroborate our analysis by examining attention patterns across models in Sec. 5. In Section 6, we show that, while shuffled models might be almost as good as their unshuffled counterparts on GLUE tasks, there exist NLU benchmarks that do require word order information to an extent that cannot be learned through fine-tuning alone. Finally, in Section 7, we describe miscellaneous experiments addressing the utility of positional embeddings when added just prior to fine-tuning. Sinha et al. (2021) train several full-scale RoBERTa language models on the Toronto Book Corpus (Zhu et al., 2015) and English Wikipedia. 1 Four of their models are trained on shuffled text, i.e., sentences in which n -grams are reordered at random. 2 We dub the original, unperturbed model ORIG , and the scrambled models SHUF . N 1, SHUF . N 2, SHUF . N 3 and SHUF . N 4 depending on the size of the shuffled n -grams: SHUF . N 1 reorders the unigrams in a sentence, SHUF . N 2 reorders its bigrams, etc. For comparison, Sinha et al. (2021) also train a RoBERTa language model entirely without position embeddings (NOPOS ), as well as a RoBERTa language model trained on a corpus drawn solely from unigram distributions of the original Book Corpus, i.e., a reshuffling of the entire corpus (SHUF .C ORPUS ). We experiment with their models, as well as with smaller models that we can train with a smaller carbon footprint. To this end, we downscale the RoBERTa architecture used in Sinha et al. (2021). Concretely, we train single-headed RoBERTa models, dividing the embedding and feed-forward dimensionality by 12, for 24 hours on a single GPU, on 100k sentences sampled from the Toronto Book Corpus. To this end, we train a custom vocabulary of size 5,000, which we use for indexing in all our subsequent experiments. While these smaller models are in no way meant to be fine-tuned and used downstream, they are useful proofs-of-concept that we later analyse. We begin by attempting to ascertain the extent to which shuffled language models are actually capable of encoding information pertaining to the naturalistic word order of sentences. We perform two simple tests on the full-scale models, in line with Wang and Chen (2020): the first of these is a classification task where a logistic regressor is trained to predict whether a randomly sampled token precedes another in an unshuffled sentence, and the second involves predicting the position of a word in an unshuffled sentence. The fact that we do not fine-tune any of the model parameters is noteworthy: the linear models can only learn word order information if it reflects in the representations the models generate somehow. Pairwise Classification For this experiment, we train a logistic regression classification model on word representations extracted from the final layer of the Transformer encoder, mean pooling over sub-tokens when required. For each word pair x and y , the classifier is given a concatenation of our model m 's induced representations m ( x )  m ( y ) and trained to predict a label indicating whether x precedes y or not. Holding out two randomly sampled positions, we use a training sets sized 2 k, 5 k, and 10 k, from the Universal Dependencies English-GUM corpus (Zeldes, 2017) (excluding sentences with more than 30 tokens to increase learnability) and a test set of size 2 , 000 . We report the mean accuracy from three runs. Regression Using the same data, we also train a ridge-regularised linear regression model to predict the position of a word p ( x ) in an unshuffled sentence, given that word's model-induced representa-Model Classification (acc.) Regression ( R 2 ) 2k 5k 10k ORIG 81.50 81.74 80.40 0.68 SHUF . tion m ( x ) . R 2 score is reported per model. To prevent the regressors from memorising word to position mappings, we perform 6-fold cross-validation, where the heldout part of the data contains no vocabulary overlap with the corresponding train set. Results For both tasks (see Table 1), our results indicate that position encodings are particularly important for encoding word order: Classifiers and regressors trained on representations from ORIG and SHUF . N 1 achieve high accuracies and R 2 scores, while those for NOPOS are close to random. Both ORIG and SHUF . N 1 appear to be better than random given only 2 k examples. These results imply that, given positional encodings and a modest training set of 2 k or more examples, a simple linear model is capable of extracting word order information, enabling almost perfect extrapolation to unseen positions. Whether the position encodings come from a model trained on natural or shuffled text does not appear to matter, emphasizing that shuffled language models do indeed contain substantial information about the original word order. In Section 3, we observed that Sinha et al. (2021)'s shuffled language models surprisingly exhibit information about naturalistic word order. That these models contain positional information can also be seen by visualizing position embedding similarity. Figure 1 displays Pearson correlations 3 for position embeddings with themselves, across positions. Here, we see that the shuffled models satisfy the idealised criteria for position embeddings described by Wang et al. (2021): namely, they appear to be a) monotonous within smaller context windows, and b) invariant to translation. If position embedding correlations are consistent across offsets over the entire space of embeddings, the model can be said to have learned' distances between tokens. Since transformers process all positions in parallel, 3 We see similar patterns with dot products for all our plots; we use Pearson correlations to constrain our range to [  1 , 1] . and since language models without position embeddings do not exhibit such information, position embeddings have to be the source of this information. In what follows, we discuss this apparent paradox. Subword vs. word shuffling An important detail when running experiments on shuffled text, is when the shuffling operation takes place. When tokens are shuffled before BPE segmentation, this leads to word-level shuffling, in which sequences of subwords that form words remain contiguous. Such sequences become a consistent, meaningful signal for language modelling, allowing models to efficiently utilise the inductive bias provided by position embeddings. Thus, even though our pretrained models have, in theory, not seen consecutive tokens in their pre-training data, they have learned to utilise positional embeddings to pay attention to adjacent tokens. The influence of this is somewhat visible in Figure 2: while models trained on text shuffled before and after segmentation both exhibit shifts in the polarity of their position correlations, only the former show bands of varying magnitude , similar to the full-scale models. Ravishankar and Sgaard (2021) discuss the implications of these patterns in a multilingual context; we hypothesise that in our context, the periodicity in magnitude is a visible artefact of the model's ability to leverage position embeddings to enable offset attention. In Section 5, we analyse the effect of shuffling the pretraining data on the models' attention mechanisms. Accidental overlap In addition to the n -gram information which results from shuffling before segmentation, we also note that short sentences tend to include original bigrams with high probability, leading to stronger associations for words that are adjacent in the original texts. This effect is obviously much stronger when shuffling before segmentation than after segmentation. Figure 3 shows how frequent overlapping bigrams (of any sort) are, comparing word and subword shuffling over 50k sentences. Sentence length Finally, we observe some preserved information about the original word order even when shuffling is performed after segmentation. We hypothesize that this is a side-effect of the non-random relationship between sentence length and unigram probabilities. That unigram probabilities correlate with sentence length follows from the fact that different genres exhibit different sentence Figure 3: (Cumulative) plot showing subword bigram overlap after shuffling either words or subwords, as a percentage of the total number of seen bigrams. length distributions (Sigurd et al., 2004; Jin and Liu, 2017). Also, some words occur very frequently in formulaic contexts, e.g., thank in thank you . This potentially means that there is an approximately learnable relationship between the distribution of words and sentence boundary symbols. To test for this, we train two smaller language models on unigram-sampled corpora: for the first, we use the first 100k BookCorpus sentences as our corpus, shuffling tokens at a corpus level (yet keeping the original sentence lengths). The stark difference in position embedding correlations between that and shuffling is seen in Figure 2. For the second, we sample from two different unigram distributions: one for short sentences and one for longer sentences (details in Appendix B). While the first model induces no correlations at all, the second does, as shown in Figure 4, implying that sentence length and unigram occurrences is enough to learn some order information. Transformer-based language models commonly have attention heads that attend to neighboring positions (Voita et al., 2019; Ravishankar et al., 2021). Such attention heads are positional and can only be learned in the presence of order information. We attempt to visualise the attention mechanism for pre-trained models by calculating, for each head and layer, the offset between a token and the token 6910 Figure 4: Similarity matrix between models with sentences sampled based on unigram corpus statistics; disjoint vocab implies a correlation between token choice and sentence length. that it pays maximum attention to 4 . We then plot how frequent each offset is, as a percentage, over 100 Book Corpus sentences, in Figure 5, where we present results for two full-scale models, and two smaller models (see 2). When compared to NOPOS , SHUF . N 1 has a less uniform pattern to its attention mechanism: it is likely, even at layer 0, to prefer to pay attention to adjacent tokens, somewhat mimicking a convolutional window (Cordon-nier et al., 2020). We see very similar differences in distribution between our smaller models: Shuffling after segmentation, i.e., at the subword level, influences early attention patterns. SuperGLUE and WinoGrande Sinha et al. (2021)'s investigation is conducted on GLUE and on the Paraphrase Adversaries from Word shuffling (PAWS) dataset (Zhang et al., 2019). For these datasets, they find that models pretrained on shuffled text perform only marginally worse than those pretrained on normal text. This result, they argue can be explained in two ways: either a) these tasks do not need word order information to be solved, or b) the required word order information can be acquired during finetuning. While GLUE has been a useful benchmark, several of the tasks which constitute it have been shown to be solvable using various spurious artefacts and heuristics (Gu-rurangan et al., 2018; Poliak et al., 2018). If, for instance, through finetuning, models are learning to rely on such heuristics as lexical overlap for MNLI (McCoy et al., 2019), then it is unsurprising that their performance is not greatly impacted by the 4 This method of visualisation is somewhat limited, in that it examines only the maximum attention paid by each token. Evaluating on the more rigorous set of SuperGLUE tasks 5 (Wang et al., 2019) and on the adversarially-filtered Winograd Schema examples (Levesque et al., 2012) of the WinoGrande dataset (Sakaguchi et al., 2020) produces results which paint a more nuanced picture compared to those of Sinha et al. (2021). The results, presented in Table 2, show accuracy or F1 scores for all models. For two of the tasks (MultiRC (Khashabi et al., 2018), COPA (Roemmele et al., 2011)), we observe a pattern in line with that seen in Sinha et al. (2021)'s GLUE and PAWS results: the drop in performance from ORIG to SHUF . N 1 is minimal (mean: 1.75 points; mean across GLUE tasks: 3.3 points) 6 , while that to NOPOS is more substantial (mean: 10.5 points; mean across GLUE tasks: 18.6 points). This pattern alters for the BoolQ Yes/No question answering dataset (Clark et al., 2019), the CommitmentBank (De Marneffe et al., 2019), the ReCoRD reading comprehension dataset (Zhang et al., 2018), both the Winograd Schema tasks, 5 Results are reported for an average of 3 runs per task. The RTE task is excluded from our results as it is also part of GLUE; RTE results can be found in Sinha et al. (2021). and to some extent the Words in Context dataset (Pilehvar and Camacho-Collados, 2018). For these tasks we observe a larger gap between ORIG and SHUF . N 1 (mean: 8.1 points), and an even larger one between ORIG and NOPOS (mean: 19.78 points). We note that this latter set of tasks requires inferences which are more context-sensitive, in comparison to the two other tasks or to the GLUE tasks. Consider the Winograd schema tasks, for example. Each instance takes the form of a binary test with a statement comprising of two possible referents (blue) and a pronoun (red) such as: Sid explained his theory to Mark but he couldn't convince him. The correct referent of the pronoun must be inferred based on a special discriminatory segment (underlined). In the above example, this depends on a) the identification of Sid as the subject of explained and b) inferring that the pronoun serving as the subject of convinced should refer to the same entity. Since the Winograd schema examples are designed so that the referents are equally associated with their context 7 , word order is crucial 8 for establishing the roles of Sid and Mark as subject and object of explained and he and him as those of convinced. If these roles cannot be established, making the correct inference becomes impossible. A similar reasoning can be applied to the Words in Context dataset and the CommitmentBank. The former task tests the ability of a model to distinguish the senses of a polysemous word based on context. While this might often be feasible via a notion of contextual association that higher-order distributional statistics are sufficient for, some instances will require awareness of the word's role as an argument in the sentence. The latter task investigates the projectivity of finite clausal complements under entailment cancelling operators. This is dependent on both the scope of the entailment operator and the identity of the subject of the matrix predicate (De Marneffe et al., 2019), both of which are sensitive to word order information. A final consideration to take into account is dataset filtering. Two of the tasks where we observe 7 e.g. Sid and Mark are both equally likely subjects/objects here. Not all Winograd schema examples are perfect in this regard, however, which could explain why scrambled models still perform above random. See Trichelair et al. (2018) for a discussion of the latter point. 8 Particularly in a language with limited morphological role marking such as English. the largest difference between ORIG , SHUF . N 1, and NOPOS  WinoGrande and ReCoRD  apply filtering algorithms to remove cues or biases which would enable models to heuristically solve the tasks. This indicates that by filtering out examples containing cues that make them solvable via higher order statistics, such filtering strategies do succeed at compelling models to (at least partially) rely on word order information. Dependency Tree Probing Besides GLUE and PAWS, Sinha et al. (2021)'s analysis also includes several probing experiments, wherein they attempt to decode dependency tree structure from model representations. They show, interestingly, that the SHUF .N4, SHUF .N3 and SHUF .N2 models perform only marginally worse than ORIG , with SHUF .N1 producing the lowest scores (lower, in fact, than SHUF .C ORPUS ). Given the findings of Section 3, we are interested in taking a closer look at this phenomenon. Here, we surmise that dependency length plays a crucial role in the probing setup, where permuted models may succeed on par with ORIG in capturing local, adjacent dependencies, but increasingly struggle to decode longer ones. To evaluate the extent to which this is true, we train a bilinear probe (used in Hewitt and Liang (2019)) on top of all model representations and evaluate its accuracy across dependencies binned by length, where length between words w i and w j is defined as | i  j | . We opt for using the bilinear probe over the Pareto probing framework (Pimentel et al., 2020), as the former learns a transformation directly over model representations, while the latter adds the parent and child MLP units from Dozat et al. (2017)  acting more like a parser. We train probes on the English Web Treebank (Silveira et al., 2014) and evaluate using UAS, the standard parsing 6912 Model BoolQ CB COPA MultiRC ReCoRD WiC WSC WinoGrande ORIG 77.6 88.2 / 87.4 61.6 67.8 / 21.9 73.5 / 72.8 67.4 73.5 62.9 SHUF . Figure 6 shows  probing accuracy across various dependency lengths for NOPOS and SHUF .N1, with respect to ORIG 9 ; we include detailed  s for all models in Appendix C. For NOPOS , parsing difficulty increases almost linearly with distance, often mimicking the actual frequency distribution of dependencies at these distances in the original treebank (Appendix C); for SHUF . N 1, the picture is a lot more nuanced, with dependencies at a distance of 1 consistently being closer in terms of parseabil-ity to ORIG , which, we hypothesise, is due to its adjacency bias. Random position embeddings are difficult to add post-training We tried to quantify the degree to which the inductive bias imparted by positional embeddings can be utilised, solely via fine-tuning. To do so, for a subset of GLUE tasks (MNLI, QNLI, RTE, SST-2, CoLA), we evaluate NOPOS , and a variant where we randomly initialised learnable position embeddings and add them to the model, with the rest of the model equivalent to NOPOS . We see no improvement in results, except for MNLI, that we hypothesise stems from position embeddings acting as some sort of regularisation parameter. To test this, we repeat the above set of experiments, this time injecting Gaussian noise instead; this has been empirically shown to have a regularising effect on the network (Bishop, 1995; Camuto et al., 2021). Adding Gaussian noise led to a slight increase in score for just MNLI, backing up our regularisation hypothesis. Models learn to expect specific embeddings Replacing the positional embeddings in ORIG with fixed, sinusoidal embeddings before fine-tuning significantly hurts scores on the same subset of 9 Note that Layer 13 refers to a linear mix of all model layers, as is done for ELMo (Peters et al., 2018). GLUE tasks, implying that the models expect embeddings that resemble the inductive bias imparted by random embeddings, and that fine-tuning tasks do not have sufficient data to overcome this. The addition of fixed, sinusoidal to NOPOS also does not improve model performance on a similar subset of tasks; this implies, given that sinusoidal embeddings are already meaningful, that model weights also need to learn to fit the embeddings they are given, and that they need a substantial amount of data to do so. In Humans It is generally accepted that a majority of languages have canonical or base' word orderings (Comrie, 1989) (e.g. Subject-Verb-Object in English, and Subject-Object-Verb in Hindi). Linguists consider word order to be a coding property  mechanisms by which abstract, syntactic structure is encoded in the surface form of utterances. Beyond word order, other coding properties include, e.g. subject-verb agreement, morphological case marking, or function words such as adpositions. In English, word order is among the most prominent coding properties, playing a crucial role in the expression of the main verb's core arguments: subject and object. For more morphologically complex languages, on the other hand, (e.g. Finnish and Turkish), word order is primarily used to convey pragmatic information such as topicalisation or focus. In such cases, argument structure is often signalled via case-marking, where numerous orderings become possible (shift in topic or focus nonwithstanding). We refer the reader to Kulmizev and Nivre (2021) for a broader discussion of these topics and their implications when studying syntax through language models. More generally, evidence for the saliency of word order in linguistic processing and comprehension comes from a variety of studies using acceptability judgements, eye-tracking data, and neu-6913 ral response measurements (Bever, 1970; Danks and Glucksberg, 1971; Just and Carpenter, 1980; Friederici et al., 2000, 2001; Bahlmann et al., 2007; Lerner et al., 2011; Pallier et al., 2011; Fedorenko et al., 2016; Ding et al., 2016). Psycholinguistic research has, however, also highlighted the robustness of sentence processing mechanisms to a variety of perturbations, including those which violate word order restrictions (Ferreira et al., 2002; Gibson et al., 2013; Traxler, 2014). In recent work, Mollica et al. (2020) tested the hypothesis that composition is the core function of the brain's language-selective network and that it can take place even when grammatical word order constrains are violated. Their findings confirmed this, showing that stimuli with shuffled word order where local dependencies were preserved  as is, roughly speaking, the case for many dependencies in the sentences SHUF . N 4 is trained on  elicited a neural response in the language network that is comparable to that elicited by normal sentences. When interword dependencies were disrupted so combinable words were so far apart that composition among nearby words was highly unlikely  as in SHUF . N 1, neural response fell to a level compared to unconnected word lists. In Machines Recently, many NLP researchers have attempted to investigate the role of word order information in language models. For example, Lin et al. (2019) employ diagnostic classifiers and attention analyses to demonstrate that lower (but not higher) layers of BERT encode word order information. Papadimitriou et al. (2021) find that Multilingual BERT is sensitive to morphosyntactic alignment, where numerous languages (out of 24 total) rely on word order to mark subjecthood (English among them). Alleman et al. (2021) implement an input perturbation framework (n-gram shuffling, phrase swaps, etc.), and employ it towards testing the sensitivity of BERT's representations to various types of structure in sentences. They report a sensitivity to larger constituent units of sentences in higher layers, which they deduce to be influenced by hierarchical phrase structure. O'Connor and Andreas (2021) examine the contribution of various contextual features to the ability of GPT-2 (Radford et al., 2019) to predict upcoming tokens. Their findings show that several destructive manipulations, including in-sentence word shuffling, applied to midand long range contexts lead only to a modest increase in usable information as defined according to the V-information framework of Xu et al. (2020). Similarly, word order information has been found not to be essential for various NLU tasks and datasets. Early work showed that Natural Language Inference tasks are largely insensitive to permutations of word order (Parikh et al., 2016; Sinha et al., 2020). Pham et al. (2020) and Gupta et al. (2021) discuss this in greater detail, demonstrating that test-time word order perturbations applied to GLUE benchmark tasks have little impact on LM performance. Following up on this, Sinha et al. (2021), which our work builds on, found that pretraining on scrambled text appears to only marginally affect model performance. Most related to this study, Clouatre et al. (2021) introduce two metrics for gauging the local and global ordering of tokens in scrambled texts, observing that only the latter is altered by the perturbation functions found in prior literature. In experiments with GLUE, they find that local (sub-word) perturbations show a substantially stronger performance decay compared to global ones. In this work, we present an in-depth analysis of these results, showing that LMs trained on scrambled text can actually retain word information and that  as for humans  their sensitivity to word order is dependent on a variety of factors such as the nature of the task and the locality of perturbation. While performance on some understanding evaluation tasks is not strongly affected by word order scrambling, the effect on others such as the Winograd Schema is far more evident. Much discussion has resulted from recent work showing that scrambling text at different stages of testing or training does not drastically alter the performance of language models on NLU tasks. In this work, we presented analyses painting a more nuanced picture of such findings. Primarily, we demonstrate that, as far as altered pre-training is concerned, models still do retain a semblance of word order knowledge  largely at the local level. We show that this knowledge stems from cues in the altered data, such as adjacent BPE symbols and correlations between sentence length and content. The order in which shuffling is performed  before or after BPE tokenization  is influential in models' acquisition of word order, which calls for caution in interpreting previous results. Finally, we show that there exist NLU tasks that are far more 6914 sensitive to sentence structure as expressed by word order. We thank Stephanie Brandl, Desmond Elliott, Yova Kementchedjhieva, Douwe Kiela and Miryam de Lhoneux for their feedback and comments. We acknowledge the CSC-IT Centre for Science, Finland, for providing computational resources. Vinit worked on this paper while on a research visit to the University of Copenhagen. Mostafa and Anders are supported by a Google Focused Research Award.
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