\section{Introduction}
\label{sec: Introduction}

\textbf{Subject-verb agreement (SVA)} is a phenomenon where the \emph{main subject} agrees in grammatical number with its \emph{associated verb}, oblivious to the presence of any other noun phrase in the sentence. An example is:

\begin{enumerate}
    \item \label{incorr} *The \textbf{keys} to the \underline{cabinet} \textbf{is} on the table.
    \item \label{corr} The \textbf{keys} to the \underline{cabinet} \textbf{are} on the table.
\end{enumerate}

The main noun and the associated verb are in bold. Intervening nouns are underlined, and * denotes a grammatically incorrect sentence. In the above example, the number of the main verb \emph{are} (plural) has to agree with the number of the main subject \emph{keys} (plural). Here, the intervening noun \emph{cabinet} has the opposite number (singular) to that of the main subject. Such intervening nouns are referred to as \textbf{agreement attractors} \cite{bock1991broken}. In natural language sentences, there can be any number of intervening nouns behaving as either agreement attractors or non-attractors (nouns with the same number as the main noun).

Previous work \cite{linzen2016assessing, marvin2018targeted, mccoy2018revisiting, kuncoro2019scalable, noji-takamura-2020-analysis, hao2020attribution} assessing the ability of RNN Language Models (LMs) to capture syntax-sensitive dependencies via SVA tasks has found that they often do quite well, despite lacking explicit tree structure. However, it is still not clear if good performance on such tasks is necessarily a result of the RNN's ability to capture the underlying syntax, and this is the question we seek to further investigate here.

For a given learning task, there may be multiple hypotheses predictive of the training set labels; the learning model's \emph{inductive bias} can play a key role in selecting one hypothesis over another.
To account for the varying inductive biases that different RNN models might encode, we look at multiple architectures -- LSTM, GRU, ONLSTM, and Decay RNN (\S \ref{sec: Architectures}). \citet{mccoy2020does,mccoy2018revisiting} showed that hierarchical bias in the models, as well as the inputs, helps to generalize to unseen sentences. On the other hand, \citet{chaves-2020-dont} and \citet{sennhauser2018evaluating} provide evidence that LSTM models are more likely to learn surface-level heuristics, such as agreeing with the most recent noun, than the underlying grammar. Following \citet{mccoy2018revisiting} who show that training on syntactically rich sentences with agreement information increases the probability of good syntactic generalization, we experiment with training RNN models on sentences with at least one attractor -- \emph{Selective Sampling} (Figure \ref{fig:dataset}). Thus, the sentences in the selectively chosen dataset are syntactically richer than naturally sampled sentences, and can hopefully impart additional hierarchical cues which prevent models from relying on simple linear heuristics.

We test the hypothesis that if these models were to capture the correct grammatical structure from syntactically rich input, then they would generalize well out-of-distribution (OOD), {\em i.e.}, when tested on sentences without attractors having been trained solely on sentences with at least one attractor. Since human learners are known to have frequent access to simple structures, our learning setup itself is not realistic for human language acquisition; but the aim is to see whether it can push RNN models towards more human-like syntactic generalisation.

In addition to the examining the accuracies of these models on natural language sentences, we perform a Representation Similarity Analysis (RSA) in \S \ref{Analysis of representations}, and find that their inductive biases appear to be overridden by the training distribution, extending the findings of \citet{mccoy2020does}. 

To evaluate the effect of the choice of training data on the ability to capture SVA on a variety of syntactic constructions, we perform Targeted Syntactic Evaluation (TSE) as proposed by \citet{marvin2018targeted}, along with surprisal analysis (\S \ref{Targeted Syntactic Evaluation},\ref{Surprisal}). We find that training on selectively sampled `hard' instances improves the model's performance on difficult constructions (sentences with clauses between the main noun and the main verb), but degrades their performance on simpler constructions. Our analysis indicates that even when RNNs are able to capture non-trivial dependency patterns, they fail to perform well on easier dependency relations (instances without agreement attractors). This suggests that RNNs tend to efficiently learn surface-level heuristics from the training distribution rather than gleaning the actual syntactic rules. 

Our major outcomes are the following:
\begin{itemize}
    \item  We show that despite providing strong hierarchical cues via a selectively sampled training set (Figure \ref{fig:dataset}), RNNs, including the ONLSTM (which has a soft hierarchical inductive bias), do not generalize to an unseen configuration of intervening nouns.
    \item We observe that training data effectively override the model's structural bias, as our model representations clearly cluster by the type of training distribution. (Figure \ref{fig:RSA}).
   
    \item We verify that our findings are consistent across multiple learning paradigms, self-supervised language modeling and supervised grammaticality judgment, as well as varied test sets, natural and constructed (Tables \ref{tab:nat}, \ref{att}).
\end{itemize}

\begin{figure}[h!]
  \centering
    \includegraphics[scale=0.5]{dataset_description.png}
  \caption{Dataset description. As structure-insensitive RNN models suffer from agreement attraction errors, our \textit{selectively sampled} dataset is syntactically challenging for such sequential models, for whom surface-level heuristics such as `agree with recent noun' are efficiently available. Hence, training RNNs on such datasets might induce them to capture hierarchical relations rather than learning shallower heuristics.}
  \label{fig:dataset}
\end{figure}


\section{Related Work}
\label{sec: Related Work}

Prior work by \citet{linzen2016assessing, gulordava2018colorless, marvin2018targeted, tran-etal-2018-importance} have shown that language models RNNs can capture hierarchical information from natural language to solve SVA tasks. However, it is still not clear if the models are necessarily capturing underlying syntactic rules to make a good prediction. 

\citet{mccoy2018revisiting} conclude that GRU with attention generalizes hierarchically despite the absence of hierarchical inductive bias on question formation task. Additionally, they find that training on agreement language helps in inducing syntactic bias. However, they could not conclude what these RNNs capture which gives rise to non-trivial performance. A subsequent study by \citet{mccoy2020does} shows that hierarchical generalization is only plausible by providing explicit hierarchical inputs (annotated parse information) to the model having an explicit hierarchical inductive bias (tree-based models). Similar observations have been made by \citet{kuncoro-etal-2018-lstms} and \citet{wilcox2020structural}, suggesting that structural supervision improves syntactic generalization in neural language models. In this work, we analyze if exposure to `hard' agreement instances, which cannot be modelled by inferring readily-available heuristics, can help RNNs to improve their syntactic abilities.
 

\citet{van-schijndel-etal-2019-quantity} showed that neural LMs lag far behind humans on Targeted Syntactic Evaluation (TSE), even when trained with a large corpus and increased model capacity. However, by virtue of high variance in the performance of LMs on TSE across different random seeds and hyperparameter tuning, \citet{kuncoro2019scalable} achieved better accuracy in the same setting. \citet{noji-takamura-2020-analysis} and \citet{kuncoro2019scalable} came up with methodologies to improve performance on TSE, via contrastive learning and knowledge distillation from models with explicit grammar induction \cite{dyer2016recurrent} respectively. It has been observed that these models have trouble capturing agreement in sentences with center embeddings, especially agreement across object relative clauses (RCs) \cite{noji-takamura-2020-analysis, mueller-etal-2020-cross}. In our work, we show that syntactically rich training sentences can also improve performance on such instances substantially (Table \ref{TSE table}, Appendix Table 5).

Studies on linguistic phenomena such as filler-gap dependencies  \cite{chaves-2020-dont} and assessing the ability of LSTMs to capture the rules of context-free grammars  \cite{sennhauser2018evaluating} argue that LSTMs learn shallower heuristics from the dataset rather than acquiring the underlying linguistic rules. In this work, we show that even a model with implicit hierarchical inductive bias (the ONLSTM) is behaviourally close to a vanilla LSTM in terms of the learned representations, for both supervised and self-supervised learning settings. 

\section{Architectures}
\label{sec: Architectures}
In this work, we conduct our experiments on four recurrent schemes -- LSTM \cite{hochreiter1997long}, GRU \cite{cho-etal-2014-learning}, Decay RNN (DRNN) \cite{bhatt-etal-2020-much}, and ONLSTM \cite{shen2018ordered}. The governing equations of these architectures are mentioned in Appendix \S A.1. The ONLSTM, unlike the other models under consideration, is a recurrent network with soft hierarchical inductive bias. The DRNN is a recurrent network without any gating mechanism that imposes biologically-inspired constraints on the neurons. Amongst all these RNN types, the DRNN is the least complex, and has been shown to outperform vanilla RNNs and perform on par with other gated networks on grammaticality judgment tasks \cite{bhatt-etal-2020-much}. 

\begin{table}[ht]
\centering
\resizebox{\linewidth}{!}{%
\begin{tabular}{l | r | r}
\textbf{Property}                                    & Natural  & Selective     \\
\hline
Training sentences~                             & 97842  & 97842    \\
Ratio of Singular to Plural main nouns      & 67\%    & 45\%     \\
Ratio of Singular to Plural nouns (total)   & 79\%    & 71\%     \\
Fraction of 0 attractors                    & 93\%    & -        \\
Fraction of 1 attractors                    & 5.6\%   & 79\%     \\
Fraction of 2 attractors                    & 1.1\%   & 15\%     \\
Fraction of 3 attractors                    & 0.3\%   & 3.7\%   \\
\hline
\hline 
Testing Sentences & 157k & 157k
\end{tabular}}
\caption{Data statistics.}
\label{appen table: data analysis}
\end{table}

\section{Dataset}
\label{sec: Dataset}

We use sentences from the Wikipedia corpus made available by \citet{linzen2016assessing}. For training, we further choose two subsets from the main dataset, based on the number of attractors in each sentence (Figure \ref{fig:dataset}). The sentences without any attractor are grammatically simple and allow for out-of-distribution testing as they are not seen while training on the selectively sampled dataset. We train our models for two objectives: language modeling and binary classification for grammaticality judgment (\S \ref{Experiments}). For uniform comparison, we keep the testing set identical across the subsets of the training data. The testing set contains $157$k sentences for both the binary classifier and the LM. Table \ref{appen table: data analysis} contains a quantitative description of the datasets. 

To perform well on the selectively sampled dataset, models cannot resort to learning simple linear heuristics such as associating the main verb with the preceding noun rather than the main noun. However, such heuristics are encouraged by a naturally sampled dataset due to a heavy skew towards sentences without attractors (Table \ref{appen table: data analysis}). The tendency to capture these shallow patterns would allow models to correctly predict the verb number in most instances, but for the wrong reasons.

For the binary classifier, we augment each sentence with its corresponding counterfactual example. Augmenting with counterfactual examples has been shown to be effective in reducing the tendency of the models to capture spurious correlations (for sentiment analysis) by \citet{Kaushik2020Learning}. Consider the example from \S \ref{sec: Introduction}: 
\begin{enumerate}
    \item \label{corr} The \textbf{keys} to the \underline{cabinet} \textbf{are} on the table.
    \item \label{incorr} *The \textbf{keys} to the \underline{cabinet} \textbf{is} on the table. 

\end{enumerate}
 Sentence \ref{incorr} is the counterfactual example for the sentence \ref{corr}. Thus our dataset will consist of pairs of a sentence and its corresponding counterfactual sentence. 

Additionally, we test our models on an artificially constructed corpus with a different distribution of sentence types than the training set. As proposed by \citet{marvin2018targeted}, this helps in evaluating if the models have mastered syntax across different syntactic constructions (\S \ref{Targeted Syntactic Evaluation}).

\section{Experiments}
\label{Experiments}
We focus on evaluating the models' ability to make number agreement judgments when trained for classification (supervised) and language modeling (self-supervised). For each task, we train models (with 5 different random seeds) on both training subsets from the corpus.\footnote{Code will be made available as part of the camera-ready version.} Training settings for our experiments are mentioned in Appendix \S A.2. 
Consider the sentences from the introduction. A classifier is expected to label sentence \ref{incorr} as ungrammatical and sentence \ref{corr} as grammatical. For grammaticality judgment via a language model (LM), we train on a standard LM objective and during inference, check if our model gives a higher probability to the grammatically correct verb form conditioned on previous tokens in the sentence.

\begin{table}[ht]
\centering
    \resizebox{\linewidth}{!}{%
\begin{tabular}{l | c c  c c| c c c c} 
Training set
       & \multicolumn{4}{c|}{Natural Sampling}         & \multicolumn{4}{c}{Selective Sampling}                           \\ 
\hline
Test attractors
      & 0          & 1          & 2          & 3          & 0          & 1          & 2          & 3           \\ 
\hline
      & \multicolumn{8}{c}{LANGUAGE MODEL}                                                                    \\ 
\hline
LSTM   & \textbf{0.98} & 0.91 & 0.84 & 0.78 & 0.89 & \textbf{0.98} & \textbf{0.98} & 0.95  \\ 
ONLSTM &\textbf{ 0.98} & 0.92 & 0.86& 0.82& 0.90 & \textbf{0.98} & \textbf{0.98} & 0.95  \\ 
GRU    & \textbf{0.97} & 0.88& 0.78 & 0.73& 0.87 & \textbf{0.98} & 0.97 & 0.94 \\ 
DRNN   & \textbf{0.96} & 0.69 & 0.47 & 0.36 & 0.83 & \textbf{0.97} & 0.94 & 0.91 \\ 
\hline
      & \multicolumn{8}{c}{BINARY CLASSIFIER}                                                                 \\ 
\hline
LSTM   &\textbf{ 0.97} & 0.93 & 0.87& 0.82& 0.60& \textbf{0.98} & 0.96 & 0.97  \\ 
ONLSTM &\textbf{ 0.97} & 0.91 & 0.84 & 0.81 & 0.64 & \textbf{0.98} & 0.97 & \textbf{0.98}  \\ 
GRU    &\textbf{ 0.97} & 0.88 & 0.76 & 0.69 & 0.62 & 0.95 & 0.94& \textbf{0.96} \\ 
DRNN   & \textbf{0.97 }& 0.90& 0.81 & 0.77& 0.70 &\textbf{ 0.97 }& 0.96 & 0.96  \\
\hline
\end{tabular}}
\caption{Accuracy of RNN architectures trained as LMs and classifiers, for test instances with an increasing number of attractors between main subject and verb; variances mentioned in Appendix Table 3. The maximum accuracy for each model and training setup across attractor counts is in bold. Note that the models trained on the selectively sampled dataset are not able to generalize well OOD (sentences without attractors).}
\label{tab:nat}
\end{table}


\subsection{Performance on Natural Sentences}
\label{Performance on Natural Sentences}

Table \ref{tab:nat} shows the main results for the described experiments. For the models trained on a naturally sampled dataset, the performance degrades quite quickly with an increasing number of attractors between the subject and the corresponding verb, for both the LM and the classifier versions. However, the reduction in the accuracy with increasing attractor count for the models trained on the selectively sampled dataset is much less than with the natural sampling training. 

For the selectively sampled dataset, the sentences without attractors serve as OOD sentences, and the performance boost on \emph{in-distribution} complex sentences comes at the cost of a reduction in the accuracy of the OOD yet relatively simple sentences.
The error rate for the ONLSTM, a model with inherent tree bias, also increases when tested on the OOD sentences, and when trained for a classification objective it performs worse than the architecturally simpler Decay RNN.

This fall-off on grammatically simpler OOD samples seems counter-intuitive. We note that the increase in error rates is much greater when training the models as classifiers rather than LMs. This shows that models with supervised training for grammaticality on syntactically rich and counterfactually augmented data are still unable to capture the actual syntactic rules and appear to be learning shallower heuristics, but ones that capture more nuanced patterns than simply going by linear distance. We can infer this because while our selectively sampled subset contains sentences with at least one attractor, many (over 30\%) of the intervening nouns in these sentences are non-attractors. Hence there are sentences in which a non-attractor noun (same number as the main subject) immediately precedes the verb rather than an attractor noun. Therefore, the agreement performance (on sentences with attractors) of the models trained on this dataset cannot arise from an overly simple heuristic like disagreeing with the most recent noun, and the observed decline in OOD performance implies that less trivial heuristics are being learned which nevertheless fail to capture the actual syntax.

\subsection{Analysis of representations}
\label{Analysis of representations}

To analyze the differences in the learned internal representations among the models trained on the two subsets of the data, we perform a representation similarity analysis (RSA) \cite{laakso2000content}. We take 2000 sentences selected randomly from the test set. As we had trained each model on five different random seeds, we compare 40 models (20 for each subset) across different learning objectives. 

Our major observation from Figure \ref{fig:RSA} is that the representations of models trained on different subsets are easily linearly separable in this space, for both the LM and the classifier objectives. This implies that the representation clustering is not so much based on model architecture or inductive bias, but is overridden by the training data. 

Additionally, we observe that the learned representations of the ONLSTM and LSTM are not well separable, neither for the LM nor for the classifier across training configurations. This shows that despite having a soft hierarchical inductive bias, the ONLSTM appears similar to the regular LSTM in terms of patterns captured at the representational level. Moreover, the learned representations for GRU and LSTM are well separable  This differentiates the two architectures, which are often used interchangeably on the representation level, and such differences may be arising due to the squashing phenomena in GRUs pointed out by \citet{mccoy2020does}. 

For the binary classifier (Figure \ref{BC RSA}), although we observe a little variance in the accuracy on the test set across the different seeds, the variance (spread of the points) in the projected space is substantial when compared to that of the LM. Quantitative analysis of the variance is available in Appendix \S A.5. This might be due to the existence of multiple valleys in the loss landscape for the binary classification objective, and we posit that an LM objective is more reliable when comparing the ability to capture the syntax sensitive dependencies in RNNs. In the following sections, we shall further analyze the performance of models trained with LM objective in greater detail.


\begin{figure}[h!]
  \centering
  \centering
  \begin{subfigure}[b]{\linewidth}
    \includegraphics[width=\textwidth]{RSA_BC_1.png}
    \caption{Binary classifier}
    \label{BC RSA}
  \end{subfigure} \hfill
  \begin{subfigure}[b]{\linewidth}
    \includegraphics[width=\textwidth]{RSA_LM_1.png}
    \caption{Language Model}
    \label{LM RSA}
  \end{subfigure}
  \caption{Representation similarity analysis of the hidden units of different RNN models (5 different seeds for each model). We observe that for both the learning objectives, one can partition the 2D space using a line that separates models trained on the two subsets of the data, natural and selective sampling.}
  \label{fig:RSA}
\end{figure}
\begin{table*}[ht]
\centering
    \resizebox{1\textwidth}{!}{%

\begin{tabular}{l|l|c c|c c|c c|c c} 
Subject Verb Agreement                    & \#sentences & \multicolumn{2}{c|}{LSTM}                            & \multicolumn{2}{c|}{ONLSTM}                          & \multicolumn{2}{c|}{GRU}                             & \multicolumn{2}{c}{DRNN}                             \\ 
\hline
Condition &            & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c|}{Selective} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c|}{Selective} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c|}{Selective} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c}{Selective}  \\ 
\hline
Simple     & 312  & \textbf{0.99} ($\pm$0.01) & 0.86 ($\pm$0.01)          & \textbf{0.98} ($\pm$0.02) & 0.86 ($\pm$0.01)          & \textbf{0.98} ($\pm$0.01) & 0.84 ($\pm$0.04)          & \textbf{0.97} ($\pm$0.02) & 0.79 ($\pm$0.05)           \\ 
Short VP                & 3432  & \textbf{0.85} ($\pm$0.02) & 0.71 ($\pm$0.06)           & \textbf{0.88} ($\pm$0.02)  & 0.73 ($\pm$0.08)           & \textbf{0.81} ($\pm$0.03) & 0.69 ($\pm$0.04)           & \textbf{0.70} ($\pm$0.05)  & 0.66 ($\pm$0.04)            \\ 
Within ORC (A)          & 9984  & \textbf{0.79} ($\pm$0.06) & 0.63 ($\pm$0.05)           & \textbf{0.78} ($\pm$0.10)   & 0.59 ($\pm$0.06)           & \textbf{0.75} ($\pm$0.02) & 0.50 ($\pm$0.02)            & \textbf{0.7} ($\pm$0.08)  & 0.46 ($\pm$0.04)            \\ 
Within ORC (IA)         & 4032  & \textbf{0.77} ($\pm$0.06) & 0.64 ($\pm$0.06)           & \textbf{0.75} ($\pm$0.08)  & 0.59 ($\pm$0.04)           & \textbf{0.73} ($\pm$0.02) & 0.50 ($\pm$0.03)            & \textbf{0.69} ($\pm$0.06) & 0.46 ($\pm$0.05)            \\ 
Within no that ORC (A)  & 9984  & \textbf{0.73} ($\pm$0.06) & 0.61 ($\pm$0.05)           & \textbf{0.72} ($\pm$0.08)  & 0.57 ($\pm$0.07)           & \textbf{0.72} ($\pm$0.03) & 0.47 ($\pm$0.04)           & \textbf{0.63} ($\pm$0.04) & 0.45 ($\pm$0.06)            \\ 
Within no that ORC (IA) & 4032  & \textbf{0.66} ($\pm$0.04) & 0.61 ($\pm$0.05)           & \textbf{0.66} ($\pm$0.06)  & 0.56 ($\pm$0.06)           & \textbf{0.62} ($\pm$0.04) & 0.47 ($\pm$0.04)           & \textbf{0.68} ($\pm$0.06) & 0.45 ($\pm$0.06)            \\ 
Long VP                 & 520   & 0.65 ($\pm$0.03)         & \textbf{0.69} ($\pm$0.07) & \textbf{0.67} ($\pm$0.04) & \textbf{0.67} ($\pm$0.06) & 0.63 ($\pm$0.04)         & \textbf{0.65} ($\pm$0.04) & 0.56 ($\pm$0.05)         & \textbf{0.65} ($\pm$0.03)  \\ 
Across Prep Phrase (A)           & 29952 & 0.86 ($\pm$0.04)          & \textbf{0.89} ($\pm$0.03)  & \textbf{0.88} ($\pm$0.03)  & \textbf{0.88} ($\pm$0.01)  & 0.81 ($\pm$0.02)          & \textbf{0.88} ($\pm$0.02)  & 0.68 ($\pm$0.04)          & \textbf{0.83} ($\pm$0.01)   \\ 
Across Prep Phrase (IA)          & 4032  & 0.87 ($\pm$0.03)          & \textbf{0.94} ($\pm$0.02)  & 0.88 ($\pm$0.02)           & \textbf{0.95} ($\pm$0.01)  & 0.86 ($\pm$0.02)          & \textbf{0.94} ($\pm$0.01)  & 0.69 ($\pm$0.06)          & \textbf{0.91} ($\pm$0.02)   \\ 
Across SRC & 9984 & 0.81 ($\pm$0.03)          & \textbf{0.89} ($\pm$0.05) & 0.81 ($\pm$0.05)          & \textbf{0.87} ($\pm$0.02) & 0.77 ($\pm$0.05)          & \textbf{0.86} ($\pm$0.05) & 0.58 ($\pm$0.04)          & \textbf{0.80} ($\pm$0.05)  \\
Across ORC (A)          & 9984  & 0.73 ($\pm$0.10)          & \textbf{0.82} ($\pm$0.07) & 0.78 ($\pm$0.07)          & \textbf{0.84} ($\pm$0.02) & 0.72 ($\pm$0.06)         & \textbf{0.79} ($\pm$0.05) & 0.63 ($\pm$0.04)         & \textbf{0.78} ($\pm$0.05)  \\ 
Across ORC (IA)         & 4032  & 0.74 ($\pm$0.09)         & \textbf{0.84} ($\pm$0.10)  & 0.81 ($\pm$0.07)          & \textbf{0.87} ($\pm$0.02) & 0.74 ($\pm$0.08)         & \textbf{0.85} ($\pm$0.05) & 0.65 ($\pm$0.07)         & \textbf{0.86} ($\pm$0.02)  \\ 
Across no that ORC (A)  & 9984  & 0.61 ($\pm$0.04)         & \textbf{0.72} ($\pm$0.08) & 0.62 ($\pm$0.05)          & \textbf{0.78} ($\pm$0.02) & 0.60 ($\pm$0.02)          & \textbf{0.68} ($\pm$0.06) & 0.64 ($\pm$0.03)         & \textbf{0.73} ($\pm$0.02)  \\ 
Across no that ORC (IA) & 4032  & 0.66 ($\pm$0.04)         & \textbf{0.77} ($\pm$0.11) & 0.66 ($\pm$0.06)          & \textbf{0.84} ($\pm$0.03) & 0.62 ($\pm$0.04)         & \textbf{0.72} ($\pm$0.07) & 0.68 ($\pm$0.06)         & \textbf{0.83} ($\pm$0.02)  \\
\hline
Average Performance                &   104296     &           0.78 ($\pm$0.03)      &  0.78 ($\pm$0.02)              &      0.79 ($\pm$0.03)           &        0.78 ($\pm$0.01)        &   0.75 ($\pm$0.01)              & 0.73 ($\pm$0.02)                &  0.66 ($\pm$0.02)                &        0.71 ($\pm$0.02)         \\
\hline
\end{tabular}} 
\caption{Accuracy of models on targeted syntactic evaluation. Quantities in bold marks the maximum accuracy for each model across the configuration. ORC: Objective Relative Clause, SRC: Subject Relative Clause, Prep Phrase: Prepositional Phrase, VP: Verb Phrase. A/IA in the parenthesis represents an animate/inanimate main subject. Models trained on selectively sampled subset perform well on the difficult sentences, but not on the simpler ones.}
\label{TSE table}
\end{table*}


\subsection{Targeted Syntactic Evaluation (TSE)}
\label{Targeted Syntactic Evaluation}

We test how training the language models on the strategically chosen inputs impacts generalisation to different syntactic constructions. Testing on such examples lets us evaluate if our models are capturing what we intend them to capture. As the subjects can be separated from their verb by long clauses, SVA requires models to capture robust hierarchical representations. The models capturing surface level regularities of the data would not be able to perform well on these constructed examples. Sentence \ref{ORC} corresponds to the agreement across an object relative clause, while the sentence \ref{SRC} corresponds to the agreement across a subject relative clause. 

\begin{enumerate}
    \item \label{ORC} The \textbf{authors} that the \underline{chef} likes \textbf{laugh}.
    \item \label{SRC} The \textbf{authors} that like the \underline{chef} \textbf{laugh}. 
\end{enumerate}
Table \ref{TSE table} mentions the results of TSE on the LM. For each model, we observe that as the difficulty of the sentences increases, models trained on the selectively sampled dataset starts surpassing those trained on the natural dataset. Difficult sentences involve number agreement across the prepositional phrase and subject/object relative clauses. However, this improvement in the performance came at a cost where their performance on simple sentences, having agreement across short verb phrases and agreement within object relative clauses, decreases. Such sentences do not have any intervening noun between the subject and the corresponding verb.

Table \ref{att} presents the performance of the LMs on the synthetic data, for sentences with 0 or 1 agreement attractors. These findings corroborate our observations on natural language sentences -- the models trained on the selectively sampled dataset performed worse on sentences without attractors which are syntactically simpler. 

As supplementary results, we present a comparison of the LSTM LM trained on the selectively sampled subset with the techniques presented by \citet{kuncoro2019scalable} in Appendix Table 5.


\begin{table}[ht]
\resizebox{\linewidth}{!}{%
\begin{tabular}{l|c|c|c|c} 
Training set & \multicolumn{2}{c|}{ Natural} & \multicolumn{2}{c}{ Selective}  \\ 
\hline
Test attractors             & 0          & 1            & 0          & 1            \\ 
\hline
LSTM         & \textbf{0.77} {($\pm$ 0.05)} & 0.66 ($\pm$ 0.04)   & 0.63 ($\pm$ 0.04) & \textbf{0.83} {($\pm$ 0.06)}   \\ 
ONLSTM       & \textbf{0.76} {($\pm$ 0.07)} & 0.70 ($\pm$ 0.06)   & 0.60 ($\pm$ 0.05) & \textbf{0.85} {($\pm$ 0.01)}   \\ 
GRU          & \textbf{0.74} {($\pm$ 0.02)} & 0.64 ($\pm$ 0.02)   & 0.51 ($\pm$ 0.02) & \textbf{0.81} {($\pm$ 0.04)}   \\ 
DRNN         & \textbf{0.67} {($\pm$ 0.04)} & 0.44 ($\pm$ 0.04)   & 0.48 ($\pm$ 0.04) & \textbf{0.79} {($\pm$ 0.03)}  \\
\bottomrule
\end{tabular}} 
\caption{Accuracy of LMs on test instances with 0 or 1 attractors from the artificial corpus. Models trained on the selectively sampled subset do not generalize well on OOD sentences without attractors.}
\label{att}
\end{table}

\subsubsection*{Fine-Grained Analysis}
\label{Fine-Grained Analysis}

To assess the performance of the models trained on the selectively sampled dataset, we take a closer look at constructed sentences that are structurally similar to in-distribution sentences but contain non-attractor intervening nouns rather than agreement attractors. Figure \ref{fig:FGA} depicts the performance of the LSTM LM on three agreement conditions -- across Object RC, Preposition Phrase, and Subject RC, each with an animate main noun. For sentences with two nouns, we have four possibilities corresponding to their combination of grammatical numbers. Consider the following examples for the sentences with object relative clause across the main noun and its verb ($\ast$ marks the incorrect verb). 

\begin{enumerate}
    \item \label{SS} (SS) The \textbf{author} that the \underline{minister} likes laughs/*laugh.
    \item \label{SP} (SP) The \textbf{author} that the \underline{ministers} like laughs/*laugh.
    \item \label{PS} (PS) The \textbf{authors} that the \underline{minister} likes laugh/*laughs.
    \item \label{PP} (PP) The \textbf{authors} that the \underline{ministers} like laugh/*laughs.
\end{enumerate}

Here SS denotes sentences having singular main noun and a singular embedded subject, and likewise for other cases. We observe that with our selective training, the performance on sentences with non-attractor intervening nouns (the SS/PP configurations, which are unobserved in the selectively sampled dataset) worsens for 2 out of 3 syntactic constructions -- across Preposition Phrase and Subject RC. This pattern highlights that the reduction in the performance on simple sentences may not be completely attributed to their difference in syntactic structure from training distribution.  

\begin{figure}[h!]
  \centering
  \begin{subfigure}[b]{\linewidth}
    \includegraphics[width=\textwidth]{K=-1.png}
    \caption{Accuracy: LSTM trained on naturally sampled subset}
    \label{FGA_a}
  \end{subfigure} \hfill
  \begin{subfigure}[b]{\linewidth}
    \includegraphics[width=\textwidth]{K=0.png}
    \caption{Accuracy: LSTM trained on selectively sampled subset}
    \label{FGA_b}
  \end{subfigure}
  \caption{Fine-grained analysis of the LSTM LM on Obj/Subj Relative Clauses and Preposition Phrases, demarcated by the inflections of the main subject and the embedded subject. P: Plural, S: Singular; thus SS denotes sentences with a singular main noun and a singular embedded subject, and likewise for the other cases.}
  \label{fig:FGA}
\end{figure}

For all the cases under consideration presented in Figure \ref{FGA_a}, the performance of the LSTM LM is worst when the main noun is singular with the plural embedded subject (SP case). This indicates that plural attractors have a stronger attraction effect than singular attractors. Note that the naturally sampled dataset has more plural attractors while the selectively sampled one has an almost equal balance of plural and singular attractors (Table \ref{appen table: data analysis}). Thus, our findings are not due to a lack of plural attractors seen during the training phase.


For completeness, we report the fine-grained analysis accuracies for all the models under consideration in the supplementary material (Tables 6, 7, and 8).


\subsection{How confident are RNN language models?}
\label{Surprisal}

From the previous experiments, it is not clear how confident neural LMs are while making predictions about the number of the upcoming verb given the context till that verb. Surprisal at a given word is defined as $-\log p(x_n \ | \ x_{[1:n-1]})$, where $x_n$ represents the $n^{th}$ token in the sentence and $x_{[1:n-1]}$ represents the sequence of preceding tokens. We define \emph{prediction confidence} as the difference in surprisal values at the verb location between the incorrect verb and the correct verb; higher values correspond to more confident correct predictions. In this section we compare the performance of models trained on the two subsets in terms of their average prediction confidence at the verb position, evaluated on 16k simple sentences from the natural corpus (testing set) of the following form:

\begin{center}
The $<$Subject$>$ $<$Verb$>...$ 
\end{center}

Note that this amounts to evaluation on sentences involving agreement without attractors. Table \ref{surp} shows the average prediction confidence and the average ratio of predicted probabilities for the grammatical verb and the ungrammatical verb. We can see that the average probability ratio of the grammatically correct verb to the incorrect verb is much lower for the models trained on the selectively sampled subset than those trained on the naturally sampled subset. Thus, in addition to the difference between the accuracies of LMs trained on the two subsets being close to 10\% on sentences with no attractors (Table \ref{tab:nat}), models trained with selective sampling are also less confident, even when they predict correctly. Moreover, we see that the ONLSTM suffers as big a drop in prediction confidence as the regular LSTM when trained on this selectively sampled dataset, despite the former having a hierarchical inductive bias which we might have hoped would help it capture the correct syntax. 

\begin{table}[ht]
\centering
\resizebox{0.8\linewidth}{!}{%
\begin{tabular}{l|c |c|c| c} 
\multicolumn{1}{c|}{Training set} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c|}{Selective} & \multicolumn{1}{c|}{Natural} & \multicolumn{1}{c}{Selective}  \\ 
\hline
Test metric                            & \multicolumn{2}{c|}{Prediction Confidence}    & \multicolumn{2}{c}{ \(\frac{P(grammatical)}{P(ungrammatical)}\)}  \\ 
\hline
LSTM   & \textbf{5.72} & 2.56 & \textbf{303.91} & 12.90  \\ 
ONLSTM & \textbf{5.80} & 2.64 & \textbf{331.83} & 14.08  \\ 
GRU    & \textbf{5.13} & 2.40 & \textbf{169.28} & 11.02  \\ 
DRNN   & \textbf{5.15} & 2.38 & \textbf{172.78} & 10.77  \\
\end{tabular}} 
\caption{Average prediction confidence and correct-to-incorrect probability ratio for agreement without attractors. Models trained on the selectively sampled dataset have lower confidence on non-attractor sentences than those trained on the natural dataset.}
\label{surp}
\end{table}


\subsection{Can fine-tuning help?}
\label{Can finetuning help?}

Fine-tuning has been shown to be an effective strategy to improve the syntactic robustness of RNNs. \citet{lepori-etal-2020-representations} fine-tuned their model on a small number of synthetic sentences which could not solved using word co-occurrence statistics. This eventually helped in decreasing their model's error on the number agreement task. We assess if a similar technique could improve the syntactic generalization ability of the models trained on the selectively sampled dataset. 

We fine-tune our LMs with artificially generated sentences following the rules of context-free grammar. We notice that our model's error rates did not decrease on sentences without attractor with fine-tuning. This observation may be the result of catastrophic forgetting during the fine-tuning phase \cite{jiang-etal-2020-smart, aghajanyan2020better, McCloskey1989}. Another possibility is that the RNNs have not been able to learn underlying syntactic rules from the given training distribution. Recent information-theoretic analysis by \citet{lovering2021informationtheoretic} points out that fine-tuning might not uncover new features that are not already captured during the pre-training phase. This suggests that training on `hard' instances might not have led the RNNs to capture dependency patterns at the level of syntax. See Appendix \S A.6 for fine-tuning results. 

\section{Discussion and Conclusion}
\label{Discussion}

In this work, we analyzed the effects of a strategically chosen training set with exclusively `hard' agreement instances, on neural language models and binary classifiers for grammaticality judgment. We observed that the models' inability to perform well on out of distribution (OOD) sentences, even those which would seem to be `easy' agreement instances, is consistent across variation in learning mechanism (supervised or self-supervised), innate architectural bias, and testing set -- natural or artificial sentences.


Our analysis showed that the error rates of models trained on sentences with at least one agreement attractor are higher on sentences with no attractors than on sentences with attractors, for both corpus sentences (Table \ref{tab:nat}) and artificial sentences (Table \ref{att}). This observation is counter-intuitive because the models were trained on syntactically rich sentences and yet failed to perform well on simpler sentences. Had our RNN models picked up the correct grammatical rules, we would not expect this behavior. We obtained a similar counter-intuitive result for targeted syntactic evaluation (Table \ref{TSE table}), where models trained on the selectively sampled dataset performed much better on difficult constructed sentences involving agreement across nested dependencies than on simpler sentences involving agreement within nested dependencies.

Our analysis of representations suggested that training set bias dominates over the model's architectural features or inductive bias in shaping representation learning; {\em e.g.}, there was no discernible difference between the learned representations of the ONLSTM and LSTM models. The reasons for this merit further exploration. Moreover, for the binary classifiers (Figure \ref{BC RSA}), although we observe little variance in test accuracy across different training seeds, the variance in the projected representation space is substantially greater than for LMs. Thus, we posit that an LM objective is more reliable when comparing the ability of different RNN models to capture syntax-sensitive dependencies. Additionally, multi-task learning may improve language modeling by predicting the CCG supertags of each word \cite{marvin2018targeted}, or by incorporating a contrastive loss term in the objective \cite{noji-takamura-2020-analysis}.   


We observed that the hierarchical inductive bias in the ONLSTM is not sufficient to perform well on OOD sentences. \citet{mccoy2020does} argued that an architecture with explicit tree bias, plus syntactically annotated inputs, are needed to capture syntax for sequence-to-sequence tasks. Here we show that the ONLSTM (soft tree bias) trained on a syntactically rich dataset (soft structural information) turns out to be insufficient to generalize well to OOD sentences and capture the underlying grammar. Our targeted syntactic evaluation pinpoints the cases which our models fail to capture, and improving performance on such cases is a key future direction. 

Our observations suggest that RNNs, being fundamentally statistical models, can efficiently capture the correlation of the output variable with the input as observed during training (even for relatively `hard' or non-linear linguistic dependencies) without necessarily learning the underlying hierarchical structure. This is consistent with the conclusions of \citet{sennhauser2018evaluating} and \citet{chaves-2020-dont}. Thus, we need to be cautious in inferring the ability of such models to capture syntax-sensitive dependencies. Performance on any particular kind of construction might always reflect some overfitting to it, even if it is syntactically rich or complex. Although we have here focused on training solely on hard instances as a means of hierarchical cueing, identifying the best mix of simpler and more complex sentences that a model should be exposed to for optimal generalisation performance across a variety of syntactic constructions remains a direction for future work. Broad-based testing on instances of diverse types and complexity levels is essential to the development of models that better capture the structure of human language in all its richness and variety.




\bibliographystyle{acl_natbib}
