Acceptability Judgements via Examining the Topology of Attention Maps
通过注意力图拓扑分析可接受性判断
Abstract
摘要
The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the attention heads’ ability to judge the grammatical acceptability of a sentence has been under explored. This paper approaches the paradigm of acceptability judgments with topological data analysis (TDA), showing that the topological properties of the attention graph can be efficiently exploited for two standard practices in linguistics: binary judgments and linguistic minimal pairs. Topological features enhance the BERTbased acceptability classifier scores by up to 0.24 Matthew’s correlation coefficient score on COLA in three languages (English, Italian, and Swedish). By revealing the topological discrepancy between attention graphs of minimal pairs, we achieve the human-level performance on the BLIMP benchmark, outperforming nine statistical and Transformer LM baselines. At the same time, TDA provides the foundation for analyzing the linguistic functions of attention heads and interpreting the correspondence between the graph features and grammatical phenomena. We publicly release the code and other materials used in the experiments 1.
注意力机制在编码语言知识中的作用一直受到自然语言处理领域的特别关注。然而，注意力头对句子语法可接受性的判断能力尚未得到充分研究。本文采用拓扑数据分析 (TDA) 方法研究可接受性判断范式，证明注意力图的拓扑特性可有效应用于语言学中的两种标准实践：二元判断和语言学最小对立对。在英语、意大利语和瑞典语三种语言的COLA数据集上，拓扑特征将基于BERT的可接受性分类器的马修斯相关系数最高提升了0.24。通过揭示最小对立对注意力图的拓扑差异，我们在BLIMP基准测试中达到人类水平表现，优于九种统计模型和Transformer语言模型基线。同时，TDA为分析注意力头的语言功能、解释图特征与语法现象之间的对应关系提供了基础。我们公开了实验中使用的代码和其他材料[1]。
1 Introduction
1 引言
Linguistic competence of neural language models (LMs) has emerged as one of the core sub-fields in NLP. The research paradigms explore whether Transformer LMs (Vaswani et al., 2017) induce linguistic generalizations from raw pre-training corpora (Warstadt et al., 2020b; Zhang et al., 2021), what properties are learned during task-specific fine-tuning (Miaschi et al., 2020; Merchant et al., 2020), and how the experimental results are connected to grammar and language acquisition theories (Pater, 2019; Manning et al., 2020).
神经语言模型的语言能力已成为自然语言处理(NLP)的核心子领域之一。该研究范式主要探索：Transformer模型(Vaswani等，2017)能否从原始预训练语料中归纳语言泛化规律(Warstadt等，2020b；Zhang等，2021)，在任务特定微调过程中学习了哪些特性(Miaschi等，2020；Merchant等，2020)，以及实验结果如何与语法和语言习得理论相关联(Pater，2019；Manning等，2020)。
One of these paradigms is centered around acce pt ability judgments, which have formed an empirical foundation in generative linguistics over the last six decades (Chomsky, 1965; Schütze, 1996; Scholz et al., 2021). Acceptability of linguistic stimuli is traditionally investigated in the form of a forced choice between binary categories or minimal pairs (Sprouse, 2018), which are widely adopted for acceptability classification (Linzen et al., 2016; Warstadt et al., 2019) and probabilistic LM scoring (Lau et al., 2017).
其中一种范式围绕可接受性判断展开，这些判断构成了生成语言学过去六十年的实证基础 (Chomsky, 1965; Schütze, 1996; Scholz et al., 2021)。传统上，语言刺激的可接受性通过二元类别或最小对立对的强制选择形式进行研究 (Sprouse, 2018)，这种方法被广泛用于可接受性分类 (Linzen et al., 2016; Warstadt et al., 2019) 和概率性大语言模型评分 (Lau et al., 2017)。
A scope of approaches has been proposed to interpret the roles of hundreds of attention heads in encoding linguistic properties (Htut et al., 2019; Wu et al., 2020) and identify how the most influential ones benefit the downstream performance (Voita et al., 2019; Jo and Myaeng, 2020). Prior work has demonstrated that heads induce grammar formalisms and structural knowledge (Zhou and Zhao, 2019; Lin et al., 2019; Luo, 2021), and linguistic features motivate attention patterns (Kovaleva et al., 2019; Clark et al., 2019). Recent studies also show that certain heads can have multiple functional roles (Pande et al., 2021) and even perform syntactic functions for typologically distant languages (Ravi shankar et al., 2021).
已有多种方法被提出，用于解释数百个注意力头(attention head)在编码语言属性中的作用 [Htut et al., 2019; Wu et al., 2020]，并识别最具影响力的头如何提升下游任务性能 [Voita et al., 2019; Jo and Myaeng, 2020]。先前研究表明，这些头能诱导语法形式体系和结构知识 [Zhou and Zhao, 2019; Lin et al., 2019; Luo, 2021]，而语言特征会驱动注意力模式 [Kovaleva et al., 2019; Clark et al., 2019]。最新研究还发现，某些头可能具有多重功能角色 [Pande et al., 2021]，甚至能为类型学差异较大的语言执行句法功能 [Ravi shankar et al., 2021]。
Our paper presents one of the first attempts to analyze attention heads in the context of linguistic acceptability (LA) using topological data analysis $(\mathrm{TDA}^{2}$ ; Chazal and Michel, 2017). TDA allows for exploiting complex structures underlying textual data and investigating graph representations of Transformer’s attention maps. We show that topological features are sensitive to well-established LA contrasts, and the grammatical phenomena can be encoded with the topological properties of the attention map.
我们的论文首次尝试在语言可接受性(LA)分析中运用拓扑数据分析(TDA)来研究注意力头机制。该方法能有效挖掘文本数据的复杂结构，并探究Transformer注意力图表的拓扑表征。研究表明，拓扑特征对经典LA对比敏感，且语法现象可通过注意力图的拓扑属性进行编码。
The main contributions are the following: (i) We adapt TDA methods to two standard approaches to LA judgments: acceptability classification and scoring minimal pairs (§3). (ii) We conduct acceptability classification experiments in three Indo-European languages (English, Italian, and Swedish) and outperform the established baselines (§4). (iii) We introduce two scoring functions, which reach the human-level performance in discr imina ting between minimal pairs in English and surpass nine statistical and Transformer LM baselines (§5). $(i\nu)$ The linguistic analysis of the feature space proves that TDA can serve as a complementary approach to interpreting the attention mechanism and identifying heads with linguistic functions $(\S4.3,\S5.3,\S6)$ .
主要贡献如下：(i) 我们将TDA方法适配至语言可接受性判断的两种标准方法：可接受性分类与最小对立对评分(第3节)。(ii) 在三种印欧语系语言(英语、意大利语和瑞典语)中开展可接受性分类实验，性能超越现有基线(第4节)。(iii) 提出两种评分函数，在英语最小对立对判别任务中达到人类水平表现，并超越九种统计方法与Transformer语言模型基线(第5节)。$(i\nu)$ 特征空间的语言学分析证明，TDA可作为解释注意力机制和识别具有语言学功能头部的补充方法(第4.3节、第5.3节、第6节)。
2 Related Work
2 相关工作
2.1 Linguistic Acceptability
2.1 语言可接受性
Acceptability Classification. Early works approach acceptability classification with classic ML methods, hand-crafted feature templates, and probabilistic syntax parsers (Cherry and Quirk, 2008; Wagner et al., 2009; Post, 2011). Another line employs statistical LMs (Heilman et al., 2014), including threshold-based classification with LM scoring functions (Clark et al., 2013). The ability of RNN-based models (Elman, 1990; Hochreiter and Schmid huber, 1997) to capture long-distance regularities has stimulated investigation of their grammatical sensitivity (Linzen et al., 2016). With the release of the Corpus of Linguistic Acceptability (COLA; Warstadt et al., 2019) and advances in language modeling, the focus has shifted towards Transformer LMs (Yin et al., 2020), establishing LA as a proxy for natural language understanding (NLU) abilities (Wang et al., 2018) and linguistic competence of LMs (Warstadt and Bowman, 2019).
可接受性分类。早期研究采用经典机器学习方法、手工制作的特征模板和概率句法分析器处理可接受性分类 (Cherry and Quirk, 2008; Wagner et al., 2009; Post, 2011)。另一方向使用统计语言模型 (Heilman et al., 2014)，包括基于阈值的语言模型评分函数分类 (Clark et al., 2013)。基于RNN的模型 (Elman, 1990; Hochreiter and Schmidhuber, 1997) 捕捉长距离规律的能力激发了对它们语法敏感性的研究 (Linzen et al., 2016)。随着语言可接受性语料库 (COLA; Warstadt et al., 2019) 的发布和语言建模技术的进步，研究重点转向Transformer语言模型 (Yin et al., 2020)，将语言可接受性作为衡量自然语言理解能力 (Wang et al., 2018) 和语言模型语言能力 (Warstadt and Bowman, 2019) 的代理指标。
Linguistic Minimal Pairs. A forced choice between minimal pairs is a complementary approach to LA, which evaluates preferences between pairs of sentences that contrast an isolated grammatical phenomenon (Schütze, 1996). The idea of discriminating between minimal contrastive pairs has been widely applied to scoring generated hypotheses in downstream tasks (Pauls and Klein, 2012; Salazar et al., 2020), measuring social biases (Nangia et al., 2020), analyzing machine translation models (Burlot and Yvon, 2017; Sennrich, 2017), and linguistic profiling of LMs in multiple languages (Marvin and Linzen, 2018; Mueller et al., 2020).
语言最小对立对。在最小对立对之间进行强制选择是语言可接受性(LA)的一种补充方法，它评估在孤立语法现象上形成对比的句子对之间的偏好 (Schütze, 1996)。区分最小对比对的思想已广泛应用于下游任务中生成假设的评分 (Pauls and Klein, 2012; Salazar et al., 2020)、测量社会偏见 (Nangia et al., 2020)、分析机器翻译模型 (Burlot and Yvon, 2017; Sennrich, 2017) 以及多语言大语言模型的语言特征分析 (Marvin and Linzen, 2018; Mueller et al., 2020)。
2.2 Topological Data Analysis in NLP
2.2 NLP中的拓扑数据分析
TDA has found several applications in NLP. One of them is word sense induction by clustering word graphs and detecting their connected components. The graphs can be built from word dictionaries (Levary et al., 2012), association net- works (Dubuisson et al., 2013), and word vector representations (Jakubowski et al., 2020). Another direction involves building class if i ers upon geometric structural properties for movie genre detection (Doshi and Zadrozny, 2018), textual entail- ment (Savle et al., 2019), and document classification (Das et al., 2021; Werenski et al., 2022). Recent works have mainly focused on the topology of LMs’ internal representations. Kushnareva et al. (2021) represent attention maps with TDA features to approach artificial text detection. Colombo et al. (2021) introduce BARYSCORE, an automatic evaluation metric for text generation that relies on Wasser stein distance and barycenter s. To the best of our knowledge, TDA methods have not yet been applied to LA.
TDA在自然语言处理(NLP)领域已有多个应用方向。其一是通过聚类词图并检测连通分量来实现词义归纳，这些词图可基于词典(Levary et al., 2012)、关联网络(Dubuisson et al., 2013)或词向量表示(Jakubowski et al., 2020)构建。另一研究方向是利用几何结构特性构建分类器，应用于电影类型检测(Doshi and Zadrozny, 2018)、文本蕴含(Savle et al., 2019)及文档分类(Das et al., 2021; Werenski et al., 2022)。近期研究主要聚焦于大语言模型内部表征的拓扑结构：Kushnareva等人(2021)采用TDA特征表示注意力图谱以进行人工文本检测；Colombo等人(2021)提出基于Wasserstein距离和质心的文本生成自动评估指标BARYSCORE。据我们所知，TDA方法尚未应用于LA领域。
3 Methodology
3 方法论
3.1 Attention Graph
3.1 注意力图 (Attention Graph)
We treat Transformer’s attention matrix $A^{a t t n}$ as a weighted graph $G$ , where the vertices represent tokens, and the edges connect pairs of tokens with mutual attention weights. This representation can be used to build a family of attention graphs called filtration, i.e., an ordered set of graphs $G^{\tau_{i}}$ filtered by increasing attention weight thresholds $\tau_{i}$ . Filtering edges lower than the given threshold affects the graph structure and its core features, e.g., the number of edges, connected components, or cycles. TDA techniques allow tracking these changes, identifying the moments of when the features appear (i.e., their “birth”) or disappear (i.e., their “death”), and associating a lifetime to them. The latter is encoded as a set of intervals called a “barcode”, where each interval (“bar”) lasts from the feature’s “birth” to its “death”. The barcode characterizes the persistent features of attention graphs and describes their stability.
我们将Transformer的注意力矩阵 $A^{a t t n}$ 视为加权图 $G$ ，其中顶点表示token，边以相互注意力权重连接token对。这种表示可用于构建一系列称为过滤 (filtration) 的注意力图，即通过递增的注意力权重阈值 $\tau_{i}$ 过滤得到的有序图集 $G^{\tau_{i}}$ 。过滤低于给定阈值的边会影响图结构及其核心特征，例如边数、连通分量或环。TDA技术可以追踪这些变化，识别特征出现（即"诞生"）或消失（即"死亡"）的时刻，并为它们关联生命周期。后者被编码为一组称为"条形码"的区间，其中每个区间（"条"）从特征的"诞生"持续到"死亡"。该条形码表征了注意力图的持久特征并描述其稳定性。
Example. Let us illustrate the process of computing the attention graph filtration and barcodes given an Example (1).
示例。让我们通过示例(1)来说明计算注意力图过滤和条形码的过程。
Figure 1: An example of attention maps, barcodes, and filtration procedure for the sentence “There is snowing today.”. Model=En-BERT-base (Devlin et al., 2019). Heads=[Layer 1; Head 11] and [Layer 9; Head 9].
图 1: 句子"There is snowing today."的注意力图、条形码和过滤过程示例。模型=En-BERT-base (Devlin et al., 2019)。注意力头=[第1层;第11头]和[第9层;第9头]。
(1) There is snowing today.
(1) 今天下雪了。
First, we compute attention maps for each Transformer head as shown in Figure 1a-1b (left). These two heads follow different attention patterns (Clark et al., 2019): attention to the next token (Figure 1a) and to the [SEP] token (Figure 1b). Next, we represent the map as a weighted graph, and conduct the filtration procedure for a fixed set of attention weight thresholds. The edges lower than each given threshold are discarded, which results in a set of six attention graphs with their maximum spanning trees (MSTs) becoming a chain (Figure 1c; $\tau{=}0.1$ ), and a star (Figure 1d; $\tau{=}0.5$ ). The families of attention graphs are used to compute persistent features (§3.2).
首先，我们为每个Transformer头计算注意力图，如图1a-1b(左)所示。这两个头遵循不同的注意力模式(Clark等人，2019)：关注下一个token(图1a)和[SEP] token(图1b)。接着，我们将注意力图表示为加权图，并对一组固定的注意力权重阈值进行过滤处理。低于每个给定阈值的边被丢弃，从而得到六组注意力图，其最大生成树(MST)分别形成链状(图1c；$\tau{=}0.1$)和星状(图1d；$\tau{=}0.5$)。这些注意力图族用于计算持久特征(§3.2)。
Figure 1a-1b (right) depict barcodes for each family of graphs. The bars are sorted by length. The number of bars equals $|T|-1$ , where $|T|$ is the number of tokens in the input sentence. The bars in yellow correspond to the 0-dimensional features acquired from the edges of the MST. The bars in blue refer to 1-dimensional features, which stand for non-trivial simple cycles. Such cycle appears in the first family (Figure 1c; $_{\tau=0.05}$ ), which is shown as a blue bar in Figure 1a. By contrast, there are no cycles in the second family (Figure 1d) and on the corresponding barcode.
图 1a-1b (右)展示了每个图族的条形码。条形按长度排序，条数等于$|T|-1$，其中$|T|$是输入句子的token数量。黄色条形对应从最小生成树(MST)边获取的0维特征，蓝色条形代表1维特征(即非平凡简单环)。这种环出现在第一图族(图1c；$_{\tau=0.05}$)，对应图1a中的蓝色条形。相比之下，第二图族(图1d)及其对应条形码中不存在环。
3.2 Persistent Features of Attention Graphs
3.2 注意力图的持久性特征
We follow Kushnareva et al. (2021) to design three groups of persistent features of the attention graph: (i) topological features, (ii) features derived from barcodes, and (iii) features based on distance to attention patterns. The features are computed on attention maps produced by a Transformer LM.
我们遵循Kushnareva等人(2021)的方法，设计了注意力图的三大类持久性特征：(i)拓扑特征，(ii)从条形码(barcode)衍生的特征，以及(iii)基于与注意力模式距离的特征。这些特征是在Transformer语言模型生成的注意力图上计算的。
Topological Features. Topological features include the first two Betti numbers of the undirected graph $\beta_{0}$ and $\beta_{1}$ and standard properties of the directed graph, such as the number of strongly connected components, edges, and cycles. The features are calculated on pre-defined thresholds over undirected and directed attention graphs from each head separately and further concatenated.
拓扑特征。拓扑特征包括无向图的前两个贝蒂数$\beta_{0}$和$\beta_{1}$，以及有向图的标准属性，如强连通分量、边和环的数量。这些特征是在预定义的阈值上分别对每个头的无向和有向注意力图进行计算，并进一步拼接而成。
Features Derived from Barcodes. Barcode is the representation of the graph’s persistent homology (Barannikov, 2021). We use the Ripser+ $^+$ toolkit (Zhang et al., 2020) to compute $0/1.$ - dimensional barcodes for $A^{a t t n}$ . Since Ripser $^{++}$ leverages upon distance matrices, we transform $A^{a t t n}$ as $A^{\prime}=1-\operatorname*{max}\left(A^{a t t n},A^{a t t n T}\right)$ .
从条形码中提取的特征。条形码是图持久同调的表现形式 (Barannikov, 2021)。我们使用 Ripser+ $^+$ 工具包 (Zhang et al., 2020) 计算 $A^{a t t n}$ 的 $0/1.$ 维条形码。由于 Ripser $^{++}$ 基于距离矩阵运算，我们将 $A^{a t t n}$ 转换为 $A^{\prime}=1-\operatorname*{max}\left(A^{a t t n},A^{a t t n T}\right)$。
Next, we compute descriptive characteristics of each barcode, such as the sum/average/variance of lengths of bars, the number of bars with the time of birth/death greater/lower than a threshold, and the entropy of the barcodes. The sum of lengths of bars $(H_{0}S)$ corresponds to the 0-dimensional barcode and represents the sum of edge weights in the $A^{\prime\prime}\mathrm{s}$ minimum spanning tree. The average length of bars $(H_{0}M)$ corresponds to the mean edge weight in this tree, i.e. $H_{0}M=1-$ (the mean edge weight of the maximum spanning tree in $A^{a t t n}$ ).
接下来，我们计算每个条形码的描述性特征，例如条带长度的总和/平均值/方差、出生/死亡时间大于/小于阈值的条带数量，以及条形码的熵。条带长度总和 $(H_{0}S)$ 对应0维条形码，表示 $A^{\prime\prime}\mathrm{s}$ 最小生成树中的边权重总和。条带平均长度 $(H_{0}M)$ 对应该树的平均边权重，即 $H_{0}M=1-$ ( $A^{a t t n}$ 中最大生成树的平均边权重 ) 。
Figure 2: A graphical representation of RTD-barcodes. In the top row given $A^{\prime}$ matrices derived from attention maps for acceptable and unacceptable sentences. Edges present in both graphs $G_{a}^{\alpha_{i}}$ and $G_{b}^{\alpha_{i}}$ at a given threshold $\alpha_{i}$ are colored in grey. Edges present only in graph $G_{b}^{\alpha_{i}}$ are colored in green.
图 2: RTD条形码的图形化表示。顶行展示了从可接受与不可接受句子的注意力图导出的$A^{\prime}$矩阵。在给定阈值$\alpha_{i}$下，同时存在于图$G_{a}^{\alpha_{i}}$和图$G_{b}^{\alpha_{i}}$中的边以灰色显示，仅存在于图$G_{b}^{\alpha_{i}}$中的边以绿色显示。
Features Based on Distance to Patterns. The shape of attention graphs can be divided into several patterns: attention to the previous/current/next token, attention to the [SEP]/[CLS] token, and attention to punctuation marks (Clark et al., 2019). We formalize attention patterns by binary matrices and calculate distances to them as follows. We take the Frobenius norm of the difference between the matrices normalized by the sum of their norms. The distances to patterns are used as a feature vector.
基于模式距离的特征。注意力图形态可分为若干模式：关注前一个/当前/后一个token、关注[SEP]/[CLS]token、关注标点符号 (Clark et al., 2019)。我们通过二元矩阵形式化注意力模式，并按如下方式计算其距离：取矩阵差值的Frobenius范数（经范数之和归一化）。模式距离被用作特征向量。
Notations. We summarize the notations used throughout the paper:
符号说明。我们总结了本文中使用的符号：
• $H_{i}$ : $i$ -th Homology Group • $\beta_{i}$ : Betti number, dimension of $H_{i}$ • $H_{0}S$ : The sum of lengths of bars • $H_{0}M$ : The average of lengths of bars • $P C A$ : Principal Component Analysis • $P C^{{i}}$ : Subset ${i}$ of principal components • MST : Maximum Spanning Tree • RTD: Representation Topology Divergence
• $H_{i}$: 第$i$个同调群
• $\beta_{i}$: 贝蒂数 (Betti number)，$H_{i}$的维度
• $H_{0}S$: 条形长度之和
• $H_{0}M$: 条形长度的平均值
• $PCA$: 主成分分析 (Principal Component Analysis)
• $PC^{{i}}$: 主成分子集${i}$
• MST: 最大生成树 (Maximum Spanning Tree)
• RTD: 表示拓扑分歧 (Representation Topology Divergence)
3.3 Representation Topology Divergence
3.3 表示拓扑差异 (Representation Topology Divergence)
Representation Topology Divergence (RTD; Barannikov et al., 2022) measures topological dissimilarity between a pair of weighted graphs with oneto-one vertex correspondence. Figure 2 outlines computation of RTD for a sentence pair in Exam
表征拓扑差异 (Representation Topology Divergence, RTD; Barannikov等, 2022) 用于衡量具有顶点一一对应关系的两个加权图之间的拓扑差异。图2展示了示例中句子对的RTD计算过程。
ple (2).
ple (2).
(2) a. Cheryl had trained Tara. b. *Cheryl had murmured Tara.
(2) a. Cheryl 训练过 Tara。 b. *Cheryl 曾低声对 Tara 说话。
First, we compute attention maps for the input sentences $S_{a}$ and $S_{b}$ with a Transformer LM, and represent them as the weighted graphs $G_{a}$ and $G_{b}$ . Next, we establish a one-to-one match between the vertices, and sort the filtration s $G_{a}^{\alpha_{i}}$ and $G_{b}^{\alpha_{i}}$ with $\alpha{=}1-\tau$ in the ascending order. We then track the hierarchical formation of connected components in the graph $G_{a}^{\alpha_{i}}\cap G_{b}^{\alpha_{i}}$ while increasing $\alpha_{i}$ . The $\mathrm{\calRTD}(G_{a},G_{b})$ feature appears at threshold $\alpha_{i}$ if an edge with the weight $\alpha_{i}$ in the graph $G_{b}$ joins two different connected components of the graph $G_{a}^{\alpha_{i}}\cap G_{b}^{\alpha_{i}}$ . This feature disappears at the threshold $\alpha_{j}$ if the two $G_{a}^{\alpha_{i}}\cap G_{b}^{\alpha_{i}}$ connected components become joined in the graph $G_{a}^{\alpha_{j}}$ .
首先，我们使用Transformer LM计算输入句子$S_{a}$和$S_{b}$的注意力图，并将其表示为加权图$G_{a}$和$G_{b}$。接着，我们在顶点之间建立一一对应关系，并按升序对过滤后的图$G_{a}^{\alpha_{i}}$和$G_{b}^{\alpha_{i}}$进行排序，其中$\alpha{=}1-\tau$。然后，在逐步增加$\alpha_{i}$的过程中，我们追踪图$G_{a}^{\alpha_{i}}\cap G_{b}^{\alpha_{i}}$中连通分量的层次形成情况。如果在图$G_{b}$中权重为$\alpha_{i}$的边连接了图$G_{a}^{\alpha_{i}}\cap G_{b}^{\alpha_{i}}$的两个不同连通分量，则$\mathrm{\calRTD}(G_{a},G_{b})$特征会在阈值$\alpha_{i}$处出现。如果这两个$G_{a}^{\alpha_{i}}\cap G_{b}^{\alpha_{i}}$连通分量在图$G_{a}^{\alpha_{j}}$中合并，则该特征会在阈值$\alpha_{j}$处消失。
Example. We can identify the “birth” of the RTD feature at $\alpha{=}0.47$ , when an edge appears in $G_{b}^{\alpha=0.47}$ between the connected component “trained/murmured” and the connected component with four vertices, namely “[SEP]”, “[CLS]”, “.”, and “Tara” (Figure 2; the appearing edge is colored in green). We observe its “death”, when the edge becomes present in both attention graphs at $\alpha{=}0.65$ (the corresponding edge changes its color to grey in the graph $G_{a}^{\bar{\alpha}=0.65}\cap G_{b}^{\alpha=0.65}.$ ). When comparing the graphs in this manner, we can associate a lifetime to the feature by computing the difference between the moments of its “death” (e.g., $\alpha_{j}{=}0.65)$ and “birth” (e.g., $\alpha_{i}{=}0.47)$ . The lifetimes are illustrated as the orange bars $[\alpha_{i},\alpha_{j}]$ in Figure 2. The resulting value of $\mathsf{R T D}(G_{a},G_{b})$ is the sum of lifetimes $\alpha_{j}-\alpha_{i}$ over all such features. A formal description of RTD is provided in Appendix A.
示例。我们可以在$\alpha{=}0.47$时识别RTD特征的"诞生"，此时$G_{b}^{\alpha=0.47}$中在连通分量"trained/murmured"与包含四个顶点("[SEP]","[CLS]",".","Tara")的连通分量之间出现了一条边(图2；新出现的边显示为绿色)。当该边在$\alpha{=}0.65$时同时出现在两个注意力图中(对应边在$G_{a}^{\bar{\alpha}=0.65}\cap G_{b}^{\alpha=0.65}$中变为灰色)，我们观察到该特征的"消亡"。通过这种方式比较图结构，我们可以通过计算特征"消亡"(如$\alpha_{j}{=}0.65$)与"诞生"(如$\alpha_{i}{=}0.47$)时刻的差值来确定其特征生命周期。这些生命周期在图2中显示为橙色区间$[\alpha_{i},\alpha_{j}]$。$\mathsf{R T D}(G_{a},G_{b})$的最终值是所有这些特征生命周期$\alpha_{j}-\alpha_{i}$的总和。RTD的形式化定义详见附录A。
4 Acceptability Classification
4 可接受性分类
4.1 Data
4.1 数据
We use three LA classification benchmarks in English (COLA; Warstadt et al., 2019), Italian (ITACOLA; Trotta et al., 2021) and Swedish (DALAJ; Volodina et al., 2021). COLA and ITACOLA contain sentences from linguistic textbooks and cover morphological, syntactic, and semantic phenomena. The target labels are the original authors’ acceptability judgments. DALAJ includes L2-written sentences with morphological violations or incorrect word choices. The benchmark statistics are described in Table 1 (see Appendix C). We provide examples of acceptable and unacceptable sentences in English (3), Italian (4), and Swedish (5) from the original papers.
我们使用了三个英语 (COLA; Warstadt等人, 2019)、意大利语 (ITACOLA; Trotta等人, 2021) 和瑞典语 (DALAJ; Volodina等人, 2021) 的语言可接受性分类基准。COLA和ITACOLA包含来自语言学教材的句子，涵盖形态、句法和语义现象，目标标签是原作者的可接受性判断。DALAJ包含存在形态违规或用词错误的二语写作句子。基准统计数据如 表 1 所示 (见附录C)。我们从原始论文中选取了英语 (3)、意大利语 (4) 和瑞典语 (5) 的可接受与不可接受句子示例。
4.2 Models
4.2 模型
We run the experiments on the following Transformer LMs: En-BERT-base (Devlin et al., 2019), It-BERT-base (Schweter, 2020), Sw-BERT- base (Malmsten et al., 2020), and XLM-Rbase (Conneau et al., 2020). Each LM has two instances: frozen (a pre-trained model with frozen weights), and fine-tuned (a model fine-tuned for LA classification in the corresponding language).
我们在以下Transformer模型上进行了实验：En-BERT-base (Devlin et al., 2019)、It-BERT-base (Schweter, 2020)、Sw-BERT-base (Malmsten et al., 2020)和XLM-Rbase (Conneau et al., 2020)。每个模型包含两种实例：冻结权重(frozen)的预训练模型，以及针对相应语言进行LA分类任务微调(fine-tuned)的模型。
Baselines. We use the fine-tuned LMs, and a linear layer trained over the pooler output from the frozen LMs as baselines.
基线方法。我们使用微调后的语言模型(LMs)，以及在冻结语言模型的池化输出(pooler output)上训练的线性层作为基线。
Our Models. We train Logistic Regression classifiers over the persistent features computed with each model instance: $(i)$ the average length of bars $(H_{0}M)$ ; (ii) concatenation of all topological features referred to as TDA (§3.2). Following Warstadt et al., we evaluate the performance with the accuracy score (Acc.) and Matthew’s Correlation Co
我们的模型。我们在每个模型实例计算的持久特征上训练逻辑回归分类器：(i) 柱状图的平均长度 $(H_{0}M)$；(ii) 所有拓扑特征的拼接，称为TDA（见3.2节）。遵循Warstadt等人的方法，我们使用准确率（Acc.）和马修斯相关系数（Matthew’s Correlation Co）评估性能。
| 模型 | 冻结语言模型 | 分布外数据/测试集 Acc.MCC | 微调语言模型 Acc.MCC | 分布内数据/开发集 分布外数据/测试集 | |||
|---|---|---|---|---|---|---|---|
| CoLA | |||||||
| En-BERT | 69.6 | 0.037 | 69.0 | 0.082 | 83.1 0.580 | 81.0 | 0.536 |
| En-BERT+HOM | 75.0 | 0.338 | 75.2 | 0.372 | 85.2 | 0.635 81.2 | 0.542 |
| En-BERT+TDA | 77.2 | 0.420 | 76.7 | 0.420 | 88.6 0.725 | 82.1 | 0.565 |
| XLM-R | 68.9 | 0.041 | 68.6 | 0.072 | 80.8 0.517 | 79.3 | 0.489 |
| XLM-R+HOM | 71.3 | 0.209 | 69.8 | 0.187 | 81.2 0.532 | 77.7 | 0.445 |
| XLM-R + TDA | 73.0 | 0.336 | 70.3 | 0.297 | 86.9 0.683 | 80.4 | 0.522 |
| ItaCoLA | |||||||
| It-BERT | 81.1 | 0.032 | 82.1 | 0.140 | 87.4 0.351 | 86.8 | 0.382 |
| It-BERT+HOM | 85.0 | 0.124 | 83.6 | 0.055 | 87.0 0.361 | 85.7 | 0.370 |
| It-BERT + TDA | 89.2 | 0.478 | 85.8 0.352 | 91.1 | 0.597 | 86.4 | 0.424 |
| XLM-R | 85.4 | 0.000 | 84.2 0.000 | 85.7 | 0.397 | 85.6 | 0.434 |
| XLM-R+ H0M | 84.7 | 0.095 | 83.3 0.072 | 86.9 | 0.370 | 86.6 | 0.397 |
| XLM-R + TDA | 88.3 | 0.411 | 84.4 | 0.208 92.8 | 0.683 | 86.1 | 0.398 |
| DaLAJ | |||||||
| Sw-BERT | 58.3 | 0.183 | 59.0 | 0.188 | 71.9 | 0.462 | 74.2 0.500 |
| Sw-BERT+HOM | 69.3 | 0.387 | 58.4 | 0.169 | 76.9 0.542 | 68.7 | 0.375 |
| Sw-BERT+TDA | 62.1 | 0.243 | 64.4 | 0.289 | 71.8 0.442 | 73.4 | 0.478 |
| XLM-R | 52.2 | 0.069 | 51.5 | 0.038 | 60.6 0.243 | 62.8 | 0.297 |
| XLM-R+ H0M | 61.1 | 0.224 | 61.8 | 0.237 | 62.5 0.256 | 64.5 | 0.295 |
| XLM-R + TDA | 51.1 | 0.227 | 54.1 | 0.218 | 62.5 0.255 | 65.5 | 0.322 |
Table 1: Acceptability classification results by benchmark. $\mathbf{ID}\mathbf{D}{=}^{\circ}$ “in domain dev” set (COLA). OODD $\vDash^{\epsilon}$ “out of domain dev” set (COLA). Dev; Test=dev and test sets in ITACOLA and DALAJ. The best score is put in bold, the second best score is underlined.
表 1: 各基准测试的 acceptability 分类结果。$\mathbf{ID}\mathbf{D}{=}^{\circ}$ 表示 "in domain dev" 集 (COLA)。OODD $\vDash^{\epsilon}$ 表示 "out of domain dev" 集 (COLA)。Dev; Test=ITACOLA 和 DALAJ 中的开发集和测试集。最佳分数加粗显示，次佳分数加下划线。
efficient (MCC; Matthews, 1975). The fine-tuning details are provided in Appendix B.
高效 (MCC; Matthews, 1975)。微调细节详见附录B。
4.3 Results
4.3 结果
Table 1 outlines the LA classification results. Our $T D A$ class if i ers generally outperform the baselines by up to $\mathrm{0.14MCC}$ for English, $\mathrm{0.24MCC}$ for Italian, and $\mathrm{0.08MCC}$ for Swedish. The $H_{0}M$ feature can solely enhance the performance for English and Italian up to 0.1, and concatenation of all features receives the best scores. Comparing the results under the frozen and fine-tuned settings, we draw the following conclusions. The TDA features significantly improve the frozen baseline performance but require the LM to be fine-tuned for maximizing the performance. However, the $T D A/H_{0}M$ classifiers perform on par with the fine-tuned baselines for Swedish. The results suggest that our features may fail to infer lexical items and word derivation violations peculiar to the DALAJ benchmark.
表1: 概述了LA分类结果。我们的TDA分类器在英语上最高提升0.14MCC，意大利语提升0.24MCC，瑞典语提升0.08MCC，整体优于基线模型。H0M特征单独使用可将英语和意大利语性能提升最高达0.1，而所有特征的组合能获得最佳分数。通过对比冻结参数和微调设置的实验结果，我们得出以下结论：TDA特征能显著提升冻结基线的性能，但需要微调语言模型以实现最大性能提升。不过对于瑞典语，TDA/H0M分类器与微调基线表现相当。这些结果表明，我们的特征可能无法有效推断DALAJ基准测试中特有的词汇项和构词违规情况。
Effect of Freezing Layers. Another finding is that freezing the Transformer layers significantly affects acceptability classification. Most of the frozen baselines score less than $0.1~\mathrm{MCC}$ across all languages. The results align with Lee et al. (2019), who discuss the performance degradation of BERT-based models depending upon the number of frozen layers. With all layers frozen, the model performance can fall to zero.
冻结层数的影响。另一个发现是冻结Transformer层会显著影响可接受性分类效果。在所有语言中，大多数冻结基线的得分都低于$0.1~\mathrm{MCC}$。该结果与Lee等人(2019)的研究一致，他们讨论了基于BERT的模型性能会随冻结层数增加而下降。当所有层都被冻结时，模型性能可能降至零。
Figure 3: Performance (MCC) of the fine-tuned EnBERT and XLM-R by major linguistic feature. Average MCC scores are represented with dashed lines. The number of sentences including the feature is placed in square brackets.
图 3: 按主要语言特征细调的EnBERT和XLM-R性能(MCC)。虚线表示平均MCC分数。包含该特征的句子数量标注在方括号中。
Results by Linguistic Features. We run a diagnostic evaluation of the fine-tuned models using a grammatically annotated version of the COLA development set (Warstadt and Bowman, 2019). Figure 3 (En-BERT and XLM-R; Figure 1 in Appendix C.1) present the results of measuring the MCC of the sentences including the major features.
基于语言特征的实验结果。我们使用经过语法标注的COLA开发集(Warstadt and Bowman, 2019)对微调模型进行诊断性评估。图3(En-BERT和XLM-R；附录C.1中的图1)展示了包含主要特征的句子MCC测量结果。
The overall pattern is that the TDA class if i ers may outperform the fine-tuned baselines, while the $H_{0}M$ ones perform on par with the latter. The per- formance is high on sentences with default syntax (Simple) and marked argument structure, including prepositional phrase arguments (Arg. Type), and verb phrases with unusual structures (Arg. Altern). The $T D A$ features capture surface properties, such as presence of auxiliary or modal verbs (Auxiliary), and structural ones, e.g., embedded complement clauses (Comp Clause) and infinitive constructions (to-VP). The models receive moderate MCC scores on sentences with question-like properties (Question), adjuncts performing semantic functions (Adjunct), negative polarity items, and comparative constructions (Determiner).
整体模式表现为：TDA 分类器可能优于微调基线模型，而 $H_{0}M$ 类模型与后者表现相当。在默认句法结构（Simple）、带标记论元结构（包括介词短语论元 (Arg. Type) 和特殊结构动词短语 (Arg. Altern)）的句子上表现优异。$T D A$ 特征能捕捉表层属性（如助动词或情态动词的存在 (Auxiliary)）和结构属性（例如嵌入式补语从句 (Comp Clause) 和不定式结构 (to-VP)）。模型在具有疑问句特性 (Question)、执行语义功能的附加语 (Adjunct)、否定极性项和比较结构 (Determiner) 的句子上获得中等MCC分数。
Analysis of the Feature Space. The LA classification experiments are conducted in the sparse feature space, where the TDA features can strongly correlate with one another, and their contribution is unclear. We run a complementary experiment to understand better how linguistic features are modeled with topology. We investigate the feature space with dimensionality reduction (principal component analysis, PCA; Pearson, 1901) by interpreting components’ structure and identifying the feature importance to the classifier’s predictions using Shapley values (Shapley, 1953), a game-theoretic approach to the attribution problem (Sun dara rajan and Najmi, 2020). Appendix C.2 describes the experiment on the fine-tuned En-BERT $+T D A$ model using the grammatically annotated COLA development set.
特征空间分析。LA分类实验在稀疏特征空间中进行，其中TDA特征之间可能存在强相关性，且其贡献尚不明确。我们通过补充实验来进一步理解如何用拓扑结构建模语言特征。采用降维方法（主成分分析，PCA；Pearson, 1901）研究特征空间，通过解释主成分结构并结合博弈论归因方法Shapley值（Shapley, 1953）(Sun dara rajan and Najmi, 2020)来识别特征对分类器预测的重要性。附录C.2描述了基于语法标注COLA开发集对微调后的En-BERT $+T D A$ 模型开展的实验。
The results show that (i) features of the higherlayer heads, such as the average vertex degree, the number of connected components, edges, and cycles, and attention to the current token, contribute most to the major linguistic features. (ii) Attention to the [CLS]/next token is important to the Determiner, Arg. Type, Comp Clause, and to-VP properties, while attention to the first token and punctuation marks has the least effect in general. (iii) The number of nodes influences the classifier behavior, which is in line with Warstadt and Bowman, who discuss the effect of the sentence length on the performance.
结果表明：(i) 高层注意力头(head)的特征（如平均顶点度数、连通组件数量、边与环的数量、对当前token的关注度）对主要语言特征贡献最大。(ii) 对[CLS]/下一token的关注度对限定词(Determiner)、论元类型(Arg. Type)、补语从句(Comp Clause)和不定式动词短语(to-VP)属性具有重要影响，而对首token和标点符号的关注度总体影响最小。(iii) 节点数量会影响分类器行为，这与Warstadt和Bowman讨论的句子长度对性能的影响一致[20]。
5 Linguistic Minimal Pairs
5 语言学最小对立对
5.1 Data
5.1 数据
BLIMP (Benchmark of Linguistic Minimal Pairs; Warstadt et al., 2020a) evaluates the sen- sitivity of LMs to acceptability contrasts in terms of a forced choice between minimal pairs, as in Example (6). The benchmark consists of 67 pair types, each including 1k pairs covering 12 language phenomena in morphology, syntax, and semantics.
BLIMP（语言最小对比基准测试；Warstadt等人，2020a）通过强制选择最小对比对（如示例(6)）来评估大语言模型对可接受性对比的敏感度。该基准包含67种对比类型，每种涵盖形态、句法和语义等12种语言现象的1000组对比对。
(6) a. Whose hat should Tonya wear? b. *Whose should Tonya wear hat?
(6) a. Tonya应该戴谁的帽子？ b. *Tonya应该戴谁的帽子？
5.2 Models
5.2 模型
We conduct the experiments using two Transformer LMs for English: BERT-base and RoBERTabase (Liu et al., 2019).
我们使用两个针对英语的Transformer语言模型进行实验：BERT-base和RoBERTabase (Liu et al., 2019)。
Baselines. We compare our methods with the results on BLIMP for human annotators and nine LMs (Warstadt et al., 2020a; Salazar et al., 2020). The baselines range from statistical N-gram LMs to Transformer LMs.
基线方法。我们将自身方法与BLIMP数据集上的人类标注结果及九种语言模型 (Warstadt et al., 2020a; Salazar et al., 2020) 进行对比，基线方法涵盖统计N元语言模型至Transformer语言模型。
Our Models. Given a minimal pair as in Example (2), we build attention graphs $G_{a}$ and $G_{b}$ from each attention head of a frozen Transformer LM. We use the $H_{0}M$ feature (§3.2) and RTD (§3.3) as scoring functions to distinguish between the sentences $S_{a}$ and $S_{b}$ . The scoring is based on empirically defined decision rules modeled after the forced-choice task:
我们的模型。给定如示例(2)中的最小对比对，我们从冻结的Transformer LM的每个注意力头构建注意力图$G_{a}$和$G_{b}$。我们使用$H_{0}M$特征(§3.2)和RTD(§3.3)作为评分函数来区分句子$S_{a}$和$S_{b}$。评分基于根据强制选择任务建模的经验定义决策规则:
We evaluate the scoring performance of each attention head, head ensembles, and all heads w.r.t. each and all linguistic phenomena in BLIMP. The following head configurations are used for each Transformer LM and scoring function:
我们评估了每个注意力头、注意力头组合以及所有注意力头在BLIMP中针对每种及所有语言现象的打分表现。针对每个Transformer语言模型和打分函数，采用了以下注意力头配置：
• Phenomenon Head and Top Head are the bestperforming attention heads for each and all phenomena, respectively. The heads undergo the selection with a brute force search and operate as independent scorers. • Head Ensemble is a group of the bestperforming attention heads selected with beam search. The size of the group is always odd. We collect majority vote scores from attention heads in the group. • All Heads involves majority vote scoring with all 144 heads. We use random guessing in case of equality of votes. This setup serves as a proxy for the efficiency of the head selection.
• Phenomenon Head 和 Top Head 分别是针对每种现象和所有现象表现最佳的注意力头。这些头通过暴力搜索进行选择，并作为独立评分器运行。
• Head Ensemble 是通过束搜索选出的表现最佳的一组注意力头。该组的大小始终为奇数。我们从组内的注意力头中收集多数投票分数。
• All Heads 涉及使用全部 144 个头进行多数投票评分。在票数相等时采用随机猜测。此设置作为头选择效率的代理指标。
Notes on Head Selection. Recall that the head selection procedure3 imposes the following limitation. Auxiliary labeled minimal pairs are required to find the best-performing Phenomenon, Top Heads, and Head Ensembles. However, this procedure is more optimal and beneficial than All Heads since it maximizes the performance when utilizing only one or 9-to-59 heads. We also analyze the effect of the amount of auxiliary data used for the head selection on the scoring performance (§5.3). Appendix D.1 presents a more detailed description of the head selection procedure.
头选择注意事项。回顾头选择过程3存在以下限制：需要辅助标记的最小对来寻找表现最佳的现象(Phenomenon)、顶部头(Top Heads)和头集成(Head Ensembles)。但该过程比全头(All Heads)更优且有益，因为仅使用1个或9至59个头时能最大化性能。我们还分析了用于头选择的辅助数据量对评分性能的影响(§5.3)。附录D.1提供了头选择过程的更详细说明。
5.3 Results
5.3 结果
We provide the results of scoring BLIMP pairs in Table 2. The accuracy is the proportion of the minimal pairs in which the method prefers an acceptable sentence to an unacceptable one. We report the maximum accuracy scores for our methods across five experiment restarts. The general trends are that the best head configuration performs on par with the human baseline and achieves the high- est overall performance (RoBERTa-base $^+$ RTD; Head Ensemble). RoBERTa predominantly surpasses BERT and other baselines, and topological scoring may improve on scores from both BERT and RoBERTa for particular phenomena.
我们在表2中提供了BLIMP配对评分的结果。准确率是指该方法在最小配对中偏好可接受句子而非不可接受句子的比例。我们报告了五次实验重启中方法的最高准确率分数。总体趋势表明，最佳头部配置与人类基线表现相当，并达到最高整体性能 (RoBERTa-base $^+$ RTD; Head Ensemble)。RoBERTa主要超越BERT和其他基线，而拓扑评分可能针对特定现象改进BERT和RoBERTa的分数。
Top Head Results. We find that $H_{0}M/\mathrm{RTD}$ scoring with only one Top Head overall outperforms majority voting of 144 heads (All Heads) by up to $10.6%$ and multiple baselines by up to $20.7%$ (5- gram, LSTM, Transformer-XL, GPT2-large). However, this head configuration performs worse than masked LM scoring (Salazar et al., 2020) for BERTbase (by $8.8%$ ; Top Head=[8; 0]) and RoBERTa- base (by $4.6%$ ; Top Head=[11; 10]).
顶级头部结果。我们发现仅使用一个顶级头部的 $H_{0}M/\mathrm{RTD}$ 评分方法在整体上优于144个头部（所有头部）多数投票（All Heads），最高提升 $10.6%$，并且优于多个基线方法（5-gram、LSTM、Transformer-XL、GPT2-large），最高提升 $20.7%$。然而，这种头部配置在BERTbase（下降 $8.8%$；Top Head=[8; 0]）和RoBERTa-base（下降 $4.6%$；Top Head=[11; 10]）上的表现不如掩码语言模型评分（Salazar et al., 2020）。
Phenomenon Head Results. We observe that the $H_{0}M/\mathrm{TDA}$ scoring performance of Phenomenon Heads insignificantly differ for the same model. Phenomenon Heads generally receive higher scores than the corresponding Top Heads for BERT/RoBERTa (e.g., Binding: $+17.1/+5.8%$ ; Quantifiers: $+17.7/+5.0%$ ; Det.- Noun agr: $+13.0/+1.7%\rangle$ , and perform best or second-best on Binding and Ellipsis. Their overall performance further adds up to $6.4/6.0%$ and is comparable with Salazar et al.. The results indicate that heads encoding the considered phenomena are distributed at the same or nearby layers, namely [3; 6-9; 11] (BERT), and [2-3; 8-11] (RoBERTa).
现象头结果。我们观察到，同一模型中现象头的 $H_{0}M/\mathrm{TDA}$ 评分表现差异不显著。对于BERT/RoBERTa，现象头通常比对应的Top Heads获得更高分数（例如：绑定(Binding): $+17.1/+5.8%$；量词(Quantifiers): $+17.7/+5.0%$；限定词-名词一致(Det.-Noun agr): $+13.0/+1.7%\rangle$，且在绑定和省略(Ellipsis)任务上表现最佳或次佳。其整体性能进一步提升至 $6.4/6.0%$，与Salazar等人的研究相当。结果表明，编码这些现象的头部分布在相同或邻近的层，即BERT的[3; 6-9; 11]层和RoBERTa的[2-3; 8-11]层。
Head Ensemble Results. Table 3 describes the most optimal Head Ensembles by Transformer LM. Most heads selected under the $H_{0}M$ and RTD scoring functions are similar w.r.t. LMs. While the selected BERT heads are distributed across all layers, the RoBERTa ones tend to be localized at the middle-to-higher layers. Although RoBERTa utilizes smaller ensembles when delivering the best overall score, some heads contribute in both LMs, most notably at the higher layers.
头集成结果。表3描述了Transformer LM最优的头集成。在$H_{0}M$和RTD评分函数下选择的大多数头对于LMs来说是相似的。虽然选择的BERT头分布在所有层中，但RoBERTa的头往往集中在中高层。尽管RoBERTa在提供最佳总体分数时使用了较小的集成，但某些头在两种LMs中都有贡献，尤其是在较高层。
Overall, the RoBERTa $H_{0}M/\mathrm{RTD}$ ensembles get the best results on Filler gap, Quantifiers, Island effects, NPI, and $S{-}V$ agr as shown in Table 2, matching the human level and surpassing four larger LMs on all phenomena by up to $7.4%$ (GPT2- medium and GPT2/BERT/RoBERTa-large).
总体而言，RoBERTa $H_{0}M/\mathrm{RTD}$ 集成模型在填充间隙 (Filler gap) 、量词 (Quantifiers) 、孤岛效应 (Island effects) 、否定极性项 (NPI) 以及 $S{-}V$ 一致性任务中取得了最佳结果（如 表 2 所示），达到人类水平，并在所有语言现象上以最高 $7.4%$ 的优势超越 GPT2-medium、GPT2/BERT/RoBERTa-large 四个更大的大语言模型。
| 模型 | 总体 | 分析一致性 | 论元结构 | 约束 | 控制/提升 | 名数一致性 | 省略 | 填充词 | 不规则 | 孤岛 | NPI | 量化 | 主谓一致性 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Warstadt et al. (2020a) | |||||||||||||
| 5-gram | 61.2 | 47.9 | 71.9 | 64.4 | 68.5 | 70.0 | 36.9 | 60.2 | 79.5 | 57.2 | 45.5 | 53.5 | 60.3 |
| LSTM | 69.8 | 91.7 | 73.2 | 73.5 | 67.0 | 85.4 | 67.6 | 73.9 | 89.1 | 46.6 | 51.7 | 64.5 | |
| Transformer-XL | 69.6 | 94.1 | 72.2 | 74.7 | 71.5 | 83.0 | 77.2 | 66.6 | 78.2 | 48.4 | 55.2 | 69.3 | |
| GPT2-large | 81.5 | 99.6 | 78.3 | 80.1 | 80.5 | 93.3 | 86.6 | 81.3 | 84.1 | 70.6 | 78.9 | 71.3 | |
| 人类基线 | 88.6 | 97.5 | 90.0 | 87.3 | 83.9 | 92.2 | 85.0 | 86.9 | 97.0 | 84.9 | 88.1 | 86.6 | |
| Salazar et al. (2020) | |||||||||||||
| GPT2-medium | 82.6 | 99.4 | 83.4 | 77.8 | 83.0 | 96.3 | 86.3 | 81.3 | 94.9 | 71.7 | 74.7 | 74.1 | |
| BERT-base | 84.2 | 97.0 | 80.0 | 82.3 | 79.6 | 97.6 | 89.4 | 83.1 | 96.5 | 73.6 | 84.7 | 71.2 | |
| BERT-large | 84.8 | 97.2 | 80.7 | 82.0 | 82.7 | 97.6 | 86.4 | 84.3 | 92.8 | 77.0 | 83.4 | 72.8 | |
| RoBERTa-base | 85.4 | 97.3 | 83.5 | 77.8 | 81.9 | 97.0 | 91.4 | 90.1 | 96.2 | 80.7 | 81.0 | 69.8 | |
| RoBERTa-large | 86.5 | 97.8 | 84.6 | 79.1 | 84.1 | 96.8 | 90.8 | 88.9 | 96.8 | 83.4 | 85.5 | 70.2 | |
| BERT-base + HoM | |||||||||||||
| [层; 头] | [8:8] | [0:8] | [7;0] | [8;0] | [7;0] | [7;11] | [9;7] | [6;1] | [11;7] | [8;9] | [3;7] | ||
| 现象头 | 81.7 | 94.9 | 75.9 | 80.4 | 79.2 | 96.7 | 89.1 | 75.9 | 93.0 | 70.5 | 84.6 | 81.2 | |
| 顶级头 [8:0] 头集成 | 75.4 | 86.8 | 75.9 | 63.4 | 79.2 | 83.7 | 72.2 | 67.3 | 90.3 | 70.0 | 83.1 | 63.5 | |
| 所有头 | 84.3 | 93.3 | 79.9 | 83.5 | 78.6 | 96.4 | 78.4 | 79.5 | 93.8 | 74.4 | 92.5 | 81.7 | |
| 64.8 | 79.6 | 69.1 | 63.9 | 62.6 | 86.2 | 70.7 | 47.3 | 90.7 | 49.5 | 61.1 | 50.0 | ||
| BERT-base + RTD | |||||||||||||
| [层; 头] | X | [8;3] | [8;0] | [7;0] | [8;0] | [7;0] | [7;11] | [9;7] | [6;1] | [9;7] | [8;9] | [3;7] | |
| 现象头 | 81.8 | 94.5 | 75.8 | 80.4 | 79.2 | 96.7 | 89.1 | 75.0 | 93.0 | 72.2 | 84.4 | 81.2 | |
| 顶级头 [8;0] | 75.4 | 86.8 93.9 | 75.8 82.5 | 63.3 85.6 | 79.2 77.0 | 83.6 96.3 | 72.1 88.1 | 67.3 | 90.2 | 70.2 | 83.1 | 63.6 | |
| 头集成 所有头 | 85.8 | 77.8 | 68.5 | 63.2 | 63.6 | 86.0 | 80.7 | 95.7 | 77.0 | 92.5 62.0 | 83.8 51.2 | ||
| 65.3 | 73.4 | 48.4 | 91.0 | 51.3 | |||||||||
| RoBERTa-base + HoM | |||||||||||||
| [层; 头] | X | [9;5] | [9;8] | [9;5] | [9;6] | [9:0] | [8;4] | [11;10] | [9:6] | [3;5] | [11;5] | [11;3] | |
| 现象头 | 86.5 | 97.6 | 79.9 | 90.5 | 80.7 | 91.6 | 89.9 | 87.1 | 95.9 | 78.9 | 91.1 | 83.4 | |
| 顶级头 [11;10] | 81.9 | 90.1 | 66.0 | 84.7 | 71.7 | 91.0 | 86.7 | 87.1 | 89.5 | 76.8 | 90.7 | 78.4 | |
| 头集成 | 87.8 | 96.3 | 79.6 | 87.6 | 82.6 | 93.6 | 84.9 | 90.4 | 94.3 | 83.0 | 94.6 | 80.6 | |
| 所有头 RoBERTa-base + RTD | 74.3 | 80.6 | 71.2 | 78.6 | 67.8 | 90.6 | 89.9 | 75.5 | 65.1 | 73.4 | 65.1 | 57.0 |
Table 2: Percentage accuracy of the baseline models, human baseline, and our methods on BLIMP. Overall is the average across all phenomena. The best score is put in bold, the second best score is underlined.
表 2: 基线模型、人类基线及我们方法在BLIMP上的准确率百分比。Overall为所有现象的平均值。最佳分数加粗显示，次佳分数加下划线。
Table 3: Results of selecting the best-performing Head Ensembles with $H_{0}M,$ /RTD-based scoring. $H_{0}M$ heads are colored in green; RTD heads are colored in yellow.
表 3: 基于 $H_{0}M$ /RTD评分选取最佳性能头组合的结果。$H_{0}M$ 头标记为绿色；RTD头标记为黄色。
Effect of Auxiliary Data. Note that the head selection can be sensitive to the number of additional examples. The analysis of this effect is presented in Appendix D.2. The results show that head ensembles, their size, and average performance tend to be more stable when using sufficient examples (the more, the better); however, using only one extra example can yield the performance above $80%$ .
辅助数据的影响。需要注意的是，头部选择对额外样本数量较为敏感。附录D.2对此效应进行了分析，结果表明：当使用充足样本时（越多越好），头部集成方案、其规模及平均性能往往更稳定；但仅使用一个额外样本仍可使性能保持在80%以上。
6 Discussion
6 讨论
Topology and Acceptability. The topological properties of the attention graph represent interpretable and versatile features for judging sentence acceptability and identifying acceptability contrasts in minimal pairs. As one of such properties, the sum length of bars $(H_{0}S)$ — and its normalized version $(H_{0}M)$ — have proved to be efficient for both LA approaches. This simple feature can serve as a profitable input for LA class if i ers and a scoring function to discriminate between minimal pairs. Figure 4 shows an example of the $H_{0}S$ sensitivity to COLA’s question-like properties, such as whmovement out of syntactic islands and matrix and embedded questions. We provide more examples in Appendix E, which demonstrate the distribution shifts between the acceptable and unacceptable sentences.
拓扑结构与可接受性。注意力图的拓扑特性为判断句子可接受性和识别最小对立对中的可接受性对比提供了可解释且通用的特征。其中，条形图总长度 $(H_{0}S)$ 及其标准化版本 $(H_{0}M)$ 已被证明对两种LA方法均有效。这一简单特征可作为LA分类器的有益输入，并作为区分最小对立对的评分函数。图4展示了 $H_{0}S$ 对COLA疑问句特性的敏感性示例，如从句法孤岛提取wh成分、主句与嵌套疑问句等。附录E提供了更多案例，展示可接受句与不可接受句之间的分布差异。
Acceptability Phenomena. The underlying structure of the attention graph encodes various well-established grammatical concepts. We observe that the persistent graph features capture surface properties, morphological agreement, structural relationships, and simple/complex syntactic phenomena well. However, with topology, lexical items, optional syntactic elements, and abstract semantic factors may be difficult to infer. Attention to the first token and punctuation marks contribute least to LA classification, while the other attention pattern features capture various phenomena.
可接受性现象。注意力图的基础结构编码了各种公认的语法概念。我们观察到，持久图特征能较好地捕捉表层属性、形态一致性、结构关系以及简单/复杂句法现象。然而，仅凭拓扑结构、词汇项、可选句法元素和抽象语义因素可能难以推断。对首个token和标点符号的关注对LA分类贡献最小，而其他注意力模式特征则捕捉了多种现象。
Figure 4: The distribution shift of the $H_{0}S$ feature between the acceptable and unacceptable sentences (Question); [L: 10; H: 0].
图 4: 可接受与不可接受句子间 $H_{0}S$ 特征的分布偏移 (Question); [L: 10; H: 0]。
Linguistic Roles of Heads. Topological tools help gain empirical evidence about the linguistic roles of heads from another perspective. Our findings on the heads’ roles align with several related studies. The results on the COLA-style and BLIMP benchmarks indicate that $(i)$ a single head can perform multiple linguistic functions (Pande et al., 2021), $(i i)$ some linguistic phenomena, e.g., phrasal movement and island effects, are better captured by head ensembles rather than one head (Htut et al., 2019), and $(i i i)$ heads within the same or nearby layers extract similar grammatical phenomena (Bian et al., 2021).
头部的语言学角色。拓扑工具从另一个角度为头部在语言学中的角色提供了实证依据。我们的研究发现与多项相关研究一致：在COLA风格和BLIMP基准测试中，结果表明$(i)$单个头部可执行多种语言功能[20]，$(ii)$某些语言现象（如短语移位和孤岛效应）更适合通过头部组合而非单一头部来捕捉[19]，$(iii)$同一层或邻近层的头部会提取相似的语法现象[21]。
7 Conclusion and Future Work
7 结论与未来工作
Our paper studies the ability of attention heads to judge grammatical acceptability, demonstrating the profitable application of TDA tools to two LA paradigms. Topological features can boost LA classification performance in three typo logically close languages. The $H_{0}M/\mathrm{RTD}$ scoring matches or outperforms larger Transformer LMs and reaches human-level performance on BLIMP, while utilizing 9-to-59 attention heads. We also interpret the correspondence between the persistent features of the attention graph and grammatical concepts, revealing that the former efficiently infer morphological, structural, and syntactic phenomena but may lack lexical and semantic information.
我们的论文研究了注意力头判断语法可接受性的能力，展示了TDA工具在两种LA范式中的有效应用。拓扑特征可以在三种类型学相近的语言中提升LA分类性能。$H_{0}M/\mathrm{RTD}$评分与更大的Transformer大语言模型相当或更优，并在仅使用9至59个注意力头的情况下，在BLIMP上达到人类水平的表现。我们还解释了注意力图的持久特征与语法概念之间的对应关系，揭示了前者能有效推断形态、结构和句法现象，但可能缺乏词汇和语义信息。
In our future work we hope to assess the linguistic competence of Transformer LMs on related resources for typo logically diverse languages and analyze which language-specific phenomena are and are not captured by the topological features. We are also planning to examine novel features, e.g., the number of vertex covers, the graph clique-width, and the features of path homology (Grigor’yan et al., 2020). Another direction is to evaluate the benefits and limitations of the $H_{0}M/\mathrm{RTD}$ features as scoring functions in downstream applications.
在我们未来的工作中，我们希望评估Transformer大语言模型在类型学多样性语言相关资源上的语言能力，并分析哪些语言特定现象能被拓扑特征捕捉或遗漏。我们还计划研究新特征，例如顶点覆盖数、图团宽度以及路径同调特征 (Grigor’yan et al., 2020)。另一个方向是评估$H_{0}M/\mathrm{RTD}$特征作为下游应用评分函数的优势与局限性。
We also plan to introduce support for new deep learning frameworks such as MindSpore4 (Tong et al., 2021) to bring TDA-based experimentation to the wider industrial community.
我们还计划引入对MindSpore4 (Tong et al., 2021) 等新深度学习框架的支持，以便将基于TDA的实验推广至更广泛的工业界。
8 Limitations
8 局限性
8.1 Computational complexity
8.1 计算复杂度
Acceptability classification. Calculation of any topological feature relies on the Transformer’s attention matrices. Hence, the computational complexity of our features is not lower than producing an attention matrix with one head, which is asymptotically $O(n^{2}d+n d^{2})$ given that $n$ is the maximum number of tokens, and $d$ is the token embedding dimension (Vaswani et al., 2017).
可接受性分类。任何拓扑特征的计算都依赖于Transformer的注意力矩阵。因此，我们特征的计算复杂度不低于生成单头注意力矩阵的复杂度，其渐进复杂度为$O(n^{2}d+n d^{2})$，其中$n$表示token的最大数量，$d$表示token嵌入维度 (Vaswani et al., 2017)。
The calculation complexity of the patternbased and threshold-based features is done in linear time $O(e+n)$ , where $e$ is the number of edges in the attention graph. In turn, the number of edges is not higher than $\frac{n(n-1)}{2}\sim n^{2}$ ) n2. The computation of the ${\bf0}^{t h}$ Betti number $\beta_{0}$ takes linear time $O(e+n)$ , as $\beta_{0}$ is equal to the number of the connected components in an undirected graph. The computation of the ${\bf1}^{s t}$ Betti number $\beta_{1}$ takes constant time, since $\beta_{1}=e-n+\beta_{0}$ . The computational complexity of the number of simple cycles and the 1-dimensional barcode features is exponential in the worst case. To reduce the computational burden, we stop searching for simple cycles after a pre-defined amount of them is found.
基于模式和基于阈值的特征计算复杂度为线性时间 $O(e+n)$ ，其中 $e$ 是注意力图中的边数。而边数不超过 $\frac{n(n-1)}{2}\sim n^{2}$ ) n2。计算第 ${\bf0}^{t h}$ 个贝蒂数 $\beta_{0}$ 需要线性时间 $O(e+n)$ ，因为 $\beta_{0}$ 等于无向图中连通分量的数量。计算第 ${\bf1}^{s t}$ 个贝蒂数 $\beta_{1}$ 只需常数时间，因为 $\beta_{1}=e-n+\beta_{0}$ 。简单环数量和1维条形码特征的计算复杂度在最坏情况下是指数级的。为了降低计算负担，我们在找到预定义数量的简单环后停止搜索。
Note that the computational costs could be reduced, e.g., by identifying the most contributing features or the best-performing heads. Consider an example in Figure 5, which illustrates how the COLA performance gets changed depending on the number of En-BERT heads. Here, the head selection is based on a simple procedure. First, we score the attention heads by calculating the maximum correlation between each head’s features and the vector of the target classes on the train set. Second, we train a linear classifier over the $T D A$ features produced by $N$ attention heads ranked by the correlation values, as specified in $\S4.2$ . Satisfactory MCC scores can be achieved when utilizing less than 40 heads with a significant speed up at the inference stage.
请注意，计算成本可以通过识别贡献最大的特征或表现最佳的注意力头来降低。以图 5 为例，它展示了 COLA 性能如何随 En-BERT 注意力头数量的变化而变化。这里的头选择基于一个简单流程：首先，我们通过计算每个头的特征与训练集上目标类别向量之间的最大相关性来对注意力头进行评分；其次，如 $\S4.2$ 所述，我们根据相关性值排序的 $N$ 个注意力头生成的 $T D A$ 特征训练线性分类器。当使用少于 40 个头时，可以在推理阶段显著加速的同时获得令人满意的 MCC 分数。
Figure 5: Performance on the COLA development set depending on the number of heads for En-BERT $^+$ $T D A$ .
图 5: En-BERT $^+$ $T D A$ 在COLA开发集上的性能随注意力头数量的变化。
Linguistic Minimal Pairs. Computation of the $H_{0}M$ and RTD features is run via the Ripser $^{++}$ GPU library. Under this library, the minimum spanning tree is found according to Kruskal’s algorithm giving the computational complexity of $H_{0}M$ as $O(n^{2}\log{n})$ . The complexity can be reduced using other algorithms, e.g., Prim’s algorithm, which takes $O(n^{2})$ . The RTD’s computational complexity is more difficult to estimate. RTD is computed via persistence barcodes of dimension 1 for a specific graph with $2n$ vertices. Many optimization techniques and heuristics are implemented in the Ripser $^{++}$ library that significantly reduce the RTD’s complexity.
语言最小对。$H_{0}M$ 和 RTD 特征的计算通过 Ripser$^{++}$ GPU 库运行。在该库中，根据 Kruskal 算法找到最小生成树，得出 $H_{0}M$ 的计算复杂度为 $O(n^{2}\log{n})$。使用其他算法（如 Prim 算法）可将复杂度降至 $O(n^{2})$。RTD 的计算复杂度较难估算，它是通过具有 $2n$ 个顶点的特定图的一维持久条形码计算的。Ripser$^{++}$ 库实现了多种优化技术和启发式方法，可显著降低 RTD 的复杂度。
Empirical estimate. Computing the $H_{0}M/\mathrm{RTD}$ features with 144 BERT heads in the worst case of a 512-token text takes 2.41 and 94.5 sec (NVIDIA Tesla K80 12GB RAM). However, the actual computation time on the considered tasks is empirically more optimal. We provide empirical estimates on the entire BLiMP and LA datasets: 2.4/15.7 hours on BLiMP $\left(H_{0}M/\mathrm{RTD}\right)$ and up to 2 hours on COLA/ITACOLA/DALAJ (estimates by the feature groups: topological features $=24%$ ; features derived from barcode $3=70%$ ; and features based on distance to patterns $=6%$ of the total time).
经验估计。在最坏情况下（512个token的文本），使用144个BERT头计算$H_{0}M/\mathrm{RTD}$特征耗时2.41秒和94.5秒（NVIDIA Tesla K80 12GB显存）。但在实际任务中，计算时间通常更为理想。我们对完整BLiMP和LA数据集进行了经验估计：BLiMP上耗时2.4/15.7小时（$\left(H_{0}M/\mathrm{RTD}\right)$），COLA/ITACOLA/DALAJ上最多2小时（按特征组估算：拓扑特征占总时间24%；条形码3衍生特征占70%；模式距离相关特征占6%）。
8.2 Application Limitations
8.2 应用限制
We also outline several application limitations of our approach. (i) The LA class if i ers require preliminary fine-tuning of Transformer LMs to extract more representative attention graph features and, therefore, achieve better performance. (ii) RTD operates upon a one-to-one vertex correspondence, which may be hindered by tokens segmented into an unequal amount of sub-tokens. As a result, identifying the topological discrepancy between pairs of attention graphs can be restricted in practice, where the graphs are of an arbitrary number of nodes. Regardless of the potential information loss due to sentence truncation in such cases, the RTD heads still receive the best overall score on BLIMP. (iii) The head selection procedure relies on auxiliary data to identify the best-performing head configurations. Annotating the auxiliary data may require additional resources and expertise for practical purposes. However, the procedure maximizes the performance and reduces the computational costs by utilizing less attention heads.
我们还概述了本方法的几项应用限制。(i) LA分类器需要对Transformer语言模型进行初步微调，以提取更具代表性的注意力图特征，从而获得更好的性能。(ii) RTD基于一对一顶点对应关系运行，当token被分割为数量不等的子token时可能受限。因此，在实际应用中识别注意力图对之间的拓扑差异可能受到限制，因为这些图可能具有任意数量的节点。尽管在这种情况下由于句子截断可能导致信息丢失，但RTD头在BLIMP上仍获得了最佳综合评分。(iii) 头选择流程依赖辅助数据来确定最佳性能的头配置。实际应用中，标注辅助数据可能需要额外的资源和专业知识。但该流程通过使用更少的注意力头，既最大化性能又降低了计算成本。
8.3 Linguistic Acceptability
8.3 语言可接受性
Acceptability judgments have been broadly used to investigate whether LMs learn grammatical concepts central to human linguistic competence. However, this approach has several methodological limitations. $(i)$ The judgments may display low reproducibility in multiple languages (Linzen and Oseki, 2018), and (ii) be influenced by an individual’s exposure to ungrammatical language use (Dabrowska, 2010). (iii) Distribution shifts between LMs’ pretraining corpora and LA datasets may introduce bias in the evaluation since LMs tend to assign higher probabilities to frequent patterns and treat them as acceptable in contrast to rare ones (Marvin and Linzen, 2018; Linzen and Baroni, 2021).
可接受性判断被广泛用于研究大语言模型是否学习了人类语言能力的核心语法概念。然而，这种方法存在若干方法论局限：(i) 这些判断在多种语言中可能表现出较低的可复现性 (Linzen and Oseki, 2018)；(ii) 可能受个体接触非规范语言使用的影响 (Dabrowska, 2010)；(iii) 大语言模型预训练语料与语言可接受性数据集之间的分布偏移可能引入评估偏差，因为模型倾向于对高频模式赋予更高概率并将其视为可接受，而低频模式则相反 (Marvin and Linzen, 2018; Linzen and Baroni, 2021)。
9 Ethical Statement
9 伦理声明
Advancing acceptability evaluation methods can improve the quality of natural language generation (Batra et al., 2021). We recognize that this, in turn, can increase the misuse potential of such models, e.g., generating fake product reviews, social media posts, and other targeted manipulation (Jawahar et al., 2020; Weidinger et al., 2021). However, the acceptability class if i ers and scoring functions laid out in this paper are developed for research purposes only. Recall that the topological tools can be employed to develop adversarial defense and artificial text detection models for mitigating the risks (Kushnareva et al., 2021).
提升可接受性评估方法可以改善自然语言生成的质量 (Batra et al., 2021)。我们认识到，这反过来可能增加此类模型的滥用潜力，例如生成虚假产品评论、社交媒体帖子和其他针对性操控 (Jawahar et al., 2020; Weidinger et al., 2021)。然而，本文提出的可接受性分类器和评分函数仅用于研究目的。值得注意的是，拓扑工具可用于开发对抗防御和人工文本检测模型以降低风险 (Kushnareva et al., 2021)。
Acknowledgements
致谢
This work was supported by Ministry of Science and Higher Education grant No. 075-10-2021-068 and by the Mindspore community. Irina Proskurina was supported by the framework of the HSE University Basic Research Program.
本研究由俄罗斯科学与高等教育部资助项目（编号075-10-2021-068）和Mindspore社区支持。Irina Proskurina的研究工作由俄罗斯高等经济大学基础研究计划框架资助。
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