## 2 Related Works
### Embedding Association Test of Bias  
Next, we introduce a commonly used computer technology that can measure biases, embedding association test (WEAT) [12]. Embedding is a semantic representation of words or sentences according to their context in the corpus [24]. Words that are closer in embedding space are supposed to be semantically similar, assuming that speakers' mental associations between concepts and attributes can be represented by the semantic similarity between the words naming the concepts and attributes. Word Embedding Association Test (WEAT) [12] is proposed to measure the bias with the distance between the embeddings of the words naming the exemplars and attributes in IAT. The details of the WEAT are as follows. It calculates the implicit association between two concept words and two sets of attribute words using Equations (1) and (2). Given two exemplar words set \(Eu_{i}\), \(Eu_{j}\) corresponding to two concepts \(C_{i}\), \(C_{j}\), respectively (e.g., _[orchid, rose,...]_ for the concept \"_Flower_\" and [_ant, spider,..._] for the concept \"_Insect_\"), and two attribute words set \(Av_{p}\), \(Av_{q}\) corresponding to two attributes \(A_{p}\), \(A_{q}\), respectively (e.g., _[happy, great, pretty,...]_ for the attribute \"_Pleasant_\" and [_awful_, _ugly, sad,..._] for the attribute \"_Unpleasant_\"), the null hypothesis is that there is no difference between \(Eu_{i}\), \(Eu_{j}\) in terms of their relative similarity to \(Av_{p}\), \(Av_{q}\). Let \(\vec{x}\) be the embedding vector of word \(x\), \(cos(\vec{x},\vec{y})\) denotes the cosine similarity between \(\vec{x}\) and \(\vec{y}\). Specifically, WEAT [12] calculated the bias on \(C_{i}\), \(C_{j}\) with respect to \(A_{p}\), \(A_{q}\) as:  
\[Bias(Eu_{i},Eu_{j},Aw_{p},Aw_{q})=\sum_{e\in Eu_{i}}s(e,Aw_{p},Aw_{q})-\sum_{e \in Eu_{j}}s(e,Aw_{p},Aw_{q}) \tag{1}\]  
where  
\[s(e,Aw_{p},Aw_{q})= \underset{a\in Au_{p}}{\text{mean}}\,cos(\vec{x},\vec{a})- \underset{a\in Au_{q}}{\text{mean}}\,cos(\vec{x},\vec{a}) \tag{2}\]  
Then, WEAT [12] measures the strength of association through the effect size. The effect size ('ES' in Equation (3)) of the bias is calculated as:  
\[ES=\frac{\underset{e\in Eu_{j}}{\text{mean}}\,s(e,Aw_{p},Aw_{q})- \underset{e\in Eu_{j}}{\text{mean}}\,s(e,Aw_{p},Aw_{q})}{\underset{e\in Eu_{ j}\cup Eu_{j}}{\text{std}}\,\underset{e\in Eu_{j}\cup Eu_{j}}{\text{dev}}\,s(e,Aw_{p},Aw_{q})} \tag{3}\]  
In this direction, SEAT [13] proposes a generalization of WEAT to sentences. SEAT generates sentences generated by inserting words from WEAT's tests into simple templates such as \"This is a[n] SwordS.\" SEAT finds evidence of human-like bias in sentence encoders like WEAT does in word encoders. Specifically, a study conducted by [25] quantifies the degree to which gender bias differs with the corpora used for the pre-trained model and fine-tuning with additional data. [PERSON] et al. [26] proposes various metrics of embedding biases and compares their strengths and weaknesses. [PERSON] et al. [27] explore biases in embeddings through the lens of geometric spaces, providing a fresh perspective on the subject. Some studies [28; 29] utilize embedding testing to investigate the evolution of biases across extensive temporal scales, revealing persistent statistical features throughout history. Furthermore, a recent study [30] reveals extensive potential for embedding testing. Beyond uncovering biases and stereotypes, embeddings also provide precise assessments of the environments in which biases manifest within human culture and thought. Although embedding-based approaches are related to IAT in connecting semantic distance and mental association, measured biases are a joint effect of explicit and implicit bias, where neither explicit nor implicit bias is correctly understood.