Contrastive Learning-based Sentence Encoders Implicitly Weight Informative Words
Authors: Hiroto Kurita
Goro Kobayashi
Sho Yokoi
Kentaro Inui
Venue: EMNLP 2023 Findings (2023)
Keywords: sentence embedding
contrastive learning
information gain
integrated gradients
TL;DR: We show that contrastive learning-based sentence encoders weight informative words by two information-theoretic quantities: information-gain and self-information through model analysis using Integrated Gradients and SHAP.

Abstract: The performance of sentence encoders can be significantly improved through the simple practice of fine-tuning using contrastive loss. A natural question arises: what characteristics do models acquire during contrastive learning? This paper theoretically and experimentally shows that contrastive-based sentence encoders implicitly weight words based on information-theoretic quantities; that is, more informative words receive greater weight, while others receive less. The theory states that, in the lower bound of the optimal value of the contrastive learning objective, the norm of word embedding reflects the information gain associated with the distribution of surrounding words. We also conduct comprehensive experiments using various models, multiple datasets, two methods to measure the implicit weighting of models (Integrated Gradients and SHAP), and two information-theoretic quantities (information gain and self-information). The results provide empirical evidence that contrastive fine-tuning emphasizes informative words.

Embedding a sentence into point in high- dimensional continuous space plays a founda- tional role in the natural language processing (NLP) (Arora et al., 2017; Reimers and Gurevych, 2019: Chuang et al., 2022, etc.). Such sentence embedding methods can also embed text of var- ious types and lengths, such as queries, pas- sages, and paragraphs; therefore, they are widely used in diverse applications such as information retrieval (Karpukhin et al., 2020; Muennighoff, 2022), question answering (Nguyen et al., 2022), and retrreeallauummented generation (Chase, 2023). Contrastive Learning-based Sentence Encoders Implicitly Weight Informative Words
Hiroto Kurita'
Goro Kobayashi Sho Yokoi Kentaro 3.12
1 Tohoku University 2 RIKEN 3 MBBUAI
(hiroto.kurita, goro. koba Jedc tchoku.ac.jp yokoi@tohoku.ac. kentaro. inui@mbzuai.ac.... ae
Abstract
Sentence cmb.
The performance sentence encoders can be significantly improved through the simple prac- tice of fine-tuning using contrastive loss. A natural question arises: what characteristics do models acquire during contrastive learning?
Contrastive fine-tuning
Embedd senteria
Cakulates word contributions
Contrastive-besse sentence encoder
Large Corpora
11
11 11 mun is playing giltar
This paper theoretically and experimentally shows that contrastive-based sentence encoders implicitly weight words based on information- theoretic quantities; that is, more informative words receive greater weight, while others re- ceive less. The theory states that, in the lower bound of the optimal value of the contrastive learning objective, the norm of word embed- ding reflects the information gain associated with the distribution of surrounding words. We also conduct comprehensive experiments using various models, multiple datasets, two meth- ods measure the implicit weighting of mod- els (Integrated Gradients and SHAP), and two information-theone quantities (information gain and self- ceff-information). The results provide empirical evidence that contrastive fine-tuning emphasizes informative words.
A
Word weighitng within encoder
Info. theoretic quantities
mon
is playing gullar
A
man
ir playing gudar
Measured by 16 or SHAP
Measured by KL(W)) or lag P(w)
Figure 1: Overview of study. We quantify the word weighting within contrastive-based sentence en- coders by XAI techniques: Integrated Gradients (IG) or Shapley additive explanations (SHAP). We found that the quantified weightings are close to infromation- theoretic quantities: information-gaii KL(w) and self- information - log P(w).
by summing its static word embeddings (SWEs; Mikolov et al., 2013; Pennington et al., 2014). Be- sides, weighing each word based on the inverse of word frequency considerably improved the quality of the sentence embeddings, exemplified by TF- IDF (Arroyo-Femánnde et al., 2019) and smoothed inverse word frequency (SIF; Arora et al., 2017).
https://gtts thub. com/kur yaan 204/ sentence-encoder-woee weighting
wordww-gtin
1 Introduction
Recent sentence embeddings are built on masked language models (MLMs; Devlin et al., 2019; Liu et al., 2019; Song et al., 2020). Although sen- tence embeddings from the additive composition of MLMs' word embeddings are inferior to those of SWES (Reimers and Gurevych, 2019), fine-tuning MLMs with contrastive learning objectives has ele- vated the quality of sentence embeddings (Reimers and Gurevych, 2019; Gao al., 2021; Chuang et al., 2022, etc.) and is now the de-facto stan- dard. Interestingly, these contrastive-basee sen- tence encoders do not employ explicit word weight- ing, which is the key in the SWE-based methods.
One of the earliest successful sentence embed- ding methods is additive composition (Mitchell and Lapata, 2010; Mikolov et al., 2013), which embeds a sentence (i.e., a sequence of words)
In this paper, we demonstrate that reason for the success contrastive- based sentence encoders is implicit word weighting. Specifically, by com-

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bining explainable AI (XAI) techniques and infor- mation theory, we demonstrate that contrastive- based sentence encoders implicitly weight each word according to two cetrmattionthhorrer quan- tities (Figure 1). To measure the contribution (i.e., implicit weighting) of each input word to the output sentence embedding within the encoders, we used two XAI techniques: Integrated Gradients (IG; Sun- dararajan al., 2017) and Shapley additive expla- nations (SHAP: Lundberg and Lee, 2017) (Sec- tion 3. To measure the ieoormatioo-thooretiii quantitics of each word, we used the two sim- plest quantities, information -aair KL(w) and self- information - log P(w) (Section 3.2). To demon- strate our hypothesis, we first provided theoret- ical connection between contrastive learning and information gain (Section 4). We then conducted comprehensive experiments with total of 12 mod- cls and 4 datasets, which found a strong empirical correlation between the encoders' implicit word weighting and the information- -heeoreticc quantities (Section 5). The results of our study provide a bridge between SWE-era explicit word weighting techniques and the implicit word weighting used by recent contrastive-based sentence encoders.
update input word embeddings to contextualized word embeddings w, + e;. (ii) The pooling layer then pools the representations [e1..... en into a single sentence embedding s E IRd. There are two major pooling methods, MEAN and CLS: MEAN averages the contextualized word embeddings, and CLS just uses the embeddings for [CLS] token after applying MLP on top of it.
Contrastive fine-tuning: The contrastive fine- tuning of MLMs is briefly described below. contrastive learning, positive pairs (s, 9pas), i.c., semantically similar pairs of sentence embeddings, are brought closer, while negative pairs (s,, $neg) are pushed apart in the embedding space. Positive examples Spos and negative examples Sneg for sentence embedding are created in different ways depending on the method. For instance, in the unsupervised SimCSE (Gao et al., 2021), a positive example pos is created by embedding the same sentence as s by applying a different dropout; and negative example Sneg is created by embedding a sentence randomly sampled from training corpus.
3 Analysis Method
2 Contrastive-Based Sentence Encoders
We compare the implicit word weighting within the contrastive-based sentence encoders with information theoretic information-thherrtiic quantities of words. Here
This section provides overview of contrastive- based sentence encoders such SBERT (Reimers and Gurevych, 2019) and SimCSE (Gao al., 2021). These models are built by fine-tuning MLMs with contrastive learning objectives.
we introduce (i) quantification of the implicit word weighting within the encoders using two XAI techniques (Section 3.1) and (ii) two information- theoretic quantities of words (Section 3.2).
Input and Output:
As shown in Figure 1, a contrastive-basee sentence encoder m: Ruxd -
3.1 Implicit Word Weighting within Encoder
Rd calculates sentence embedding E IRdd from sequence of input word embeddings W (wi,..., wn] Rand corresponding words and special tokens. For example, for the sen- tence "I like playing the piano," the input to the en- coder m is W = [CLs]] Wy, Wikee... ..., W[SEP]]. and sentence embedding s is calculated as follows:
Contrastive-baset sentence encoders are not given explicit word weighting externally but are expected to implicitly weight words through the complicated internal network. We quantify the implicit word weighting using two widely used feature attribution methods (Molnar, 2022): Integrated gradients (Sun- dararajan et al., 2017) and Shapley additive expla- nations (Lundberg and Lee, 2017).
input
-==1 == W) = [mi (W), .,, ma( (W),. (1)
where m,: paxd + R denotes the computation of the i-th element of s.
3.1.1 Integrated Gradients (IG)
Integrated Gradients (IG) is widely XAI tech- nique used to calculate the contribution of each input feature to the output in neural models. IG has two major advantages: (i) is based on the gradient calculations and thus can be used to arbitrary neural models; and (ii) it satisfies several desirable proper- ties, for example, the sum of the contributions for
The encoder architecture consists of (i) Transformer layers (same as MLM architec- ture) and (ii) a pooling layer. (i) Transformer layers
Architecture:
'A classification loss is used in the training of SBERT; however, this can he roughly regarded as a contrastive loss (see Appendix A).

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each input feature matches the output value (Com- pleteness described in Sundararajan et al., 2017). It has also been actively applied to the analysis of MLMM-based models (Hao et al., 2021; Prasad et al.,
output to the contribution of each input (Lund- berg and Lce, 2017). Its formal definition and application to the word weighting calculation of contrastive-based sentence encoders are shown in Appendix D.
2021; Bastings et al., 2022; Kobayashi et al., 2023). The formal definition of IG is as follows: Let f: Raxd + R be model (e.g., each element of sentence encoder) and X' E Rnxd be certain input (e.g., word vectors). IG calculates contribu- tion score jGr for the (i,j) element of the input X' [ (e.g.. each element of each input word vec- tor) to the output f(X'):
Though we can apply SHAP to analyze sen- tence encoders, SHAP is often claimed to be unre- liable (Prasad al., 2021). Thus, we discuss the experimental results using IG in the main text and show the results using SHAP in Appendix E.
3.2 Cntormation-Thertii Quantities
Here, introduce two information-theoreticc quan- tities that represent the amount of information a word conveys.
d f(x') = ΣΣ
IG (X' B), ((B) (2)
i=1
IG X ff: B)B = (x [1,1] -B(,,))
3.2.1 Information Gain KL(w)
xf" 0X (
0f
The first quantity is the information gain, which measures how much probability distribution (e.g., the unigram distribution in some sentences) changes after observing a certain event (e.g., a certain word). Information gain of observing a word w in a sentence is denoted as KL(w) := KL sent (-ww) || P(-)), where (-ent(-|un (w) is the word frequency distribution in sentences contain- ing word w. and P(-) is distribution without con- ditions. Intuitively, KL(w) represents the extent to which the topic of sentence determined by observing a word w in the sentence. For exam- ple, if uc is "the", KL( "tt"""e") becomes small be- cause the information that sentence contains "the" does not largely change the word frequency dis- tribution in the sentence from the unconditional distribution (Psen "the"" ") ze P(-)). On the other hand, if w is "NLP", larger than (L("thee) because the information that a sentence contains "NLP" expected to sig- nificantly change the word frequency distribution (. * P(-)). Recently, Oyama et al. (2023) showed that KL(w) is encoded in the norm of SWE. Also, x2-measure, which is a similar quan- tity to KL(w). is useful in keyword extraction (Mat- suo and Ishizuka, 2004). We provide theoretical connection between KL(w) and contrastive learn- ing in Section 4.
da. (3)
X= X=B+a(X'
Here B denotes baseline vector, often uninfor- mative neutral input is employed. Notably, IG decomposes the output value into the sum of the contribution scores of each input (Equation 2).
Application to the sentence encoder: We aim to measure the contribution of each input word to the output sentence embedding. However, when applying IG to the sentence encoder (its k-th element is m&) and input W = [w,,-.., ..., w.... it can only compute the fine contribution score of the j-th element of the each input word vector w, the k-th element of the sentence vector 8 = m (W). Thus, we aggregates the contribution scores across all the (j, k) pairs by the Frobenius norm:
becomes much
d GG ( mk: B)
c:(W ( m. B)
B (WCLs, WPADs WPAD, UPAD: WSEP..
(4)
where we used a sequence of input word vectors for an uninformed sentence "[CLS] [PAD] [PAD] [PAD] [SEP]" as the bascline input B. In addition, the word contribution is normalized with respect to the sentence length n to compare contributions equally among words in sentences of different lengths: d; a/ (4) cj).
3.2.2 Self-Information log P(w)
3.1.2 SHapley Additive exPlanations (SHAP) Shapley additive explanations (SHAP) is feature attribution method based on Shapley values (Shap- lcy, 1953). Similar to IG, SHAP satisfies the desir- able property: it linearly decomposes the model
The second quantity which naturally represents the information of word is self-information log P(w). log P(w) is based on the inverse of word frequency and actually very similar to word weighting techniques used in SWE-based sen-

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lence encoding methods such TF-IDF (Arroyo- Fernández et al., 2019) and SIF weighting (Arora
Model (pooling)
R² 100
x 100 f
BERT (CLS)
0.2
et al., 2017). Note that the information gain (L(w)
U.SimCSE-BBR
32.4 (+332.4)
17.3 (+17.1)
introduced Section 3.2.1 is also correlated with
S.SIISEEBERR
30.8 (4-30.8)
16.9 (6.7)
RIfICSE-BERT
31.6 (+31.66
13.1 (+12.9)
the inverse of word frequency (Oyama et al., 2023), and both quantities introduced in this section are close to the word weighting techniques. Detailed comparison between the two quantities and the word weighting techniques is shown in Appendix B. If the contrastive- sentence encoder's word weighting close (L) and log ((w), the post-hoc word weighing used in SWE-based meth- ods is implicitly learned via contrastive learning.
BERT (MEAN)
24.4
7.9
SBERT
22.9 (-1.5)
16.1 (+8.1)
RoBERTa (CLS)
2.0
5.0
+ U. U.SimCSE-RoBBER
29.7 (4-27.7)
17.5 (4-12
+ S.SimCSE-RoBERT
29.1 (+27.11
20.2 (+
DiAICSE-ROBRRT
28.4 (+26.4)
16.5 (+11.4)
RoBERTa (MEAN)
4.2
5.5
+ SRoBERTa
31.4 (4-27.2)
24.0 (+18.4)
MPNet (MEAN) - >aall-mmm all-mpnet-base--2 21.6 (4-210) 21.0 (+23.55
0.6
2266
4 Theoretical Analysiss
Table Coefficient of determination (S²²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by IG the information gain KL for the STS-B dataset. The It and 33 is reported as R² 100 and x 100. The values inside the brackets represent the gain from pre-trained models.
This section provides brief explanations of the theo- retical relationship between (L(w) and contrastive learning. Given a pair of sentences (s,s') s'), con- trastive learning can be regarded as problem of discriminating whether a sentence s' is positive (semantically similar) negative (not similar) ex- ample of another sentence We reframe this dis- crimination problem using word frequency distribu- tion. After observing w in s, the positive example is likely to contain words that co-occur with w; i.c., the word distribution the positive example likely follows Psent (-| (-lw)). Contrary, the negative example is likely to contain random words from corpus regardless of the observation of w; i.e., the word distribution of the negative example likely follows P(.). Hence, (T.n (-Iw) || (P()) KT((w) approximately represents the objective of the dis- crimination problem (i.e., contrastive learning). See Appendix C for a more formal explanation.
analyzed 3 pre-trained MLMs: BERT (Devlin et al., 2019), RoBERTa (Liu et al., 2019) and MP- Net (Song et al., 2020). All models are base size.
Dataset: We used STS-Benchmark (Cer et al., 2017), a widely used dataset to evaluate sentence representations, for input sentences to encoders and calculating log P(w) and KL(w). We used the validation set, which includes 3,000 sentences. We also conducted experiments using Wikipedia, STS12 (Agirre et al., 2012), and NLI datasets (Bow- man et al., 2015; Williams et al., 2018) for the generalizability, which are shown in Appendix F.2.
Experimental procedure: First, we fed all sen- tences to the models and caleulated the word weightings by IG or SHAP (Section 3.1). Then applied OLS regression the calculated word weightings on log P(w) or KL((w) (Section 3.2) for each model. Although we experimented with all four possible combinations from the two XAI meth- ods and two quantities for each model, we report here the results only for the combination of IG and KL(w). Other results are shown in Appendix E.
5 Experiments
In this section, we investigate the empirical relation- ship between the implicit word weighting within contrastive-based sentence encoders (quantified by IG or SHAP) and the information-thcorrtiec quanti- ties (KL(w) or log P(w)).
5.1 Experimental Setup
Models: We used the following 9 sentence en- coders: SBERT (Reimers and Gurevych, 2019), UnsuperviseddSSpprriied SimCSE (Gao et al., 2021), DifiCSE (Chuang et al., 2022), both for BERT and RoBERTa-based versions, and all bassme----- As baselines, we also
5.2 Quantitative Analysis
Table lists the coefficient of determination (R²2) and regression coefficient (3) of the linear regres- sion on IG and KT.(w). Figure/ 2 shows the plots of the word weightings and their regression lines for BERT and Unsupervised SimCSE.
'https://hugginffaat ace. co/ssentence-ttaasffreeeerr transformers/ all all-mpnet-base-1

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BERT (CLS)
Unsup. SimCSE
KL(w)
Word weighting (IG)
RERT (CIS)
2.5
y 0.00z 1.00
0.177 4 0.69
2.0
1.5
1.0
0.5
2
0.0
Word weighting
man
playing guitar
2.5
2.0
1.5
0
2
1.0
0.5
(L(w)
0.0
with
hand hat daaccnng
2.0
Figure 2: Linear regression plots between (L) and the word weighting of BERT (CLS) (left) and Unsper- vised (U.) SimCSE-BERS (right) using IG. We plot- ted subsampled 3000 tokens from the tokens with the top 99.5% of small KL values for visibility. The plots - log P(w) experiments are shown Figure in Ap- pendix E.
1.0
0.5
0.0
a
young child is
riding
horse
Figure 3: Sentence-level examples of the word weight- ing of BERT (CLS) and Unsupervised SiMCSSE-BERT using IG. Same as IG, KL(w) is normalized so that the sum of KI((w) becomes the sentence length for visi- bility. For words like "man". "child", "guitar", "is", "har", "horse" and "." the word weightings of the con- trastive fine-tuned model (A) are closer to KL(w) (I) than the pre-trained model ), which means that con- trastive fine-tuning induces word weighting by KL(w).
Table 1 shows that R2 and | are much higher in cnntrastive-baeed encoders than pre-trained mod- els. Similar trends were obtained with other XAI method, information-theoreti quantity, and datasets (Appendix E, F.2). These indicate that contrastive learning for sentence encoders induces word weighting according to the information- theoretic quantities (Figure 2). In other words, contrastive-based encoders acquired the inner mechanism to highlight informative words more. Furthermore, given that (T,(w) and log P(w) are close to the weighting techniques employed in the SWE-based sentence embeddings (Section 3.2), these results suggest that the contrastive-based sen- tence encoders learn implicit weightings similar to the explicit ones of the SWE-based methods.
discounted by contrastive learning the other hand, weights for words such as "a" and "with" ", whose KL(w) is very small, are not changed so much. Investigating the effect of POS on word weighting, which is not considered on KL(w) and - log P(w), is an interesting future direction.
On
Conclusion
5.3 Qualitative Analysis
Figure shows the word weighting within BERT and Unsupervised SimCSE (A) and KL(w) for three sentences: "a man playing guitar." "a man with hard hat is dancing.". ", and "a young child is riding a horse.". ". The contrastive- based en- coder (Unsup. SimCSE: A) has more similar word weighting to KL((w)
We showed that contrastive learning-based sen- tence encoders implicitly weight informative words based information-theoree quantities. This in- dicates that the recent sentence encoders learn im- plicit weightings similar the explicit ones used in the SWE-based methods. We also provided the theoretical proof that contrastive learning induces models to weight each word by KL(w). These pro- vide insights into why contrastive-basst sentence encoders succeed in a wide range of tasks, such as information retrieval (Muennighoff,, 2022) and question answering (Nguyen et al., 2022), where emphasizing some informative words is effective. Besides sentence encoders, investigating the word weighting of retrieval models is an interesting fu- ture direction.
than the MLM (BERT; which is consistent with the R² in the Table 1. Also, the contrastive- annred encoder (A) tends to weight input words more extremely than the MLM (0), which is consistent with the in Table 1. For ex- ample, weights for nouns such as "guitar", "hat",
"child", and "horse" are enhanced, and weights for non-informative words such as "is", and " are
"Fxceptionally, R does not change much from BERT (MEAN) to SBERT, while B indeed increases.

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Limitations
Sanjeev Arora, Yingyu Liang, and Tengyu Ma. 2017. A Simple but Tough-to- Bough-to-Beat Baseline for Sentence Embeedingg.. In Sth International Conference on Learning Representations (ICLR).
There are three limitations in this study. First is the limited experiment for baseline input of IG. For the IG experiment, we only tested the baseline input with PAD tokens explained in Section 3.1.1. Although there is consensus on the appropriate baseline inputs of IG for contrastive- sentence encoders, a comparison of results with different baseline inputs is left to future work. Second, our findings do not cover contrastive text embeddings from retrieval models. Analyzing contrastive-based retrieval models such as DPR (Karpukhin et al., 2020), Contriever (Izacard et al., 2022), and inves- tigating the effect on text length would also be an interesting future direction. Third is the assump- tions made in the sketch of proof in Section C. In our proof, we assume that the similarity of sentence embeddings is calculated via inner product. How- ever, in practice, cosine similarity is often used instead. Also, we do not consider the contextual- ization effect of Transformer models on the word embeddings in the proof. The theoretical analysis using cosine similarity or considering the contextu- alization effect is left to future work.
Ignacio Arroyo-Fernnndez, Carlos Francisco Méndez- Cruz, Gerardo Sierra, Juan Manuel Torres-Moreno, and Grigori Sidorov. 2019. Unsupervised sentence representations as word information series: Revisit- ing TF-IDE Computer Speech and Language, pages 107-129.
Giuseppe Attanasio, Eliana Pastor, Chiara Bonaven- tura, and Debora Nozza. 2023. ferret: Framework for Benchmarking Explainers on Transformers. In Proceedings of the 17th Conference of the European Chapter of the Association for Computational Lin- guistics (EACL); System Demonstrations, pages 256- 266.
Jasmijn Bastings, Sebastian Ebert, Polina Zablotskaia,
Anders Sandholm, and Katja Filippova. 2022. "Will You Find These Shortcuts?" A Protocol for Evaluat- ing the Faithfulness of Input Salience Methods for Text Classification. In Proceedings of the 2022 Con- ference on Empirical Methods in Natural Language Processing (EMNLP), pages 976-991.
Samuel R. Bowman, Gabor Angeli. Christopher Potts. and Christopher D. Manning. 2015. A large anno- tated corpus for learning natural language inference. In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing (EMNLPP, pages 632-642.
Ethics Statement
Our study showed that sentence encoders im- plicitly weight input words by frequency-baad information- thhorrtic quantities. This suggests that sentence encoders can be affected by biases in the training datasets, and our finding a step forward in developing trustful sentence embeddings without social or gender biases.
Daniel Cer, Mona Diab, Eneko Agirre, lnigo Lopez- Gazpio, and Lucia Specia. 2017. SemEval-2011 task I: Semantic Textual Similarity Multilingual and Crosslingual Focused Evaluation. In Proceedings of the 11th International Workshop Semantic Évalu- ation (SemEval), pages 1-14.
Harrison Chase. 2023. LangChain. Accessed 2023-10- 15.
Acknowledgements
Yung-Sund Sung Chuang, Rumen Dangovski, Hongyin Luo, Yang Zhang. Shiyu Chang, Marin Soljacic. Shang- Wen Li, Scott Yih, Yoon Kim, and James Glass. 2022.
We would like to thank the members of the Tohoku NLP Group for their insightful comments. This work was supported by JSPS KAKENHI Grant Number PP22J21492, JP22H05106, JST ACT-X Grant Number JPMIAX200S; and IST CREST Grant Number JPMJCR20D2, Japan.
DiffCSE: Difference-based Contrastive Learning for Sentence Embeddings. In Proceedings of the 2022
Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLD) pages 4207- 4218.
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Nils Reimers and Iryna Gurevych. 2019. Sentence- BERT: Sentence embeddings using Siamese BERT- networks. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natu- ral Language Processing (EMNIP--JCNIPP) pages 3982-3992.
Scott M Lundberg and Su-In Lee. 2017. A Unified Approach to Interpreting Model Predictions. In Ad- vances Neural Information Processing Systems 30 (NIPS), volume 30.
Yutaka Matsuo and Mitsuru Ishizuka. 2004. Keyword extraction from single document using word co- occurrence statistical information. International Journal on Artificial Intelligence Tools, 13(01):157- 169.
Lloyd S. Shapley. 1953. A Value for N-Person Games. In Contributions to the Theory of Games 2.28.
Kaitao Song, Xu Tan, Tao Qin, Jianfeng Lu, and Tie- Yan Liu. 2020. MPNet: Masked and Permuted Pre- training for Language Understanding. In Advances in Neural Information Processing Systems 33 (NPS), pages 16857-16867.
Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Cor- rado, and Jeff Dean. 2013. Distributed Representa- tions of Words and Phrases and their Compositional- ity. In Advances in Neural Information Processing Systems 26 (NIPS).
Mukund Sundararajan and Amir Najmi. 2020. The Many Shapley Values for Model Explanation. In Proceedings of the 37th International Conference Machine Learning (ICML), pages 9269-9278
Jeff Mitchell and Mirella Lapata. 2010. Composition in Distributional Models of Semantics. Cognitive science, 34(8):1388-142
Mukund Sundararajan, Ankur Taly, and Qiqi Yan. 2017. Axiomatic Attribution for Deep Networks. In Pro- ceedings of the 34th International Conference on Machine Learning (ICML), page 3319-3328.
Christoph Molnar. 2022. Interpretable Machine Learn- ing, 2nd edition.

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Adina Williams, Nikita Nangia, and Samuel Bowman. 2018. A Broad- Coverage Challenge Corpus for Sen- tence Understanding through Inference. In Proceed- ings of the 2018 Conference of the North American Chapter of the Association for Computational Lin- guisticy: Human Language Technologies (NAACI- H...T) pages 1112-1122.
0.8
Word weighting
0.6
0.4
Yuanmeng Yan, Rumei Li, Sirui Wang, Fuzheng Zhang, Wei Wu, and Weiran Xu. 2021. ConSERT: con- trastive framework for self seff-super sentence repre- sentation transfer. In Proceedings the 59th Annual Meeting of the Association for Computational Lin- guistics and the I 11th International Joint Conference Natural Language Processing (ACL-IICNLP), pages 5065-5075.
0.2
IDF
SiF-weighiing
0.0
KLiw)
2
KL(w)
Figure 4: Scatter plot of KL(w) IDF, and SIF- Weighting, All weightings are normalized within the same weighting method.
Sho Yokoi, Ryo Takahashi, Reina Akama, Jun Suzuki, and Kentaro Inui. 2020. Word Rotator's s Distance. In Proceedings of the 2020 Conference on Empirical Methods Natural Language Processing (EMNLP), pages 2944-2960.
1.0
IDF
Sif-weighting -log((w)
0.8
Word weighting
A The classification loss in SBERT/ROBERTa
SBERT and SRoBERTa (Reimers and Gurevych, 2019) are fine-tuned with softmax classifiers top of original MLMs architectures. Before the soft- max, the models calculate the element-wise differ- ence of two sentence embeddings and concatenate them with the original two sentence embeddings. Then the concatenated embedding is linearly trans- formed and fed into a softmax classifier. Here, the element wise difference is expected to work as an implicit similarity function. Thus, SBERT and SRoBERTa can be roughly regarded contrastive- based sentence encoders.
0.0
3
10
log P (w)
Figure 5: Scatter plot of - log P(w) IDF, and SIF- Weighting. All weightings are normalized within the same weighing method.
- log P(w) are highly correlated with existing word weighting TF-IDF (Arroyo-Fernánder) et al., 2019) and SiF-wwighting (Arora al., 2017).
B Comparison of (Lww) and log Pww) with Existing Weighting Methods
C The Theoretical Relationship between Contrastive Learning and Information Gain
Here, compare the two information-theoreti quantities KL(w) and - log P(w) with existing weighting methods used in SWE-based sentence embedding: TF-IDF (Arroyo-Feenández et al., 2019) and SIF-weighting (Arora et al., 2017). Fig- ure 4 and 5 are the scatter plots of IDF and SIF- weighitng against KL(w) and log (ww), respec- tively. We removed the term frequency part in TF-IDF and only used IDF to climinate contex- tual effects and reduce the variance of the values for the comparison, and all quantities were cal- culated on the STS-Benchmark (Cer al., 2017) dataset. From the figures, we can see that the two informatiin-theorrtie quantities KL(w) and
Formally, the following theorem holds:
Theorem 1. Let S be the set of sentences. {((,,s)), C}} be the dutaset constructed from S where S, s' = (when C 1), and s' S (when C 0). Suppose that the sentence en- coder parametrized by takes sentence (wi....; w|+)) as the input and returns word embed- dings (Wl.... (| and its mean-pooled sentence embedding = Ibsl wi as the output, and the contrastive fine-tuning maximizes Ceontrastive (0), the log- aigliikl of P(C((s, s'): = o((s, s')) Then, in the lower bound of the optimal value of Lcontrastive (4), w/| 2 KL(w).

---

In other words, KL(w)) ) encoded in the norm of word embeddings, which construct the sentence embedding. The proof is shown Section C.2.
Sentence embedding is not normalized.
C.1 Assumptions
For assumption 2, one can also use the inner prod- uct instead of cosine similarity, as discussed in Gao et al. (2021), for example. Using the inner prod- uct for calculating sentence embedding similarity is an important assumption for the proof 4, and extending our theory to cosine similarity a chal- lenging and interesting future work. Assumption makes the conclusion of our theory meaningful, which uses the norm of word embedding. Typical contrastive sentence encoders compute sentence embedding without normalization (Reimers and Gurevych, 2019; Gao et al., 2021, etc.).
Dataset: Let S be the training corpus for con- trastive learning. When training a sentence encoder with contrastive fine-tuning, the set of sentence pairs {() is used as the training data, and the sentence encoder is trained with the objective which discriminates whether the sentence pair is positive example (the pair of semantically similar sentences) or negative example (the pair of seman- tically dissimilar sentences). For the theoretical analysis, we make the following three reasonable assumptions:
1. An anchor sentence is sampled from S.
2. Positive exmaple For semantically similar sentence s' with 8, 8 itself is used (s' = 8).
C.2 Proof
3. Negative example For semantically dissimi- lar sentence s' with s, randomly sampled sen- tence s' from is used (s' ~ S).
First, P(C - 1l(s,s/); bound:
has the following lower
Assumption 1 is commonly used setting for the training data of contrastive fine-tuning of sentence encoders (Gao al., 2021; Chuang et al., 2022, etc.). Assumption 2 considers data augmentation techniques based on perturbations such as token shufffing (Yan et al., 2021) or dropout augmen- tation (Gao et al., 2021). Noting that these data augmentations do not affect the word frequency distributions, this simplification has little effect on the theory. Assumption 3 considers the most simple way to create dissimilar sentence s' of the anchor sentence 8, especially in unsupervised set- tings (Yan al., 2021; Gao et al., 2021; Chuang al., 2022, etc.). In typical supervised settings, hard negatives are often created with NLI supervi- sion, and considering these settings the theory is an important future work. Also, for simplicity, we assume the sentence length is fixed to n in the proof ([s] = |s'| n).
P(C (((s))))0)
(()
(5)
=
||||s|| (w, w'))
(6)
wEs weeK
II II WCs u'
((w,, w')) [লाل
)'))
(7)
II WE w'Ee'
II
P(C = 1| w ())
(8)
Here, we used the mean pooling assumption and the property of bilinear form for Equation 6 and Theorem 3.2 Nantomah (2019) for Equation
Model: We make the following three assump- tions on contrastive-baser sentence encoders (Sec-
Then the objective function Lcontrastive (0) of the probabilistic model P has the following approxi-
tion 2):
1. The sentence embedding is constructed by the mean pooling (Section 2).
"More accurately, our theory requires the similarity func- tion for the sentence embeddings to be a bilinear form. The inner product is a (symmetrie) bilinear form, while cosine is not.
2. The inner product is used to calculate the sim- ilarity of sentence embeddings s and s'

---

mated lower bound:
considered sampled from the unigram distribution P(-), followed from s' S and w' s'. By using the property of the trained SGNS model shown in Oyama et al. (2023), we have
Coontrastive (0)
II (s,0))pos
P = =((sss)))))
II
P(C 5():)')::0)
(9)
1
| ~ (L pas por (-120) || Purg( (-110)
(15)
2
II (1,6)) pops AwCa w'Ex
II
II P(C 11(5, =(((,,"):0))xin)))
=
KKI(P (aamesmeeentt (-mmsent(-/ww) [/w)) || P(.))
_ (16)
II
II
II P(C. 0i(s, 1
C.3 Discussion
(s.d" yooee w'Es'
(10) Here, we discuss the two implications from Theo- rem 1.
II (wn,ae") Joupos
P(C= = 1[( 0))
First, Equation 16 represents the intuition (II) exaplined in Section 4. That is, the difference of the word frequency distribution of the similar sentence s' and the dissimilar sentence s' after observing the word w in the anchor sentence s is implicitly en- coded in |w]], |. In other words, the information gain the word frequency distribution of the similar sentence s' is encoded in || by observing w E s. Secondly, the conclusion of our proof that the in- formation gain KL((w) is encoded in the norm of justifies the means of quantifying the implicit word weighting of the model using Integrated Gradients (IG) or SHAP to a certain extent. When construct- ing a sentence embedding by additive composition (MEAN pooling), the contribution of each word is approximately determined by the norm of the word embedding (Yokoi et al., 2020). IG and SHAP also additively decomposes the contribution of each in- put feature (input word embedding) to the model output (sentence embedding) (Sundararajan et al., 2017; Lundberg and Lee, 2017). From the perspec- tive of the additive propertics, the result that IG and SHAP can capture the contributions implicitly encoded in the norm is natural. To preserve the additive properties of IG and SHAP more properly, further sophisticating the aggregation methods of contributions (Equation 4, 20) is an interesting fu- ture work.
II
P(C Ol(w, w/ 0)
x (we,w))
II Jmppos
P(C' =
+
x Eso poupo
II P(C = 0[(w,, O[[w,
(12)
Here, Equation 10 follows from Equation 6 to 8, and |s| |s'| is used in Equation 11. Hence, the optimal value for Lcontrastive is bounded as follows:
max Ccontrastive (0)
II P(C. 1|(w, w 0)
max
(s0,
= p(C.=0(wv, ww)) #t2
x II
(13)
(vopon))ppo
max (13)
II P(C, 1[ w')
arg max
x
II P(C,=0(mm = (ww, w')):
(14)
Noting that arg max (13) arg max, (14).
Equation 14 corresponds the objective function of the skip-gram with negative sampling (SGNS) model (Mikolov et al., 2013) with taking the con- text window as a sentence. In other words, the optimal value of the lower bound (Equation 13) cor- responds to the optimal value of the SGNS model (Equation 14).
D Quantifying word weighting within sentence encoders with SHAP
In this section, we briefly describe Shapley aaddi- tive explanations (SHAP: Lundberg and Lee, 2017), the feature attribution method introduced in Sec- tion 3. 1.2, and then describe how to apply SHAP quantification word weighting within sentence encoders.
(i) If (s, s') is a positive example, the words w/ in s' can be considered sampled from the distribution of words, co-occurring with w in sentences: w/ P-pa(-lus (-ww) Psame sent (-lw). (ii) If s' is a negative example, the word in a negative example can be

---

D.I Shapley value
is generally calculated through an approximation. One of the typical approximated calculation of SHAP is PartitionSHHA implemented shap library", which hierarchically clusters input fea- tures (or words) to decide coalitions, reducing the total number of the permutations in Equation 17. PartitionSHAA is widely used in interpreting NLP models (Mosca et al., 2022; Attanasio et al., 2023; Eksi al., 2021, etc.); hence, also in our experiments.
SHAP is an extension for XAI of Shapley value (Shapley, 1953), the classic method proposed in the context of cooperative game theory. We first explain Shapley value. Let us consider a co- operative game, where set of players forms coalition and gains payofts. Shapley value is method to distribute the payofí's gained by coopera- tion (forming coalition) fairly among the players. Let == [1, .....,,) n be the set of players in the game and v: 2 + be the function that deter- mines the payoff gained based on a subset (coali- tion) of players. Note that the empty set does not gain payoff, v(6) = O. To compute the payoff (con- tribution) Φ; distributed the i-th player, Shapley value calculates the expectation of the difference of the payoff before and after the i-th player joins each of the possible coalitions (all subsets made from permutations of players). Formally, Φ; calculated as follows:
D.4 Application sentence encoder
When applying SHAP to NLP models, instead of replacing a feature with its expected value, an input word is often replaced with uninformative token (e.g., [MASK] for BERT-based models). For sen- tence encoders, SHAP calculates the contribution of each input word to the output my (W) form of decomposing my (W) into sum:
(w() in the
12
my m = Σ SHAP, mj M) + f(M)
| 18| 11! -M(SU(0))
(b(
Σ
N!
SENVA
(18)
(17)
M [[[MAK]] ...., w [MASK]] RR
(19)
Shapley value satisfies some ideal properties; for example, the summation of each caleulated contri- bution & becomes the payoff of the case where all players join, i.e., v(N) E. es (v()).
where M denotes masked input. Then, we can calculate the contribution of i-th word to j-th ele- ment of by SHAP in the same aggregation as for IG (see Section 3. 3.1.1):
D.2 SHAP
SHAP is an extension of the Shapley value to inter- preting machine learning models. Let : Ih + IR be model and X E R" be a certain input. SHAP maps machine learning models to coopera- tive games: the input X corresponds to the set of players N and the model corresponds the set function in Equation 17. However, in coopera- tive games the input (subset of players) is discrete, while in machine learning models the input (vector) is continuous. SHAP fills this discrepancy as fol- lows: the situation "the i-th player is not included in the input subset" is mapped to "the i-th feature of the input vector is replaced with its expected value." See the original SHAP paper (Lundberg and Lee, 2017) for details.
c: (W; m, M) =
SHAP, W my, M)²
(20)
In addition, the word contribution o; is normalized with respect the sentence length same as IG
(see Section 3.1.1): d, = c/((, Ej 93).
E Omitted results in Section 5
Tables 2 4 are the results of (IG, log P(w)), (SHAP, KL(w)) and (SHAP, log P(w)) experi- ments, respectively, and Figure 6 is the linear re- gression plots between - log P(w) and IG.
D.3 Approximate calculation of SHAP
'tt thttps///shap. rewtteedoeseeecseeeco reatthedoss.io//e/latees
The exact calculation of Shapley value compu- tationally expensive (time complexity of (22)) because it calculates all the permutations of the input players (Equation 17). Its extension, SHAP,
genera weterrated/shpp.PParee tortttitinxxpaiee..... html
"https://gtt //githbb.tbb.... http://gtthu....ssaa///.../// com/shap/shap
"The approach replacing inputs with a certain baseline is an instance of Baseline SHAP (BSHAP; Sundararajan and Najmi, 2020).

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Model (pooling)
x 100 7
B x 100 1
Model (pooling)
R² 100
3 x 100 1
BERT (CLS)
0.2
00.5
BERT (CLS)
0.3
U. BERT
37.9 (+37.7)
10.3 (+-0.8)
7 U.SimCSE-BBE
1.2 (+1.11
2.0 (+1.6)
L.SimCSE-BERR
36.7 (-36.5)
10.1 (+-10.7)
+ S.SImCSE-BERT
(4-1911
15.9 (+-15.6
CAICSS-BERR
39.5 (-39.3)
8.0 (+8.6)
7 BIICSE-BERTT
0.7 (+0.7)
1.3 (+0.9)
BERT (MEAN)
29.9
4.8
BERT (MEAN)
0.5
-1.3
SBERT
28.4 (-1.5)
9.8 (+5.0)
SBERT
10.7 (+10022)
18.6 (+119.9)
RoBERTa (CLS)
1.9
3.1
RoBERTa (CLS)
1.3
6.5
U.SimCSE-RoBBE
36.1
34.2)
12.0 (+-8.9)
-> U.S.IISEERROBERS
11.2 (4-9.8)
7.8 (4-14.3)
..iiCSSERROBERT
36.8
(-3199
14.0 (+11.0)
+ SSiISSSERBBBRRT
14.5
10.7 (+17.2)
SERCCSF-ROBERT
35.1 (-33.1)
11.3 (+8.2)
+ SHHICSE-ROBERT
(+1.8)
5.0 (+11.5)
RoBERTa (MEAN)
4.7
3.6
RoBERTa (MEAN)
0.0
0.3
- SRoBERTa
39.2
34.5)
16.6 (+12.99
-> SRoBERTa
14.4 (+-144)
13.4 (+11..1)
MPNet (MEAN) all-mpnet-base-
MPNet (MEAN) all-mpnet-base-e
0.7
2.8
22.4 (-20.9) 11.7 (+11.0)
30.8 (4-30.1) 21.9 (+19.0)
Table 2: Coefficient of determination (R²²) and regres- sion coefficient (3) the linear regression the words' weightings calculated by IG the self-infone self-information - log ((w) for the STS-B dataset. The It2 and | is reported R² 100 and 100. The values inside the brackets represent the gain from pre-trained models.
Table 3: Coefficient of determination (R²²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by SHAP the information gain KL for the STS-B dataset. The It and 3 is reported as R² 100 and 100. The values inside the brackets represent the gain from pre-trained models.
Word weighting (IG)
BERT
UiSCCSE-BERT 0.17x 0.69
NLI: concatenation of SNLI (Bowman et al., 2015) and MNLI (Williams et al., 2018) datasets used in the SimCSE paper (Gao et al., 2021).² , We further randomly sampled 3000 sentences.
-001x 1.04
STS12: randomly sampled 3000 sentences from the test set of STS12 (Agirre et al., 2012) dataset.
10
log P (ww
Figure 6: Linear regression plots between - log (ww) and the word weighting of BERT (CLS) (left) and Un- spervised (U.) SimCSE-BERR BERT (right) using IG. We plot- ted subsampled 3000 tokens from the tokens with the top 99.5% of small KL values for visibility.
We followed the same setting for models and word weighting calculation in Section 5 and we experimented with all the combinations of ((IG, SHAP),(KL(w)) log P(w))).
F.2 Results
F Experiments with Wikipedia, NLI, and STS12 datasets
Tables 5 16 the results of the three datasets. Except for SBERT the IG experi- ments 10 and U.SimCSE-BERT/ROBBBBE
Here, conduct experiments with Wikipedia, NLI, and STS12 datasets other than STS-B datasets in Section 5 for generalizability.
DiffCSE- BERT/RoBERTa in the SHAP experiments, the coefficient of determination R2 and regression co- efficient 3 of contrastive-based sentence encoders are higher than pre-trained models across all the three datasets, verifying the consistency with the experiments with STS-B in Section 5 and E. The results suggest that contrastive-batt sentence en- coders learn to weight each word according to the
F.1 Experimental setup
The following datasets were used:
Wikipedia: randomly sampled sentences of Wikipedia used in the SimCSE paper (Gao et al., 2021). We further randomly sampled 3000 sentences.
phttps://huggingface http://nnnaaccccccataceeeeeeeeee co/datasets/ heinncetoonnpp/dttttttt-----ee wtt.s/rorssiinneeeeseeeeeeeeeeee
hhttps://huggingee http://wgggingaaa...ccaaaaaaaaaa co/datasets/ siincetornnll/taaasets----- hatass/sooosssiineeeeee/e///iiia wikiln_for_sinee cimoosssmmseeeeeee txt
ili_for_ for_simcse. csv
R2 does not increase from BERT(MEAN), while / indeed increases.

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Model (pooling)
x 100 7
B x 100
BERT (CLS)
0.0
-0.1
U. BERT
(+0.8)
0.9 (+0.9)
L.SiCCS--BERR
(-.3.))333)
9.7 (+9.7)
Model (pooling)
n² 100
3 x 100 f
CHICSE--ERR
(+0.5)
0.6 (+0.77
BERT (CLS)
2.2
BERT (MEAN)
1.4
- -12
- U.S.iCSEEBBBL
39.3 (+-38.7)
22.7 (+-20.4)
SBERT
14.1 (+12.8)
11.7 (+-13.0)
+ S.SImCSE-BERT
36.5 (4-35.9)
20.7 (+18.55)
RoBERTa (CLS)
3.2
6.3
+ DifCCSF- BERT
40.1 (+39.44
16.8 (+ 14.6)
U.
11.9 (4-8.6)
4.9 (4-1.))
BERT (MEAN)
32.4
10.0
..SimCSE-ROBERT
18.8 (-15.)
7.5 (3..7)
SBERT
23.6 (-8.8)
19.6 (+9.6)
DiACCFF- ROBERTA
2.1 (-1.)
2.5 (+8.8)
RoBERTa (CLS)
0.8
5.5
RoBERTa (MEAN)
0.1
0.7
- U.SImCSEEROBERTT
34.1 (+-33.2
22.3 (4-16.8)
- SRoBERTa
20.0
19.9)
9.8 (+10.5)
+ S.SinCSE-RoBERR
(+31111
24.3 (+18.8)
MPNet (MEAN) all-mpnet-base- 37.0 (-36.4) 13.2 (+11.7)
0.6
DifICE-RRBBRTA
31.5 (+30.6)
20.6 (+15.1)
RoBERTa (MEAN) + SRoBERTa
1.9
5.9
37.7 (+335.8
26.8 (+-21.0)
Table 4: Coefficient of determination (Re²) and regres- sion coefficient (3)
MPNet (MEAN) all All-mpnet-base-e
0.2
2.0
linear regression the words' weightings calculated by SHAP the self-information log ((w) for the STS-B dataset. The It² and | is reported R² 100 and 100. The values inside the brackets represent the gain from pre-trained models.
23.0 (+22.88) 25.4 (+227.5)
Table 5: Coefficient of determination (R²) and regres- sion coefficient (3) of the linear regression of words' weightings calculated by IG on the information gain KL for the Wikipedia dataset. The /t2 and , is reported as R 100 and 100. The values inside the brackets represent the gain from pre-trained models.
information-theoreticc quantities of words, irrespec- tive of dataset domains.
Model (pooling)
R²
100
BERT (CLS)
0.2
0.6
U.SimCSF
41.1 (+-40.9)
11.3 (+10.8)
S.SinCSE-BBR
39.5 (+-39.4)
10.5 (+10.00
DiACSE-BERT
43.8 (+433.7)
8.6 (+8.0)
BERT (MEAN)
32.8
4.9
+ SBERT
26.9 (-5.9)
10.2 (+5.3)
RoBERTa (CLS)
0.9
3.0
+ U.SimCSE ROBERTa
36.0 (+35.2)
12.5 (+9.5)
+ S. S.SimCSE-RoBIE RoBRRTa
35.0 (+-34.1)
13.8 (+-10.8)
+ DifICSE RoBERTa
34.5 (+33.77)
11.7 (+8.7)
ROBERTA (MEAN)
3.4
> SRoBERTa
41.3 (+-39.1)
(+11199)
MPNet (MEAN)
0.4
-1.3
oll-mpnet-base-eee
22.4(+22.0) 12.3 (+13.66
Table Coeffiiient of determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by IG on the self-information log (ww) for the Wikipedia dataset. The R and is reported as R22 x 100 and 3 x 100. The values inside the brackets represent the gain from pre-trained models.

---

Model (pooling)
x 100 7
B x 100 1
Model (pooling)
n² 100
3 x 100
BERT (CLS)
0.2
BERT (CLS)
0.0
U. SimCSE- -ERT
1.3 (+-1.1)
2.9 (+4.5)
- U.SiMCSE-BBLL
34.9 (+349))
19.1 (+19.11)
S.SimCSE-BERS
(-11.2)
(+-1.0)
+ S.SImCSE-BERT
31.0 (4-10))
18.5 (+18,4)
CHICSE-BERT
0.0 (-0.1)
0.3 (+1.9)
+ DifCCSF- BERT
32.8 (+32.88
14.2 (+14.2)
BERT (MEAN)
0.5 6.2 (4-5.)
BERT (MEAN)
29.5
9.3
SBERT
15.4 (4-16.9)
SBERT
24.8 (-1.7)
18.2 (+8.9)
RoBERTa (CLS)
1.7
10.3
RoBERTa (CLS)
1.8
5.8
U.SimCSE-RoBEER
4.7 (4-3.0)
6.9 (4
- U.SimCSE-RoBERTI
32-9(+311.1
20.0
(+12)2)
(++6.)
9.3 19.66)
+ S.SSCSSE-RBBRRT
31.5 (+-2977)
23.1 (+17.3)
DiACCE RoBERTa
2.5
5.2 (+55
DifICSE DiAICSE-ROBERT
30.2 (+28.4)
18.8 (+13.0)
RoBERTa (MEAN)
0.2
-1.9
RoBERTa (MEAN)
4.2
6.5
- SRoBERTa
8.2 (+-8.0)
11.7 (+13.6)
- SRoBERTa
34.1 (+229.8)
28.2 (+-21.7)
MPNet (MEAN) all-mpnet-base-v2 21.5 (-21.4) 20.5 (+22.00)
0.1
-1.4
MPNet (MEAN) all-mpnet-base-e
0.6
33.0
23.0 (+22.4) 22.4 (+25.44
Table 7: Coefficient of determination (R²) and regres- sion coefficient (3) linear regression the words' weightings calculated by SHAP on the information gain KL for the Wikipedia dataset. The 1t2 and | is reported R2 100 and 3 100. The values inside the brackets represent the gain from pre-trained models.
Table 9: Coefficient of determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by IG the information gain KL for the NLI dataset. The /12 and / is reported as R 100 and 100. The values inside the brackets represent the gain from pre-trained models.
Model (pooling)
R² 100
8 100
Model (pooling)
R²
T
100
BERT (CLS)
0.3
-1.1
BERT (CLS)
0.3
-0.6
U.SimCSF-RR BERTRT
1.4 (+1.1)
1.5 (+2.66)
U.SimCSF
40.1 (+39.9)
10.2 (+10.88)
S.SimCSE-BERR
13.8 (-13.5)
7.2 (+88.)
+ S.SSCSSEBBBBR
36.0 (+35.77
9.9 (+110.5)
DiACSF-BERR BERT
0.0 (-0.3)
0.1 (+1.2)
DiANSEE-BRRT
39.2 (+38.9)
7.7 (+8.3)
BERT (MEAN)
0.8
-1.0
BERT (MEAN)
34.3
5.0
SBERT
8.3 (+7.5)
8.7 (+9.6)
+ SBERT
29.8 (-4.6)
9.9 (++..9)
RoBERTa (CLS)
2.8
-7.1
RoBERTa (CLS)
1.9
3.3
U. Si ROBERTa
3.9 (++12)
3.4 10.55
+ U.SimCSE ROBERTa
38.8 (+36.9)
12.1 (+8.8)
SSiCCSE-ROBEKTH
9.1 (+-.3)
5,4 (+.15)
+ S. SSinCE-RRBBRRR
38.6 (4-36.7)
14.2 (++10.9)
DifICSE RoBERTa
(-0.8)
2.5 (+9.6)
+ DifICSE RoBERTa
36.2 (+34.3)
11.4 (+8.1)
RoBERTa (MEAN) SRoBERTa
0.6
-2.0 6.9 (+8.9)
RoBERTA (MEAN)
5.0
3.9
9.7 (+9.1))
-> SRoBERTa
41.1 (+36.11
17.2 (+13.3)
MPNet (MEAN) all-monet-base-
0.2
-1 -1.3
MPNet (MEAN) bll-n-net-base-v2
1.4
-2.2
23.9
(3.7) 10.6
11.9)
24.2 (+-288) 11.5 (+13.77
Table 8: Coefficient of determination (RP) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by SHAP on the self-information log P(w) (w) for the Wikipedia dataset. The R and reported 122 x 100 and 3 100. The values inside the brackets represent the gain from pre-trained models.
Table 10: Coefficient of determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by IG on the self-information log ((w) for the NLI dataset. The R² and / is ported as 1?3 x 100 and I 100. The values inside the brackets represent the gain from pre- treitrained models.
-

---

Model (pooling)
x 100 7
B x 100 1
Model (pooling)
n² 100
3 x 100 t
BERT (CLS)
0.2
BERT (CLS)
-04
U. SimCSEE- -ERT
1.2 (+009)
2.1 (+0.5)
+ U.S.MCSE-BBLL
37.9 (+37.9)
19.3 (+-19.8)
S.SimCSE-BERS
18.4 (-18.2)
17.5 (+-1.8)
+ S.SimCSE-BERT
31.5 (4-315)
17.3 (+17.8)
DiACCEE-BRRY
1.8 (+1.6)
2.0 (+0.4)
+ DifCCSF- BERT
37.1 (+37.00)
14.9 (+15.3)
BERT (MEAN) SBERT
0.6
BERT (MEAN)
28.6
9.2
10.7 (+100.1
20.3 (+-21.8
SBERT
24.0 (-1.6)
17.3 (+8.00)
RoBERTa (CLS)
1.3
-7.2
RoBERTa (CLS)
1.6
5.3
U.SimCSE-ROBEER
8.7 (+-.3)
7.6 (+1488)
- U.SimCSE-RoBERTI
36.6 (4-35.1)
21.1 (+.888)
15.1
11.8 19.0))
+ S.SSISSS-RBBRRT
33.9 (+32.3)
23.5 (+18.2)
DiACCE RoBERTa
(+1.9)
5.1 (+12)3)
DiAACSE-ROBERTa
35.6 (+34.1)
20.2 (+14.9)
RoBERTa (MEAN) - SRoBERTa
0.0
0.2
RoBERTa (MEAN)
4.1
6.4
14.1 (-11.1)
14.8 (+14.6)
- SRoBERTa
38.3 (+33111
28.6 (+-22.2)
MPNet (MEAN)
0.8
3.1
MPNet (MEAN) all-mpnet-basee
0.8
-3.2
all-mpnet-baser 30.9 (-30.1) 23.3 (+-20.2)
24.1 (+23.33 23.1 1 (+266.3
Table 11: Coefficient of determination (R²) and regres- sion coefficient (3)
Table 13: Coefficient of determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by IG the information gain KL for the STS 12 dataset. The 1t2 and , is reported as R 100 and 100. The values inside the brackets represent the gain from pre-trained models.
linear regression the words' weightings calculated by SHAP on the information gain KL for the NLJ dataset. The !t? and / is reported as R2 100 and B 100. The values inside the brackets represent the gain from pre-trained models.
Model (pooling)
R² 100
8 100
Model (pooling)
R²
100
BERT (CLS)
0.2
0.8
BERT (CLS)
0.4
0..7
U.SimCSF -BRRTT
0.9 (++0.7)
0.9 (+0.2)
U.SimCSF
39.9 (+39.6)
10.4 (+11.11
S.SimCSE-BERR
23.3 (-23.1)
9.8 (+-9.0)
+ S.SSCCSEBBBE
33.6 (+33.22)
9.4 (+110.1)
DiACSF-BERR
1.9 (+1.7)
1.0 (+0.3)
DIACSE-BERT
40.7 (+40033)
8.2 (+8.9)
BERT (MEAN)
1.5
-1.1
BERT (MEAN)
29.6
4.9
SBERT
14.8 (-13.3)
11.8 (+12
+ SBERT
27.0 (-2.6)
9.6 (+4.77)
RoBERTa (CLS)
2.7
RoBERTa (CLS)
1.3
2.7
U. Si ROBERTa
9.4 (+6.7)
4.4 (+.01)
+ U.SimCSE ROBERTa
38.0 (+36.7)
12.3 (+9.6)
SBinCSE-ROBERTH
19.5
(-16.9)
(+1.1)
+ S. SSinCS--ROBERR
36.7 (4-35.4)
14.0 (+11.33
DifICSE RoBERTa
2.4(00.3
2.5 (+8.1)
+ DifICSE RoBERTa
37.6 (+36.3)
11.9 (+9.2)
RoBERTa (MEAN)
0.0
-0.4
RoBERTA (MEAN)
3.6
SRoBERTa
19.4 (-19.4)
9.7 1+.10.1)
SRoBERTa
40.4 (+36.5)
(+13.3)
MPNet (MEAN)
0.8
1.5
MPNet (MEAN) all-mpnet-base-eeee.
1.3
-2.2
all-monet-based 38.0 (--733) 12.9 (+11)44
23.3 (+-2.9) 11.9 (+14.11
Table Coefficient determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by SHAP on the self-information log ((w) (w) for the NLI dataset. The 2 and ported as 1t2 x 100 and 3 x 100. The values inside the brackets represent the gain from pre-traine trained models.
Table 14: Coefficient of determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by IG on the self-information log (ww) for the STS12 dataset. The R² and / is reported as R?2 x 100 and 3 x 100. The values inside the brackets represent the gain from pre-trained models.
re-

---

Model (pooling)
x 100 7
B x 100
BERT (CLS)
U. S.SiCSSE -EREET
0.9 (++0.8
1.9 (+2.44
S.SimCSE-BERT
(-211)
(+-7.5)
DiACCEE-BERT
0.4 (+0.44
1.0 (+1.6)
BERT (MEAN) SBERT
1.2
2.3
11.8 (-10.6)
20.0
(+.2.33
RoBERTa (CLS)
2.4
9.6
U.SimCSE-ROBER
11.0
8.6 (+)))2)
(-14.9)4.9)
12.9 (+2))
DiACCE RoBERTa
2+8..)
5.0 (+14)))
RoBERTa (MEAN) - SRoBERTa
0.1
-1.2 -1.2
19.1 (-19.00
16.7 (+17.9)
MPNet (MEAN) all-mpnet-base- 34.1 (-33.6) 23.6 (+21.1)
0.4
2.5
Table 13: Coefficient of determination (R²) and regres- sion coefficient (3)
linear regression the words' weightings calculated by SHAP on the information gain KL for the STS 12 dataset. The 1t2 and 8 is reported as R² 100 and 8 100. The values inside the brackets represent the gain from pre-trained models.
Model (pooling)
R² 100 1
8 100
BERT (CLS)
0.1
00.5
U.SimCSF-BB -ERRRT
0.7 (+00.))
0.8 (+1.3)
S.SimCSE-BERK
22.7 (-22.7)
9.2 (+-9.7)
DiACCF-BERT
0.2 (+0.2)
0.4 (+0.9)
BERT (MEAN)
2.0 13.8 (-11.8)
1.5
SBERT
11.3 (+ 12.9)
RoBERTa (CLS)
3.8
-7.0
U.SimCSE-ROBERTA
10.7 (+6.9)
4.8 (1.8)
SSiICSE-RoBERE
(-.0(2)
7.7 (4.7)
DifICSE-Roon RoBERTa
(-1.8)
2.4 (+9.4)
RoBERTa (MEAN) SRoBERTa
0.3
-1.4
22.1 (+21.8)
10.3 (+ (1.7)
MPNet (MEAN) all-monet-base- 36.7 (-36.5) 12.8
0.3
1.0
1+.8)
Table Coefficient determination (R²) and regres- sion coefficient (3) of the linear regression of the words' weightings calculated by SHAP on the self-information log ((w) (w) for the STS12 dataset. The R2 and reported R22 x 100 and 3 100. The values inside the brackets represent the gain from pre-trained models.


Reviews:
[{"review_id": "LUWXSiWwSK", "reviewer": "Reviewer_un9Z", "summary": "", "questions": "- Is there any paper for the state given in lines 40-41 on the first page?\n\n- Is there any extra method to quantify the word weighting addition to Integrated Gradients? If yes, what is the reason of choosing this method?\n\n- What is your conclusion about the higher scores of sBERT/SRoBERTA compared to SimCSE BERT/SimCSE RoBERTa?", "limitations": "", "rating": 3, "confidence": 2, "soundness": 3, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the thoughtful review! We appreciate the positive feedback on our mathematical proof of why contrastive learning induces word weighting by information gain.\nAlso, thank you for pointing out important points in the experimental settings.\n\n# Additional experiments using STS-12 and other datasets to validate our claim.\nThank you for suggesting this! \nWe fully agree that our result should be confirmed with other datasets than STS-B (ll.302-307).\nSTS-12, which differs in domains from STS-B, would be helpful to confirm the generalizability.\n\n## Experimental setting\nFollowing your suggestion, we conducted experiments using STS-12 dataset for BERT-based models to validate the generalizability of our claim. \nWe used test set of STS-12 to calculate the word weighting of the model (IG), self-information and information gain.\n\nWe also experimented with Wikipedia and NLI datasets whose domains differ from STS-B/STS-12 for further validation.\nWe followed the same setting with SimCSE ([Gao et al., 2021](https://aclanthology.org/2021.emnlp-main.552/)): \n- Wikipedia: randomly sampled 30k sentences.\n- NLI: concatenation of SNLI ([Bowman et al., 2015](https://aclanthology.org/D15-1075/)) and MNLI([Williams et al., 2018](https://aclanthology.org/N18-1101/)) datasets.\n\nWhole datasets were used to calculate self-information and information gain. \nFor calculating IG, we randomly sampled the 1500 sentences from each dataset.\n\n## Results\nThe experimental results show that coefficient of determination $R^2$ and regression coefficient $\\beta$ for contrastive-finetuned encoders are higher than those for pre-trained models across almost all datasets, models, and information-theoretic quantities combinations (denoted as ✔︎).\nThese results are consistent with the results of STS-B, validating our claim that contrastive learning induces encoders to weight words according to $-\\log{P(w)}$ and $\\mathrm{KL}(w)$. We will include these results in the camera-ready version as well. Again, thank you for the constructive feedback.\n\n###  Result for STS-12\n| Model (pooling)         | $R^2$ w.r.t. $-\\log{P(w)}$ ↑ | $\\beta$ w.r.t. $-\\log{P(w)}$ ↑ | $R^2$ w.r.t. $\\mathrm{KL}(w)$ ↑ | $\\beta$ w.r.t. $\\mathrm{KL}(w)$ ↑ |\n|----------------------|-----------------|----------------|--------------|-------------|\n| BERT(CLS)            | 0.059           | 0.023          | 0.065        | 0.046       |\n| → Unsup. SimCSE-BERT(CLS) | 0.397 ✔︎           | 0.102 ✔︎         | 0.377 ✔︎        | 0.190 ✔︎      |\n| → Sup. SimCSE-BERT(CLS)   | 0.326 ✔︎           | 0.091 ✔︎         | 0.306 ✔︎      | 0.168 ✔︎      |\n| BERT(MEAN)           | 0.296           | 0.049          | 0.286        | 0.092       |\n| → SBERT(MEAN)              | 0.270           | 0.096 ✔︎         | 0.240        | 0.173 ✔︎      |\n\n### Result for Wikipedia\n| Model (pooling)         | $R^2$ w.r.t. $-\\log{P(w)}$ ↑ | $\\beta$ w.r.t. $-\\log{P(w)}$ ↑ | $R^2$ w.r.t. $\\mathrm{KL}(w)$ ↑ | $\\beta$ w.r.t. $\\mathrm{KL}(w)$ ↑ |\n|----------------------|-----------------|----------------|--------------|-------------|\n| BERT(CLS)            | 0.090           | 0.0314         | 0.128        | 0.248       |\n| → Unsup. SimCSE-BERT(CLS) | 0.427 ✔︎           | 0.106 ✔︎         | 0.409 ✔︎       | 0.686 ✔︎      |\n| → Sup. SimCSE-BERT(CLS)   | 0.399 ✔︎          | 0.096 ✔︎         | 0.352 ✔︎       | 0.598 ✔︎      |\n| BERT(MEAN)           | 0.333           | 0.046          | 0.333        | 0.304       |\n| → SBERT(MEAN)              | 0.269           | 0.095 ✔︎        | 0.213        | 0.556 ✔︎      |\n\n### Result for NLI\n| Model (pooling)         | $R^2$ w.r.t. $-\\log{P(w)}$ ↑ | $\\beta$ w.r.t. $-\\log{P(w)}$ ↑ | $R^2$ w.r.t. $\\mathrm{KL}(w)$ ↑ | $\\beta$ w.r.t. $\\mathrm{KL}(w)$ ↑ |\n|----------------------|-----------------|----------------|--------------|-------------|\n| BERT(CLS)            | 0.066           | 0.022          | 0.079        | 0.110       |\n| → Unsup. SimCSE-BERT(CLS) | 0.403 ✔︎          | 0.092 ✔︎         | 0.413 ✔︎       | 0.426 ✔︎      |\n| → Sup. SimCSE-BERT(CLS)   | 0.347 ✔︎          | 0.087 ✔︎         | 0.325 ✔︎       | 0.387 ✔︎      |\n| BERT(MEAN)           | 0.330           | 0.045          | 0.302        | 0.198       |\n| → SBERT(MEAN)              | 0.296           | 0.090 ✔︎         | 0.266        | 0.391 ✔︎      |\n\n\n# Explicit word weighting techniques to improve sentence embedding quality\nThank you for the question! \nWeighting static word embeddings by the quantities based on the inverse of word frequency, such as TF-IDF ([Arroyo-Fernández et al., 2019](https://linkinghub.elsevier.com/retrieve/pii/S0885230817302887)) and smoothed inverse frequency (SIF; [Arora et al., 2017](https://openreview.net/forum?id=SyK00v5xx)), are strong baselines, outperforming more complicated sentence encoders based on LSTM or RNN (ll.21-26). In the era of BERT-based sentence encoder, it is reported that weighting each word of SBERT model further improves the embedding qualities ([Wang and Kuo, 2020](https://ieeexplore.ieee.org/document/9140343)).\n\n# Reasons for using Integrated Gradients / Additional experiments with SHAP\nThank you for the question regarding Integrated Gradients (IG) and other posibble methods!\n\nWe chose IG because IG is a widely used technique among feature attribution methods for differentiable neural networks (ll.111-118).　\nIG satisfies desirable axioms, such as sensitivities, while other gradient-based methods often violate these axioms ([Sundararajan et al., 2017](https://proceedings.mlr.press/v70/sundararajan17a.html)).\n\nBesides gradient-based feature attribution methods, SHAP ([Lundberg and Lee, 2017](https://papers.nips.cc/paper_files/paper/2017/hash/8a20a8621978632d76c43dfd28b67767-Abstract.html)), which is based on the Shapley Value used in game theory ([Lloyd S, 1953](https://www.jstor.org/stable/j.ctt1b9x1zv.24)), is also a widely used feature attribution method in the NLP field as well ([Mosca et al., 2022](https://aclanthology.org/2022.coling-1.406/)).\n\nTo validate that our claim also holds for methods other than IG, we conducted experiments using SHAP. In addition to models analyzed in the paper, we added DiffCSE ([Chuang et al., 2022](https://aclanthology.org/2022.naacl-main.311/)) which is an extension of SimCSE, and [all-mpnet-base-v2](https://huggingface.co/sentence-transformers/all-mpnet-base-v2) ([Reimers and Gurevych, 2019](https://aclanthology.org/D19-1410/)), which is one of SoTA sentence transformer models based on MPNet ([Song et al., 2020](https://proceedings.neurips.cc/paper/2020/hash/c3a690be93aa602ee2dc0ccab5b7b67e-Abstract.html)) for the analysis. \n\nAs a result, we confirmed that the $R^2$ and $\\beta$ of contrastive-based sentence encoders are higher than those of models before contrastive fine-tuning for almost all experimental combinations (denoted as ✔), supporting the generalizability of our claim.\n\n| Model (pooling)         | $R^2$ w.r.t. $-\\log{P(w)}$ ↑ | $\\beta$ w.r.t. $-\\log{P(w)}$ ↑ | $R^2$ w.r.t. $\\mathrm{KL}(w)$ ↑ | $\\beta$ w.r.t. $\\mathrm{KL}(w)$ ↑ |\n|-------------------------|----------------------|---------------------|-------------------|------------------|\n| BERT(CLS)               | 0.006                | -0.009              | 0.002             | -0.010           |\n| → Unsup. SimCSE-BERT(CLS)    | 0.006                | 0.008 ✔︎              | 0.010 ✔︎             | 0.018 ✔︎           |\n| → Sup. SimCSE-BERT(CLS)     | 0.227 ✔︎                 | 0.094 ✔︎              | 0.186 ✔︎            | 0.154 ✔︎           |\n| → DiffCSE-BERT(CLS)          | 0.006                | 0.006 ✔︎              | 0.008 ✔︎             | 0.013 ✔︎           |\n| BERT(MEAN)              | 0.014                | -0.012              | 0.005             | -0.013           |\n| → SBERT(MEAN)           | 0.131 ✔︎                | 0.117 ✔︎              | 0.107 ✔︎             | 0.186 ✔︎           |\n| RoBERTa(CLS)            | 0.029                | -0.056              | 0.012             | -0.057           |\n| → Unsup. SimCSE-RoBERTa(CLS) | 0.119 ✔︎                 | 0.050 ✔︎              | 0.113 ✔︎              | 0.078 ✔︎           |\n| → Sup. SimCSE-RoBERTa(CLS)   | 0.189 ✔︎                | 0.074 ✔︎              | 0.146 ✔︎              | 0.106 ✔︎           |\n| RoBERTa(MEAN)           | 0.000                | -0.007              | 0.000             | 0.003            |\n| → SRoBERTa(MEAN)              | 0.200 ✔︎                 | 0.098 ✔︎              | 0.144 ✔︎             | 0.134 ✔︎           |\n| mpnet(CLS)              | 0.000                | 0.004               | 0.002             | 0.014            |\n| mpnet(MEAN)             | 0.005                | 0.014               | 0.007             | 0.028            |\n| →　all-mpnet-base-v2(MEAN)    | 0.370 ✔︎                 | 0.132 ✔︎              | 0.308 ✔︎             | 0.219 ✔︎           |\n\n\n\n# Scores of SBERT/SRoBERTA compared to SimCSE BERT/SimCSE RoBERTa\nThank you for the question! In Table 1 in the paper, the $R^2$ values are SBERT > SimCSE-BERT while SRoBERTa < SimCSE-RoBERTa. This result suggests that the score of $R^2$, which indicates how strong IG and $-\\log{P(w)}$ or ${\\mathrm{KL(w)}}$ are linearly associated, is not a perfect proxy for how good the sentence encoder is.\nThere might be more appropriate quantities that can explain the word weighting of the model (IG) other than $-\\log{P(w)}$ and ${\\mathrm{KL(w)}}$, which we have yet to be aware of, and it is left to future work (ll.288-290).", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "The paper presents solid proof of contrastive learning word weighting by information gain.", "reasons_to_reject": "- The experimental results by using only STS-B are very limited. There are several STS datasets, especially it would be nice to see the results of STS12 which has lower scores compared to other datasets.", "questions_to_authors": "- Is there any paper for the state given in lines 40-41 on the first page?\n\n- Is there any extra method to quantify the word weighting addition to Integrated Gradients? If yes, what is the reason of choosing this method?\n\n- What is your conclusion about the higher scores of sBERT/SRoBERTA compared to SimCSE BERT/SimCSE RoBERTa?", "paper_topic_and_main_contributions": "The paper explores the weighting of input words in encoders for contrastive learning.\nThe mathematical background of the method is very strong and very detailed.\n\n\nThe experimental results are limited.", "excitement": 3, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"Typos_Grammar_Style_and_Presentation_Improvements": "line 159 discriimination\nline 181 ward w\nline 222 OLS -> the full version of OLS ?"}, "extra_text": {}}, {"review_id": "Pv6ujUZPZU", "reviewer": "Reviewer_4dqe", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 2, "soundness": 2, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the insightful review! We appreciate the positive feedback on our idea and tackling demystifying the contrastive learning of sentence encoder. We also appreciate the constructive feedback on the insights of our work.\n\n# Qualitative analysis of word weighting of the models\nThank you for commenting about the qualitative analysis! \n\nThe \"onion\" in Figure 3 is actually a good example from the information theory perspective. Our writing might have confused you, so let us briefly explain here.\n\nOur hypothesis throughout the paper is that contrastive-based sentence encoders weight each word according to information-theoretic quantities $-\\log{P(w)}$ or $\\mathrm{KL}(w)$. Thus, in Figure 3, we would like to see if blue (before contrastive fine-tuning) has a different word weighting trend from gray lines (information-theoretic quantities) and if orange (after contrastive fine-tuning) has a similar trend with gray (information-theoretic quantities) lines.\n\nThrough this perspective with Figure 3, we can observe the following trends that support our hypothesis:\n- Blue (before contrastive fine-tuning) assigns high weight to low informative words such as *is* and punctuation. \n- However, orange (after contrastive fine-tuning) assigns high weight to informative words such as *woman*, *cutting* and *onion* when constructing sentence embedding.\n\nA similar trend is also observed in Figure 25 in the appendix.\n\nBesides, this interesting phenomenon of contrastive sentence encoders' weighting informative words is observed in the whole corpus (Section 4.2), not only in the specific sentence in Figure 3. The increase of $R^2$ and $\\beta$ in Table 1 quantitatively explains that contrastive-based sentence encoders weight informative words when constructing sentence embedding.\n\nBased on your feedback, we will add the discussion here to the caption of Figure 3 in the camera-ready version.\n\n# Insights of the inner mechanism of contrastive learning for sentence embedding\nThank you for your important perspective! \nTo summarize our work, we estimated how each input word contributes to the output (sentence embedding) in sentence encoders trained with contrastive learning and compared it with information theoretic quantities. Our results show the macro-level characteristic that \"sentence encoders learn to focus on informative words via contrastive fine-tuning.\"\n\nWe believe our insight further advances the understanding of contrastive learning for sentence embedding from previous micro-level analysis, which focuses on the inner mechanism of representations: [Gao et al., 2021](https://aclanthology.org/2021.emnlp-main.552/) showed that contrastive learning induces representations for semantically similar sentences to be distributed closer and vice versa in sentence embedding space.\nOur work further attempts to demystify how contrastive learning works from the word-level contribution in sentence encoders and association with information theory.\n\nOur insight is also helpful for understanding the practical success of contrastive learning. For example, our insight that the sentence encoders learn IDF-like word weighting ($-\\log{P(w)}$) through contrastive fine-tuning provides the understanding of why contrastive fine-tuning is also effective in tasks such as passage retrieval where the similarity of the topics should be considered.\n\nIn the camera-ready version, we will add one paragraph about the point discussed here using an additional page. Again, thank you very much for the important suggestion! If anything is unclear, let us discuss it in the discussion phase!", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- Easy idea to follow.\n- Paper easy to read. (Short paper)\n- (Perhaps) first paper that tackles to understand why contrastive learning works the ways it works", "reasons_to_reject": "- Qualitative analysis is very limited and ambiguous. (\"cutting\" is clear, but how about \"onion\"? For 'onion', -log P(w) is lower than SimCSE-BERT. )\n- What do we know about the inner working of contrastive learning by comparing word's contribution (from IG) against self-information and information gain? The authors need to take one more step to interpret the results further.", "questions_to_authors": "", "paper_topic_and_main_contributions": "Main contribution: it tries to explain how contrastive learning gives weights to input words in a given sentence\n- It compares a word's contribution to contrastive learning's sentence encoding with two information-theoretic quantities: self-information & information gain.\n- It computes a word's contribution to sentence encoding using Integrated Gradients.", "excitement": 3, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "HG1LEbbTag", "reviewer": "Reviewer_aaka", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": 2, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are thankful for your comprehensive review! We appreciate the positive feedback on bridging contrastive learning for sentence embedding and information-theoretic quantities. \nWe also appreciate the helpful feedback on the experimental setting of IG and other possible methods besides the models to be analyzed.\n\n# Additional experiment with other contrastive-based sentence encoders\nThank you for the constructive feedback on the varieties of models to be analyzed! \nWe fully agree that our experiments are limited to BERT & RoBERTa and their SimCSE versions, and adding more models to be analyzed would help us understand more about the contrastive learning of sentence encoders (ll.307-313).\n\nTo validate the generalizability of our claim, we conducted additional experiments with contrastive-based sentence encoders other than SimCSE/SBERT.\nWe choose DiffCSE ([Chuang et al., 2022](https://aclanthology.org/2022.naacl-main.311/)), an extension of the SimCSE model, incorporating an ELECTRA-like training objective.\nWe also select [all-mpnet-base-v2](https://huggingface.co/sentence-transformers/all-mpnet-base-v2) ([Reimers and Gurevych, 2019](https://aclanthology.org/D19-1410/)), one of the SoTA sentence transformer models. It is fine-tuned from MPNet ([Song et al., 2020](https://proceedings.neurips.cc/paper/2020/hash/c3a690be93aa602ee2dc0ccab5b7b67e-Abstract.html)) using contrastive learning with various labeled pair sentences.\n\nAs a result, we confirmed that the coefficient of determination $R^2$ and regression coefficient $\\beta$ of contrastive-based sentence encoders are higher than those of models before contrastive fine-tuning for all contrastive-based models (denoted as ✔), supporting the generalizability of our claim.\nWe will include these results in the camera-ready version! Again, thank you for the constructive feedback.\n\n| Model (pooling)         | $R^2$ w.r.t. $-\\log{P(w)}$ ↑ | $\\beta$ w.r.t. $-\\log{P(w)}$ ↑ | $R^2$ w.r.t. $\\mathrm{KL}(w)$ ↑ | $\\beta$ w.r.t. $\\mathrm{KL}(w)$ ↑ |\n|----------------------|-----------------|----------------|--------------|-------------|\n| BERT(CLS)            | 0.066           | 0.022          | 0.079        | 0.110       |\n| → DiffCSE(CLS)            | 0.393 ✔︎          | 0.080 ✔︎         | 0.334 ✔︎       | 0.153 ✔︎      |\n| MPNet(CLS)           | 0.016           | -0.028         | 0.006        | -0.030      |\n| MPNet(MEAN)          | 0.0142          | -0.022         | 0.006        | -0.026      |\n| →　all-mpnet-base-v2(MEAN) | 0.224 ✔︎          | 0.117 ✔︎         | 0.216 ✔︎       | 0.210 ✔︎      |\n\n# Reasons for using Integrated Gradients / Additional experiments with SHAP\nThank you for pointing out the reasons for using Integrated Gradients (IG) and the potential usage of other methods!\n\nWe chose IG because IG is a widely used technique among feature attribution methods for differentiable neural networks (ll.111-118).　\nIG satisfies desirable axioms, such as sensitivities, while other gradient-based methods often violate these axioms ([Sundararajan et al., 2017](https://proceedings.mlr.press/v70/sundararajan17a.html)).\n\nBesides gradient-based feature attribution methods, SHAP ([Lundberg and Lee, 2017](https://papers.nips.cc/paper_files/paper/2017/hash/8a20a8621978632d76c43dfd28b67767-Abstract.html)), which is based on the Shapley Value used in game theory ([Lloyd S, 1953](https://www.jstor.org/stable/j.ctt1b9x1zv.24)), is also a widely used feature attribution method in the NLP field as well ([Mosca et al., 2022](https://aclanthology.org/2022.coling-1.406/)).\n\nTo validate that our claim also holds for methods other than IG, we conducted experiments using SHAP. In addition to models analyzed in the paper, we added DiffCSE ([Chuang et al., 2022](https://aclanthology.org/2022.naacl-main.311/)) which is an extension of SimCSE, and [all-mpnet-base-v2](https://huggingface.co/sentence-transformers/all-mpnet-base-v2) ([Reimers and Gurevych, 2019](https://aclanthology.org/D19-1410/)), which is one of SoTA sentence transformer models based on MPNet ([Song et al., 2020](https://proceedings.neurips.cc/paper/2020/hash/c3a690be93aa602ee2dc0ccab5b7b67e-Abstract.html)) for the analysis. \n\nAs a result, we confirmed that the $R^2$ and $\\beta$ of contrastive-based sentence encoders are higher than those of models before contrastive fine-tuning for almost all experimental combinations (denoted as ✔), supporting the generalizability of our claim.\n\n| Model (pooling)         | $R^2$ w.r.t. $-\\log{P(w)}$ ↑ | $\\beta$ w.r.t. $-\\log{P(w)}$ ↑ | $R^2$ w.r.t. $\\mathrm{KL}(w)$ ↑ | $\\beta$ w.r.t. $\\mathrm{KL}(w)$ ↑ |\n|-------------------------|----------------------|---------------------|-------------------|------------------|\n| BERT(CLS)               | 0.006                | -0.009              | 0.002             | -0.010           |\n| → Unsup. SimCSE-BERT(CLS)    | 0.006                | 0.008 ✔︎              | 0.010 ✔︎             | 0.018 ✔︎           |\n| → Sup. SimCSE-BERT(CLS)     | 0.227 ✔︎                 | 0.094 ✔︎              | 0.186 ✔︎            | 0.154 ✔︎           |\n| → DiffCSE-BERT(CLS)          | 0.006                | 0.006 ✔︎              | 0.008 ✔︎             | 0.013 ✔︎           |\n| BERT(MEAN)              | 0.014                | -0.012              | 0.005             | -0.013           |\n| → SBERT(MEAN)           | 0.131 ✔︎                | 0.117 ✔︎              | 0.107 ✔︎             | 0.186 ✔︎           |\n| RoBERTa(CLS)            | 0.029                | -0.056              | 0.012             | -0.057           |\n| → Unsup. SimCSE-RoBERTa(CLS) | 0.119 ✔︎                 | 0.050 ✔︎              | 0.113 ✔︎              | 0.078 ✔︎           |\n| → Sup. SimCSE-RoBERTa(CLS)   | 0.189 ✔︎                | 0.074 ✔︎              | 0.146 ✔︎              | 0.106 ✔︎           |\n| RoBERTa(MEAN)           | 0.000                | -0.007              | 0.000             | 0.003            |\n| → SRoBERTa(MEAN)              | 0.200 ✔︎                 | 0.098 ✔︎              | 0.144 ✔︎             | 0.134 ✔︎           |\n| mpnet(CLS)              | 0.000                | 0.004               | 0.002             | 0.014            |\n| mpnet(MEAN)             | 0.005                | 0.014               | 0.007             | 0.028            |\n| →　all-mpnet-base-v2(MEAN)    | 0.370 ✔︎                 | 0.132 ✔︎              | 0.308 ✔︎             | 0.219 ✔︎           |", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- Attempted to explain the inner workings of contrastive methods for sentence representation learning, with the introduction of simple but intuitive information-theoretic concepts such as self-information and information gain.", "reasons_to_reject": "- The paper lacks a compelling rationale for the specific use of the Integrated Gradients method to determine the implicit weights of individual words, leaving unanswered questions about the potential outcomes or advantages of employing alternative approaches.\n- Given a wide array of contrastive methods for sentence representation learning that extend SimCSE, a simple comparison between the original BERT & RoBERTa models and their SimCSE versions may be insufficient for drawing a robust and well-grounded conclusion.\n", "questions_to_authors": "", "paper_topic_and_main_contributions": "This paper endeavors to unravel the underlying mechanisms of contrastive methods used in sentence representation learning. \nIt does so by introducing nuanced concepts grounded in information theory, such as self-information and information gain. \nSpecifically, the proposed methodology leverages the Integrated Gradients (IG) technique to assess the implicit weightings attributed to individual words within a sentence, as calculated by various sentence encoders. \nSubsequently, the relationship between these computed weights and key information-theoretic quantities (namely, self-information and information gain) is examined. This analysis facilitates a comparative evaluation of sentence embeddings derived from different sentence encoders, shedding light on their distinct characteristics and behavior.", "excitement": 3, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "HARvA77Hdd", "reviewer": "Reviewer_3ibg", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for the detailed and thoughtful feedback! We appreciate the positive feedback on the intuitiveness of our method, the conciseness of our experimental setting, writing, and math presentation. We will brush up our work more on the camera-ready version!", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "\n1. The method is intuitive and makes sense.\n2. The experimental setup is reasonable and well-executed. The results support their claim.\n3. The writing and math presentation is clear and easy to follow.", "reasons_to_reject": "N/A", "questions_to_authors": "", "paper_topic_and_main_contributions": "This paper studies the interpretability of the contrastive learning-based sentence encoder. \n\nMore specifically, the authors use the integrated gradients method to analyze the SimCSE contrastive learning model and investigate how the encoders internally weigh input words to encode a sentence. Their experiments reveal that contrastive learning induces the encoders to weight input words according to information-theoretic quantities, which are somewhat similar to previous sentence embedding methods.", "excitement": 4, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper studies the interpretability of the contrastive learning-based sentence encoder. More specifically, the authors use the integrated gradients method to analyze the SimCSE contrastive learning model and investigate how the encoders internally weigh input words to encode a sentence. The experiments reveal that contrastive learning induces the encoders to weight input words according to information-theoretic quantities, which are somewhat similar to previous sentence embedding methods.

I did not find in the reviews any strong reason to reject the paper except that its most important contribution is theoretical rather than empirical. To me, this is not an actual limitation and I think this paper can make a good contribution to the EMNLP audiance.
Decision: Accept-Findings