Probing neural language models for understanding of words of estimative probability
Year: 2023

Abstract:
Words of Estimative Probability (WEP) are phrases used to express the plausibility of a statement. Examples include terms like probably, maybe, likely, doubt, unlikely, and impossible. Surveys have shown that human evaluators tend to agree when assigning numerical probability levels to these WEPs. For instance, the term highly likely equates to a median probability of 0.90±0.08 according to a survey by Fagen-Ulmschneider (2015). In this study, our focus is to gauge the competency of neural language processing models in accurately capturing the consensual probability level associated with each WEP. Our first approach is utilizing the UNLI dataset (Chen et al., 2020), which links premises and hypotheses with their perceived joint probability p. From this, we craft prompts in the form: "[PREMISE]. [WEP], [HYPOTHESIS]." This allows us to evaluate whether language models can predict if the consensual probability level of a WEP aligns closely with p. In our second approach, we develop a dataset based on WEP-focused probabilistic reasoning to assess if language models can logically process WEP compositions. For example, given the prompt "[EVENTA] is likely. [EVENTB] is impossible.", a wellfunctioning language model should not conclude that [EVENTA&B] is likely. Through our study, we observe that both tasks present challenges to out-of-the-box English language models. However, we also demonstrate that fine-tuning these models can lead to significant and transferable improvements.

heading: 1 Introduction
text: Expression of uncertainty is an important part of communication. Formal statistics are the rigorous way to quantify uncertainty but do not fit all communication styles. Words of estimative probability (WEP) such as maybe and believe are adverbs or verbs that are informal alternatives. Kent (1964) noted the importance of clarifying WEP meaning
for intelligence analysis in the Central Intelligence Agency, and provided guidelines for mapping WEP to numerical probabilities. Several studies then measured the human perceptions of probability words and discovered some agreement with Kent (1964)’s guidelines. In this work, we use the scale derived from a survey (Fagen-Ulmschneider, 2015), which is the largest and most recent WEP perception survey available. 123 participants were asked to label WEP with numerical probabilities. We use the median of the participant answers to assign a consensual value to each WEP. Associated probabilities for the 19 WEP we use are available in Appendix A, table 2.
Here, we assess whether neural language models learn the consensual probability judgment of WEP from language modeling pretraining. We develop datasets and a methodology to probe neural language model understanding of WEP. The first dataset leverages previously annotated probability scores between a premise and a hypothesis, in order to measure a language model’s ability to capture the agreement between numerical probabilities and WEP-expressed probabilities. The second dataset is based on compositions of facts with WEP-expressed probabilities, and measures verbal probabilistic reasoning in language models.
Our contributions are as follows: (i) two datasets and methods to measure understanding of WEP; and (ii) evaluation of the ability of neural language models (GPT2, RoBERTa-trained on MNLI) to tackle WEP-related problems, showing that offthe-shelf models are very little influenced by them, even though fine-tuning on our constructed datasets quickly leads to high accuracies. The code and generated datasets are publicly available1
1/hf.co/.../probability_words_nli
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heading: 2 Related work
text: Our work probes a particular aspect of language understanding. We do not analyze the inside of the models (Rogers et al., 2020). We focus on the models’ ability to perform controlled tasks (Naik et al., 2018; Richardson et al., 2020) involving WEP. WEP were studied in the context of intelligence analysis and linguistics, our work is the first to look at them through natural language processing (NLP) models. Our study also pertains to NLP analyses of logical reasoning and probability problems, and to uncertainty in natural language inference tasks.
Linguistics study of WEP Kent (1964)’s seminal work was the first to link WEP and numerical probability estimates, with intelligence analysis motivations (Dhami and Mandel, 2021) and a prescriptivist approach. This inspired further quantifications of human perceptions of WEP, in the context of medical reports (O’Brien, 1989; Ott, 2021) and weather reports (Lenhardt et al., 2020). FagenUlmschneider (2015) proposed the largest survey up to date with 123 participants about generaldomain WEP perception.
Logical and probabilistic reasoning Another strand of work probes NLP text encoders capabilities, notably reasoning abilities. Weston et al. (2015) probed understanding of specific problems like negation, spatial and temporal reasoning with the bAbI dataset. Richardson et al. (2020) probe understanding of first-order logic reasoning, Sileo and Lernould (2023) probe epistemic logic reasoning. Our work is the first to address probabilistic logic, alongside Dries et al. (2017); Suster et al. (2021) who construct a dataset of natural language probability problems, e.g., "A bag has 4 white and 8 blue marbles. You pull out one marble and it is blue. You pull out another marble, what is the probability of it being white?". They also rely on the ProbLog solver (De Raedt et al., 2007), but focus on numeric probability problems. By contrast, our work targets WEP, and textual probabilistic logical reasoning.
Natural language inference, uncertainty, modality, evidentiality Uncertainty was also studied in the context of natural language inference tasks. Zhou et al. (2022) study the disagreement across annotators when labeling entailment relationships. Zhang et al. (2017) annotate graded entailment with 5 probability levels, and the UNLI dataset (Chen
et al., 2020) go further by annotating numerical probabilities. Our work also pertains to the study of modality (Palmer, 1992; Saurí et al., 2006) and more particularly evidentiality (Su et al., 2010), but where previous work focused on WEP.

heading: 3 Probing WEP understanding

heading: 3.1 Verbalization and distractor generation
text: Our goal is to measure the understanding of WEP. One requirement of WEP understanding is capturing the consensual probability level. To test that, we use contexts (PREMISE) paired with a conclusions (HYPOTHESIS). The likelihood of a conclusion, p, depends on the associated context. One example from UNLI (Chen et al., 2020), which annotates that, is (A man in a white shirt taking a picture , A man takes a picture , 1.0).
We convert a triplet (PREMISE, HYPOTHESIS, p) to the following verbalization:
PREMISE. Tp(HYPOTHESIS). (1)
where Tp is a text template assigned to the probability p. To select a template, we find the WEP whose associated median probability (see table 2) is the closest to p. We then use handcrafted templates to construct a modal sentence from the selected WEP and the hypothesis, e.g., "It is certain that a man takes a picture". Table 3 in appendix B displays the templates that we associate with each WEP.
We also generate an invalid verbalization by randomly selecting an incorrect WEP (a WEP whose consensual probability differs from p by at least 40%)2, e.g., It is unlikely that a man takes a picture. We hypothesize that language models and entailment recognition models should give a higher score (respectively likelihood and entailment probability) to the correct valid verbalization than to the invalid verbalization of p.

heading: 3.2 WEP-UNLI: probability/WEP matching
text: The UNLI dataset annotates (PREMISE, HYPOTHESIS) pairs from the SNLI dataset (Bowman et al., 2015) with joint probability scores p, totaling 55k training examples, 3k/3k validation/test examples. We use these examples to generate WEPunderstanding dataset with verbalization validity prediction as shown in the previous subsection.
2This threshold ensures sufficient distance, while also ensuring that each WEP has at least one possible distractor.

heading: 3.3 WEP-Reasoning: WEP compositions
text: Here, our goal is to assess models’ ability to reason over combinations of probabilistic statements. We construct synthetic (PREMISE, HYPOTHESIS, p) examples from random factoids extracted from the bAbI dataset (Weston et al., 2015). Figure 1 illustrates the construction of WEP-reasoning examples:
We randomly sample initial facts and associated probability levels, and we verbalize them with the previously mentioned templates from Table 3 (Round 1). We further compose them with randomly sampled logical operators (and, or, xor). We then generate a hypothesis with logical combinations of the previous round. Finally, we feed the constructed premise and hypothesis to a probabilistic soft reasoning engine in order to derive the likelihood of the hypothesis given the premise. We rely on the ProbLog (De Raedt et al., 2007) reasoner which implements Dantsin (1992) semantics.
To evaluate different complexities of reasoning, we propose two variants: 2-hop reasoning, where facts in Round 2 combine facts from Round 1, and the final hypothesis combines facts from Round 2. and 1-hop reasoning where facts from the hypothesis combine Round 1 facts (Round 2 is skipped).
Since we want to sample more than two facts and we cannot a priori use text from the UNLI dataset,
because UNLI only provides entailment likelihood for specific pairs. Combining several sentences could cause unaccounted interference. Therefore, we sample subject/verb/object factoids from the bAbI (Weston et al., 2015) datasets instead, which is built with handwritten arbitrary factoids such as John went to the kitchen. To sample multiple factoids, we prevent any overlap of concepts (verb, subject, object) between any pair of facts to make the facts independent of one another.
We sample probability levels from the list of medians of all WEP to prevent sampling the levels that too distant from a known WEP. When we assign a WEP to a probability level, we assume that the correct semantics is the consensual one, but humans differs slightly from this consensus. Still, when adding random perturbations of 20% to sampled p1...6, the hypothesis probability is perturbed by less than 40% for 98% of examples.
We generate 5k examples using the template depicted in Figure 1, and use 10%/10% of the data for the validation/test splits. Appendix C shows the distribution of correct WEP for each dataset.

heading: 4 Experiments
text: We conduct verbalization validity prediction (binary classification task of WEP correctness detection between two candidates) under two settings.

heading: 4.1 Zero-shot models
text: We use off-the-shelf language models to assign likelihood scores to a context and its conclusion. We evaluate the rate at which valid verbalization is scored higher than invalid verbalization. We refine the scores by also considering the average likelihood per token (Brown et al., 2020; Schick and Schütze, 2021) and calibrated scores (Brown et al., 2020; Zhao et al., 2021) where we divide the score of a PREMISE. Tp(HYPOTHESIS). by the score of Tp(HYPOTHESIS). We evaluate the normalized, length-normalized, and calibrated likelihood on the validation sets of each dataset and select the most accurate method for each dataset and model.
We also consider a pretrained natural language inference model, which is trained to predict entailment scores between a context and a conclusion.
GPT2 We use the pretrained GPT2 base version with 127M parameters (Radford et al., 2019), which is a causal language model trained to estimate text likelihood. We concatenate the premise and hypothesis and compute their likelihood as a plausibility score.
RoBERTa We also use the pretrained RoBERTa base model with 123M parameters (Liu et al., 2019) to score the masked language modeling likelihood of the premise/hypothesis pair.
RoBERTa-MNLI We fine-tune RoBERTa on the MNLI entailment detection dataset (Williams et al., 2018) with standard hyperparameters (see the following subsection).
Human baseline To establish human baseline performance on the constructed dataset, we had two NLP researchers annotate 100 examples randomly sampled from the test set of each dataset, with a multiple-choice question answering setting.
Overall inter-annotator agreement is relatively high, with a Fleiss’s κ of 0.70/0.68/0.71 for WEP Reasoning 1 hop, 2 hops and WEP-UNLI respectively.

heading: 4.2 Fine-tuning and transfer across probes
text: We fine-tune RoBERTa-base models on our datasets, using standard (Mosbach et al., 2021) hyperparameters3 (3 epochs, sequence length of 256, learning rate of 2.10−5 batch size of 16. We use length-normalization with GPT2 likelihood and calibration with RoBERTa likelihood as they worked best on the validation sets.). We use a multiplechoice-question answering setup (we predict logit scores for the valid and invalid verbalization, combine their score with a softmax, then optimize the likelihood of the valid verbalization). The same format is applied to all tasks, so we can also study the transfer of capacities acquired during fine-tuning of each probe, for instance, between probability matching and compositional reasoning.

heading: 4.3 Results and discussion
text: Table 1 shows the results of our experiments. The very low accuracy of causal and masked language models (first two rows) demonstrates how challenging the WEP-understanding tasks are.
RoBERTa fine-tuned on MNLI dataset performs better than chance for WEP-UNLI. MNLI contains 814 instances of probably in the MNLI dataset, but we found little to no evidence of WEP compositions among them, which can explain the results.
Finally, fine-tuning on the dataset of a particular probe leads to high test accuracy on the associated test set. More surprisingly, fine-tuning on one dataset also causes substantial accuracy gain on other probes. This suggests that our datasets can
3Deviation from these hyperparameters did not yield significant improvement on the validation sets.
be incorporated in text encoder training in order to improve WEP handling.

heading: 5 Conclusion
text: We investigated WEP understanding in neural language models with new datasets and experiments, showing that WEP processing is challenging but helped by supervision which leads to transferable improvement. Future work could extract WEP probability scales from the UNLI dataset as an alternative to human perception surveys, but our work suggests that this requires language modeling progress.

heading: 6 Acknowledgements
text: This work is part of the CALCULUS project, which is funded by the ERC Advanced Grant H2020ERC-2017 ADG 7885064.

heading: B WEP verbalization template

heading: A Associated probabilities

heading: C WEP frequencies on the generated datasets

heading: Future Work
text: Future work could extract WEP probability scales from the UNLI dataset as an alternative to human perception surveys, but our work suggests that this requires language modeling progress