Source-linked AI summary
Surface Form Competition: Why the Highest Probability Answer Isn't Always Right
Ari Holtzman, Peter West, Vered Shwartz, Yejin Choi, Luke Zettlemoyer
TL;DR
String-probability ranking in zero-shot multiple choice is distorted when synonymous surface forms compete for finite probability mass, lowering the score of a listed correct answer. The paper introduces Domain Conditional Pointwise Mutual Information, which reweights options using task-domain likelihoods. PMIDC consistently outperforms raw, normalized, and calibrated scoring methods across GPT-2 and GPT-3 models and more than a dozen datasets.
Problem
Surface form competition can lower a listed correct answer’s probability because other valid strings representing the same concept also receive probability mass.
Method
PMIDC reweights each answer by dividing its question-conditioned probability by an estimate of its unconditional probability within the task domain.
Results
PMIDC consistently outperforms raw, normalized, and calibrated scoring methods across more than a dozen zero-shot multiple-choice datasets and every GPT-2 and GPT-3 model.
Takeaways & Limitations
Compensating for surface form competition improves zero-shot multiple-choice scoring across the evaluated models and datasets.
Takeaways & Limitations
PMIDC does not consistently outperform other methods on HellaSwag, ARC Easy, and BoolQ.
Abstract
from arXiv · showhide
Large language models have shown promising results in zero-shot settings (Brown et al.,2020; Radford et al., 2019). For example, they can perform multiple choice tasks simply by conditioning on a question and selecting the answer with the highest probability. However, ranking by string probability can be problematic due to surface form competition-wherein different surface forms compete for probability mass, even if they represent the same underlying concept, e.g. "computer" and "PC." Since probability mass is finite, this lowers the probability of the correct answer, due to competition from other strings that are valid answers (but not one of the multiple choice options). We introduce Domain Conditional Pointwise Mutual Information, an alternative scoring function that directly compensates for surface form competition by simply reweighing each option according to a term that is proportional to its a priori likelihood within the context of the specific zero-shot task. It achieves consistent gains in zero-shot performance over both calibrated (Zhao et al., 2021) and uncalibrated scoring functions on all GPT-2 and GPT-3 models over a variety of multiple choice datasets.
1 Introduction
Zero-shot multiple-choice scoring can undervalue correct options when synonymous surface forms compete for finite probability mass. The paper introduces PMIDC to compensate for task-specific competition and reports consistent gains across GPT-2 and GPT-3 models and many datasets.
- 1 Introduction: Surface form competition distributes probability across different strings expressing the same concept, including valid answers not listed among the options.This can reduce the probability assigned to the listed correct answer.
- 1 Introduction: PMIDC reweights answer scores by how much more likely each hypothesis becomes given the question within the specific task domain.It estimates an answer’s domain-specific unconditional likelihood using a domain premise and divides the conditional probability by that estimate.
- 1 Introduction: In CommonsenseQA, “Whirlpool bath” is correct, but easier-to-generate alternatives such as “Bathtub” compete for probability mass.The listed option is rarer despite representing the same underlying answer concept.
- 1 Introduction: PMIDC consistently outperforms raw, normalized, and calibrated scoring methods on zero-shot multiple choice across more than a dozen datasets and every GPT-2 and GPT-3 model.The improvement also holds across different prompts and preliminary few-shot experiments.
2 Background and Related Work
Prior work shows that generative models’ broad output distributions and prompt sensitivity complicate multiple-choice selection when synonymous answer strings receive unequal probabilities. Related approaches address option comparison, calibration, or probability bias, while PMIDC targets task-specific surface-form competition and remains subject to language-model biases.
- Surface Form Competition: Generative language models assign probability across all possible strings, so synonymous valid answers can receive substantially different probabilities in multiple-choice tasks.This differs from open-ended generation, where probability mass across multiple valid strings can still yield a correct response.
- Surface Form Competition: Earlier work emphasizes considering multiple-choice options jointly, whereas left-to-right language models implicitly compete over a much wider set of strings than the dataset contains.Pretraining on expansive corpora exacerbates this surface-form competition.
- Surface Form Competition: Replacing a common correct option such as “USA” with the rarer “U.S. of A.” can change probability-based multiple-choice selection.The underlying answer remains correct, but the surface form’s rarity affects its score.
- PMI and Contextual Calibration: PMIDC differs from contextual calibration by dividing by each answer’s domain-conditional probability, directly compensating for common token bias.Brown et al. (2020) used a related scoring function but estimated unconditional probability with the generic prompt “A:”.
- Interpreting Language Models: PMIDC aims to better measure agreement with human judgments but remains subject to the limits and biases of the language model being used.The paper also notes that language models may model selectional preferences and thematic fit rather than semantic plausibility.
3 Zero-shot Scoring Strategies
The paper reviews standard zero-shot scoring strategies and proposes Domain Conditional PMI to address surface form competition. It estimates answer likelihood within the task domain and compares this approach with probability-based, unconditional, and calibrated alternatives.
- Standard Methods: LM selects the highest-probability option, while AVG selects the option with the highest length-normalized log-likelihood.These are presented as common scoring strategies for generative language models.
- Motivation: Direct probability scoring can mis-rank multiple-choice answers because valid surface forms compete for finite probability mass.The paper argues that this competition can favor answers with fewer lexical paraphrases and reduce the score of a listed answer.
- Standard Methods: PMI scores how much more likely a hypothesis becomes given a premise, equivalently relating the premise and hypothesis through conditional probabilities.In multiple-choice settings, the premise is fixed across hypotheses, making premise-based scoring proportional to P(x|y).
- Domain Conditional PMI: Unconditional probability estimates vary widely because GPT-2 and GPT-3 are not trained to produce reliable unconditional estimates of document excerpts.Rare answers in large web scrapes make these estimates poorly calibrated for a given task.
- Domain Conditional PMI: Domain Conditional PMI estimates answer likelihood within a task domain using a short domain premise string and reweights conditional answer scores accordingly.For a causal relation, the method can use “because” to estimate how likely an answer is as a cause.
- Comparison Methods: UNC scores answers using only the domain premise, whereas Contextual Calibration applies an affine transform to LM using content-free inputs.UNC ignores the question premise completely; Contextual Calibration aims to make a closed answer set equally likely without evidence.
4 Multiple Choice Experiments
Experiments across multiple-choice datasets compare PMIDC with uncalibrated and calibrated scoring methods for GPT-2 and GPT-3, including prompt-robustness and few-shot evaluations. PMIDC consistently performs strongly across datasets, prompts, and models, although it is not always best.
- Main results: The smallest GPT-3 175B margin over the best competing method exceeds 40 percentage points in datasets won or tied for first place.This comparison uses the summarized percentage-of-wins-or-ties view; the result does not imply PMIDC is always better or better by a large margin.
- Prompt robustness: Across fifteen SST-2 prompts, PMIDC maintains the highest mean, often by a substantial margin, although scores are lower for prompts optimized for few-shot use.The prompt-robustness evaluation reports means and standard deviations over the templates considered by Zhao et al. (2021).
- Few-shot robustness: In four-shot SST-2 and CQA experiments, the overall trend favors PMIDC, though LM is superior for two models on SST-2.Results average over five randomly sampled sets of four priming examples and include both closed-set and open-set datasets.
5 Removing Surface Form Competition
The section tests scoring-by-premise by flipping COPA’s premise and hypothesis, removing competition among answer surface forms. Results support surface form competition as a primary explanation for LM and AVG’s lower performance than PMIDC, while manual flipping is not generally applicable.
- 5 Removing Surface Form Competition: Scoring-by-premise reverses the conditional direction, choosing the premise most probable given each hypothesis rather than the hypothesis most probable given the premise.The approach measures a shared surface form across options, reducing competition among continuations.
- 5 Removing Surface Form Competition: Causal language models cannot directly compute premise-given-hypothesis probabilities because they condition only on past tokens.The paper therefore exploits COPA’s cause-effect structure to construct COPA Flipped.
- 5 Removing Surface Form Competition: COPA Flipped reverses cause-effect pairs and swaps “because” with “so,” transforming which clause is the continuation being scored.Figure 3 illustrates the transformation and an additional distractor used for the in-depth example.
- 5.1 Results: On COPA Flipped, LM, AVG, and PMIDC obtain the same score because they compare different contexts with one fixed continuation.The caption reports that LM performs better on COPA Flipped than COPA because surface form competition is removed.
- 5.1 Results: When surface form competition is removed, all methods perform similarly to PMIDC on the unflipped version because only the likelihood of each answer making the question probable matters.A single scored continuation does not compete with other strings for probability mass.
- 5.1 Results: PMIDC is theoretically symmetric between COPA and COPA Flipped, but phrasing differences from imperfect inverses and shuffled references can produce different predictions.The authors attribute PMIDC’s better COPA performance to more natural phrasing in the original dataset.
- 5.2 In-depth Example: The in-depth example shows that scoring-by-premise selects the right answer and PMIDC successfully simulates scoring-by-premise.The example contrasts probabilities for alternative premises and hypotheses, including a lower-probability but correct answer.
- 5.2 In-depth Example: Different correct answers score nearly identically in COPA Flipped, unlike in COPA, where “it was 3 AM” and “it was 3:30AM” score very differently.This stability indicates that eliminating surface form competition lets multiple valid answers achieve high scores.
6 Analysis
The analysis identifies three datasets where PMIDC is not consistently best and examines why other scoring methods fit their task-specific properties. It also discusses possible explanations for AVG’s effectiveness through length bias and unconditional probability.
- Failure Cases: PMIDC does not consistently outperform other methods on HellaSwag, ARC Easy, and BoolQ.Each dataset is dominated by a different alternative method.
- Failure Cases: AVG is most suitable for HellaSwag, which emphasizes internal hypothesis coherence rather than premise-hypothesis matching.The dataset contains on-topic but intrinsically strange hypotheses generated by GPT-2 and filtered with BERT.
- Failure Cases: LM performs best on ARC Easy, whose questions can be solved through retrieval or word co-occurrence and contain many stock answers.These properties suggest a bias toward a priori likely phrases.
- Failure Cases: An unconditional baseline best solves BoolQ, where answers are only “yes” or “no” and most methods do not exceed the majority baseline.Only PMIDC with the largest GPT-3 model surpasses the majority baseline among the reported methods.
- Why does length normalization work?: Length normalization may compensate for probability assigned to irrelevant options at each time-step, producing a possible explanation for AVG’s success.The passage presents length bias as a proposed explanation rather than an established mechanism.
- Why does length normalization work?: AVG may also approximate unconditional probability because BPE-token length can roughly correlate with unigram log-probability.This explanation is not mutually exclusive with length bias, although AVG adjusts log terms differently from PMIDC.
7 Discussion
Generative models assign probabilities to strings, not directly to the concepts those strings express, creating surface form competition when multiple strings represent one idea. PMIDC better aligns scoring with selecting the hypothesis that explains the premise, but does not model interactions among answer options.
- Discussion: Generative-model string probability is not equivalent to selecting the underlying concept when multiple strings can express the same idea.The paper expects surface form competition wherever generative models represent concepts through multiple possible strings.
- Discussion: PMIDC reframes multiple-choice prediction as choosing the hypothesis that explains the premise rather than generating its exact surface form.This aligns the scoring objective more closely with the task posed by multiple-choice questions.
- Discussion: PMIDC still cannot consider the given answer options jointly, which matters when answers interact, such as with “all of the above.”The paper identifies this as a remaining limitation of the scoring approach.
8 Conclusion
The paper compares scoring functions for zero-shot inference across GPT-2 and GPT-3 models and multiple-choice datasets. It finds that PMIDC consistently outperforms prior methods, while suggesting future work on surface form competition in generation.
- PMIDC consistently outperforms previous scoring functions across GPT-2 and GPT-3 models on a wide variety of multiple-choice datasets.
- Eliminating surface form competition makes other scoring methods perform as well as PMIDC, supporting the proposed explanation for its performance gains.
- Future work will examine whether surface form competition contributes to overly generic outputs when model uncertainty is high.
A GPT-2 Results
The paper presents GPT-2 results for zero-shot multiple-choice inference.
- Table 6 reports zero-shot multiple-choice results using GPT-2.
B Templates
This section presents GPT-2 scoring results and describes the templates used across tasks. The templates distinguish premises, hypotheses, and domain premises, with long premises abbreviated.
- Table 7 gives an example of each template used for each dataset.
- Table 6 compares scoring algorithms for GPT-2 zero-shot inference on multiple-choice questions.
- The templates show original premises in blue and original answers in red, while long premises are abbreviated with “[...]”.
- Full premises, conditional hypotheses, and domain premises are marked as [·]P, [·]UH, and [·]DP, respectively.