Domain Conditional Pointwise Mutual Information (PMI_DC) Scoring
Evaluation Methods AIMech:PMIDCDomainConditionalPointwiseMutualInformation DRAFT
Aliases: Domain Conditional Pointwise Mutual Information, PMI_DC, Domain Conditional PMI Scoring, Surface Form Competition PMI_DC Scoring
A zero-shot and few-shot multiple-choice scoring method for generative language models that compensates for surface form competition—the rationing of finite probability mass across distinct strings representing the same concept—by selecting the candidate hypothesis y_i that maximizes Domain Conditional Pointwise Mutual Information: arg max_i PMI_DC(x, y_i, domain) = arg max_i log [P(y_i | x) / P(y_i | x_domain)], where P(y_i | x_domain) is the a priori probability of hypothesis y_i within the task domain estimated by conditioning on a short task-specific domain premise string x_domain (typically the trailing cue of the prompt template x, such as 'because' or 'the answer is:').
Identity Notes & Concept Scope
Distinct from standard direct probability arg max_i P(y_i | x) and length-normalized average log-likelihood AVG = (1/l_i) sum_j log P(y_i^j | x, y_i^{<j}), which do not factor out surface-form rarity, and from Contextual Calibration (Zhao et al., ICML 2021, AIMech:CalibrateBeforeUseContextualCalibration), which fits an affine matrix over a fixed closed label set using multiple content-free inputs rather than computing the symmetric log-probability difference log P(y_i | x) - log P(y_i | x_domain) for arbitrary open-set per-question answer options.
Claims & Grounded Evidence
4 Claims
Mechanism
#r730-claim-surface-form-competition-and-symmetry
Because generative LMs allocate probability mass across all valid surface paraphrases of a concept (e.g., 'Bathtub' vs. 'Whirlpool bath', or 'it was 3 AM' vs. 'it was 3:30AM'), direct scoring P(y_i | x) penalizes rare surface forms; by Bayes' rule symmetry arg max_i [P(y_i | x, domain) / P(y_i | domain)] = arg max_i P(x | y_i, domain), PMI_DC simulates scoring-by-premise without requiring the question and options to be manually inverted.
Mechanism
#r730-claim-copa-flipped-eradication-proof
On 'COPA Flipped'—where cause and effect clauses are swapped with inverted connectives ('because' <-> 'so') so that the LM scores a single fixed premise continuation given each candidate option as context—surface form competition is completely removed, causing uncalibrated LM and AVG scoring to jump to the exact same accuracy as PMI_DC across all 8 GPT-2 and GPT-3 model scales.
Application
#r730-claim-zero-and-few-shot-benchmark-application
Across 16 splits of 13 open-set and closed-set multiple-choice benchmarks (COPA, StoryCloze, HellaSwag, RACE-M/H, ARC-E/C, OpenBookQA, CommonsenseQA, BoolQ, RTE, CB, SST-2, SST-5, AG's News, TREC) and 8 model sizes (GPT-2 125M-1.6B and GPT-3 2.7B-175B), PMI_DC wins or ties on 62.5% to 86.7% of datasets per model scale (outperforming LM, AVG, and Contextual Calibration by >40 percentage points in win rate).
Limitation
#r730-claim-internal-coherence-and-joint-option-limitation
PMI_DC underperforms AVG on HellaSwag (where adversarial machine-generated distractors test internal continuation coherence rather than premise-hypothesis mutual information) and underperforms direct LM scoring on ARC Easy (which favors a priori likely stock textbook phrases), and PMI_DC still scores each option y_i independently rather than jointly reasoning over the entire set of candidate options (e.g., failing on meta-options like 'all of the above').
⚠️ Curated Limitations & Negative Results
- Underperforms average log-likelihood (AVG) on benchmarks dominated by internal continuation fluency rather than premise conditioning (such as HellaSwag) and underperforms raw probability (LM) on retrieval-style questions with stock textbook answers (such as ARC Easy).
- Scores each multiple-choice candidate option independently rather than jointly comparing all options in context, and doubles inference queries on open-set datasets where P(y_i | x_domain) cannot be cached across questions.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:ArtificialNeuralNetwork
Artificial Neural Network
|
related_match | Domain Conditional PMI scores multiple-choice hypotheses generated by autoregressive neural language models by normalizing against domain-premise likelihoods. |
Evidence Sources & Primary Literature
3 Sources| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
r730-primary-pdf
|
Ari Holtzman, Peter West, Vered Shwartz, Yejin Choi, Luke Zettlemoyer
|
primary paper
full_text
|
ID: https://dblp.org/search/publ/api?q=Surface+Form+Competition+Why+the+Highest+Probability+Answer+Holtzman&format=xml
sha256:810c26ceec85…
|
r730-arxiv-abs
|
Ari Holtzman, Peter West, Vered Shwartz, Yejin Choi, Luke Zettlemoyer
|
primary paper
abstract_only
|
ID: https://arxiv.org/abs/2104.08315
sha256:158504202d26…
|
r730-metadata-cr
|
Ari Holtzman, Peter West, Vered Shwartz, Yejin Choi, Luke Zettlemoyer
|
primary paper
abstract_only
|
ID: https://dblp.org/search/publ/api?q=Surface+Form+Competition+Why+the+Highest+Probability+Answer+Holtzman&format=xml
sha256:c5e89a324d8f…
|
Ontology & Grounding Topology
Open in interactive network graph →Curation Provenance
Curator: Antigravity
Method: ai_assisted
Model: Gemini
Created: 2026-10-19T13:33:00Z
Updated: 2026-10-19T13:33:00Z
Source File:
data/curated/PMIDCDomainConditionalPointwiseMutualInformation.yaml
· Schema:
curated_concept.yaml
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