QFrCoRE: Quebec-French Benchmark & Quantile Entropy

• QFrCoRE is an acronym representing two distinct constructs: a Quebec-French idiom benchmark for NLP dialect assessment and a quantile-based formulation of fractional cumulative residual entropy.
• The Quebec-French corpus evaluates idiom interpretation via multiple-choice tasks using curated expressions and AI-generated distractors to probe cultural lexical knowledge.
• The quantile-based model redefines residual entropy for nonnegative variables, offering enhanced sensitivity to tail risks in financial and reliability analyses.

QFrCoRE designates two distinct technical constructs in recent arXiv literature: a Quebec-French dialect benchmark for idiom interpretation in natural language processing, and a quantile-based formulation of fractional cumulative residual entropy in reliability theory and financial data analysis. In the first sense, QFrCoRE expands to “Quebec-French Corpus of Regional Expressions” and operationalizes dialect understanding as multiple-choice interpretation of idiomatic expressions. In the second, QFrCoRE denotes quantile-based fractional cumulative residual entropy, a functional defined through the quantile function and its density, together with a dynamic residual-life version. The shared acronym does not imply methodological continuity; it marks two unrelated lines of work with different objects, evaluation regimes, and mathematical apparatus (Beauchemin et al., 6 Oct 2025, Sebastian et al., 1 Feb 2025).

1. Dual usage and conceptual scope

In NLP, QFrCoRE is a benchmark centered on Quebec French idiomatic expressions. Its stated purpose is to evaluate dialect understanding via idiom interpretation, on the premise that regional idioms probe dialect proficiency better than grammar or syntax because idioms derive from local culture and history and are not easily inferred from the prestige variety. The benchmark is paired with QFrCoRT, which targets idiomatic words rather than multi-word expressions (Beauchemin et al., 6 Oct 2025).

In information theory and reliability analysis, QFrCoRE is the shorthand used for quantile-based fractional cumulative residual entropy. This formulation recasts fractional cumulative residual entropy in the quantile framework, making it usable when the distribution function is unavailable in explicit form but the quantile function is available in closed form. The same paper also introduces a dynamic version and studies its properties, estimation, and applications to financial returns (Sebastian et al., 1 Feb 2025).

This dual usage suggests that QFrCoRE should be treated as an acronym with domain-dependent meaning rather than as a single research program.

2. Quebec-French Corpus of Regional Expressions

QFrCoRE, in the dialect-benchmark sense, is a benchmark for dialect understanding via idiom interpretation in Quebec French. The task is multiple-choice idiom interpretation: given a Quebec expression and 10 candidate definitions, a model must select the correct definition by index, with zero-based indexing. This task format is intended to isolate lexical–cultural knowledge instead of syntactic prowess (Beauchemin et al., 6 Oct 2025).

The released corpus contains 4,633 idiomatic expressions. Reported corpus statistics are an average instance word count of 5.01, an average answers word count of 9.69, a vocabulary size of 25,181, and an average lexical richness of 0.65. Lexical richness is computed as the ratio of unique words in an instance over the corpus vocabulary cardinality, without stop-word removal or normalization. The benchmark is not annotated for parts of speech, semantic classes, domains, register or formality, or usage constraints, and it does not include per-expression regional sub-tags or registers in the released version (Beauchemin et al., 6 Oct 2025).

The instance schema used for evaluation comprises four fields: expression, definitions, correct_index, and source. The benchmark is intended for evaluation rather than supervised training, and no train/dev/test splits are defined. It is released through the Hugging Face dataset graalul/QFrCoRE_QFrCoRT (Beauchemin et al., 6 Oct 2025).

QFrCoRE is complemented by QFrCoRT, which contains 171 regional instances of idiomatic words. Although QFrCoRE contains longer phrases and a much larger vocabulary, the reported model behavior on QFrCoRE and QFrCoRT is similar, which the authors interpret as evidence that the main difficulty lies in regional lexical knowledge rather than in surface length or syntactic complexity (Beauchemin et al., 6 Oct 2025).

3. Corpus construction, distractor design, and benchmark findings

The expressions in QFrCoRE were manually extracted primarily from DesRuisseaux’s Dictionnaire des expressions québécoises (2009), augmented with DesRuisseaux’s Dictionnaire des proverbes, dictons et adages québécois (2008) and the Canada-Media portal. Anglicisms and duplicates were manually removed. Beyond that, no normalization is applied for lexical richness computation (Beauchemin et al., 6 Oct 2025).

A central design feature is distractor generation. For each idiom, nine distractors are generated by GPT-4o-mini from a prompt designed to be semantically plausible but incorrect. Distinctness from the true definition is enforced by a weighted similarity gate,

$$S = 0.353 \cdot \mathrm{BLEU} + 0.176 \cdot \mathrm{ROUGE} + 0.47 \cdot \mathrm{BERTScore},$$

with regeneration triggered when $S > 0.45$. The fallback model is GPT-4.1, and the temperature increases by $0.1$ per regeneration round up to a maximum of $1.6$. The correct definition is randomly placed among the 10 options to avoid positional bias (Beauchemin et al., 6 Oct 2025).

The evaluation protocol is zero-shot. A fixed prompt template instructs models to return only the zero-based index of the correct definition. Across 94 LLMs, the reported random baselines are 12.28% accuracy for QFrCoRE and 9.93% for QFrCoRT. The experimental summary reports that 25 proprietary models exceeded 65% accuracy on both benchmarks, 40 models performed below the random baseline on at least one benchmark, and 29 models occupied an intermediate region. The result table includes top QFrCoRE accuracies up to 97.66%, while QFrCoRT peaks at approximately 93–95% for top proprietary systems. The average score difference per model between QFrCoRE and QFrCoRT is 3.4%, and the score correlation between the two benchmarks is described as near-linear (Beauchemin et al., 6 Oct 2025).

The same study reports that French-tuned models did not dominate the benchmark; none appeared among the top-performing group, and some were below baseline on both benchmarks. The authors attribute this to fine-tuning on prestige French rather than Quebec French. They also report that access paradigm is the strongest separator: the worst proprietary model remained 9.1% above the best open-source model on QFrCoRT and 14.6% above it on QFrCoRE (Beauchemin et al., 6 Oct 2025).

4. Interpretive scope, replicability, and limitations of the benchmark

QFrCoRE is designed to test definitional mapping rather than pragmatic appropriateness. The study explicitly notes that the benchmark evaluates definitional understanding, not social register or appropriateness, such as sacres usage. This matters because a correct choice among definitions does not imply competence in production, sociolinguistic placement, or contextual acceptability (Beauchemin et al., 6 Oct 2025).

The benchmark is also presented as a replicable methodology for other dialects. The reported recipe is: curate idioms from authoritative dictionaries and credible online sources, manually extract idioms and canonical definitions, remove duplicates and non-dialectal borrowings, generate nine plausible distractors with an LLM, enforce distinctness via the BLEU–ROUGE–BERTScore gate, randomize answer order, and publish sources and prompts. This suggests that QFrCoRE is as much a benchmark-construction protocol as a static dataset (Beauchemin et al., 6 Oct 2025).

Several limitations are stated. AI-generated distractors may carry detectable artifacts; coverage is partial even at 4,633 expressions; evaluation is zero-shot only; online sources may have appeared in model pretraining corpora, creating contamination risk; very large open-source models above 70B were excluded for hardware reasons; and ethical concerns include dual-use risks, representational harms, and provenance or licensing issues for reused lexicographic content. These limitations constrain strong claims about “understanding” and indicate that QFrCoRE is best viewed as a targeted probe of dialectal lexical–cultural knowledge rather than a complete dialect-competence benchmark (Beauchemin et al., 6 Oct 2025).

5. Quantile-based fractional cumulative residual entropy

In a different literature, QFrCoRE denotes quantile-based fractional cumulative residual entropy. This quantity generalizes cumulative residual entropy and fractional cumulative residual entropy into the quantile framework. For a nonnegative absolutely continuous random variable $X$ with quantile function $Q(u)=F^{-1}(u)$ and quantile density $q(u)=dQ(u)/du$, the quantile-based FCRE is defined by

$$\mathcal{E}_{\alpha}^{Q}(X) = \int_{0}^{1}(1-p)\bigl(-\log(1-p)\bigr)^{\alpha}\,dQ(p) = \int_{0}^{1}(1-p)\bigl(-\log(1-p)\bigr)^{\alpha} q(p)\,dp, \quad 0 \le \alpha \le 1.$$

Using the hazard quantile function

$H(u)=\frac{1}{(1-u)q(u)},$

the same functional can be written as

$$\mathcal{E}_{\alpha}^{Q}(X) = \int_{0}^{1}\frac{1}{H(p)}\bigl(-\log(1-p)\bigr)^{\alpha}\,dp.$$

The corresponding dynamic version is

$S > 0.45$0

Finite QFrCoRE requires the associated integrability conditions in the quantile domain (Sebastian et al., 1 Feb 2025).

This formulation recovers classical quantities at the endpoints of $S > 0.45$1. Specifically,

$S > 0.45$2

so the family interpolates between the mean and quantile-based cumulative residual entropy. The paper further states that $S > 0.45$3 is nonnegative, nonadditive, and convex in $S > 0.45$4 (Sebastian et al., 1 Feb 2025).

6. Properties, estimation, and applications of quantile QFrCoRE

The quantile formulation inherits several transformation properties. If $S > 0.45$5 with $S > 0.45$6, then $S > 0.45$7, while for $S > 0.45$8 with $S > 0.45$9,

$0.1$0

The paper also gives additivity under quantile addition, product-form identities, reciprocal-transformation formulas, and a general monotone-transformation rule for $0.1$1 with positive increasing $0.1$2 (Sebastian et al., 1 Feb 2025).

Several inequalities and order relations are developed. One reported upper bound is

$0.1$3

with equality at $0.1$4. The paper also defines an order $0.1$5 through comparison of $0.1$6 values, and states that hazard-quantile order implies QFrCoRE order (Sebastian et al., 1 Feb 2025).

For estimation, the paper adopts a plug-in estimator based on empirical quantiles and order statistics. With order statistics $0.1$7, the reported summation form is

$0.1$8

Simulation tables in the paper report decreasing bias and mean squared error with increasing $0.1$9 (Sebastian et al., 1 Feb 2025).

Closed forms are given for standard models. For the exponential distribution,

$1.6$0

and for $1.6$1,

$1.6$2

The paper also reports formulas for Weibull-type, Pareto I, and rescaled Beta constructions, and gives the lognormal case as a quantile-domain integral without a closed form (Sebastian et al., 1 Feb 2025).

The main application is to DJIA daily closing prices from 2014-01-01 to 2019-12-31, transformed into shifted nonnegative log returns. The reported finding is that smaller $1.6$3 values, especially below $1.6$4, are more sensitive to instability, whereas the $1.6$5 limit is less sensitive. Among the examined years, 2018 exhibits the highest complexity or instability, with $1.6$6 for $1.6$7. The paper interprets this as evidence that QFrCoRE can act as a tail-aware, quantile-weighted uncertainty score complementing conventional financial risk summaries (Sebastian et al., 1 Feb 2025).

Taken together, the two uses of QFrCoRE illustrate a rare acronymic overlap between a dialect benchmark and an entropy functional. In NLP, it is a structured probe of Quebec-French lexical–cultural knowledge through multiple-choice idiom interpretation. In reliability and financial analysis, it is a quantile-domain entropy family with explicit transformation rules, estimation procedures, and sensitivity to tail behavior.