Dilaprix: Dialogue Language Proficiency Index

• Dilaprix is a dialogue language proficiency index that quantifies utterance difficulty for L2 learners using readability, syntactic, and lexical features.
• It integrates metrics from standardized formulas and constituency parsing to provide an interpretable, normalized difficulty score for dialogue responses.
• Empirical validation shows a high Pearson correlation (0.950) with expert judgments, outperforming traditional CEFR-based methods in dialogue quality control.

Searching arXiv for the cited papers to ground the article in the current record. Dilaprix, short for the Dialogue Language Proficiency Index, is a metric introduced to quantify how difficult a dialogue utterance is from an L2-learning perspective and to support controllable language generation in educational dialogue systems. It was proposed in the context of LLMs used for speaking practice, where matching generated responses to learner proficiency remains difficult. In the cited formulation, Dilaprix is not a generic readability score for arbitrary text; it is a dialogue-oriented index built from readability, syntactic, and lexical features, with the explicit goals of interpretable measurement and controllable generation of textbook dialogues (Xu et al., 18 Sep 2025).

1. Origin and problem setting

Dilaprix was introduced because existing language-difficulty evaluation methods are usually built for passages, essays, or reading materials with pre-assigned proficiency labels, and those resources do not transfer cleanly to conversational dialogue (Xu et al., 18 Sep 2025). The central problem is that interactive dialogue requires utterance-level difficulty estimation under conversational constraints, rather than document-level assessment under exogenous labels.

The associated framework addresses two coupled tasks. The first is measurement: assigning an interpretable scalar difficulty score to a dialogue response without relying on pre-labeled proficiency corpora. The second is control: conditioning LLM-generated responses so that textbook dialogues can be matched to learners’ proficiency levels. The paper reports that training LLMs on linguistically annotated dialogue data enables precise modulation of language proficiency and outperforms prompt-based methods in both flexibility and stability (Xu et al., 18 Sep 2025).

A plausible implication is that Dilaprix occupies an intermediate position between classical readability estimation and generation-time controllability: it is simultaneously an evaluation metric and a control target. That dual role is a defining feature of the proposal.

2. Linguistic feature basis

Dilaprix is constructed from 11 linguistic features grouped into readability, syntactic, and lexical categories (Xu et al., 18 Sep 2025).

Category	Features	Brief note
Readability	$F_R, F_G, G_F, C_L$	Standard formulas
Syntactic	$T_D, L_N, N_D, S_C, U_L$	Constituency-parse and length measures
Lexical	$S_W, I_W$	Ratios from curated word lists

The readability group contains Flesch Reading Ease $(F_R)$, Flesch-Kincaid Grade Level $(F_G)$, Gunning Fog Index $(G_F)$, and Coleman-Liau Index $(C_L)$. The paper explicitly notes that Flesch-Kincaid Grade Level estimates the US grade level needed to understand a text; Gunning Fog is based on average sentence length and the proportion of complex words; and Coleman-Liau relies on character counts per word and sentence length rather than syllables (Xu et al., 18 Sep 2025).

The syntactic group consists of Tree Depth $(T_D)$, Leaf Node Count $(L_N)$, Non-terminal Diversity $(N_D)$, Subtree Complexity $T_D, L_N, N_D, S_C, U_L$0, and Utterance Length $T_D, L_N, N_D, S_C, U_L$1. Tree Depth is described as the maximum syntactic-tree depth across the sentences in an utterance, and the other syntactic measures are similarly computed from constituency parses at the utterance level (Xu et al., 18 Sep 2025).

The lexical group contains Simple Word Ratio $T_D, L_N, N_D, S_C, U_L$2 and Intermediate Word Ratio $T_D, L_N, N_D, S_C, U_L$3, based on expert-curated word lists: roughly 2,000 simple words and an expanded 6,000-word intermediate inventory. The paper highlights simple word ratio as a key example of lexical difficulty. This feature design suggests that the metric is intentionally interpretable at the level of recognizable linguistic constructs rather than latent embeddings or black-box regressors.

3. Formal definition and computation

Dilaprix is defined as a normalized average over the full feature set:

$T_D, L_N, N_D, S_C, U_L$4

with

$T_D, L_N, N_D, S_C, U_L$5

Here

$T_D, L_N, N_D, S_C, U_L$6

and

$T_D, L_N, N_D, S_C, U_L$7

are the features inversely related to difficulty (Xu et al., 18 Sep 2025).

The parameters $T_D, L_N, N_D, S_C, U_L$8 and $T_D, L_N, N_D, S_C, U_L$9 are the 5th and 95th percentiles, respectively, computed from the textbook dialogue corpus. The clamp function forces values into $S_W, I_W$0. Operationally, each feature is extracted from a dialogue response, normalized by percentile-based scaling, inverted when lower values correspond to greater difficulty, and then averaged. For syntactic features, the procedure uses a constituency parser; for lexical features, it checks the proportion of words appearing in the curated word lists (Xu et al., 18 Sep 2025).

This normalization scheme has two notable properties. First, it is robust in the sense that it uses corpus percentiles rather than unbounded raw scales. Second, it is feature-direction aware, since readability and simple-word prevalence are treated as inversely related to difficulty. The resulting scalar is therefore interpretable as an aggregate over heterogeneous but explicitly specified linguistic dimensions.

4. Empirical validation against expert judgment

To validate Dilaprix against expert judgment, the authors created a human-evaluation set of 100 utterances and performed pairwise comparisons, yielding 4,950 utterance pairs. Three experts independently judged which utterance in each pair was harder. Each utterance was assigned a score based on its winning rate, defined as the fraction of comparisons in which it was judged more difficult, and the final gold score was the average across the three experts (Xu et al., 18 Sep 2025).

On this benchmark, Dilaprix showed a Pearson correlation coefficient of 0.950 with the ground-truth difficulty scores. The paper reports this as stronger than the average expert-to-expert PCC of 0.935. It also reports that a CEFR-based sentence difficulty annotator, CEFR-SP, achieved a lower PCC of 0.839 on the same 100-utterance set (Xu et al., 18 Sep 2025).

These results are significant in two distinct senses. Empirically, they indicate that the metric tracks expert pairwise preferences very closely. Methodologically, they support the claim that dialogue difficulty can be estimated without pre-labeled proficiency corpora if the estimation is grounded in interpretable linguistic features. A plausible implication is that Dilaprix functions not merely as a proxy for readability but as a dialogue-specific difficulty estimator with human-aligned behavior.

5. Role in controllable dialogue generation

Dilaprix is used as the central metric for assessing controllability of LLM-generated dialogue difficulty. During inference, the model is prompted with target linguistic-feature values, and the paper often sets all features to share a common control parameter $S_W, I_W$1 by choosing values $S_W, I_W$2 such that $S_W, I_W$3. This allows generation at different target difficulty levels and evaluation of how closely outputs match those levels (Xu et al., 18 Sep 2025).

In the reported experiments, feature-controlled models such as QWEN-DPO span a wide Dilaprix range, from 0.073 to 0.883, whereas CEFR-based instruction tuning covers a narrower range, from about 0.211 to 0.685. The feature-controlled models also show lower variability, with QWEN-DPO reporting Dilaprix standard deviation 0.084 versus 0.155 for QWEN-CEFR, indicating more stable control. To summarize the quality-control tradeoff across difficulty levels, the paper introduces an AUC measure over the curve of response success rate versus Dilaprix. The best overall model, QWEN-DPO, achieves AUC 0.786, difficulty range 0.810, and STD 0.084 (Xu et al., 18 Sep 2025).

The paper also shows that response success rate generally rises with Dilaprix and uses fitted curves to analyze this relationship. This suggests a nontrivial coupling between linguistic difficulty and task completion in textbook dialogue generation: harder responses may also be more successful in satisfying dialogue requirements, although the paper does not frame this as a universal law.

A further property of the framework is category-level control. It can independently manipulate lexical/readability versus syntactic difficulty by choosing different $S_W, I_W$4 values for feature groups, enabling fine-grained control such as “simple vocabulary but complex syntax,” or the reverse (Xu et al., 18 Sep 2025). This is important because it shows that Dilaprix is not restricted to one-dimensional monotone simplification; it can serve as part of a more granular control interface.

6. Ablations, limitations, and scope of the term

Ablation analysis further supports Dilaprix’s role as a controllability measure. Removing most linguistic features hurts performance, and removing Simple Word Ratio causes the largest drop among the single-feature ablations, while removing Utterance Length can improve dialogue quality metrics, suggesting that length constraints can conflict with the task-completion requirement of textbook dialogue (Xu et al., 18 Sep 2025). This result indicates that lexical simplicity is especially consequential for the framework, whereas raw length is a more ambiguous control variable.

The paper notes several limitations. The approach requires substantial training data with linguistic-feature annotations, which may not always be easy to obtain. Dilaprix is also said to be not directly transferable to other text types such as essays or reading passages without adaptation; for example, the paper suggests that a feature like Tree Depth, computed as a maximum across dialogue sentences, might be better averaged in non-dialogue settings. In addition, the AUC metric used alongside Dilaprix gives equal weight to difficulty control and dialogue quality, which the authors caution may not always reflect real-world priorities, since naturalness and task completion can matter more than perfectly matching a target difficulty score. Finally, while using the same $S_W, I_W$5 for all features works well, the framework is intentionally more flexible and can assign different values to different feature categories when finer control is desired (Xu et al., 18 Sep 2025).

There is also a useful boundary on the term’s interpretation. A separate paper on mathematical modelling of drug release from multi-layer capsules does not mention Dilaprix by name, although it provides a mechanistic diffusion framework that would be relevant if one were interpreting Dilaprix as a multilayer or coated capsule rather than as a dialogue-difficulty metric (Kaoui et al., 2017). This suggests that, in the current arXiv record represented here, “Dilaprix” is specifically the dialogue-oriented proficiency index, not an identified pharmaceutical formulation.

Taken together, these points position Dilaprix as a specialized, interpretable, corpus-normalized metric for dialogue difficulty estimation and control. Its contribution lies not only in its reported human alignment but also in its integration into generation-time control, where linguistic features become explicit steering variables rather than post hoc diagnostics.