DSV-CF: Semantic Visibility & Fidelity

• DSV-CF is Dual-Axis Semantic Visibility and Content Fidelity, a framework that quantifies both the presence and faithful attribution of source documents in generative responses.
• The metric combines two aggregates—Surface Semantic Visibility and Intrinsic Semantic Impact—with explicit penalties for attribution errors to balance exposure and factual grounding.
• Empirical evaluations across multiple engines show that DSV-CF aligns with human assessments, optimizing both visible citation and semantic integrity in generative outputs.

DSV-CF denotes Dual-Axis Semantic Visibility and Content Fidelity, a GEO evaluation framework introduced in the context of multi-agent Generative Engine Optimization (GEO) to measure two properties jointly: the extent to which a target source document becomes visible and influential in a generative engine’s answer, and the extent to which that influence is faithfully attributed and semantically grounded rather than hallucinated or spuriously cited (Wu et al., 21 Apr 2026). The framework is defined as a dual-axis score combining a visibility aggregate, an impact-and-fidelity aggregate, and an explicit penalty for attribution errors. Within the same work, DSV-CF functions both as an evaluation metric and as the optimization target used to select document edits under a controlled intervention protocol (Wu et al., 21 Apr 2026).

1. Definition and formal score

The paper defines DSV-CF through the statement that it proposes the “Dual-Axis Semantic Visibility and Content Fidelity (DSV-CF) framework” (Wu et al., 21 Apr 2026). Its top-level score is

$$S_{DSV-CF} = \lambda \cdot \bar{S}_{SSV} + (1-\lambda) \cdot \bar{S}_{ISI} - \gamma (1 - AA),$$

where $\bar{S}_{SSV}$ is the normalized aggregate for Surface Semantic Visibility, $\bar{S}_{ISI}$ is the normalized aggregate for Intrinsic Semantic Impact, $AA$ is Attribution Accuracy, $\lambda$ balances visibility and quality, and $\gamma$ penalizes citation errors (Wu et al., 21 Apr 2026).

The default parameter values reported are $\lambda=0.5$ and $\gamma=0.5$. The paper states that $\lambda=0.5$ imposes a symmetric prior between visibility gain and fidelity preservation, and that $\gamma=0.5$ gave the best overall DSV-CF on the test set (Wu et al., 21 Apr 2026).

This formulation makes DSV-CF structurally different from visibility-only or fidelity-only GEO metrics. A visibility increase is not sufficient on its own; it must survive the attribution penalty. Conversely, a faithful source that remains semantically negligible in the generated answer will not obtain a strong overall score. A plausible implication is that DSV-CF was designed as a compromise objective for settings where optimization pressure can otherwise induce unsupported claims or citation hallucination.

2. Motivation: the GEO evaluation gap

The stated motivation is that existing GEO evaluation schemes do not jointly capture semantic visibility and faithful attribution. The paper argues that in generative engines, a document’s contribution is not reducible to classical rank-based exposure because a source may matter by being explicitly cited, by contributing answer content, by occupying prominent structural positions, or by shaping the answer semantically, and these effects may or may not be properly attributed (Wu et al., 21 Apr 2026).

The authors explicitly criticize prior evaluation by noting that “many metrics treat surface visibility and semantic influence separately without jointly enforcing faithful attribution, allowing exposure gains to coincide with miscitation or hallucination” (Wu et al., 21 Apr 2026). This is the central problem DSV-CF addresses. In the framework’s terms, GEO success is two-dimensional: a target document should become more visible in the answer, but that visibility must correspond to genuine semantic contribution and accurate attribution.

The paper therefore presents DSV-CF as a fidelity-aware alternative to metrics that reward only surface exposure. This suggests a broader methodological position: GEO should be evaluated at the level of answer formation, not only at the level of document retrieval or citation count, because generative engines collapse retrieval, synthesis, and attribution into a single output object.

3. The two axes and their submetrics

DSV-CF is decomposed into two aggregates, each consisting of four submetrics (Wu et al., 21 Apr 2026).

Axis	Submetrics	Intended role
Surface Semantic Visibility (SSV)	WLV, DPA, CP, SI	Visible and perceptual source presence
Intrinsic Semantic Impact (ISI)	AA, $\bar{S}_{SSV}$0, KC, AD	Truthful semantic influence

The first axis, Surface Semantic Visibility (SSV), is defined as measuring “the extent to which the target document physically occupies the generated response” (Wu et al., 21 Apr 2026). Its four submetrics are:

• Word-Level Visibility (WLV): how much response text is attributed to the target source, with normalization when multiple sources are cited in the same sentence.
• Decayed Positional Authority (DPA): a visibility measure discounted by sentence position, rewarding earlier citations more strongly.
• Citation Prominence (CP): an LLM-judged estimate of whether the citation occurs in visually prominent areas such as headers, bullet points, or bold text.
• Subjective Impression (SI): an LLM-based estimate of how important the target source appears to a human reader.

The second axis, Intrinsic Semantic Impact (ISI), is defined as measuring “the depth of influence and truthfulness” (Wu et al., 21 Apr 2026). Its four submetrics are:

• Attribution Accuracy (AA): whether claims attributed to the target document are actually entailed by that source.
• Response-level Faithfulness ($\bar{S}_{SSV}$1): whether the optimized document or response remains semantically faithful and does not introduce unsupported content during editing.
• Key-Point Coverage (KC): how many important information points from the target document are transferred into the answer.
• Answer Dominance (AD): especially for recommendation or comparative queries, whether the target source is presented as the primary solution.

The division between SSV and ISI is conceptually important. SSV concerns presence, prominence, and salience in the rendered answer. ISI concerns semantic control, truthfulness, and source-groundedness. The penalty term $\bar{S}_{SSV}$2 then explicitly suppresses cases where visibility gains arise through incorrect attribution rather than legitimate semantic uptake.

4. Mathematical specification and computable components

The paper provides explicit formulas for two submetrics, WLV and DPA (Wu et al., 21 Apr 2026). Let the generated response be $\bar{S}_{SSV}$3, let $\bar{S}_{SSV}$4 if sentence $\bar{S}_{SSV}$5 cites the target document and $\bar{S}_{SSV}$6 otherwise, let $\bar{S}_{SSV}$7 be the number of sources cited in $\bar{S}_{SSV}$8, and let $\bar{S}_{SSV}$9 denote sentence length. Then

$\bar{S}_{ISI}$0

This definition assigns credit only to target-citing sentences, divides credit among co-cited sources, and increases with attributed textual mass (Wu et al., 21 Apr 2026).

For DPA, the paper gives

$\bar{S}_{ISI}$1

The source text is reported as slightly malformed, but the intended structure is clear: DPA is WLV with an exponential position decay so that earlier sentences receive higher weight (Wu et al., 21 Apr 2026). The exact final denominator syntax is therefore not fully recoverable from the provided text, but the weighting principle is explicit.

The remaining six submetrics are specified procedurally rather than by full formulas. CP and SI are LLM-judged visibility-related measures. AA is computed by extracting claims attributed to the target document and checking whether they are entailed by the original source. $\bar{S}_{ISI}$2 checks whether optimization introduced unsupported content. KC extracts key points from the target document and measures their recall in the answer. AD determines whether the target source is framed as the primary solution in comparative or recommendation settings (Wu et al., 21 Apr 2026).

The paper also states that $\bar{S}_{ISI}$3 and $\bar{S}_{ISI}$4 are normalized aggregates, but it does not specify the exact normalization formula, the internal weights among the four submetrics within each axis, or whether fixed-range, min-max, or some other normalization is used (Wu et al., 21 Apr 2026). This omission is consequential for exact reproducibility: the framework is formally clear at the top level, but its full implementation details are only partially specified in the text provided.

5. Role in optimization and the Twin Branch protocol

DSV-CF is not only a reporting metric. The paper defines the optimization objective as

$\bar{S}_{ISI}$5

where $\bar{S}_{ISI}$6 is the query, $\bar{S}_{ISI}$7 is the fixed retrieval list, $\bar{S}_{ISI}$8 is the target document, $\bar{S}_{ISI}$9 ranges over candidate edits, and $AA$0 denotes replacing the original target document with the edited candidate (Wu et al., 21 Apr 2026). In other words, DSV-CF is the score by which the best edit is selected.

This optimization is embedded in the Twin Branch Evaluation Protocol, whose purpose is to isolate the causal effect of document edits from retrieval variance. The protocol compares a baseline branch, using the original retrieval list and original document, against an optimization branch, using the same retrieval list except that the target document is replaced by an edited variant (Wu et al., 21 Apr 2026). Because the retrieval context is frozen, changes in DSV-CF can be attributed more plausibly to the edit itself rather than to exogenous retrieval changes, rank drift, or engine-side instability.

Within this setup, DSV-CF serves as the response-side causal outcome measure. Twin Branch controls the intervention; DSV-CF measures the intervention’s effect along visibility and fidelity dimensions. The paper presents this as central to reusable GEO strategy learning, because only gains that remain valid under controlled attribution should be retained as reusable optimization skills (Wu et al., 21 Apr 2026).

6. Empirical behavior, validation, and sensitivity

The paper reports that DSV-CF is used across experiments on three target engines—GPT-5.2, Gemini-3 Pro, and Qwen-3 Max—and two benchmarks, MSME-GEO-Bench and GEO-Bench (Wu et al., 21 Apr 2026). It does not provide a single scalar $AA$1 column for every method in every table, but it reports the constituent submetrics and states that MAGEO substantially outperforms heuristic baselines under DSV-CF evaluation (Wu et al., 21 Apr 2026).

On MSME-GEO-Bench with GPT-5.2, MAGEO achieves WLV $AA$2, DPA $AA$3, CP $AA$4, SI $AA$5, AA $AA$6, FA $AA$7, KC $AA$8, and AD $AA$9 (Wu et al., 21 Apr 2026). On Gemini-3 Pro, the reported values are WLV $\lambda$0, DPA $\lambda$1, CP $\lambda$2, SI $\lambda$3, AA $\lambda$4, FA $\lambda$5, KC $\lambda$6, and AD $\lambda$7 (Wu et al., 21 Apr 2026). On Qwen-3 Max, MAGEO improves from no-GEO WLV/DPA $\lambda$8 to $\lambda$9 while maintaining CP $\gamma$0, SI $\gamma$1, AA $\gamma$2, FA $\gamma$3, KC $\gamma$4, and AD $\gamma$5 (Wu et al., 21 Apr 2026).

Human validation is particularly important because six of the eight submetrics are LLM-judged. On 100 sampled instances, the paper reports Spearman $\gamma$6 for DSV-CF, compared with $\gamma$7 for WLV and $\gamma$8 for CF, with highly significant $\gamma$9-values; it also reports 81.5% agreement between the LLM judge and human experts in pairwise comparison over 50 response pairs (Wu et al., 21 Apr 2026). These numbers are used as evidence that DSV-CF aligns reasonably well with human assessment, though the paper also treats LLM judging as an approximation rather than a substitute for human audit in high-risk settings.

The appendix further reports a $\lambda=0.5$0-sensitivity analysis:

$\lambda=0.5$1	DSV-CF	WLV	CF
0.25	4.41	4.09	0.031
0.50	4.52	4.52	0.043
1.00	4.43	4.62	0.048
2.00	4.37	4.71	0.058

The paper concludes that DSV-CF peaks at $\lambda=0.5$2 (Wu et al., 21 Apr 2026). The textual interpretation is somewhat awkward, because increasing $\lambda=0.5$3 strengthens the penalty on attribution error, but the table itself is explicitly reported and therefore fixes the empirical claim.

A concrete case study concerns the query “How can we mitigate the impact of ocean acidification on coral reef ecosystems?” on Gemini 3 Pro. From initial response to best optimized version, SI increases from $\lambda=0.5$4 to $\lambda=0.5$5, WLV from $\lambda=0.5$6 to $\lambda=0.5$7, DPA from $\lambda=0.5$8 to $\lambda=0.5$9, CP from $\gamma=0.5$0 to $\gamma=0.5$1, AA from $\gamma=0.5$2 to $\gamma=0.5$3, FA from $\gamma=0.5$4 to $\gamma=0.5$5, KC from $\gamma=0.5$6 to $\gamma=0.5$7, and AD from $\gamma=0.5$8 to $\gamma=0.5$9 (Wu et al., 21 Apr 2026). The authors use this to illustrate DSV-CF’s dual-axis logic: both visibility and fidelity-oriented measures rise simultaneously.

7. Scope, limitations, and disambiguation

The framework has several explicit or strongly implied limitations. First, substantial parts of DSV-CF depend on LLM-as-a-judge scoring—specifically CP, SI, AA, FA, KC, and AD—so the metric inherits judge calibration and prompt sensitivity issues (Wu et al., 21 Apr 2026). Second, the paper does not provide exact formulas for six of the eight submetrics, nor the exact normalization and aggregation rules for $\lambda=0.5$0 and $\lambda=0.5$1, making exact reimplementation difficult from text alone (Wu et al., 21 Apr 2026). Third, the operational distinction among Attribution Accuracy, Response-level Faithfulness, and the document-level fidelity gate is not fully formalized in the provided text, leaving some ambiguity in how these checks interact (Wu et al., 21 Apr 2026).

The framework is also engine-specific and context-dependent. Because DSV-CF is computed on answers produced by a particular engine under a frozen retrieval list, its values are not intrinsic properties of the source document alone (Wu et al., 21 Apr 2026). Metrics such as CP and SI likely depend on formatting conventions and judge prompts, which are not fully specified. The paper also reports over-optimization fatigue, where additional editing rounds can reduce faithfulness; DSV-CF is intended to detect this trade-off, but it remains a practical failure mode (Wu et al., 21 Apr 2026).

A separate source of confusion is terminological. The exact string “DSV-CF” is explicitly defined in the GEO paper as Dual-Axis Semantic Visibility and Content Fidelity (Wu et al., 21 Apr 2026). Other arXiv papers use DSV for unrelated concepts, including an alignment validation loss for self-supervised outlier model selection (Yoo et al., 2023) and a dynamic sparsity framework for video DiT training (Tan et al., 11 Feb 2025). Likewise, CF appears in unrelated number-theoretic work as shorthand for continued fraction, including a randomness measure for sequences based on continued-fraction length (Aileni, 2010). These uses are unrelated to DSV-CF as defined in GEO. The 2023 and 2025 DSV papers explicitly state that they do not define any method or component called DSV-CF (Yoo et al., 2023, Tan et al., 11 Feb 2025).

In that sense, DSV-CF is a specialized evaluation construct for generative-engine settings rather than a general-purpose metric transferable without modification to anomaly detection, sparse attention, or continued-fraction analysis. Its distinguishing feature is precisely the coupling of answer-level visibility measurement with attribution-sensitive semantic fidelity under a controlled document-edit intervention framework (Wu et al., 21 Apr 2026).