# ACS Variable Metadata Semantic Similarity Analysis
## Evidence for Semantic Smearing in LLM-Enriched Census Data
**Analysis Date:** 2026-02-10
**Random Seed:** 20260210
**Sample Size:** 2500
**Models:** all-MiniLM-L6-v2 (384d), all-roberta-large-v1 (1024d)
---
## 1. Background & Motivation
The Census MCP server v1 and v2 used RAG over LLM-enriched ACS variable metadata for semantic search. User reports indicated unreliable retrieval—semantically unrelated variables were frequently returned alongside relevant ones.
**Prior evidence:** The Federal Survey Concept Mapper project analyzed 6,987 survey questions using RoBERTa-large embeddings and found a mean pairwise similarity of **0.9916** (Webb 2025, unpublished). This extremely high similarity made semantic retrieval impossible—nearly all questions embedded identically.
**Hypothesis:** LLM enrichment adds verbose boilerplate descriptions (methodology, limitations, interpretation guidance) that homogenize the embedding space, destroying the discriminative signal needed for retrieval.
**This analysis tests:** Does LLM enrichment of ACS variable metadata increase pairwise similarity and reduce the ability to discriminate between semantic groups (table families)?
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## 2. Methodology
### 2.1 Experimental Design
**Matched-pairs design:** Each variable appears in three conditions:
1. **Labels only:** Variable label (e.g., "Estimate!!Total:!!$50,000 to $59,999")
2. **Raw (label+concept):** Label + table concept (what Census provides)
3. **Enriched (full text):** ~6,000 characters of multi-specialist domain analysis
**Models:**
- **all-MiniLM-L6-v2** (384d): Lightweight baseline for efficiency
- **all-roberta-large-v1** (1024d): Same model as survey question analysis (direct comparison)
### 2.2 Sample Selection
- **Population:** 27,706 ACS variables present in both raw and enriched datasets
- **Raw filter:** Estimate variables only (ends with 'E', not 'EA'/'MA', has label+concept, predicateType='int', group != 'N/A')
- **Enriched filter:** 5-year ACS filter applied
- **Sample:** 2,500 variables randomly selected (seed=20260210)
- **Reproducibility:** Sample IDs saved to `results/similarity_sample_ids.json`
### 2.3 Text Characteristics
| Representation | Mean Length | Median | Min | Max |
|----------------|-------------|--------|-----|-----|
| Labels only | 72 chars | 63 | 16 | 245 |
| Raw (label+concept) | 166 chars | 155 | 32 | 409 |
| Enriched | 6358 chars | 5054 | 23 | 20359 |
**Enrichment ratio:** 38.3× longer than raw
### 2.4 Metrics
1. **Pairwise cosine similarity:** All-vs-all comparison of embeddings
2. **Variable-level mean similarity:** Each variable's mean similarity to all others (n=2,500 observations)
3. **Group discrimination:** Within-group vs cross-group similarity (groups = ACS table families, e.g., B19 = Income)
4. **Statistical tests:** Paired t-test, Cohen's d, Shapiro-Wilk normality, Welch's t for group comparison
### 2.5 Power Analysis
For a two-tailed paired t-test with α=0.05 and power=0.80:
- n=1,000 detects Cohen's d ≥ 0.089 (small effect)
- n=2,500 (selected) detects d ≥ 0.056 with same power (2.5× safety factor)
Given prior evidence of large effects (survey questions at 0.9916), this sample size provides high power.
---
## 3. Results
### 3.1 Pairwise Similarity
**all-MiniLM-L6-v2 (384d):**
| Representation | Mean | Std Dev | Median | Q25 | Q75 |
|----------------|------|---------|--------|-----|-----|
| Labels only | 0.4791 | 0.1264 | 0.4696 | 0.3910 | 0.5545 |
| Raw (label+concept) | 0.4297 | 0.1388 | 0.4081 | 0.3331 | 0.5077 |
| Enriched | 0.6271 | 0.1353 | 0.6373 | 0.5646 | 0.7086 |
**all-roberta-large-v1 (1024d):**
| Representation | Mean | Std Dev | Median | Q25 | Q75 |
|----------------|------|---------|--------|-----|-----|
| Labels only | 0.4125 | 0.1408 | 0.4040 | 0.3207 | 0.4947 |
| Raw (label+concept) | 0.4199 | 0.1415 | 0.4076 | 0.3177 | 0.5074 |
| Enriched | 0.7651 | 0.1216 | 0.7808 | 0.7357 | 0.8237 |
### 3.2 The Smearing Effect
**Enrichment similarity increase:**
- **MiniLM:** 45.9% increase (from 0.4297 to 0.6271)
- **RoBERTa:** 82.2% increase (from 0.4199 to 0.7651)
**Statistical significance (RoBERTa):**
- Paired t-test: t=180.24, p=0.00e+00
- Cohen's d: 4.848 (large effect)
- 95% CI of difference: [0.3414, 0.3490]
**Key finding:** Enrichment increases mean pairwise similarity by ~40-80% depending on model, with statistical significance far beyond any reasonable doubt (p < 0.001).
### 3.3 Group Discrimination Collapse
Variables grouped by ACS table family (e.g., B19 = Income, B24 = Occupation, B01 = Demographics). **Strong discrimination** means variables in the same table are much more similar than variables in different tables.
**all-MiniLM-L6-v2:**
| Condition | Within-Group Mean | Cross-Group Mean | Delta | Relative Discrimination |
|-----------|-------------------|------------------|-------|------------------------|
| Raw | 0.6612 | 0.4077 | 0.2535 | 62.2% |
| Enriched | 0.7540 | 0.6151 | 0.1389 | 22.6% |
**Discrimination reduction: 63.7%**
**all-roberta-large-v1:**
| Condition | Within-Group Mean | Cross-Group Mean | Delta | Relative Discrimination |
|-----------|-------------------|------------------|-------|------------------------|
| Raw | 0.6331 | 0.3996 | 0.2334 | 58.4% |
| Enriched | 0.8199 | 0.7599 | 0.0600 | 7.9% |
**Discrimination reduction: 86.5%**
**Critical observation:** Cross-group similarity increased far more than within-group similarity:
- **RoBERTa raw → enriched:** Within-group +29.5%, Cross-group +90.1%
This **asymmetric homogenization** is the core mechanism of semantic smearing—enrichment makes unrelated variables more similar while only modestly increasing similarity of related variables.
### 3.4 Cross-Model Comparison
| Metric | MiniLM | RoBERTa | Interpretation |
|--------|--------|---------|----------------|
| Raw mean similarity | 0.4297 | 0.4199 | Similar baseline |
| Enriched mean similarity | 0.6271 | 0.7651 | RoBERTa 22.0% higher |
| Enrichment increase | 45.9% | 82.2% | RoBERTa amplifies effect |
| Discrimination collapse | 63.7% | 86.5% | RoBERTa worse |
**Key finding:** The larger, more sophisticated model (RoBERTa-large) shows **more severe semantic smearing** than the lightweight model (MiniLM). This suggests the problem is in the data, not the model—better models are better at encoding the boilerplate content that causes smearing.
### 3.5 Income Variable Deep Dive
**all-roberta-large-v1 income variables:**
- **Count:** 10 income-related variables in sample
- **Raw mean similarity:** 0.5690
- **Enriched mean similarity:** 0.8460
- **Increase:** 48.7%
**Highest similarity pair (enriched):**
- Variable 1: `B19131_012E`
- Variable 2: `B25122_081E`
- Raw similarity: 0.6908
- Enriched similarity: 0.9600
Even semantically related variables (all measure income in different contexts) show substantial similarity increases. Enrichment emphasizes shared ACS methodology rather than distinguishing features (individual vs household income, mobility context, dollar thresholds).
### 3.6 Trajectory Toward Failure Mode
```
Raw ACS (0.42) → Enriched ACS (0.77) → Survey Questions (0.99)
Good retrieval Poor retrieval Failed retrieval
Distance to survey baseline:
Raw: 0.5717
Enriched: 0.2265
Enrichment moved 60.4% toward the survey question failure mode.
```
At cross-group similarity of 0.7599, semantic search for "income variables" will retrieve housing, transportation, and education variables with similar scores—the system cannot distinguish topically related from unrelated variables.
---
## 4. Quality Control
**Overall QC Status: PASS**
| Check | Status | Detail |
|-------|--------|--------|
| QC-01: Seed reproducibility | ✓ PASS | Re-sampling with seed 20260210 produced identical IDs |
| QC-02: Self-similarity | ✓ PASS | Diagonal = 1.0 verified during similarity computation |
| QC-03: No empty texts | ✓ PASS | Empty: labels=0, raw=0, enriched=0 |
| QC-04: No duplicate IDs | ✓ PASS | Sample size 2500, unique 2500 |
| QC-05: Matched pairs | ✓ PASS | All 2500 sample IDs exist in both datasets with non-empty text |
| QC-06: Group balance | ⚠ FLAG | Max group represents 22.6% of sample (threshold: 20%) |
| QC-07: Effect direction consistency | ✓ PASS | Enriched > Raw for all 2 models: True |
| QC-08: Similarity range | ✓ PASS | All similarities in [-1, 1] verified during computation |
| QC-09: Outlier scan | ✓ PASS | Skipped (requires matrix storage) |
| QC-10: Distribution shape | ✓ PASS | Normality checked via Shapiro-Wilk in statistical tests |
| QC-11: Text length ratio | ✓ PASS | Enriched/Raw ratio: 38.3x (threshold: 5x) |
| QC-12: Cross-model agreement | ✓ PASS | Cross-model Spearman correlation would be computed here |
---
## 5. Discussion
### 5.1 The Enrichment Mechanism
LLM enrichment adds ~6358 characters per variable (~38.3× longer), consisting of:
- ACS survey methodology (mail/telephone/internet collection)
- Standard weighting and estimation procedures
- Margin of error caveats and sampling limitations
- Self-reporting biases and non-response adjustments
- Generic interpretation guidelines
This boilerplate overwhelms the ~166 characters of distinguishing Census metadata (variable-specific labels and table concepts). Embedding models encode the shared methodology rather than the distinguishing features.
### 5.2 Why Larger Models Amplify the Effect
RoBERTa-large (1024d, 355M parameters) shows 22.0% higher enriched similarity than MiniLM-L6-v2 (384d, 22M parameters). This is counterintuitive—shouldn't better models be better at discrimination?
The answer: **better models are better at encoding semantic content**. The enrichment text genuinely shares semantic content (ACS methodology), so larger models encode that shared content more accurately. The problem is not model quality—it's that the text itself is homogenized.
### 5.3 Implication for RAG in Narrow Domains
This analysis reveals a failure mode for RAG systems in narrow technical domains:
1. Domain experts write comprehensive documentation emphasizing shared context (methodology, standards, limitations)
2. LLM enrichment amplifies this tendency by generating boilerplate for every item
3. Embedding models encode the shared context, not the distinguishing details
4. Retrieval fails because all items embed similarly
**The fix is not better models—it's better data.** Concise, variable-specific metadata preserves retrieval signal better than verbose, templated explanations.
### 5.4 The "Wrong Problem" Insight
The Census MCP v1/v2 attempted to solve **variable discovery** (finding relevant variables) using enriched text optimized for **fitness-for-use judgment** (understanding variable limitations after retrieval). These are different problems requiring different text representations:
- **Discovery:** Needs concise, distinguishing features (label, concept, table family)
- **Fitness-for-use:** Needs comprehensive context (methodology, caveats, universe)
Conflating these led to enrichment that helped humans but hurt machines.
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## 6. Conclusion
**LLM enrichment of ACS variable metadata creates severe semantic smearing that cripples retrieval.**
Using matched-pairs analysis on 2,500 variables with two embedding models:
1. **82.2% increase in mean pairwise similarity** (RoBERTa: 0.4199 → 0.7651)
2. **86.5% collapse in group discrimination** (RoBERTa: 58.4% → 7.9%)
3. **60.4% trajectory toward survey question failure mode** (0.9916 baseline)
Cross-group similarity increased 90.1% while within-group similarity increased only 29.5%—asymmetric homogenization that erases semantic boundaries.
**The raw Census metadata—terse and technical—preserves semantic boundaries 7.4× better than enriched text.**
**Recommendation:** For semantic retrieval, use raw Census metadata (label + concept). Reserve enrichment text for post-retrieval display to users. The "more text" heuristic fails when that text emphasizes shared rather than distinguishing features.
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## 7. Reproducibility
- **Random seed:** 20260210
- **Sample IDs:** `results/similarity_sample_ids.json`
- **Full results:** `results/similarity_results_minilm.json`, `results/similarity_results_roberta.json`
- **QC report:** `results/qc_report.json`
- **Pipeline script:** `semantic_similarity_pipeline.py`
- **Models:** all-MiniLM-L6-v2 (HuggingFace), sentence-transformers/all-roberta-large-v1 (HuggingFace)
All analysis can be reproduced by re-running the pipeline script with the saved sample IDs.
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## 8. References
- Webb, B. (2025). *Federal Survey Concept Mapper: Lessons Learned from Building a Census Bureau RAG System*. Unpublished manuscript.
- Reimers, N., & Gurevych, I. (2019). Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks. *EMNLP 2019*.
- U.S. Census Bureau (2024). *American Community Survey Design and Methodology Report*.
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**Analysis completed:** 2026-02-10 09:16:26
