Text Metrics

Text-Metrics: Probability-Based Text Analysis

Overview

A utility skill providing advanced statistical and model-based text analysis for AI detection. Implements three core capabilities grounded in peer-reviewed research:

1. Token Rank Histograms (GLTR-style): Analyzes token probability distributions
2. DetectGPT Curvature Probes: Measures log-probability curvature through perturbations
3. Cohesion Metrics (Coh-Metrix-inspired): Evaluates discourse connectives, lexical diversity, and referential cohesion

Primary Use Case

This skill is designed to compose with the ai-check skill to provide Dimension 5 (Probability-Based) detection features. It can also be used standalone for text analysis research.

Auto-Invoke Conditions

This skill is typically invoked by other skills (particularly ai-check) rather than directly by users. It may be invoked when:

• AI-check requests probability-based metrics
• User explicitly requests "token rank analysis" or "GLTR"
• User mentions "DetectGPT" or "curvature probe"
• User asks for "lexical diversity" or "cohesion metrics"

Scientific Foundation

1. GLTR Token Rank Histograms

Reference: Gehrmann, S., Strobelt, H., & Rush, A. M. (2019). "GLTR: Statistical Detection and Visualization of Generated Text." ACL 2019.

Principle: LLM-generated text tends to select higher-probability tokens (lower ranks) more consistently than human writing, which exhibits more variability and surprisal.

Method:

1. For each token in text, compute its rank given preceding context using a language model
2. Bin tokens into: top-10, top-100, top-1000, rest
3. LLM text shows higher concentration in top bins

Typical Patterns:

• AI-generated: Top-10 > 40%, Top-100 > 85%
• Human-written: Top-10 ~ 20-30%, Top-100 ~ 70-80%

2. DetectGPT Curvature Probes

Reference: Mitchell, E., et al. (2023). "DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvature." ICML 2023.

Principle: Generated text sits at local maxima in the model's probability distribution, while human text does not. Random perturbations of generated text tend to have lower probability.

Method:

1. Compute log-probability of original text: log P(x)
2. Generate random perturbations: x'₁, x'₂, ..., x'ₙ
3. Compute mean perturbed log-probability: mean(log P(x'ᵢ))
4. Curvature = log P(x) - mean(log P(x'ᵢ))
5. Positive curvature suggests generation

Interpretation:

• Curvature > 0.5: Likely generated
• Curvature ~ 0: Ambiguous
• Curvature < -0.5: Likely human

3. Coh-Metrix Cohesion Metrics

Reference: McNamara, D. S., et al. (2014). "Automated Evaluation of Text and Discourse with Coh-Metrix." Cambridge University Press.

Principle: Discourse cohesion patterns (connectives, referential overlap, lexical diversity) differ between human and AI writing.

Metrics:

• Connective Density: Additive, temporal, causal, adversative connectives per 1,000 tokens
• Lexical Diversity: Type-token ratio, unique lemmas, hapax legomena
• Referential Cohesion: Pronoun rate, unique pronoun types

Functions

1. token_rank_hist(text, model_name="gpt2")

Compute GLTR-style token rank histogram.

Input:

• text: String to analyze
• model_name: HuggingFace model identifier (default: "gpt2")

Output:

{
  "top10_pct": 45.2,
  "top100_pct": 87.3,
  "top1000_pct": 96.1,
  "rest_pct": 3.9,
  "mean_rank": 182.4,
  "median_rank": 34.0
}

Usage:

from scripts.text_metrics import token_rank_hist

result = token_rank_hist("Your text here", model_name="gpt2")
print(f"Top-10 concentration: {result['top10_pct']:.1f}%")

2. detectgpt_score(text, model_name="gpt2", num_perturbations=10)

Compute DetectGPT curvature criterion.

Input:

• text: String to analyze
• model_name: HuggingFace model (default: "gpt2")
• num_perturbations: Number of random perturbations (default: 10)

Output:

{
  "original_logprob": -2.34,
  "mean_perturbed_logprob": -3.12,
  "curvature": 0.78
}

Usage:

from scripts.text_metrics import detectgpt_score

result = detectgpt_score("Your text here", num_perturbations=20)
if result['curvature'] > 0.5:
    print("Likely AI-generated")

3. cohesion_bundle(text)

Compute Coh-Metrix-inspired cohesion metrics.

Input:

• text: String to analyze

Output:

{
  "connectives": {
    "additive_rate": 12.5,
    "temporal_rate": 8.3,
    "causal_rate": 6.2,
    "adversative_rate": 9.1,
    "total_rate": 36.1
  },
  "lexical_diversity": {
    "type_token_ratio": 0.62,
    "unique_lemmas": 142,
    "hapax_legomena": 78
  },
  "referential_cohesion": {
    "pronoun_rate": 45.2,
    "unique_pronoun_types": 12
  }
}

Usage:

from scripts.text_metrics import cohesion_bundle

result = cohesion_bundle("Your text here")
diversity = result['lexical_diversity']['type_token_ratio']
print(f"Lexical diversity: {diversity:.2f}")

4. full_analysis(text, model_name="gpt2", num_perturbations=10)

Run all three analyses in one call.

Output: Combined dictionary with all metrics.

Integration with AI-Check

When ai-check skill invokes text-metrics:

# ai-check calls text-metrics for Dimension 5
token_data = invoke_skill("text-metrics", "token_rank_hist", text)
curvature = invoke_skill("text-metrics", "detectgpt_score", text)
cohesion = invoke_skill("text-metrics", "cohesion_bundle", text)

# Use results in probability dimension scoring
if token_data['top10_pct'] > 40:
    flag_high_probability_concentration()

if curvature['curvature'] > 0.5:
    flag_curvature_anomaly()

Model Selection

Supported Models (HuggingFace)

• gpt2 (default): Fast, lightweight, good baseline
• gpt2-medium: Better accuracy, slower
• gpt2-large: Best accuracy, requires GPU
• facebook/opt-125m: Alternative small model
• facebook/opt-1.3b: Alternative medium model

Recommendation: Use gpt2 for speed, gpt2-medium for accuracy.

GPU Acceleration

Text-metrics benefits significantly from GPU:

• CPU: ~2-5 seconds per 500-token document
• GPU: ~0.3-0.8 seconds per 500-token document

Install PyTorch with CUDA support for GPU acceleration.

Performance Characteristics

Times for ~500 token documents, gpt2 model.

Limitations

1. Model Dependency: Results depend on choice of language model. Mismatch between evaluation model and generation model affects accuracy.

2. Short Text: DetectGPT requires ~100+ tokens for reliable results. Token rank histograms need ~50+ tokens.

3. Computational Cost: Model inference is expensive. Cache results when possible.

4. Perturbation Quality: Simple word replacement perturbations used here. Production systems should use mask-filling with dedicated models.

5. Language: Currently English-only. Multilingual models needed for other languages.

6. Post-Editing: Heavily edited AI text may evade detection as curvature flattens.

Example Usage

Standalone Analysis

from scripts.text_metrics import full_analysis

text = """
Your sample text here. Should be at least 100 tokens
for reliable DetectGPT results.
"""

results = full_analysis(text, model_name="gpt2", num_perturbations=20)

print("Token Rank Histogram:")
print(f"  Top-10: {results['token_ranks']['top10_pct']:.1f}%")
print(f"  Top-100: {results['token_ranks']['top100_pct']:.1f}%")

print("\nDetectGPT Curvature:")
print(f"  Curvature: {results['curvature']['curvature']:.2f}")

print("\nCohesion Metrics:")
print(f"  Type-Token Ratio: {results['cohesion']['lexical_diversity']['type_token_ratio']:.2f}")
print(f"  Connective Rate: {results['cohesion']['connectives']['total_rate']:.1f}/1000")

Integration with AI-Check

# In ai-check skill, invoke text-metrics for probability dimension
token_metrics = invoke_text_metrics("token_rank_hist", test_text)
curvature_metrics = invoke_text_metrics("detectgpt_score", test_text)
cohesion_metrics = invoke_text_metrics("cohesion_bundle", test_text)

# Score probability dimension
probability_score = compute_probability_dimension(
    token_metrics,
    curvature_metrics,
    cohesion_metrics
)

Files & Resources

• Implementation: scripts/text_metrics.py
• Dependencies: scripts/requirements.txt
• Examples: examples/usage_example.md

Installation

cd skills/utility/text-metrics/scripts
pip install -r requirements.txt

# First run will download model (~500MB for gpt2)
python text_metrics.py

Troubleshooting

Issue: "Model download failed"

Solution: Ensure internet connection. Model cached in ~/.cache/huggingface/.

Issue: "Out of memory"

Solution: Use smaller model (gpt2 instead of gpt2-large) or reduce num_perturbations.

Issue: "Slow inference"

Solution: Install PyTorch with CUDA for GPU acceleration, or use CPU-optimized build.

Issue: "Results differ from GLTR web demo"

Solution: Different models produce different ranks. Ensure same model as reference.

References

1. Gehrmann, S., Strobelt, H., & Rush, A. M. (2019). "GLTR: Statistical Detection and Visualization of Generated Text." Proceedings of ACL 2019.

2. Mitchell, E., Lee, Y., Khazatsky, A., Manning, C. D., & Finn, C. (2023). "DetectGPT: Zero-Shot Machine-Generated Text Detection using Probability Curvature." Proceedings of ICML 2023.

3. McNamara, D. S., Graesser, A. C., McCarthy, P. M., & Cai, Z. (2014). "Automated Evaluation of Text and Discourse with Coh-Metrix." Cambridge University Press.

Version: 1.0.0 License: MIT Maintained by: Claude Skills Library

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