WARP-benchmark

The benchmark to test logical reasoning and pattern generalisation in large language models through formal SMT constraints.

Overview

We propose a benchmark designed to evaluate a language model's ability to generalise worst-case path constraints for all input sizes. Each example asks a model to generate a formal constraint for a specific target size after being shown examples of constraints for smaller input sizes.

Github Repository

You can find the link here at: WARP-benchmark

Dataset Statistics

Basic Statistics

• Total samples: 671
• Format: Parquet file
• Difficulty tiers:
  • Small: 333 samples (49.6%)
  • Medium: 333 samples (49.6%)
  • Large: 5 samples (0.7%)

Token Statistics (using Qwen2.5-3B tokenizer)

	Questions	Answers
Minimum	117	27
Maximum	4,086	14,476
Mean	1,684	994
Median	1,521	493
Total tokens	1,130,153	666,709

Target N Distribution

• Range: 5 to 30
• Mean: 19.9
• Median: 20
• Unique values: 25 different values

Examples Per Question

• Range: 3 to 18 examples
• Mean: 6.7
• Median: 6
• Most common: 3 examples (168 questions)

Dataset Structure

Each example in the dataset follows this structure:

• Question: A prompt showing examples of constraints for smaller input sizes N, asking for constraints at target N
• Answer: The formal constraint for the target size
• Constants: Variable declarations for the target size
• Tier: Difficulty level ("small", "medium", or "large")

Example question format:

Given the following examples of constraints for increasing input sizes:
N=3: (assert (and (and ...)))
N=4: (assert (and (and ...)))
...
What is the constraint for N={target}?

Dataset Creation

The dataset is generated from SMT2 files using the following process:

1. Discovery: Finds SMT2 files following the naming pattern {prefix}.{problem}_{number}.smt2
2. Combination Generation: For each problem and target N value, generates combinations of smaller N values to use as examples
3. Prompt Construction: Creates prompts with selected examples and targets, ensuring they fit within token limits
4. Difficulty Assignment: Assigns difficulty tiers based on the "jump" between example N and target N:
   • Small: ≤ 5
   • Medium: 6-15
   • Large: > 15
5. Balanced Sampling: Uses reservoir sampling to balance the dataset across difficulty tiers

Dataset Profiling

Use the included profiler to analyze the dataset:

python profiler.py dataset.parquet --visualize

This will generate comprehensive statistics and visualizations about token lengths, difficulty distribution, and other metrics.

Dependencies

• pandas
• pyarrow
• transformers (Qwen2.5-3B tokenizer)
• tqdm
• matplotlib (for visualization)
• seaborn (for visualization)