shreeman-iyer/llm_multiplication_training
Triple-Tier Multiplication Curriculum (Area Model) A structured curriculum for teaching multiplication to small language models. This dataset moves from rote memorization to logical decomposition. Curriculum Structure Tier 1: Basic Tables (1-100) - Sequential and shuffled pairs for results up to 1000 to establish "Instant Recall" weights. Tier 2: Sign Logic - Explicitly teaches the rules of arithmetic signs: $(+) \times (+)$, $(-) \times (+)$, and $(-) \times… See the full description on the dataset page: https://huggingface.co/datasets/shreeman-iyer/llm_multiplication_training.
Triple-Tier Multiplication Curriculum (Area Model)
A structured curriculum for teaching multiplication to small language models. This dataset moves from rote memorization to logical decomposition.
Curriculum Structure
- Tier 1: Basic Tables (1-100) - Sequential and shuffled pairs for results up to 1000 to establish "Instant Recall" weights.
- Tier 2: Sign Logic - Explicitly teaches the rules of arithmetic signs: $(+) \times (+)$, $(-) \times (+)$, and $(-) \times (-)$.
- Tier 3: Distributive Property (Large) - Uses the "Area Model" to split 4-digit by 2-digit problems into manageable partial products.
Why this works
By splitting a problem like $450 \times 12$ into $(450 \times 10) + (450 \times 2)$, the model avoids "Dimensionality Collapse" and learns a scalable algorithm for any number size.