Minnow-Math-1.5B

Minnow-Math-1.5B is a ~1.5B parameter decoder-only transformer trained from scratch on raw arXiv LaTeX sources across mathematics, computer science, and theoretical physics.

📄 Paper: https://arxiv.org/abs/2602.17288
💻 Github: https://github.com/kitefishai/Minnow-Math-1.5B

This is a base scientific language model (not instruction-tuned).

Overview

Minnow-Math-1.5B explores what it takes to train a domain-specialized scientific language model directly from structured LaTeX archives.

Training Scale

• ~52B pretraining tokens
• ~5B additional post-training tokens
• ~200GB processed scientific corpus
• LLaMA-compatible tokenizer (~102k vocab)
• 2× NVIDIA A100 (80GB) GPUs
• 24 experimental training runs

The focus of this project is scientific language modeling robustness, not benchmark optimization.

Model Architecture

• 24 Transformer layers
• Hidden size: 2048
• FFN size: 5504
• 16 attention heads
• Context length: 4096 (trained at 768 tokens)
• Dense LLaMA-style architecture

Optimization

• AdamW
• Learning rate: 2e-4
• Warmup: 500 steps
• Weight decay: 0.1
• Gradient accumulation: 32
• bf16 mixed precision
• Gradient checkpointing enabled

Validation Perplexity: ~4.2 (held-out scientific corpus)

Intended Use

Minnow-Math-1.5B is suitable for:

• Scientific text modeling research
• Mathematical language modeling experiments
• Pretraining initialization for domain fine-tuning
• Tokenization and symbolic modeling research
• Studying LaTeX structure modeling

It is not optimized for:

• Instruction following
• Chat-based applications
• General conversational AI
• Benchmark leaderboard performance

Performance Notes

This model was trained under moderate compute constraints and without instruction tuning or alignment stages.

Observed characteristics:

• Strong familiarity with scientific writing style
• Stable LaTeX structural modeling
• Reasonable symbolic fluency
• Limited reasoning depth
• Low downstream benchmark accuracy without fine-tuning

Performance improves significantly with supervised fine-tuning (SFT), LoRA adaptation, or domain-specific instruction tuning.

Limitations

• Not instruction-tuned
• No RLHF or preference alignment
• Trained at 768-token sequence length
• Domain restricted to selected arXiv categories
• Not optimized for reasoning benchmarks
• General NLP benchmark scores may be low

This release is intended primarily for research and experimentation.

Example Usage

from transformers import AutoTokenizer, AutoModelForCausalLM
import torch

model_id = "KiteFishAI/Minnow-Math-1.5B"

tokenizer = AutoTokenizer.from_pretrained(model_id)
model = AutoModelForCausalLM.from_pretrained(model_id)

prompt = "Prove that the sum of two continuous functions is continuous."
inputs = tokenizer(prompt, return_tensors="pt")

with torch.no_grad():
    outputs = model.generate(**inputs, max_new_tokens=200)

print(tokenizer.decode(outputs[0], skip_special_tokens=True))

Citation

If you use this model in your research, please cite:

@article{kitefish_a1_2026,
  title={KiteFish-A1: Training a Scientific Language Model from Raw LaTeX Archives},
  author={...},
  year={2026},
  eprint={2602.17288},
  archivePrefix={arXiv}
}