IPO (Inverse Preference Optimization) fine-tuned model for the Countdown arithmetic reasoning task, built on top of an SFT baseline. Trained as part of Stanford CS224R (Spring 2026).

Model Description

This model is preference-tuned using IPO on pairwise chosen/rejected completions for Countdown problems. Given a target number and a set of allowed numbers, the model produces chain-of-thought reasoning inside <think> tags and a final answer inside <answer> tags.

Training Details

Hyperparameter	Value
Base model	ba144220/cs224r-default-project-sft (SFT-tuned Qwen2.5-0.5B)
Dataset	asingh15/countdown_tasks_3to4-dpo
Loss type	IPO
Beta	0.1
Epochs	1
Learning rate	5e-6
LR schedule	Cosine with 5% warmup
Batch size	64 (gradient accumulation = 16)
Weight decay	0.01
Precision	bfloat16
Gradient checkpointing	Enabled
Hardware	1x NVIDIA H100 (Modal)
Max prompt length	512
Max response length	1024

Evaluation

Evaluated on asingh15/countdown_tasks_3to4 test split (40 prompts) using vLLM with temperature 0.6, top-k 20, top-p 0.95, sampling K=16 responses per prompt.

Metric	SFT Baseline	IPO (this model)
Average Score	0.3660	0.4080
Pass@1	0.30	0.375
Pass@16	0.75 (30/40)	0.75 (30/40)
Correct (score=1.0)	244/800	287/800

Usage

python

from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained("ba144220/cs224r-default-project-ipo")
tokenizer = AutoTokenizer.from_pretrained("ba144220/cs224r-default-project-ipo")

messages = [{"role": "user", "content": "Using the numbers [3, 4, 6, 8], create an equation that equals 24."}]
input_text = tokenizer.apply_chat_template(messages, add_generation_prompt=True, tokenize=False)
inputs = tokenizer(input_text, return_tensors="pt").to(model.device)

outputs = model.generate(**inputs, max_new_tokens=1024, temperature=0.6, top_k=20, top_p=0.95, do_sample=True)
print(tokenizer.decode(outputs[0][inputs["input_ids"].shape[1]:], skip_special_tokens=True))

Limitations

Trained and evaluated only on the Countdown arithmetic task; not intended for general-purpose use.
Performance degrades on harder problems with more numbers or larger targets.
The 0.5B parameter size limits reasoning capacity compared to larger models.

Authors

Yuchi Hsu (yuchihsu@stanford.edu) and Ryan He (ryanhe@stanford.edu), Stanford CS224R Spring 2026.