ZR1-1.5B

ZR1-1.5B is a small reasoning model trained extensively on both verified coding and mathematics problems with reinforcement learning. The model outperforms Llama-3.1-70B-Instruct on hard coding tasks and improves upon the base R1-Distill-1.5B model by over 50%, while achieving strong scores on math evaluations and a 37.91% pass@1 accuracy on GPQA-Diamond with just 1.5B parameters.

Data

For training we utilized the PRIME Eurus-2-RL dataset which combines the following math and code datasets:

• NuminaMath-CoT
• APPS, CodeContests, TACO, and Codeforces train set

We filtered math data by validating that questions are correctly graded when calling the evaluator with reference ground truth, and we removed all code examples with an empty list of test cases. Our final dataset comprised roughly 400k math + 25k code samples.

Training Recipe

We employ PRIME (Process Reinforcement through IMplicit rEwards), an online RL algorithm with process rewards, motivated by the improvement over GPRO demonstrated in the paper, as well as potentially more accurate token-level rewards due to the learned process reward model. We used the training batch accuracy filtering method from PRIME for training stability, and the iterative context lengthening technique demonstrated in DeepScaleR for faster training, which has also been shown to improve token efficiency. After a warmup period with maximum generation length set to 12k tokens, we sequentially increased the maximum generation length during training, starting at 8k tokens before increasing to 16k and 24k.

We trained on a single 8xH100 node with the following specific algorithmic details.

• PRIME + RLOO with token-level granularity
• No <think> token prefill. 0.1 format reward/penalty
• Main train batch size 256 with n=4 samples per prompt. veRL dynamic batch size with max batch size set per GPU to support training with large generation length
• Max prompt length 1536, generation length increase over training. Started with 12k intended to ease model into shorter generation length training
• 12384 -> 8192 -> 16384 -> 24448
• Start with 1 PPO epoch, increase to 4 during 24k stage
• Accuracy filtering 0.2-0.8 and relax to 0.01-0.99 during 24k stage
• Oversample batches 2x for accuracy filtering

And the following training hyperparameters:

• KL coefficient 0 (no KL divergence term)
• Entropy coefficient 0.001
• Actor LR 5e-7
• Reward beta train 0.05
• Reward LR 1e-6
• Reward grad clip 10
• Reward RM coefficient 5

Evaluation

Coding

	Leetcode	LCB_generation
ZR1-1.5B	40%	39.74%
R1-Distill-Qwen-1.5B	12.22%	24.36%
DeepCoder-1.5B	21.11%	35.90%
OpenHands-LM-1.5B	18.88%	29.49%
Qwen2.5-1.5B-Instruct	20.56%	24.36%
Qwen2.5-Coder-3B-Instruct	35.55%	39.74%
Llama-3.1-8B-Instruct	14.44%	23.08%
Llama-3.1-70B-Instruct	37.22%	34.62%
Eurus-2-7B-PRIME	34.44%	32.05%
Mistral-Small-2503	-	38.46%
Gemma-3-27b-it	-	39.74%
Claude-3-Opus	-	37.18%

LiveBench

Model	AMPS Hard	Math_Comp	LCB_Generation	Coding_Completion
ZR1-1.5B	74%	60.42%	39.74%	12%
DeepCoder-1.5B	69%	61.46%	35.90%	12%
DeepScaleR-1.5B	64%	50%	24.36%	6%
OpenHands-LM-1.5B	24%	29.48%	29.49%	8%
R1-Distill-1.5B	54%	37.50%	24.36%	6%
Qwen2.5-1.5B-Instruct	38%	20.83%	24.36%	4%
Qwen2.5-Math-1.5B-Instruct	49%	36.46%	0%	0%
Qwen2.5-3B-Instruct	41%	17.71%	28.21%	10%
R1-Distill-7B	74%	61.46%	44.87%	14%
Qwen2.5-7B-Instruct	56%	29.17%	38.46%	40%
Qwen2.5-Math-7B-Instruct	62%	45.83%	16.67%	4%
R1-Distill-14B	77%	69.79%	64.10%	18%
Qwen2.5-14B-Instruct	59%	43.75%	46.15%	54%
R1-Distill-32B	74%	75%	60.26%	26%
QwQ-32B-Preview	78%	67.71%	52.56%	22%
QwQ-32B	83%	87.5%	87.18%	46%
Qwen2.5-32B-Instruct	62%	54.17%	51.23%	54%
Qwen2.5-Coder-32B-Instruct	48%	53.13%	55.13%	58%
R1-Distill-Llama-70B*	65%	78.13%	69.23%	34%
Qwen2.5-72B-Instruct	66%	52.08%	50%	62%
Qwen2.5-Math-72B-Instruct	56%	59.38%	42.31%	42%
DeepSeek-R1*	88%	88.54%	79.48%	54%

General Math

model	AIME24	AIME25	AMC22_23	AMC24	GPQA-D	MATH500	Minerva	Olympiad
ZR1-1.5B	33.75%	27.29%	72.06%	59.17%	37.91%	88.34%	33.52%	56.87%
ZR1-1.5B (greedy)	40%	26.67%	71.08%	53.33%	37.88%	89.40%	32.72%	57.93%
DeepScaleR-1.5B	42.92%	27.71%	74.40%	60.69%	34.66%	89.36%	35.50%	59.37%
DeepScaleR-1.5B (greedy)	33.33%	33.33%	67.47%	57.77%	29.29%	84.60%	31.62%	52.44%
DeepCoder-1.5B	41.88%	24.79%	75.30%	59.72%	36.46%	83.60%	32.01%	56.39%
Still-3-1.5B	31.04%	23.54%	65.51%	56.94%	34.56%	86.55%	33.50%	53.55%
Open-RS3-1.5B	31.67%	23.75%	64.08%	51.67%	35.61%	84.65%	29.46%	52.13%
R1-Distill-1.5B	28.96%	22.50%	63.59%	50.83%	33.87%	84.65%	31.39%	51.11%
R1-Distill-1.5B (greedy)	26.67%	13.33%	51.81%	24.44%	30.81%	73.40%	25.74%	40%
Qwen2.5-Math-1.5B-Instruct (greedy)	10%	6.67%	42.17%	26.67%	28.28%	75.20%	28.31%	40.74%
Qwen2.5-Math-7B-Instruct (greedy)	20%	3.33%	46.99%	31.11%	32.32%	83%	37.13%	42.22%
Qwen2.5-Math-72B-Instruct (greedy)	26.67%	6.67%	59.04%	46.67%	43.94%	85.40%	42.65%	50.37%
Eurus-2-7B-PRIME (greedy)	20%	13.33%	56.62%	40%	36.36%	81.20%	36.76%	44.15%
DeepHermes-3-Llama-3-3B (think prompt, greedy)	0%	3.33%	12.05%	11.11%	30.30%	34.40%	10.66%	10.52%
OpenHands-LM-1.5B (greedy)	0%	0%	10.84%	4.44%	23.74%	36.80%	12.50%	10.22%

Short CoT

Our direct answer system prompt was: “Give a direct answer without thinking first.”

The table reports the average greedy pass@1 score across the following math evals: AIME24, AIME25, AMC22_23, AMC24, GPQA-Diamond, MATH-500, MinervaMath, OlympiadBench

	avg pass@1	max_tokens
ZR1-1.5B	51.13%	32768
ZR1-1.5B (truncated)	46.83%	4096
ZR1-1.5B (direct answer prompt)	45.38%	4096
ZR1-1.5B (truncated)	40.39%	2048
ZR1-1.5B (direct answer prompt)	37%	2048
Qwen-2.5-Math-1.5B-Instruct	32.25%	2048
Qwen-2.5-Math-7B-Instruct	37.01%	2048

For Leetcode and LiveBench, we report pass@1 accuracy with greedy sampling. For the rest of the evaluations we report pass@1 accuracy averaged over 16 samples per question, with temperature 0.6 and top_p 0.95.

We use the following settings for SGLang:

python -m sglang.launch_server --model-path <model> --host 0.0.0.0 --port 5001 --mem-fraction-static=0.8 --dtype bfloat16 --random-seed 0 --chunked-prefill-size -1 --attention-backend triton --sampling-backend pytorch --disable-radix-cache --disable-cuda-graph-padding  --disable-custom-all-reduce --disable-mla --triton-attention-reduce-in-fp32

For vllm we disable prefix caching and chunked prefill.