Objective: Train a model to solve math problems correctly while penalizing unnecessarily long responses, using a combined reward signal with length penalty.

Reward Function (Sum-then-Normalize GDPO): For each group of rollouts from the same prompt:

Compute raw combined score: correctness + lambda * length_penalty
- correctness: 1.0 if answer matches ground truth, 0.0 otherwise
- length_penalty: -num_tokens / max_completion_length
Z-normalize the combined scores within each group (zero mean, unit variance)
Use normalized scores as advantages for GRPO policy gradient update

This "sum-then-normalize" approach ensures the length penalty signal is proportional to lambda relative to correctness before normalization, rather than independently normalizing each component.

Training Configuration

Parameter	Value
Base Model	Qwen/Qwen3-4B
Method	GRPO with GDPO length penalty
Lambda (length penalty weight)	0.5
LoRA rank	16
LoRA alpha	16
LoRA target modules	all-linear (q, k, v, o, gate, up, down proj)
Learning rate	5e-5 (constant schedule)
KL penalty (beta)	0.0
Temperature	1.0
Top-p	0.95
Prompts per step	6
Rollouts per prompt	8
Batch size	48 (6 x 8)
Max completion length	15,000 tokens
Total steps	200
Optimizer	AdamW (weight_decay=0.1, betas=[0.9, 0.99])
Max grad norm	1.0
PPO epochs	1
Clip ratio	0.2
Framework	Verl v0.6.1 + FSDP2
Hardware	4x NVIDIA H200

Dataset

Source: DeepScaleR math reasoning dataset (agentica-org/DeepScaleR-Preview-Dataset)
Difficulty filter: 99-100% solved percentage (easiest problems)
Size: 1,840 problems after filtering
System prompt: "Please reason through this problem for yourself, and then when giving your answer ONLY provide your final answer within \boxed{} and DO NOT provide any reasoning."

Key Training Metrics

Metric	Step 1	Step 100	Step 199
Mean response length	1,414	61	92
Max response length	4,289	134	204
KL divergence	0.0	0.29	0.22
Policy loss	0.032	0.003	0.007
Grad norm	0.019	0.195	0.149
Entropy	0.140	0.057	0.061

The model learned to produce dramatically shorter responses (from ~1,400 tokens to ~60-90 tokens average) while maintaining correctness on easy math problems.

Checkpoints

LoRA adapters are saved every 20 steps:

checkpoints/global_step_20/ through checkpoints/global_step_200/

Each checkpoint contains:

adapter_model.safetensors (~127MB) - LoRA adapter weights
adapter_config.json - PEFT/LoRA configuration

Usage

python

from transformers import AutoModelForCausalLM, AutoTokenizer
from peft import PeftModel

base_model = AutoModelForCausalLM.from_pretrained("Qwen/Qwen3-4B")
tokenizer = AutoTokenizer.from_pretrained("Qwen/Qwen3-4B")

# Load a specific checkpoint
model = PeftModel.from_pretrained(base_model, "brikdavies/deepscaleR/checkpoints/global_step_200")

Run Details

Run ID: 20260223_182638_deepscaler_gdpo_lambda0.5
Training time: ~71 minutes (200 steps)
Wandb project: grpo-deepscaler