Model Description

Traditional reinforcement learning alignment (like standard GRPO) backpropagates formatting and correctness gradients across all layers of a language model. In smaller models (1.5B to 3B parameters), this triggers Central Engine Disruption—the destructive corruption of core mathematical and logical representations in early and middle layers ($L0$--$L23$).

LF-GRPO solves this by strictly freezing the model's central logic core ($L0$--$L23$) and confining parameter updates to the late-layer behavioral periphery ($L24$--$L27$). This allows the model to learn complex reasoning layout boundaries (such as step-by-step <think> tag monologues) without corrupting its underlying arithmetic capability.

Functional Behaviors:

• Structured Thinking: The model breaks down word problems step-by-step using logical numbering arrays.
• Conciseness Penalization: Through step-decay relative rewards, the model maintains a short, high-density reasoning path, preventing verbosity drift.
• Intact Core Arithmetic: Avoids the standard post-alignment reasoning decay, preserving raw calculation precision.

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How to Get Started with the Model

You can load this adapter on top of the base Qwen-1.5B model using peft and transformers.

python
Copy code
import torch
from transformers import AutoModelForCausalLM, AutoTokenizer
from peft import PeftModel

# Load the base model
base_model = AutoModelForCausalLM.from_pretrained(
    "Qwen/Qwen2.5-1.5B-Instruct",
    torch_dtype=torch.float16,
    device_map="auto"
)

# Load the LF-GRPO adapter
model = PeftModel.from_pretrained(base_model, "kridaydave/Qwen-1.5B-LFGRPO-OPTIM")
tokenizer = AutoTokenizer.from_pretrained("Qwen/Qwen2.5-1.5B-Instruct")

model.eval()

# Prompt format (Zero-Shot CoT with system guidance)
SYSTEM_PROMPT = (
    "A conversation between User and Assistant. The Assistant must think step-by-step "
    "inside <think>...</think> tags to solve the mathematical problem, and then provide "
    "the final numeric answer outside the tags."
)

prompt = f"<|im_start|>system\n{SYSTEM_PROMPT}<|im_end|>\n<|im_start|>user\nJanet has 16 eggs. She eats 3 for breakfast and bakes muffins with 4. She sells the rest for $2 each. How much does she make?<|im_end|>\n<|im_start|>assistant\n<think>\n"

inputs = tokenizer(prompt, return_tensors="pt").to("cuda")
with torch.no_grad():
    outputs = model.generate(**inputs, max_new_tokens=300, do_sample=False)

print(tokenizer.decode(outputs[0][inputs.input_ids.shape[1]:]))

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Training Details

Training Data

The model was trained on a 1,000-sample subset of the OpenAI GSM8K dataset, optimized specifically for step-by-step math logic.

Training Procedure

• Regime: Two-stage optimization. Stage 1 (steps 0-100) focuses on format-priming and monologue tag alignment. Stage 2 (steps 101-300) optimizes for final math correctness and conciseness.
• Group Relative Search: Group size ($N=4$) is used to compute advantages relative to the group mean and standard deviation, bypassing the memory-heavy critic model.
• Autograd Periphery Insulation: Hard gradient masking applied at layer 24. 100% of parameters in layers 0-23 were kept frozen.

Training Hyperparameters

• LoRA Target Modules: q_proj, k_proj, v_proj, o_proj, gate_proj, up_proj, down_proj
• LoRA Rank / Alpha: 32 / 32
• Targeted Layers: [24, 25, 26, 27]
• Trainable Parameters: 5,275,648 (0.34% of base model)
• Optimizer: paged_adamw_8bit (with CUDA page offloading)
• Learning Rate: 1.5e-5
• Batch Configuration: Batch=1, Accumulation=4 (effective batch size = 4)
• Sequence Limits: Prompt=512, Completion=384

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Evaluation Results

Evaluated on the OpenAI GSM8K test split (held-out prompts) under a zero-shot ChatML reasoning format:

• Qwen2.5-1.5B-Instruct (Base Baseline): ~42.0% - 50.0%
• Standard GRPO (Full-Layer LoRA): ~42.0% (degraded due to alignment tax / engine disruption)
• LF-GRPO (This Work - Step 100): ~50.0%
• LF-GRPO (This Work - Step 200/300): ~58.0% - 65.0% OOD accuracy (highly structured, concise CoT)

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Environmental Impact

• Hardware Type: 1 x Tesla T4 GPU (16GB VRAM)
• Hours used: ~2.0 hours
• Cloud Provider: Google Colab
• Compute Region: us-central1

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Technical Specifications

Model Architecture

The underlying architecture is based on Qwen2.5 (RoPE embeddings, SwiGLU gating, and RMSNorm layers) using a 28-layer parameter layout.

Software

• TRL (Transformer Reinforcement Learning)
• Unsloth (Fast language model training & Triton kernels)
• vLLM (Fast CUDA graph decoders for advantage rollouts)

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