The Hidden Flaw Crippling Your LLM’s Reasoning Power
Large language models (LLMs) promise revolutionary reasoning capabilities, yet most hit an invisible wall. Traditional training forces a brutal trade-off:
- Knowledge Distillation (KD) rapidly imitates teacher models but fails catastrophically on unseen problems (↓ 3.1% accuracy vs RL).
- Reinforcement Learning (RL) enables creative problem-solving yet guzzles compute resources, struggling to explore high-reward paths.
Enter KDRL—a Huawei/HIT-developed framework merging KD and RL into a single unified pipeline. Results from 6 reasoning benchmarks reveal:
- 57.2% average accuracy—outperforming GRPO (↑2.6%) and KD-RKL (↑1.1%)
- 20% shorter responses than pure distillation
- 80-hour training convergence—2.3× faster than RL-only systems
How KDRL Shatters the KD-RL Deadlock
Proposed model breakthrough lies in Reverse KL Divergence (RKL) + Policy Gradient Optimization—forcing alignment between teacher guidance and environmental rewards.
The 3-Pillar Architecture
- Teacher Supervision
- On-policy sampling from student rollouts
- Token-level reverse KL loss (RKL) minimizes divergence from teacher
- Rule-Based Reinforcement
- Binary verifier rewards (format + accuracy)
- GRPO advantage function scales self-exploration
- Dynamic Balancing
- Annealing KL coefficient: Shifts focus from imitation (β=5e⁻³) → reward optimization (β=1e⁻³)
- Reward-guided masking: Suppresses KD on correct responses to avoid over-regularization
Critical Insight: Unlike Qwen3’s distillation, KDRL’s k2 estimator provides unbiased gradients—accelerating convergence by 17% vs k3 approximations.
Benchmark Domination:
Tests across MATH500, AIME24, and OlympiadBench prove proposed model supremacy:
| Method | AIME24 (%) | Avg. Length | Training Hours |
|---|---|---|---|
| SFT (Reject Sampling) | 33.5 | 4,812 | 80 |
| GRPO (RL-only) | 38.3 | 5,109 | 68 |
| KD-RKL (Qwen3-style) | 41.0 | 8,642 | 92 |
| KDRL (Ours) | 42.9 | 6,203 | 80 |
| MODEL | AIME24 AVG@16 | MATH PASS@1 | AMC23 AVG@16 |
|---|---|---|---|
| GRPO (Pure RL) | 38.3% | 88.6% | 79.5% |
| KD-RKL (On-Policy KD) | 41.0% | 89.0% | 80.2% |
| KDRL (Ours) | 42.1% | 90.0% | 81.3% |
| KDRL-Annealing | 42.9% | 90.4% | 82.2% |
Takeaway : Proposod model outperforms all baselines, achieving a 5.7% gain over SFT and 2.6% over GRPO
3 Unmatched Advantages
- Token Efficiency
- Response-level masking cuts redundant outputs by 1,400 tokens (↓11%)
- No accuracy trade-off: 42.9% AIME24 score retained
- Training Stability
- Annealing β prevents early length explosion (truncation ↓15% vs KD-RKL)
- Group-level sampling eliminates “gradient conflict” in correct responses
- Scalability
- Works for “Zero-RL” (direct pretrained model tuning) and distilled backbones
- 32.5% accuracy on Qwen2.5-3B—outperforming GRPO by 1.2%
Implement KDRL: Your 4-Step Blueprint
Deploy model using Huawei’s VeRL framework with these optimizations:
# Pseudo-code for KDRL joint loss (PyTorch-style)
def kdrl_loss(policy_logits, teacher_logits, advantages):
# 1. Compute k2 KL approximation
rkl = 0.5 * (log(teacher_probs) - log(policy_probs))**2
# 2. Anneal KL coefficient (β from 5e-3 → 1e-3)
beta = max(5e-3 - 5e-5 * step, 1e-3)
# 3. Reward-guided masking
mask = (rewards == 0).float() # Suppress KD on correct responses
masked_rkl = rkl * mask
# 4. Combine with GRPO objective
return grpo_loss - beta * masked_rkl.mean()
Critical Hyperparameters
| Parameter | Value | Effect |
|---|---|---|
| KL scheduler (β) | 5e⁻³ → 1e⁻³ | Balances imitation/reward phases |
| Rollouts per prompt | 16 | Optimal exploration-compute balance |
| Top-K tokens | 50 | Prevents memory overflow in KL calc |
If you’re Interested in Vehicle Routing, you may also find this article helpful: MTL-KD: 5 Breakthroughs That Shatter Old Limits in AI Vehicle Routing (But Reveal New Challenges)
The Future of Reasoning LLMs Starts Here
KDRL isn’t just incremental—it’s a paradigm shift. By fusing teacher wisdom with environment rewards, it solves the “generalization-efficiency paradox” plaguing LLMs. As Huawei’s team confirms:
“KDRL enables smaller models (1.5B) to achieve 80% of 7B teacher performance—democratizing high-level reasoning.”
Ready to deploy?
➔ Download our KDRL implementation kit (VeRL scripts + difficulty-balanced datasets)
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Free Resource: Get the PDF: “5 KDRL Tweaks for 90% Faster LLM Training”
Transform your LLM from a memorizing machine to a reasoning powerhouse—today.
Here’s the complete PyTorch implementation of KDRL based on the research paper. This code integrates knowledge distillation (KD) with reinforcement learning (RL) using the GRPO algorithm and reverse KL divergence:
import torch
import torch.nn as nn
import torch.nn.functional as F
from transformers import AutoModelForCausalLM, AutoTokenizer
from collections import deque
import numpy as np
class KDRL:
def __init__(self, student_model, teacher_model, kl_coef_init=5e-3, kl_coef_min=1e-3,
kl_annealing_rate=5e-5, gamma=0.99, top_k=50):
"""
KDRL: Unified Knowledge Distillation and Reinforcement Learning
Args:
student_model: Pretrained student model (to be optimized)
teacher_model: Frozen teacher model for knowledge distillation
kl_coef_init: Initial KL coefficient (β)
kl_coef_min: Minimum KL coefficient after annealing
kl_annealing_rate: Linear decay rate for KL coefficient
gamma: Discount factor for reward calculation
top_k: Top-K tokens for KL approximation
"""
self.student = student_model
self.teacher = teacher_model
self.kl_coef = kl_coef_init
self.kl_init = kl_coef_init
self.kl_min = kl_coef_min
self.kl_annealing_rate = kl_annealing_rate
self.gamma = gamma
self.top_k = top_k
# Freeze teacher model
for param in self.teacher.parameters():
param.requires_grad = False
def anneal_kl_coef(self, step):
"""Linearly anneal KL coefficient"""
self.kl_coef = max(self.kl_init - self.kl_annealing_rate * step, self.kl_min)
def k2_kl_approximation(self, student_logits, teacher_logits, mask):
"""
Compute k2 KL divergence approximation
Args:
student_logits: [batch_size, seq_len, vocab_size]
teacher_logits: [batch_size, seq_len, vocab_size]
mask: [batch_size, seq_len] (1 for valid tokens, 0 for padding)
Returns:
kl_loss: Scalar tensor
"""
# Apply top-K filtering to teacher logits
topk_values, topk_indices = torch.topk(teacher_logits, self.top_k, dim=-1)
filtered_teacher_logits = torch.full_like(teacher_logits, -float('inf'))
filtered_teacher_logits.scatter_(-1, topk_indices, topk_values)
# Compute probabilities
student_probs = F.softmax(student_logits, dim=-1)
teacher_probs = F.softmax(filtered_teacher_logits, dim=-1)
# Calculate reverse KL using k2 approximation
log_ratio = torch.log(teacher_probs + 1e-8) - torch.log(student_probs + 1e-8)
kl_div = 0.5 * (log_ratio ** 2)
# Apply mask and average
kl_loss = (kl_div * mask.unsqueeze(-1)).sum() / mask.sum()
return kl_loss
def compute_advantage(self, rewards, values):
"""
Compute generalized advantage estimation (GAE)
Args:
rewards: [batch_size, seq_len]
values: [batch_size, seq_len]
Returns:
advantages: [batch_size, seq_len]
"""
advantages = torch.zeros_like(rewards)
last_advantage = 0
# Calculate advantages in reverse
for t in reversed(range(rewards.size(1))):
delta = rewards[:, t] + self.gamma * values[:, t+1] - values[:, t]
advantages[:, t] = last_advantage = delta + self.gamma * last_advantage
# Normalize advantages
advantages = (advantages - advantages.mean()) / (advantages.std() + 1e-8)
return advantages
def reward_guided_masking(self, kl_loss, rewards, response_level=True):
"""
Apply reward-guided masking to KL loss
Args:
kl_loss: Original KL loss tensor
rewards: Reward values for each response
response_level: True for response-level masking, False for group-level
Returns:
masked_kl_loss: Masked KL loss
"""
if response_level:
# Response-level masking: Suppress KL for successful responses
mask = (rewards == 0).float()
return kl_loss * mask.unsqueeze(-1)
else:
# Group-level masking: Suppress if any response in group succeeds
group_mask = (rewards.mean(dim=0) == 0).float()
return kl_loss * group_mask.unsqueeze(-1).unsqueeze(-1)
def grpo_loss(self, student_logits, old_logits, actions, advantages, mask):
"""
Compute Group Relative Policy Optimization (GRPO) loss
Args:
student_logits: Current model logits [batch, seq, vocab]
old_logits: Old model logits [batch, seq, vocab]
actions: Selected token indices [batch, seq]
advantages: Computed advantages [batch, seq]
mask: Padding mask [batch, seq]
Returns:
policy_loss: GRPO loss value
"""
# Get log probabilities
student_log_probs = F.log_softmax(student_logits, dim=-1)
old_log_probs = F.log_softmax(old_logits, dim=-1).detach()
# Calculate importance ratio
action_log_probs = student_log_probs.gather(-1, actions.unsqueeze(-1)).squeeze(-1)
old_action_log_probs = old_log_probs.gather(-1, actions.unsqueeze(-1)).squeeze(-1)
ratio = torch.exp(action_log_probs - old_action_log_probs)
# Compute clipped policy loss
policy_loss = -torch.min(
ratio * advantages,
torch.clamp(ratio, 0.8, 1.2) * advantages
)
# Apply mask and average
return (policy_loss * mask).sum() / mask.sum()
def train_step(self, prompts, optimizer, step, response_level_mask=True):
"""
Perform single KDRL training step
Args:
prompts: Batch of input prompts
optimizer: Model optimizer
step: Current training step (for KL annealing)
response_level_mask: Type of reward masking
Returns:
total_loss: Combined KDRL loss
"""
# Generate rollouts with current policy
rollouts, old_logits, actions, masks = self.generate_rollouts(prompts)
# Compute rewards (format + correctness)
rewards = self.compute_rewards(rollouts)
# Get student and teacher logits
student_logits = self.student(prompts).logits
with torch.no_grad():
teacher_logits = self.teacher(prompts).logits
# Calculate KL divergence with k2 approximation
kl_loss = self.k2_kl_approximation(student_logits, teacher_logits, masks)
# Apply reward-guided masking
masked_kl_loss = self.reward_guided_masking(kl_loss, rewards, response_level_mask)
# Estimate value function (simplified)
values = torch.ones_like(rewards) * rewards.mean() # Placeholder
# Compute advantages
advantages = self.compute_advantage(rewards.unsqueeze(0), values.unsqueeze(0))
# Calculate GRPO policy loss
policy_loss = self.grpo_loss(
student_logits,
old_logits,
actions,
advantages,
masks
)
# Anneal KL coefficient
self.anneal_kl_coef(step)
# Combine losses: J_KDRL = J_GRPO - β * D_KL
total_loss = policy_loss - self.kl_coef * masked_kl_loss
# Optimization step
optimizer.zero_grad()
total_loss.backward()
optimizer.step()
return total_loss.item()
# Helper functions would be implemented below:
# - generate_rollouts()
# - compute_rewards()
# - format_checker()
# - answer_verifier() def generate_rollouts(self, prompts, num_rollouts=16, max_length=2048):
"""
Generate on-policy rollouts with current student model
Args:
prompts: Batch of input prompts [batch, seq]
num_rollouts: Responses per prompt
max_length: Maximum response length
Returns:
rollouts: Generated responses
old_logits: Logits from generation
actions: Selected token indices
masks: Attention masks
"""
self.student.eval()
rollouts = []
all_logits = []
all_actions = []
all_masks = []
with torch.no_grad():
for prompt in prompts:
# Repeat prompt for multiple rollouts
repeated_prompt = prompt.repeat(num_rollouts, 1)
# Generate responses
outputs = self.student.generate(
repeated_prompt,
max_length=max_length,
do_sample=True,
top_k=50,
output_scores=True,
return_dict_in_generate=True
)
# Store results
rollouts.append(outputs.sequences)
all_logits.append(torch.stack(outputs.scores, dim=1))
all_actions.append(outputs.sequences[:, prompt.size(-1):])
# Create masks
mask = torch.ones_like(outputs.sequences)
mask[outputs.sequences == self.tokenizer.pad_token_id] = 0
all_masks.append(mask)
self.student.train()
return (
torch.cat(rollouts),
torch.cat(all_logits),
torch.cat(all_actions),
torch.cat(all_masks)
) def generate_rollouts(self, prompts, num_rollouts=16, max_length=2048):
"""
Generate on-policy rollouts with current student model
Args:
prompts: Batch of input prompts [batch, seq]
num_rollouts: Responses per prompt
max_length: Maximum response length
Returns:
rollouts: Generated responses
old_logits: Logits from generation
actions: Selected token indices
masks: Attention masks
"""
self.student.eval()
rollouts = []
all_logits = []
all_actions = []
all_masks = []
with torch.no_grad():
for prompt in prompts:
# Repeat prompt for multiple rollouts
repeated_prompt = prompt.repeat(num_rollouts, 1)
# Generate responses
outputs = self.student.generate(
repeated_prompt,
max_length=max_length,
do_sample=True,
top_k=50,
output_scores=True,
return_dict_in_generate=True
)
# Store results
rollouts.append(outputs.sequences)
all_logits.append(torch.stack(outputs.scores, dim=1))
all_actions.append(outputs.sequences[:, prompt.size(-1):])
# Create masks
mask = torch.ones_like(outputs.sequences)
mask[outputs.sequences == self.tokenizer.pad_token_id] = 0
all_masks.append(mask)
self.student.train()
return (
torch.cat(rollouts),
torch.cat(all_logits),
torch.cat(all_actions),
torch.cat(all_masks)
) def compute_rewards(self, rollouts):
"""
Compute binary rewards (format + correctness)
Args:
rollouts: Generated responses
Returns:
rewards: Tensor of rewards [batch_size]
"""
rewards = []
for response in rollouts:
text = self.tokenizer.decode(response, skip_special_tokens=True)
# Format checking
format_ok = self.format_checker(text)
# Answer verification
answer_correct = self.answer_verifier(text)
# Combined binary reward
rewards.append(1.0 if format_ok and answer_correct else 0.0)
return torch.tensor(rewards, device=self.student.device)
def format_checker(self, text):
"""Check response format validity"""
return "<think>" in text and "</think>" in text and "\\boxed" in text
def answer_verifier(self, text):
"""Verify answer correctness (simplified)"""
# In practice, integrate with math_verify library
return "CORRECT" in text # Placeholder logic# Training Loop Integration
student = AutoModelForCausalLM.from_pretrained("DeepSeek/R1-Distill-Qwen-1.5B")
teacher = AutoModelForCausalLM.from_pretrained("Skywork/Skywork-OR1-Math-7B")
tokenizer = AutoTokenizer.from_pretrained("DeepSeek/R1-Distill-Qwen-1.5B")
# Initialize KDRL trainer
kdrl = KDRL(
student_model=student,
teacher_model=teacher,
kl_coef_init=5e-3,
kl_coef_min=1e-3,
kl_annealing_rate=5e-5
)
# Initialize optimizer
optimizer = torch.optim.AdamW(student.parameters(), lr=1e-6)
# Training loop
for step, batch in enumerate(dataloader):
prompts = tokenizer(batch["questions"], return_tensors="pt", padding=True).input_ids
loss = kdrl.train_step(
prompts=prompts,
optimizer=optimizer,
step=step,
response_level_mask=True
)
# Logging and checkpointing
if step % 50 == 0:
print(f"Step {step}: Loss={loss:.4f}, KL Coef={kdrl.kl_coef:.6f}")
if step % 1000 == 0:
torch.save(student.state_dict(), f"kdrl_checkpoint_step{step}.pt")# Top-K filtering implementation
topk_values, topk_indices = torch.topk(teacher_logits, self.top_k, dim=-1)
filtered_teacher_logits = torch.full_like(teacher_logits, -float('inf'))
filtered_teacher_logits.scatter_(-1, topk_indices, topk_values)
# Response-level masking
mask = (rewards == 0).float()
return kl_loss * mask.unsqueeze(-1)
#Adaptive KL Annealing
self.kl_coef = max(self.kl_init - self.kl_annealing_rate * step, self.kl_min)# Usage instrunctions
student = AutoModelForCausalLM.from_pretrained("your-base-model")
teacher = AutoModelForCausalLM.from_pretrained("powerful-teacher-model")
kdrl = KDRL(
student_model=student,
teacher_model=teacher,
kl_coef_init=5e-3, # Initial KL weight
kl_coef_min=1e-3, # Minimum KL weight
kl_annealing_rate=5e-5, # Annealing rate
top_k=50 # Top-K for KL approx
)
for step, batch in enumerate(dataloader):
loss = kdrl.train_step(
prompts=batch["inputs"],
optimizer=optimizer,
step=step,
response_level_mask=True
)References
Xu et al. (2025). KDRL: Post-Training Reasoning LLMs via Unified KD and RL. arXiv:2506.02208
Agarwal, R. et al. (2024). On-Policy Distillation of Language Models. ICLR
Guo, D. et al. (2025). DeepSeek-R1: Boosting Reasoning via RL. arXiv:2501.12948