Knowledge Distillation: Compressing LLMs

When to Use This Skill

Use Knowledge Distillation when you need to:

• Compress models from 70B → 7B while retaining 90%+ performance
• Transfer capabilities from proprietary models (GPT-4) to open-source (LLaMA, Mistral)
• Reduce inference costs by deploying smaller student models
• Create specialized models by distilling domain-specific knowledge
• Improve small models using synthetic data from large teachers

Key Techniques: Temperature scaling, soft targets, reverse KLD (MiniLLM), logit distillation, response distillation

Papers: Hinton et al. 2015 (arXiv 1503.02531), MiniLLM (arXiv 2306.08543), KD Survey (arXiv 2402.13116)

Installation

# Standard transformers
pip install transformers datasets accelerate

# For training
pip install torch deepspeed wandb

# Optional: MiniLLM implementation
git clone https://github.com/microsoft/LMOps
cd LMOps/minillm
pip install -e .

Quick Start

Basic Knowledge Distillation

import torch
import torch.nn.functional as F
from transformers import AutoModelForCausalLM, AutoTokenizer, Trainer, TrainingArguments

# 1. Load teacher (large) and student (small) models
teacher = AutoModelForCausalLM.from_pretrained(
    "meta-llama/Llama-2-70b-hf",  # Large teacher
    torch_dtype=torch.float16,
    device_map="auto"
)

student = AutoModelForCausalLM.from_pretrained(
    "meta-llama/Llama-2-7b-hf",  # Small student
    torch_dtype=torch.float16,
    device_map="cuda:0"
)

tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-70b-hf")

# 2. Define distillation loss
def distillation_loss(student_logits, teacher_logits, labels, temperature=2.0, alpha=0.5):
    """
    Combine hard loss (cross-entropy) with soft loss (KL divergence).

    Args:
        temperature: Softens probability distributions (higher = softer)
        alpha: Weight for distillation loss (1-alpha for hard loss)
    """
    # Hard loss: Standard cross-entropy with true labels
    hard_loss = F.cross_entropy(student_logits.view(-1, student_logits.size(-1)), labels.view(-1))

    # Soft loss: KL divergence between student and teacher
    soft_targets = F.softmax(teacher_logits / temperature, dim=-1)
    soft_student = F.log_softmax(student_logits / temperature, dim=-1)
    soft_loss = F.kl_div(soft_student, soft_targets, reduction='batchmean') * (temperature ** 2)

    # Combined loss
    return alpha * soft_loss + (1 - alpha) * hard_loss

# 3. Training loop
for batch in dataloader:
    # Teacher forward (no grad)
    with torch.no_grad():
        teacher_outputs = teacher(**batch)
        teacher_logits = teacher_outputs.logits

    # Student forward
    student_outputs = student(**batch)
    student_logits = student_outputs.logits

    # Compute distillation loss
    loss = distillation_loss(
        student_logits,
        teacher_logits,
        batch['labels'],
        temperature=2.0,
        alpha=0.7  # 70% soft, 30% hard
    )

    # Backward and optimize
    loss.backward()
    optimizer.step()
    optimizer.zero_grad()

MiniLLM (Reverse KLD)

Source: arXiv 2306.08543 (2024)

Innovation: Use reverse KLD instead of forward KLD for better generative model distillation.

def reverse_kl_loss(student_logits, teacher_logits, temperature=1.0):
    """
    Reverse KL divergence: KL(Teacher || Student)
    Better for generative models than forward KL.
    """
    # Teacher distribution (target)
    p_teacher = F.softmax(teacher_logits / temperature, dim=-1)

    # Student distribution (model)
    log_p_student = F.log_softmax(student_logits / temperature, dim=-1)

    # Reverse KL: Sum over teacher, student learns to cover teacher's modes
    reverse_kl = -(p_teacher * log_p_student).sum(dim=-1).mean()

    return reverse_kl * (temperature ** 2)

# Training with MiniLLM
for batch in dataloader:
    with torch.no_grad():
        teacher_logits = teacher(**batch).logits

    student_logits = student(**batch).logits

    # Reverse KLD (better for generation)
    loss = reverse_kl_loss(student_logits, teacher_logits, temperature=1.0)

    loss.backward()
    optimizer.step()

Why reverse KL?

• Forward KL (standard): Student learns to match teacher's mean
• Reverse KL (MiniLLM): Student learns to cover all teacher's modes
• Better for diverse text generation

Response Distillation

# Generate synthetic data from teacher, train student to imitate

# 1. Generate synthetic responses from teacher
prompts = ["Explain AI:", "What is ML?", "Define NLP:"]

teacher_responses = []
for prompt in prompts:
    inputs = tokenizer(prompt, return_tensors='pt').to(teacher.device)
    outputs = teacher.generate(**inputs, max_new_tokens=256, do_sample=True, temperature=0.7)
    response = tokenizer.decode(outputs[0], skip_special_tokens=True)
    teacher_responses.append(response)

# 2. Train student on teacher's responses (standard fine-tuning)
train_dataset = [
    {"text": f"{prompt}\n{response}"}
    for prompt, response in zip(prompts, teacher_responses)
]

# 3. Fine-tune student
trainer = Trainer(
    model=student,
    args=TrainingArguments(output_dir="./student", num_train_epochs=3, learning_rate=2e-5),
    train_dataset=train_dataset,
)
trainer.train()

Core Concepts

1. Temperature Scaling

Purpose: Soften probability distributions to expose teacher's uncertainty.

# Low temperature (T=1): Sharp distribution
logits = [3.0, 2.0, 1.0]
probs_T1 = softmax(logits / 1.0)  # [0.67, 0.24, 0.09]

# High temperature (T=4): Soft distribution
probs_T4 = softmax(logits / 4.0)  # [0.42, 0.34, 0.24]

# Higher T reveals more information about relative rankings

Rule: Use T=2-5 for distillation (2 is common default).

2. Loss Function Components

# Total loss = alpha * soft_loss + (1 - alpha) * hard_loss

# Soft loss: Learn from teacher's knowledge
soft_loss = KL(student || teacher)

# Hard loss: Learn from ground truth labels
hard_loss = CrossEntropy(student_output, true_labels)

# Typical values:
alpha = 0.5  # Balanced
alpha = 0.7  # More emphasis on teacher
alpha = 0.3  # More emphasis on labels

3. Forward vs Reverse KLD

# Forward KL: KL(Student || Teacher)
# - Student matches teacher's average behavior
# - Mode-seeking: Student focuses on teacher's highest probability modes
# - Good for classification

# Reverse KL: KL(Teacher || Student)
# - Student covers all of teacher's behaviors
# - Mode-covering: Student learns diverse behaviors
# - Good for generation (MiniLLM)

Training Strategies

Strategy 1: Logit Distillation

# Train student to match teacher's logits directly

def logit_distillation_trainer(student, teacher, dataloader, temperature=2.0):
    optimizer = torch.optim.AdamW(student.parameters(), lr=2e-5)

    for epoch in range(3):
        for batch in dataloader:
            # Get logits
            with torch.no_grad():
                teacher_logits = teacher(**batch).logits

            student_logits = student(**batch).logits

            # MSE on logits (alternative to KLD)
            loss = F.mse_loss(student_logits, teacher_logits)

            # Or use KLD
            # loss = F.kl_div(
            #     F.log_softmax(student_logits/temperature, dim=-1),
            #     F.softmax(teacher_logits/temperature, dim=-1),
            #     reduction='batchmean'
            # ) * (temperature ** 2)

            loss.backward()
            optimizer.step()
            optimizer.zero_grad()

    return student

Strategy 2: Two-Stage Distillation

# Stage 1: Distill from teacher
student = distill(teacher, student, epochs=5)

# Stage 2: Fine-tune on task-specific data
student = fine_tune(student, task_data, epochs=3)

# Results in better task performance than single-stage

Strategy 3: Multi-Teacher Distillation

# Learn from multiple expert teachers

def multi_teacher_dist