Puzzle 20: Kernel Fusion and Custom Backward Pass

Kernel fusion and autograd integration

We’re continuing Part IV with a focus on kernel fusion and autograd integration.

Building on Puzzle 19, you’ll now explore how to combine multiple operations into a single efficient kernel and integrate it with PyTorch’s autograd system. You’ll learn:

  • How kernel fusion improves performance in both forward and backward passes
  • Why custom backward passes are crucial for fused operations
  • How to design fused kernels with proper gradient flow
  • The performance implications of different fusion strategies

This puzzle demonstrates that how you combine operations can be as important as how you implement them.

Overview

In this puzzle, you’ll implement fused LayerNorm + Linear operations with both forward and backward passes. While both fused and unfused implementations produce identical results, they use different strategies that lead to significant performance differences.

You’ll compare:

  • Unfused approach: Separate kernels for LayerNorm and Linear
  • Fused kernel: Combined operation in a single kernel
  • Custom backward pass: Gradient computation for fused operations

This comparison teaches the critical importance of kernel fusion and proper gradient computation in deep learning operations.

Background: LayerNorm + Linear operations

LayerNorm and Linear are fundamental operations in transformer architectures, particularly in attention mechanisms and feed-forward networks. Here’s how they’re typically used:

import torch
import torch.nn.functional as F

# Input: hidden states
x = torch.randn(batch_size, seq_len, hidden_dim)

# LayerNorm parameters
ln_weight = torch.ones(hidden_dim)  # scale parameter (γ)
ln_bias = torch.zeros(hidden_dim)   # shift parameter (β)

# Linear layer parameters
linear_weight = torch.randn(output_dim, hidden_dim)
linear_bias = torch.zeros(output_dim)

# Unfused operations (with autograd)
ln_output = F.layer_norm(x, [hidden_dim], weight=ln_weight, bias=ln_bias)
output = F.linear(ln_output, linear_weight, linear_bias)

# Fused operation (custom implementation)
# This is what you'll implement in this puzzle
output_fused = fused_layernorm_linear(x, ln_weight, ln_bias, linear_weight, linear_bias)

When fused, these operations are combined into a single efficient kernel that:

  • Reduces memory bandwidth usage
  • Minimizes kernel launch overhead
  • Improves cache utilization
  • Eliminates intermediate allocations

In practice, this fusion can provide up to 1.5-2x speedup in both forward and backward passes, which is crucial for transformer training efficiency.

Why custom backward passes matter

PyTorch’s autograd system automatically computes gradients for individual operations, but fused operations require custom backward passes to:

  • Maintain numerical stability
  • Ensure proper gradient flow
  • Optimize memory access patterns
  • Handle atomic operations for gradient accumulation

Learning path

This puzzle is structured in two parts to build your understanding systematically:

Forward pass implementation

Start here to implement the fused forward kernel and understand kernel fusion benefits.

What you’ll do:

  • Implement both unfused and fused forward kernels
  • Learn fundamental kernel fusion techniques
  • See the same operations implemented with different strategies
  • Understand performance implications of fusion
  • Master memory access patterns for optimal performance

Backward pass implementation

Deep dive into autograd integration and gradient computation.

What you’ll learn:

  • How to implement custom backward passes
  • Why proper gradient flow is crucial
  • Real-world implications for training efficiency
  • Optimization strategies for backward operations
  • Mathematical foundations of gradient computation
  • Atomic operations for gradient accumulation
  • Numerical stability in backward passes

Getting started

Ready to explore kernel fusion and autograd integration? Start with the Forward pass implementation to implement the fused kernel, then move to Backward pass implementation to understand gradient computation.

The puzzle includes a comprehensive testing framework that verifies:

  • Numerical correctness against PyTorch’s implementation for both forward and backward passes
  • Performance comparison between our CPU and GPU implementations
  • Gradient computation accuracy for all parameters (input, LayerNorm weights/bias, Linear weights/bias)
  • Memory usage optimization through kernel fusion

💡 Success tip: Pay attention to how the different implementations (fused vs unfused) affect both forward and backward pass performance - this insight applies to many deep learning operations beyond LayerNorm + Linear. The backward pass implementation is particularly important as it directly impacts training efficiency and numerical stability.