EnzymeAD For JAX: Automatic Differentiation Support
Enzyme is a powerful automatic differentiation (AD) tool that has garnered significant attention for its ability to efficiently compute derivatives of programs. A user recently inquired about the possibility of extending Enzyme's capabilities to JAX code, specifically to derive Vector-Jacobian Products (VJPs) and Jacobian-Vector Products (JVPs). This article delves into the potential of using Enzyme with JAX, exploring the benefits, challenges, and possible implementation strategies.
The Power of EnzymeAD with JAX
The core question revolves around whether Enzyme can be leveraged to automatically derive VJPs and JVPs of JAX functions, rather than being limited to C++ code. This is particularly relevant in scenarios where reverse-mode AD, the traditional approach, may exhibit suboptimal performance. A key area where Enzyme shines is in optimizing functions composed of numerous small operations. In such cases, reverse-mode AD can become inefficient due to the need to propagate derivatives through each intermediate node in the computational graph, requiring at least one read and write operation per node.
To illustrate this point, consider a scenario where a hand-derived VJP results in a performance speedup of over 2x compared to the standard reverse-mode AD. This highlights the potential benefits of using Enzyme to automatically generate custom JVPs/VJPs for arbitrary JAX code, especially when standard reverse-mode AD leads to slow execution. Enzyme's ability to directly analyze and differentiate code at the LLVM IR level offers a unique advantage. It can identify and eliminate unnecessary memory accesses and operations, resulting in highly optimized derivative computations. This is especially crucial for complex JAX functions where manual derivation of VJPs and JVPs can be a time-consuming and error-prone task.
Addressing Performance Bottlenecks with Enzyme
The primary motivation behind exploring Enzyme's integration with JAX stems from addressing performance bottlenecks associated with reverse-mode AD in certain situations. Reverse-mode AD, while widely used, can suffer from performance degradation when applied to functions comprising a multitude of small operations. This is because the process of propagating derivatives backward through the computational graph necessitates storing and retrieving intermediate values, leading to increased memory traffic and computational overhead. Enzyme offers a compelling alternative by enabling the automatic generation of custom VJPs and JVPs, tailored to the specific structure of the JAX code. This approach has the potential to significantly improve performance, particularly in scenarios where the computational graph exhibits complex dependencies or involves a large number of operations. By leveraging Enzyme's capabilities, developers can potentially achieve substantial speedups in their JAX code, enabling faster training of machine learning models and more efficient execution of numerical simulations.
Practical Example: Custom VJP for Performance Improvement
To demonstrate the potential performance gains, a practical example is provided, comparing a standard JAX function with a custom VJP implementation. The function f_standard(x, a) calculates (sin(a * x) ** 2) / a, while f_custom(x, a) represents the same function but with a custom-defined VJP. The custom VJP, f_custom_bwd, is hand-derived and optimized for performance. A benchmarking function, bench, is used to measure the execution time of both the standard and custom VJP implementations. The results clearly show that the custom VJP achieves a significant speedup compared to the standard reverse-mode AD, especially for larger input sizes. For instance, with an input size of (32, 16384, 64), the custom VJP exhibits a 2.25x speedup over the standard approach. This example underscores the potential of using Enzyme to automatically derive such custom VJPs for JAX code, enabling substantial performance improvements in computationally intensive tasks.
import time
import jax
import jax.numpy as jnp
from jax import custom_vjp
def f_standard(x, a):
return jnp.sin(a * x) ** 2 / a
@custom_vjp
def f_custom(x, a):
return jnp.sin(a * x) ** 2 / a
def f_custom_bwd(res, g):
x, a = res
ax = a * x
sin_ax = jnp.sin(ax)
sin_2ax = jnp.sin(2 * ax)
grad_x = g * sin_2ax
grad_a_local = g * (ax * sin_2ax - sin_ax**2) / (a**2)
grad_a = grad_a_local.sum(axis=tuple(range(grad_a_local.ndim - 1)))
return grad_x, grad_a
f_custom.defvjp(lambda x, a: (f_custom(x, a), (x, a)), f_custom_bwd)
def bench(fn, x, a, n=100):
@jax.jit
def vjp_fn(x, a, g):
_, vjp = jax.vjp(fn, x, a)
return vjp(g)
g = jnp.ones_like(x)
for _ in range(10):
vjp_fn(x, a, g)[0].block_until_ready()
start = time.perf_counter()
for _ in range(n):
vjp_fn(x, a, g)[0].block_until_ready()
return (time.perf_counter() - start) / n * 1000
key = jax.random.PRNGKey(0)
B, C = 32, 64
x = jax.random.normal(key, (B, 512, C))
a = jax.random.uniform(key, (C,), minval=0.5, maxval=2.0)
print(jax.jit(f_standard).lower(x, a).as_text())
print(f"{(B,T,C):<20} {'Std (ms)':>10} {'Cust (ms)':>10} {'Speedup':>10}")
for T in [512, 1024, 2048, 4096, 8192, 16384]:
x = jax.random.normal(key, (B, T, C))
a = jax.random.uniform(key, (C,), minval=0.5, maxval=2.0)
t_std = bench(f_standard, x, a)
t_cst = bench(f_custom, x, a)
print(f"{str((B, T, C)):<20} {t_std:>10.3f} {t_cst:>10.3f} {t_std / t_cst:>9.2f}x")
module @jit_f_standard attributes {mhlo.num_partitions = 1 : i32, mhlo.num_replicas = 1 : i32} {
func.func public @main(%arg0: tensor<32x512x64xf32>, %arg1: tensor<64xf32>) -> (tensor<32x512x64xf32> {jax.result_info = "result"}) {
%0 = stablehlo.broadcast_in_dim %arg1, dims = [2] : (tensor<64xf32>) -> tensor<1x1x64xf32>
%1 = stablehlo.broadcast_in_dim %0, dims = [0, 1, 2] : (tensor<1x1x64xf32>) -> tensor<32x512x64xf32>
%2 = stablehlo.multiply %1, %arg0 : tensor<32x512x64xf32>
%3 = stablehlo.sine %2 : tensor<32x512x64xf32>
%4 = stablehlo.multiply %3, %3 : tensor<32x512x64xf32>
%5 = stablehlo.broadcast_in_dim %arg1, dims = [2] : (tensor<64xf32>) -> tensor<1x1x64xf32>
%6 = stablehlo.broadcast_in_dim %5, dims = [0, 1, 2] : (tensor<1x1x64xf32>) -> tensor<32x512x64xf32>
%7 = stablehlo.divide %4, %6 : tensor<32x512x64xf32>
return %7 : tensor<32x512x64xf32>
}
}
(B,T,C) Std (ms) Cust (ms) Speedup
(32, 512, 64) 0.076 0.060 1.27x
(32, 1024, 64) 0.077 0.061 1.25x
(32, 2048, 64) 0.123 0.085 1.46x
(32, 4096, 64) 0.622 0.299 2.08x
(32, 8192, 64) 1.184 0.543 2.18x
(32, 16384, 64) 2.293 1.021 2.25x
StableHLO MLIR and Enzyme Integration
The user's inquiry touches upon the technical feasibility of integrating Enzyme with JAX. JAX, being a powerful framework for numerical computation, compiles functions into StableHLO MLIR (Multi-Level Intermediate Representation). This MLIR representation serves as a crucial bridge for Enzyme integration. The user correctly points out that the necessary components for this integration might already be in place, given Enzyme's ability to operate on LLVM IR and the straightforward process of obtaining StableHLO MLIR from compiled JAX functions. Enzyme works by analyzing the program's intermediate representation (IR), identifying differentiable operations, and generating code for the derivatives. By leveraging the StableHLO MLIR from JAX, Enzyme can potentially apply its AD capabilities to JAX functions, enabling automatic derivation of VJPs and JVPs.
Exploring the API and Future Plans
The discussion raises the question of whether an API for this functionality is planned or if the developers would be interested in adding it. This is a crucial point for the JAX and Enzyme communities. An API that allows seamless integration between JAX and Enzyme would open up new avenues for performance optimization and automatic differentiation in JAX-based projects. Such an API could potentially provide a way to specify JAX functions for Enzyme to differentiate, control the differentiation process, and retrieve the generated VJPs and JVPs. The development of such an API would require careful consideration of the design and implementation details, ensuring that it is both user-friendly and efficient. Furthermore, it would be beneficial to explore different approaches for integrating Enzyme with JAX, such as directly operating on StableHLO MLIR or leveraging JAX's existing custom derivative mechanisms.
Challenges and Future Directions
While the potential benefits of integrating Enzyme with JAX are significant, there are also challenges to consider. One challenge is the complexity of JAX's compilation pipeline and the intricacies of StableHLO MLIR. Enzyme needs to be able to effectively analyze and transform this representation to generate correct and efficient derivatives. Another challenge is the handling of JAX's functional programming paradigm, which may require specific adaptations in Enzyme's differentiation algorithms. Furthermore, the integration needs to be carefully designed to avoid introducing overhead or compatibility issues. Despite these challenges, the potential rewards of integrating Enzyme with JAX are substantial. It could lead to significant performance improvements in JAX code, enable new applications of automatic differentiation, and foster closer collaboration between the JAX and Enzyme communities. Future research could focus on developing new differentiation techniques tailored to JAX's specific features and exploring the use of Enzyme for higher-order differentiation and other advanced AD tasks.
Conclusion
The prospect of using Enzyme for automatic differentiation of JAX code is an exciting one. The ability to automatically derive custom VJPs and JVPs for JAX functions could lead to significant performance improvements, particularly in scenarios where reverse-mode AD falls short. While there are technical challenges to overcome, the potential benefits of this integration make it a worthwhile endeavor. The development of an API for Enzyme-JAX integration would be a major step forward, enabling developers to leverage the power of Enzyme in their JAX projects.
For more information on automatic differentiation, you can visit the EnzymeAD Project Website. 🚀
