numpy.einsum的优化方案是什么？优化方向与optimize选项疑问

Great question! Let's unpack how einsum optimization works, what it focuses on, and demystify that optimize parameter you're curious about.

What Does the Optimization Target? #

First off, it’s designed to tackle two big pain points of unoptimized einsum:

• Memory consumption: Unoptimized einsum often creates unnecessary intermediate arrays when computing complex sums, which can eat up RAM quickly for large tensors.
• CPU performance: The naive implementation of Einstein summation doesn’t leverage highly optimized linear algebra routines (like BLAS/LAPACK under the hood). Optimization rewrites operations to use these fast, low-level tools.

Specific Optimization Schemes #

The core idea is to rewrite your einsum expression into a sequence of more efficient NumPy operations, rather than executing the raw summation step-by-step. Here’s how it does that:

• Eliminate intermediate arrays: Instead of computing partial sums and storing them as separate arrays, the optimizer combines operations to compute the final result directly. For example, a sum that would normally create 2-3 intermediate tensors can be done in one pass.
• Leverage optimized linear algebra: When possible, the optimizer converts einsum operations into calls to matmul, dot, or tensordot—these functions use hand-tuned BLAS/LAPACK routines that are way faster than naive summation on CPU.
• Reorder operations for minimal computation: For multi-dimensional sums with multiple indices, the optimizer calculates the cheapest order to perform summations. For example, summing over a small dimension first reduces the size of the tensor for subsequent operations, cutting down total CPU cycles.

Decoding the optimize Parameter #

This parameter controls how aggressive (and how computationally expensive) the optimization is. Here are the main options you’ll encounter:

• optimize=False: Turns off all optimization. Useful for debugging, or for very simple sums where the overhead of optimization isn’t worth it.
• optimize=True: Enables the default optimization (in recent NumPy versions, this maps to the 'greedy' strategy). It’s a good middle ground for most use cases.
• optimize='greedy': Uses a fast greedy algorithm to find a reasonably efficient operation path. It doesn’t check every possible combination, so it’s quick to compute the optimized plan.
• optimize='optimal': Uses dynamic programming to find the globally optimal operation order. This is great for complex, multi-index sums, but note that calculating the optimal path has a small computational cost upfront.
• You can also pass a custom path (generated via np.einsum_path) to manually specify exactly how you want the operations to be reordered.

As a quick example: If you run np.einsum('ij,jk->ik', a, b) with optimization enabled, it will directly call np.matmul(a, b) under the hood—way faster and more memory-efficient than the naive einsum implementation.

内容的提问来源于stack exchange，提问作者Stéphane