PyTorch Approx Top-k

Approximate algorithms for computing top-k faster on machine learning accelerators, by using bucketing to increase parallelism. Rather than computing a single top-k over the sequence:

1. split the sequence into $b$ interleaved buckets
2. take $k_b$ elements from each bucket
3. if $k_b \cdot b > k$: take a final top-k

You can get pretty nice speedups (e.g. several times) with little loss in recall! See our paper for detailed benchmarks and analysis of the cost/quality trade-off:

Approximate Top-k for Increased Parallelism; O Key, L Ribar, A Cattaneo, L Hudlass-Galley, D Orr

The implementation is quite fast, but we welcome any contributions from CUDA experts. In Figure 1, we compare against torch.argmax(), which is a reasonable upper-bound on how fast this kernel could be. There's still room for improvement!

Using the library

Requires: Python >3.10, PyTorch >=2.4, Ninja (ninja-build), CUDA toolkit matching your version of PyTorch

pip install git+https://github.com/graphcore-research/pytorch-approx-topk.git

Usage:

from approx_topk import topk as approx_topk
import torch

x = torch.randn(128, int(2**20), device="cuda")
values, indices = approx_topk(x, k=int(2**16), dim=-1, j=2, k_mult=1)

(the kernel is compiled on first use, which might take a while)

Note that, when comparing to the paper, j is $k_b$ and k_mult is $k_b \cdot b / k$.

Repository highlights

• approx_topk.priority_queue: main CUDA kernel supporting $k_b \in {1,2,4}$, implemented using a priority queue algorithm
• approx_topk.experimental.bucketed_argmax: implementations for $k_b=1$ only, using torch.argmax() and custom Triton kernels
• benchmarks.measure_speed: benchmarks speed of our implementation vs exact top-ks (Figure 1 in paper)
  • requires additional dependencies, see below
• notebooks: experimental results notebooks (theoretical performance analysis, figure plotting)

Reproducing benchmarks + development

To set up the environment, install the dependencies:

• CUDA toolkit 12.4
• Ninja (ninja-build)
• Python 3.11
• Python Poetry

Then run poetry install --with benchmarks

To make it easier to install the CUDA dependencies, we provide an Apptainer image recipe in environment.simg:

• Build: apptainer build environment.sif environment.simg
• Run:
  • apptainer exec --nv environment.sif python benchmarks/measure_speed.py
  • apptainer exec --nv environment.sif python benchmarks/plot_bandwidth.py

Code tools:

• Type checking: mypy --ignore-missing-imports -p approx_topk
• Formatting Python: ruff format **/*.py
• Formatting CUDA: clang-format -i **/*.cu

License

Copyright (c) 2024 Graphcore Ltd and Oscar Key. Licensed under the MIT License.