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The Limited Multi-Label Projection Layer

This repository is by Brandon Amos, Vladlen Koltun, and J. Zico Kolter and contains the PyTorch library and source code to reproduce the experiments in our tech report on The Limited Multi-Label Projection Layer.

We provide the LML layer as a PyTorch module in You can install it with:

pip install git+git://

A simple usage example to project a 5-dimensional vector onto the LML polytope with two active elements is:

import torch
from lml import LML

x = 10.*torch.randn(5) # tensor([ -4.0695,  10.8666,  13.0867,  -7.1431, -14.7220])
y = LML(N=2)(x) # tensor([5.8745e-04, 9.9945e-01, 9.9994e-01, 2.7187e-05, 1.3897e-08]))

Top-k Image Classification

In the smooth-topk directory, we have connected the LML layer to the PyTorch experiments in the oval-group/smooth-topk repository. We ran these experiments with PyTorch 1.0.

A single LML training run can be done from the smooth-topk/src directory with

./ --dataset cifar100 --model densenet40-40 --out-name /tmp/lml-cifar --loss lml --noise 0.0 --seed 0 --no-visdom

Coordinating all of the CIFAR-100 experiments can be done with the ./scripts/cifar100_noise_*.sh scripts.

We have also added an option to use the NVIDIA/DALI library for pre-processing ImageNet images on the GPU, but DALI currently has known memory leaks that currently cause the experiments to crash and run out of memory.

Neural Motifs: Scene Graph Generation

In the neural-motifs directory, we have connected the LML layer to the PyTorch experiments in the rowanz/neural-motifs repository. The README in this directory provides more details about setting up and running the experiments. The original code has not been updated to the latest version of PyTorch and these experiments should be run with PyTorch 0.3.

A single LML training run can be done from the neural-motifs directory with

python3 models/ -m predcls -model motifnet -order leftright -nl_obj 2 -nl_edge 4 -b 6 -clip 5 -p 10 -hidden_dim 512 -pooling_dim 4096 -lr 1e-3 -ngpu 1 -ckpt checkpoints/vg-faster-rcnn.tar -save_dir /tmp/lml-nm -nepoch 50 -use_bias --lml_topk 20

Coordinating all of the experiments can be done with /scripts/

Licensing and Citations

Our LML layer in is licensed under the MIT license. All other code in this repository remains under the original licensing.

If you find this repository helpful in your publications, please consider citing our paper.

  title={{The Limited Multi-Label Projection Layer}},
  author={Brandon Amos and Vladlen Koltun and J. Zico Kolter},
  journal={arXiv preprint arXiv:1906.08707},