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McTorch, a manifold optimization library for deep learning

McTorch is a Python library that adds manifold optimization functionality to PyTorch.


  • Leverages tensor computation and GPU acceleration from PyTorch.
  • Enables optimization on manifold constrained tensors to address nonlinear optimization problems.
  • Facilitates constrained weight tensors in deep learning layers.


More about McTorch

McTorch builds on top of PyTorch and supports all PyTorch functions in addition to Manifold optimization. This is done to ensure researchers and developers using PyTorch can easily experiment with McTorch functions. McTorch's manifold implementations and optimization methods are derived from the Matlab toolbox Manopt and the Python toolbox Pymanopt.

Using McTorch for Optimization

  1. Initialize Parameter - McTorch manifold parameters are same as PyTorch parameters (torch.nn.Parameter) and requires just addition of one property to parameter initialization to constrain the parameter values.
  2. Define Cost - Cost function can be any PyTorch function using the above parameter mixed with non constrained parameters.
  3. Optimize - Any optimizer from torch.optim can be used to optimize the cost function using same functionality as any PyTorch code.

PCA Example

import torch
import torch.nn as nn

# Random data with high variance in first two dimension
X = torch.diag(torch.FloatTensor([3,2,1])).matmul(torch.randn(3,200))

# 1. Initialize Parameter
manifold_param = nn.Parameter(manifold=nn.Stiefel(3,2))

# 2. Define Cost - squared reconstruction error
def cost(X, w):
    wTX = torch.matmul(w.transpose(1,0), X)
    wwTX = torch.matmul(w, wTX)
    return torch.sum((X - wwTX)**2)

# 3. Optimize
optimizer = torch.optim.Adagrad(params = [manifold_param], lr=1e-2)

for epoch in range(30):
    cost_step = cost(X, manifold_param)

Using McTorch for Deep Learning

Multi Layer Perceptron Example

import torch
import torch.nn as nn
import torch.nn.functional as F

# a torch module using constrained linear layers
class ManifoldMLP(nn.Module):
    def __init__(self):
        super(ManifoldMLP, self).__init__()
        self.layer1 = nn.Linear(in_features=28*28, out_features=100, weight_manifold=nn.Stiefel)
        self.layer2 = nn.Linear(in_features=100, out_features=100, weight_manifold=nn.PositiveDefinite)
        self.output = nn.Linear(in_features=100, out_features=10, weight_manifold=nn.Stiefel)

    def forward(self, x):
        x = F.relu(self.layer1(x))
        x = F.relu(self.layer2(x))
        x = F.log_softmax(self.output(x), dim=0)
        return x

# create module object and compute cost by applying module on inputs
mlp_module = ManifoldMLP()
cost = mlp_module(inputs)

More examples added - here

Functionality Supported

This would be an ever increasing list of features. McTorch currently supports:


  • Stiefel
  • Positive Definite

All manifolds support k multiplier as well.


  • SGD
  • Adagrad
  • ConjugateGradient


  • Linear
  • Conv1d, Conv2d, Conv3d
  • Conv1d_transpose, Conv2d_transpose, Conv3d_transpose


This is same as PyTorch installation from source. I have tried the installation with Python 3.7 and it will be preferred version for installation.

If you are installing from source, we highly recommend installing an Anaconda environment.

  • Download anaconda installer from here - Anaconda and follow GUI steps to install
  • Create an environment, from anaconda console prompt: conda create -n myenv python=3.7
  • Activate the environment: source activate myenv
  • Install current release branch i.e. mctorch_1_5


source activate myenv
conda install numpy ninja pyyaml mkl mkl-include setuptools cmake cffi typing
# Add LAPACK support for the GPU if needed
conda install -c pytorch magma-cuda90 # or [magma-cuda80 | magma-cuda92 | magma-cuda100 ] depending on your cuda version
pip install git+git://

Mac OS

source activate myenv
conda install numpy ninja pyyaml mkl mkl-include setuptools cmake cffi typing
MACOSX_DEPLOYMENT_TARGET=10.9 CC=clang CXX=clang++ pip install git+git://

Installation FAQs

  1. ModuleNotFoundError: No module named 'torch._C': After installation when using McTorch make sure you have activate the conda environment and not in the same folder as McTorch as import torch tries to refer to the module in torch folder and throws an error.

For other os and optional dependencies go through Installation.

Release and Contribution

McTorch is currently under development and any contributions, suggestions and feature requests are welcome. We'd closely follow PyTorch stable versions to keep the base updated and will have our own versions for other additions.

McTorch is released under the open source 3-clause BSD License.



Please cite [1] if you found this code useful.

McTorch, a manifold optimization library for deep learning

[1] M. Meghawanshi, P. Jawanpuria, A. Kunchukuttan, H. Kasai, and B. Mishra, McTorch, a manifold optimization library for deep learning

  title={McTorch, a manifold optimization library for deep learning},
  author={Meghwanshi, Mayank and Jawanpuria, Pratik and Kunchukuttan, Anoop and Kasai, Hiroyuki and Mishra, Bamdev},
  institution={arXiv preprint arXiv:1810.01811},