NCET

NCET (Neural-network Constraint Embedding Toolkit) converts supported PyTorch neural networks into exact mixed-integer linear constraints. It preserves graph connectivity, including branches and residual/skip connections, rather than restricting models to sequential structures.

NCET is partly supported by Engineering and Physical Sciences Research Council grant number [EP/Y025946/1].

Documentation: https://xuwkk.github.io/ncet/

Declarations: Codex has been used to refine the codebase, generate the documentation and the pytest cases.

Installation

Install NCET from PyPI:

pip install ncet

For a local editable installation, run from the repository root:

pip install -e .

Quick start

This example exactly encodes a small residual network and maximizes its first output over a bounded input box:

import cvxpy as cp
import numpy as np
import torch
from torch import nn

from ncet import Bounds, form_milp

# Define a simple residual MLP
class ResidualMLP(nn.Module):
    def __init__(self) -> None:
        super().__init__()
        self.linear = nn.Linear(2, 2)
        with torch.no_grad():
            self.linear.weight.copy_(
                torch.tensor([[1.0, -1.0], [0.5, 1.0]])
            )
            self.linear.bias.copy_(torch.tensor([0.0, -0.25]))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return torch.relu(self.linear(x)) + x


model = ResidualMLP().eval()
# Define the bounds of the input. Bounds describe one sample; do not include a batch dimension.
bounds = Bounds(
    lower=np.array([-1.0, -1.0]),
    upper=np.array([1.0, 1.0]),
)

# Convert the model to a MILP encoding
encoding = form_milp(model, bounds, relu_binary_mode="reduced")

# Connect the encoding to a CVXPY problem
x = encoding.inputs["x"]
y = encoding.outputs[0]
problem = cp.Problem(cp.Maximize(y[0]), encoding.constraints)
problem.solve(solver=cp.SCIPY)

print(problem.status, problem.value)  # optimal 3.0
print(x.value)                        # [ 1. -1.]

See the complete form_milp() user interface for all arguments, accepted bound forms, return fields, and public exceptions.

Modeling scope

NCET captures static PyTorch FX graphs and normalizes the supported operations into a canonical graph intermediate representation (IR). The current operator set is Linear, Conv2d, BatchNorm1d/2d, AdaptiveAvgPool2d, AvgPool2d, MaxPool2d, ReLU, LeakyReLU, Add, Sub, fixed-constant Add/Sub/Mul/Div, Concat, Flatten, ReduceMean, Reshape/View/Squeeze/Unsqueeze, Permute, Transpose, Identity/evaluation-mode Dropout, and static GetItem/Slice. Graph-based interval bound propagation and the CVXPY/MILP encoder support this operator set. See the current operator boundary for the accepted semantics and restrictions of each operator.

• Input bounds use a single sample's shape, such as (features,) or (channels, height, width), without a batch dimension.
• lower and upper define elementwise box bounds $\mathrm{lower} \leq x \leq \mathrm{upper}$. The symmetric box $[x_0-\epsilon, x_0+\epsilon]$ is an $L_\infty$ ball. Coupled $L_1$, $L_2$, and other norm bounds are not currently accepted.
• relu_binary_mode="reduced" (the default) introduces binaries only for unstable ReLU/LeakyReLU elements. "full" introduces one binary per activation element. Both modes are exact; see ReLU binary handling.
• MaxPool2d uses the full exact formulation, with one binary selector for every valid candidate in each pooling window.

Comparison with OMLT

OMLT is a broader Pyomo-based package for embedding trained machine-learning models in optimization problems. NCET focuses on direct, graph-preserving encoding of supported PyTorch networks as exact CVXPY LP/MILP constraints.

The packages are therefore complementary: choose NCET when direct PyTorch and graph-preserving CVXPY encoding are central, and consider OMLT when Pyomo or its broader formulation ecosystem is the priority.

Requirements

NCET requires Python 3.10+, CVXPY 1.7.5+, NumPy 1.26+, SciPy 1.13+, and PyTorch 2.2+. See pyproject.toml for the supported upper bounds.

Examples

License

NCET is licensed under the Apache License 2.0.

Citation

If you use NCET in your research, please cite:

@ARTICLE{xu2026learning,
  author={Xu, Wangkun and Chu, Zhongda and Teng, Fei},
  journal={IEEE Transactions on Power Systems}, 
  title={Learning-Augmented Power System Operations: A Unified Optimization View}, 
  year={2026},
  volume={},
  number={},
  pages={1-21},
  doi={10.1109/TPWRS.2026.3726363}}