torchverif

Multiple pytorch tools towards formal verification of neural networks

Tools

• PyTorch to PVS theory generation
• Interval propagation through PyTorch network
• Statistical Model Analysis (SMA) neural network verification

Prerequisites (if needed)

Install dependencies with:

pip install -r requirements.txt

Install

pip install torchverif

Usage

See tests/ for examples

Cite this

If you use this repository in your works, please cite the following papers:

@article{rossi2024closedloop,
title = {Neural networks in closed-loop systems: Verification using interval arithmetic and formal prover},
journal = {Engineering Applications of Artificial Intelligence},
volume = {137},
pages = {109238},
year = {2024},
issn = {0952-1976},
doi = {https://doi.org/10.1016/j.engappai.2024.109238},
url = {https://www.sciencedirect.com/science/article/pii/S0952197624013964},
author = {Federico Rossi and Cinzia Bernardeschi and Marco Cococcioni},
keywords = {Cyber–physical systems, Neural networks, Closed-loop control systems, Formal verification, Interval arithmetic},
}

TorchVerif API Documentation

torchverif/interval_tensor/v2/__init__.py

Classes

• IntervalTensor: Represents tensors where each element holds an interval instead of a single value, used for interval arithmetic. The IntervalTensor class defines operations on interval tensors, supporting various tensor operations directly on intervals.

Functions

• Tensor Operations: Functions like Linear, Pad, Conv2d, MaxPool2D, BatchNorm2D, Cat, Sum, Squeeze, Unsqueeze, Flatten, RepeatInterleave, Max, Min, Matmul, and Var provide interval-based versions of these tensor operations, essential for neural network layers.
• Activation Functions: ReLU, Sigmoid, Tanh, Sqrt, and Square implement activation functions designed to handle intervals.
• Arithmetic Functions: Functions such as Add, Sub, Mean, Max, Min, and Var support interval arithmetic across tensors.
• Utility Methods: Functions like from_np_supinf, interval_from_infsup, from_raw, and check_interval assist with constructing and validating intervals. Operators like __add__, __sub__, __mul__, and __truediv__ are overloaded to support interval-based arithmetic directly on IntervalTensor objects.

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torchverif/net_interval/v2/__init__.py

The net_interval module provides interval analysis methods for neural network verification.

Functions

• bounds_from_v2_predictions: Computes the interval bounds of the output given the network predictions. This function is used to verify that the network’s predictions stay within certain bounds.
• class_bounds_from_net_outputs: Extracts the bounds of each class’s output from network predictions, aiding in robustness verification by determining if outputs stay within secure intervals.
• interval_plot_scores_helper: Provides interval-based scoring for plotting, useful for visualizing bounds across classes or network layers.
• interval_time_plot_helper: Assists with plotting intervals over time, observing how bounds evolve during network evaluation or training.

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torchverif/pvs/torch2pvs.py

This module provides functionality for converting Torch models into PVS-compatible format, enabling formal verification processes.

Functions

• get_leaky_relu_string: Generates a string representation for the Leaky ReLU activation function in PVS syntax.
• gen_vector_matrix_product: Generates PVS code for vector-matrix products, a common operation in neural network computations.
• gen_network_operation_sequence: Produces a sequence of network operations in PVS format, encoding the layers and structure of a Torch model.
• gen_theorem and gen_theorem_eval: Generate theorems for PVS verification, defining formal properties for the network to satisfy, and evaluate these theorems.
• gen_constraint_expressions: Produces PVS expressions that represent constraints, such as bounds or inequalities, for use in theorem proving.
• emit_pvs_from_pth: Converts a PyTorch model (.pth file) to PVS format, enabling formal verification of trained models in PVS.

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torchverif/smc/plot_helper.py

The plot_helper module provides functions to visualize interval analysis and verification results.

Functions

• format_query_bounds: Prepares bounds for queries in a readable format, suitable for visualization and interpretation in plots.
• format_query_output: Structures output data for display and annotations in plots.
• sure_class: Identifies the most certain class based on interval bounds, useful for classification tasks where bounds indicate confidence levels.
• plot_cdf: Plots the cumulative distribution function (CDF) of a given interval, a valuable visualization tool for probabilistic or distributional data in interval analysis.
• interval_plot_scores_helper: Provides interval-based scoring for visual plots, highlighting ranges across different network outputs.
• finalize_plot: Finalizes plot aesthetics (axes, labels, legends) before rendering, ensuring clarity for interval or CDF visualizations.
• show_plot: Renders the plot, displaying interval or CDF results.
• save_plot: Saves the plot to a file, preserving interval analysis visualizations for reporting or documentation.

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torchverif/smc/__init__.py

This module contains tools for simulation-based verification methods.

Classes

• Simulator: The main class for performing simulations and querying statistical bounds, allowing verification of probabilistic or interval-based properties.

Functions (in Simulator)

• __init__: Initializes the simulator with configurations for simulations and statistical model checking.
• simulate: Runs a simulation, often involving interval-based testing or statistical verification.
• query: Executes a query on the simulation, retrieving bounds or probability estimates as needed.
• cdf: Calculates the cumulative distribution function (CDF) for simulation results, supporting probabilistic analysis.
• minmax_query: Queries minimum and maximum bounds in a simulation, useful for interval-based robustness verification.

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