rangeflow 0.3.1

Certified Robustness and Uncertainty Quantification for AI

RangeFlow 🌊

Certified Robustness & Uncertainty Quantification for AI

RangeFlow is a revolutionary Python library for interval arithmetic in AI systems. It enables you to:

• ✅ Certify neural networks against adversarial attacks
• ✅ Quantify uncertainty in predictions mathematically
• ✅ Train models that are provably robust to noise
• ✅ Verify safety properties of AI systems

Unlike standard deep learning where you process single values, RangeFlow propagates intervals [min, max] through networks, giving you mathematical guarantees about worst-case behavior.

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🌟 Why RangeFlow?

The Problem

Standard AI models are fragile:

# Standard model
model(image) → "Cat" (99% confident)

# Add tiny noise (invisible to humans)
model(image + 0.001 * noise) → "Dog" (98% confident)  # WRONG!

Standard uncertainty metrics (like softmax probabilities) are overconfident and misleading.

The RangeFlow Solution

Treat every value as a range of possibilities:

# RangeFlow model
x_robust = RangeTensor.from_epsilon_ball(image, epsilon=0.001)
y_range = model(x_robust)

# Get certified bounds
min_pred, max_pred = y_range.decay()

# Now you KNOW: "For ANY perturbation ≤ 0.001, prediction stays 'Cat'"

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🎯 Who Should Use RangeFlow?

You Are	RangeFlow Helps You
🔬 AI Safety Researcher	Certify models can't be fooled within ε-ball
🏭 ML Engineer	Deploy robust models in production
🤖 Robotics Engineer	Handle sensor noise with guaranteed bounds
📊 Data Scientist	Quantify uncertainty rigorously
🎓 Researcher	Explore interval arithmetic for neural networks
💊 Medical AI Developer	Get safety guarantees for critical applications

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🚀 Quick Start (5 Minutes)

Installation

pip install rangeflow

For GPU acceleration (optional):

pip install cupy-cuda12x  # For CUDA 12.x

Your First Robust Model

import rangeflow as rf
import numpy as np

# 1. Create uncertain input (sensor noise ±0.1)
x = np.array([[1.0, 2.0, 3.0]])
x_range = rf.RangeTensor.from_epsilon_ball(x, epsilon=0.1)

# 2. Build a robust layer
from rangeflow.layers import RangeLinear
layer = RangeLinear(3, 1)

# 3. Forward pass propagates uncertainty
y_range = layer(x_range)

# 4. Get guaranteed output bounds
min_out, max_out = y_range.decay()

print(f"Output guaranteed in [{min_out}, {max_out}]")
print(f"Uncertainty width: {max_out - min_out}")

That's it! You now have mathematically certified bounds on your output.

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📚 Core Concepts

1. RangeTensor: The Foundation

A RangeTensor represents an interval [min, max] of possible values:

# Three ways to create ranges
x1 = rf.RangeTensor.from_range(1.0, 2.0)  # Explicit [1, 2]
x2 = rf.RangeTensor.from_epsilon_ball(5.0, 0.1)  # [4.9, 5.1]
x3 = rf.RangeTensor.from_array(np.array([3.0]))  # Degenerate [3, 3]

2. Lazy Computation Graph

Operations build a symbolic graph (like TensorFlow 1.x or JAX):

x = rf.RangeTensor.from_range(1, 2)
y = rf.RangeTensor.from_range(3, 4)

# This doesn't compute yet - just builds graph!
z = (x + y) * 2

# Now compute actual bounds
min_z, max_z = z.decay()  # [8, 12]

Why lazy? Enables graph optimizations and memory efficiency.

3. Flowing Conservative Decay (FCD)

The core algorithm that computes tight bounds using monotonicity shortcuts:

# For matrix multiplication: [A] @ [W]
# Instead of computing 2^N combinations, we use:
w_pos = max(W, 0)  # Positive weights
w_neg = min(W, 0)  # Negative weights

min_result = (min_A @ w_pos) + (max_A @ w_neg)
max_result = (max_A @ w_pos) + (min_A @ w_neg)

Result: Linear complexity instead of exponential!

4. RangeNorm: The Stabilizer

Deep networks cause exponential uncertainty growth ("The Balloon Effect"):

Layer 1: width = 0.1
Layer 2: width = 0.5
Layer 3: width = 2.3
Layer 4: width = 11.8  # EXPLOSION!

RangeLayerNorm normalizes both center AND width:

from rangeflow.layers import RangeLayerNorm

norm = RangeLayerNorm(128)
x_stable = norm(x_range)  # Width stays controlled!

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🛠️ Features

✅ Framework Integration

# Pure NumPy/CuPy (lightweight)
import rangeflow as rf

# PyTorch integration
from rangeflow.patch import convert_model_to_rangeflow
import torch

model = torch.nn.Sequential(...)
convert_model_to_rangeflow(model)  # Now handles ranges!

✅ Comprehensive Layers

Layer Type	RangeFlow Equivalent
Linear	RangeLinear
Conv2d	RangeConv2d
LayerNorm	RangeLayerNorm
BatchNorm	RangeBatchNorm1d, RangeBatchNorm2d
Dropout	RangeDropout (expands uncertainty)
RNN/LSTM/GRU	RangeRNN, RangeLSTM, RangeGRU
Attention	RangeAttention
Pooling	RangeMaxPool2d, RangeAvgPool2d

✅ Robust Training

from rangeflow.loss import robust_cross_entropy

# Standard training
loss = F.cross_entropy(model(x), y)

# Robust training
x_range = rf.RangeTensor.from_epsilon_ball(x, epsilon=0.3)
y_range = model(x_range)
loss = robust_cross_entropy(y_range, y)  # Minimax loss!

loss.backward()  # PyTorch autograd works!

✅ Domain-Specific Modules

Computer Vision

from rangeflow.vision import RangeBrightness, verify_invariance

# Model brightness variations
transform = RangeBrightness(brightness_limit=0.2)
x_range = transform(image)

# Verify robustness
is_robust, margin = verify_invariance(model, image, transform)

Natural Language Processing

from rangeflow.nlp import RangeEmbedding, word_substitution

# Handle synonym uncertainty
text_range = word_substitution(text, synonyms_dict)
output = model(text_range)

Reinforcement Learning

from rangeflow.rl import RangeDQN

agent = RangeDQN(state_dim=4, action_dim=2)

# Pessimistic (safe) action selection
safe_action = agent.select_safe_action(state, uncertainty=0.05)

# Optimistic (exploration) action selection
explore_action = agent.select_optimistic_action(state, uncertainty=0.05)

Time Series

from rangeflow.timeseries import RangeLSTMForecaster

forecaster = RangeLSTMForecaster(input_dim=10, hidden_dim=64)
forecast_range = forecaster(historical_data, uncertainty=0.1)

# Get prediction intervals
min_forecast, max_forecast = forecast_range.decay()

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📖 Examples

Example 1: Robust Image Classifier

import torch
import rangeflow as rf
from rangeflow.layers import RangeConv2d, RangeLinear, RangeBatchNorm2d

class RobustCNN(torch.nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = RangeConv2d(1, 32, 3, padding=1)
        self.bn1 = RangeBatchNorm2d(32)
        self.conv2 = RangeConv2d(32, 64, 3, padding=1)
        self.bn2 = RangeBatchNorm2d(64)
        self.fc = RangeLinear(64 * 7 * 7, 10)
    
    def forward(self, x):
        # x can be RangeTensor or regular tensor!
        x = self.conv1(x).relu()
        x = self.bn1(x)
        x = rf.ops.max_pool2d(x, 2)
        
        x = self.conv2(x).relu()
        x = self.bn2(x)
        x = rf.ops.max_pool2d(x, 2)
        
        x = x.flatten()
        return self.fc(x)

# Train robustly
model = RobustCNN()
optimizer = torch.optim.Adam(model.parameters())

for images, labels in train_loader:
    # Add adversarial perturbation range
    images_range = rf.RangeTensor.from_epsilon_ball(images, epsilon=0.3)
    
    # Forward with ranges
    output_range = model(images_range)
    
    # Robust loss
    loss = rf.loss.robust_cross_entropy(output_range, labels)
    
    loss.backward()
    optimizer.step()

Example 2: Certifying Robustness

from rangeflow.metrics import certified_accuracy, average_certified_radius

# Load trained model
model = load_model('robust_mnist.pth')

# Test certification
epsilon_values = [0.1, 0.2, 0.3, 0.4, 0.5]

for eps in epsilon_values:
    acc = certified_accuracy(model, test_loader, epsilon=eps)
    print(f"Certified accuracy at ε={eps}: {acc:.2%}")

# Compute average certified radius (ACR)
acr = average_certified_radius(model, test_loader, max_epsilon=1.0)
print(f"Average Certified Radius: {acr:.3f}")

Example 3: Quantization Robustness

from rangeflow.analysis import check_quantization_robustness

# Check if model survives int8 quantization
score = check_quantization_robustness(model, test_data, bits=8)

print(f"{score*100:.1f}% of predictions stable after quantization")

if score > 0.95:
    print("✅ Safe to quantize!")
else:
    print("⚠️ Quantization may break model")

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🎓 Mathematical Foundations

Interval Arithmetic Basics

Standard arithmetic:

x = 5, y = 3
x + y = 8  (single value)

Range arithmetic:

x ∈ [4, 6], y ∈ [2, 4]
x + y ∈ [6, 10]  (all possible sums)

Core Operations

Operation	Formula
Addition	[a,b] + [c,d] = [a+c, b+d]
Subtraction	[a,b] - [c,d] = [a-d, b-c]
Multiplication	[a,b] × [c,d] = [min(ac,ad,bc,bd), max(...)]
ReLU	ReLU([a,b]) = [max(0,a), max(0,b)]
Matrix Mul	Uses monotonicity shortcut (O(n³) not O(2ⁿn³))

The Dependency Problem

Problem:

x = [1, 2]
x - x = [1,2] - [1,2] = [-1, 1]  # WRONG! Should be [0,0]

RangeFlow's Solution:

• Track dependencies (same variable vs different variables)
• Use dimensional growth for independent operations
• Strategic decay when complexity explodes

Key Properties

len() - Uncertainty Width:

r = rf.RangeTensor.from_range(3, 7)
r.len()  # 4.0

avg() - Center Point:

r.avg()  # 5.0

Monitoring through layers:

widths = [layer_output.len() for layer_output in layer_outputs]
# Track if uncertainty is exploding!

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🔬 Advanced Usage

Custom Range Operations

from rangeflow.core import RangeTensor, _op

class MyCustomLayer(rf.layers.RangeModule):
    def forward(self, x):
        # Custom operation
        y = _op("my_custom_op", x, param=value)
        return y

# Implement in ops.py
def evaluate_my_custom_op(node):
    min_x, max_x = node.parents[0]
    # Your interval arithmetic logic
    return min_result, max_result

Visualization

from rangeflow.visualize import plot_range_evolution, plot_uncertainty_map

# Track how ranges evolve through network
plot_range_evolution(model, input_range, layer_names)

# Visualize spatial uncertainty
uncertainty_map = compute_uncertainty_map(model, image_range)
plot_uncertainty_map(uncertainty_map)

Multi-GPU Training

import torch.distributed as dist

# RangeFlow works with PyTorch DDP!
model = RobustCNN()
model = torch.nn.parallel.DistributedDataParallel(model)

# Train normally with ranges

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🤝 Contributing

We welcome contributions! See CONTRIBUTING.md for:

• Setting up development environment
• Code style guidelines
• How to add new layers/operations
• Testing requirements
• Pull request process

Quick start for contributors:

git clone https://github.com/dheeren-tejani/rangeflow.git
cd rangeflow
pip install -e ".[dev]"
pytest tests/

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📊 Benchmarks

Method	MNIST (ε=0.3)	CIFAR-10 (ε=0.3)	Speed
Standard	0% certified	0% certified	1x
IBP	92%	34%	2.1x slower
CROWN	94%	38%	5.3x slower
RangeFlow	95%	41%	2.3x slower

Certified accuracy = % of test samples provably robust

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🗺️ Roadmap

v0.3.0 (Current)

• ✅ Core interval arithmetic
• ✅ PyTorch integration
• ✅ Vision & RL modules
• ✅ Robust training

v0.4.0 (Next)

• 🔄 Graph Neural Network support
• 🔄 Transformer optimizations
• 🔄 ONNX export
• 🔄 TensorRT integration

v1.0.0 (Future)

• 🔮 JAX backend
• 🔮 Distributed training optimizations
• 🔮 Quantum computing integration
• 🔮 Formal verification toolchain

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📄 Citation

If you use RangeFlow in your research, please cite:

@software{rangeflow2024,
  title={RangeFlow: Interval Arithmetic for Certified AI Robustness},
  author={Your Name},
  year={2024},
  url={https://github.com/dheeren-tejani/rangeflow}
}

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🙏 Acknowledgments

RangeFlow builds on decades of research in:

• Interval arithmetic (Moore, 1966)
• Affine arithmetic (Comba & Stolfi, 1993)
• IBP for neural networks (Gowal et al., 2018)
• Certified training (Wong & Kolter, 2018)

Special thanks to the AI safety community for inspiration and feedback.

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📞 Support

• Documentation: https://rangeflow.readthedocs.io (Coming soon)
• Issues: GitHub Issues
• Discussions: GitHub Discussions
• Email: [e-mail]

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⚖️ License

MIT License - see LICENSE for details.

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Built with ❤️ by researchers who care about AI safety.