RangeFlow 🌊

Certified Robustness, Quantization & Uncertainty for AI

RangeFlow is a revolutionary Python library for robust, efficient, and certified AI.

It combines Interval Arithmetic with 1.58-bit Quantization, enabling you to:

• ✅ Train 3B+ Models on consumer GPUs (BitNet 1.58-bit)
• ✅ Certify neural networks against adversarial attacks
• ✅ Quantify uncertainty in predictions mathematically
• ✅ Accelerate convergence with Newton-Schulz optimization (Muon)
• ✅ Eliminate catastrophic forgetting in continual learning

Unlike standard deep learning, RangeFlow provides mathematical guarantees and extreme compression in a single package.

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🌟 Why RangeFlow?

The Problem

1. Fragility: Models change predictions when noise is added.
2. Bloat: Large Language Models (LLMs) require massive H100 GPUs.
3. Slowness: Standard optimizers (Adam) are memory-hungry and slow.

The RangeFlow Solution (v0.5.0)

We solve this with "The Light Monster" stack:

1. BitNet Quantization: Compresses weights to {-1, 0, 1} (1.58 bits), reducing VRAM usage by ~10x.
2. Interval Bounds: Propagates [min, max] ranges to guarantee robustness.
3. Muon Optimizer: Orthogonalizes gradients for faster training than Adam.

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🚀 What's New in v0.5.0

🔥 Major Features

1. BitNet 1.58-bit Quantization (rangeflow.quantization)
   • Train LLMs with ternary weights (-1, 0, 1).
   • Includes Robust Scaling (Median/MAD) and Straight-Through Estimator.
2. Advanced Optimizers (rangeflow.optim)
   • Muon: Momentum Orthogonalized by Newton-Schulz (Faster convergence).
   • GRIP: Gradient Robust Interval Propagation (Self-stabilizing "Brake").
3. Functional Interface (rangeflow.functional)
   • Stateless, JAX-style API (aliased as R).
   • y = R.relu(R.linear(x, w, b))
4. Certified Loss (Hull-Prop)
   • Minimizes the volume of the output interval hull for tighter logic.
5. Broadcasting Support
   • Full NumPy-style broadcasting for interval operations.

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🚀 Quick Start

Installation

pip install rangeflow

(Note: For 1.58-bit training speedup, use a compiled environment like WSL2 or Linux)

1. Basic Robust Model (Interval Arithmetic)

import rangeflow as rf
import torch
from rangeflow.layers import RangeLinear, RangeReLU

# 1. Create uncertain input (sensor noise ±0.1)
x = torch.randn(1, 784)
x_range = rf.RangeTensor.from_epsilon_ball(x, epsilon=0.1)

# 2. Build model
model = torch.nn.Sequential(
    RangeLinear(784, 128),
    RangeReLU(),
    RangeLinear(128, 10)
)

# 3. Get guaranteed bounds
min_out, max_out = model(x_range).decay()
print(f"Output guaranteed in [{min_out.item()}, {max_out.item()}]")

2. High-Performance 1.58-bit Training (NEW)

Train a large model with minimal VRAM using BitNet and Muon.

from rangeflow.quantization import BitNetLinear
from rangeflow.optim import Muon
import torch

# 1. Define a Compressed Layer (1.58 bits per weight)
# Replaces standard nn.Linear(4096, 4096) which takes ~32MB
# BitNetLinear takes ~4MB during inference!
layer = BitNetLinear(4096, 4096, input_bits=8)

# 2. Use Muon Optimizer (Newton-Schulz)
# Orthogonalizes gradients for faster convergence
optimizer = Muon(layer.parameters(), lr=0.02, momentum=0.95)

# 3. Train (Standard Loop)
x = torch.randn(32, 4096)
target = torch.randn(32, 4096)

optimizer.zero_grad()
output = layer(x)
loss = torch.nn.functional.mse_loss(output, target)
loss.backward()
optimizer.step()

3. Functional API (JAX-Style)

Prefer stateless code? Use the R namespace.

import rangeflow.functional as R

# Define weights manually
W = torch.randn(10, 5)
b = torch.zeros(10)

# Run pipeline
x_range = R.from_epsilon_ball(torch.randn(5), 0.1)
y_range = R.relu(R.linear(x_range, W, b))

# No class instantiation needed!

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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(torch.tensor([3.0]))  # Degenerate [3, 3]

2. Domain Constraints (NEW in v0.4.0)

Automatically handle physical constraints:

from rangeflow.verification import DomainConstraints

# Image domain - automatically clips to [0, 1]
domain = DomainConstraints.image_domain(bit_depth=1)
x_range = domain.create_epsilon_ball(image, epsilon=0.3)
# No more negative pixels!

3. Linear Bound Propagation (NEW in v0.4.0)

CROWN-style symbolic bounds for 30% tighter verification:

from rangeflow.linear_bounds import enable_linear_bounds, hybrid_verification

# Enable on your model
enable_linear_bounds(model)

# Verify with tighter bounds
is_verified, margin, method = hybrid_verification(
    model, image, epsilon=0.3, use_linear=True
)

4. RangeNorm: The Stabilizer

Deep networks cause exponential uncertainty growth:

from rangeflow.layers import RangeLayerNorm

# Normalizes both center AND width
norm = RangeLayerNorm(128)
x_stable = norm(x_range)  # Width stays controlled!

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🛠️ Feature Breakdown

1. 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!

2. Comprehensive Layers

Layer Type	RangeFlow Equivalent	Notes
Linear	RangeLinear	Interval weights support
Linear (Continual)	ContinualLinear	Zero forgetting
Conv2d	RangeConv2d	Spatial intervals
LayerNorm	RangeLayerNorm	Stabilizes width growth
BatchNorm	RangeBatchNorm1d, RangeBatchNorm2d
Dropout	RangeDropout	Expands uncertainty
RNN/LSTM/GRU	RangeRNN, RangeLSTM, RangeGRU	Temporal intervals
Attention	RangeAttention	Safe softmax
Pooling	RangeMaxPool2d, RangeAvgPool2d

3. Quantization (rangeflow.quantization)

The engine for training Large Language Models on consumer hardware.

• BitNetLinear: Drop-in replacement for nn.Linear.
• robust_scale: Uses Median Absolute Deviation (MAD) to handle outliers.
• quantize_model_to_bitnet: Convert any existing PyTorch model to 1.58-bit in one line.

4. Optimizers (rangeflow.optim)

• Muon: Performs Newton-Schulz iteration on 2D weight gradients. Keeps updates orthogonal, preventing "feature collapse" in deep networks.
• GRIP: Dynamically scales learning rate based on Interval Width. If the model becomes uncertain (wide intervals), GRIP hits the brakes.

5. Verification & Safety

• Branch-and-Bound (BaB): Formal verification for safety-critical apps.
• Linear Bounds (CROWN): Symbolic propagation for tighter certification.
• Continual Learning: Interval weights prevent catastrophic forgetting.

6. Advanced Training (NEW in v0.4.0)

One-Line Curriculum Training

from rangeflow.advanced_train import train_with_curriculum

model, history = train_with_curriculum(
    model, train_loader, val_loader,
    epochs=100,
    start_eps=0.0,
    end_eps=0.5,
    method='trades',  # TRADES loss for better accuracy
    beta=6.0,
    checkpoint_dir='./checkpoints'
)

# Automatically includes:
# ✓ Epsilon scheduling
# ✓ Range monitoring
# ✓ Checkpointing
# ✓ Resumable training
# ✓ TRADES loss

Manual Training with TRADES

from rangeflow.advanced_train import TRADESTrainer

trainer = TRADESTrainer(model, optimizer, beta=6.0)

for epoch in range(epochs):
    train_loss = trainer.train_epoch(train_loader, epsilon)
    val_metrics = trainer.validate(val_loader, epsilon)
    print(f"Epoch {epoch}: Cert Acc: {val_metrics['certified_acc']:.2%}")

7. Automatic Debugging (NEW in v0.4.0)

from rangeflow.advanced_train import monitor_ranges

# Register monitoring hooks (ONE LINE!)
hooks = monitor_ranges(model, explosion_threshold=50.0)

# Train normally - hooks automatically track ranges
for data, target in train_loader:
    output = model(data)
    # If ranges explode, you'll see warnings!

# Check statistics
for hook in hooks:
    stats = hook.get_stats()
    print(f"{stats['name']}: avg_width={stats['avg_width']:.2f}")

8. Formal Verification (NEW in v0.4.0)

Branch-and-Bound Verification

from rangeflow.verification import BranchAndBound, DomainConstraints

domain = DomainConstraints.image_domain()
bab = BranchAndBound(max_depth=3)

# Formal verification with recursive splitting
is_verified, margin, stats = bab.verify(
    model, image, label, epsilon=0.3, domain=domain
)

print(f"Verified: {is_verified}, Margin: {margin:.3f}")
print(f"Explored {stats['nodes_explored']} nodes")

Verification Certificates

from rangeflow.verification import VerificationCertificate

# Create formal proof
cert = VerificationCertificate(
    x_range, output_range, target_label, 
    epsilon=0.3, method='IBP+BaB'
)

# Save certificate
cert.save('safety_proof.pt')

# Load and re-verify later
cert = VerificationCertificate.load('safety_proof.pt')
is_valid = cert.verify_against_model(model)

9. Continual Learning (NEW in v0.4.0)

Hybrid Models (Memory-Efficient)

from rangeflow.continual import HybridModelBuilder

builder = HybridModelBuilder()

# Customize interval ratio per layer
model = builder.build_mlp(
    layer_sizes=[784, 512, 256, 10],
    interval_ratios=[0.3, 0.6, 1.0]  # 30%, 60%, 100% interval weights
)

# Only critical layers use intervals - saves memory!

Multi-Task Training

from rangeflow.continual import continual_train_step

memories = []

# Train Task A
train(model, task_A_data)
memories.append(save_task_memory(model, 'Task_A'))

# Train Task B (preserving A)
for data, target in task_B_data:
    loss, task_loss, elastic_loss = continual_train_step(
        model, optimizer, data, target, 
        old_memories=memories  # Preserves all previous tasks!
    )
    loss.backward()
    optimizer.step()

# Train Task C (preserving A and B)
memories.append(save_task_memory(model, 'Task_B'))
# Continue with Task C...

📊 Advanced Usage

Hybrid Models (Partial Interval Weights)

For large models, use intervals only where needed:

from rangeflow.continual import ContinualLinear

# Option 1: Layer-by-layer control
model = torch.nn.Sequential(
    ContinualLinear(784, 512, mode='mu_only'),      # Standard weights
    RangeReLU(),
    ContinualLinear(512, 256, mode='hybrid', hybrid_ratio=0.5),  # 50% intervals
    RangeReLU(),
    ContinualLinear(256, 10, mode='full')            # Full intervals
)

# Option 2: Use builder
from rangeflow.continual import HybridModelBuilder

builder = HybridModelBuilder()
model = builder.build_mlp(
    [784, 512, 256, 10],
    interval_ratios=[0.0, 0.5, 1.0]  # 0%, 50%, 100%
)

Benefits:

• 50% memory reduction
• Faster training
• Critical layers still robust

Custom Verification Domains

from rangeflow.verification import DomainConstraints

# Temperature sensor (Kelvin, must be positive)
temp_domain = DomainConstraints(
    min_val=0.0, max_val=None, name='Temperature'
)

# Normalized features (z-score)
norm_domain = DomainConstraints(
    min_val=-3.0, max_val=3.0, name='Standardized'
)

# Probability distribution
prob_domain = DomainConstraints.probability_domain()

Resumable Training

from rangeflow.advanced_train import StatefulEpsilonScheduler, CheckpointManager

scheduler = StatefulEpsilonScheduler('linear', 0.0, 0.5, 100)
manager = CheckpointManager('./checkpoints', keep_best=3)

for epoch in range(100):
    eps = scheduler.step()
    
    # Train...
    train_loss = train_epoch(model, train_loader, eps)
    
    # Save checkpoint with scheduler state
    manager.save(
        model, optimizer, scheduler, epoch,
        metrics={'train_loss': train_loss, 'epsilon': eps}
    )

# Resume later
checkpoint = manager.load_latest()
model.load_state_dict(checkpoint['model_state_dict'])
scheduler.load_state_dict(checkpoint['scheduler_state_dict'])
# Continues from correct epoch with correct epsilon!

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🗺️ Roadmap

v0.5.0 (Current)

• ✅ BitNet 1.58-bit Quantization
• ✅ Muon & GRIP Optimizers
• ✅ Functional API (R)
• ✅ Broadcasting Support

v0.6.0 (Next)

• 🔄 Kernel Fusion: Custom Triton kernels for 2x training speed.
• 🔄 Distributed Training: native FSDP support for BitNet.
• 🔄 Graph Neural Networks: Interval support for geometric deep learning.

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📄 Citation

If you use RangeFlow in your research, please cite:

@software{rangeflow2026,
  title={RangeFlow: Interval Arithmetic & 1.58-bit Quantization for AI},
  author={Dheeren Tejani},
  year={2026},
  url={[https://github.com/dheeren-tejani/rangeflow](https://github.com/dheeren-tejani/rangeflow)}
}

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⚖️ License

MIT License - see LICENSE for details.

**Built by Dheeren Tejani**