mobiu-q 2.7

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q v2.7

Mobiu-Q wraps your existing optimizer with Soft Algebra to filter noise and improve convergence. Same API, better results.

---

🚀 What's New in v2.7

• MobiuOptimizer: Universal wrapper - auto-detects PyTorch optimizers!
• Hybrid Mode: Cloud intelligence + local PyTorch performance
• Zero Friction: One-line integration for PyTorch users
• Full Backward Compatibility: All existing code continues to work

---

⚡ Quick Start

PyTorch Users (NEW in v2.7!)

import torch
from mobiu_q import MobiuOptimizer

# Your existing code
model = MyModel()
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)

# Wrap with Mobiu-Q (one line!)
opt = MobiuOptimizer(base_opt, method="adaptive")

# Training loop stays the same
for epoch in range(100):
    loss = criterion(model(x), y)
    loss.backward()
    opt.step(loss.item())  # Pass loss for Soft Algebra
    opt.zero_grad()

opt.end()

Quantum Users (unchanged)

from mobiu_q import MobiuQCore

opt = MobiuQCore(method="standard")
for step in range(100):
    params = opt.step(params, energy_fn)
opt.end()

---

🏆 Verified Benchmark Results

All benchmarks compare Optimizer + Soft Algebra vs Optimizer alone. Same learning rate, same seeds, fair A/B test.

🎮 Reinforcement Learning

Environment	Improvement	p-value	Win Rate
LunarLander-v3	+129.7%	<0.001	96.7%
MuJoCo InvertedPendulum	+118.6%	0.001	100%
MuJoCo Hopper	+41.2%	0.007	80%

📐 Classical Optimization

Function	Improvement	Description
Rosenbrock	+75.8%	Valley navigation
Beale	+62.0%	Plateau escape
Sphere	+31.1%	Convex baseline

⚛️ Quantum VQE - Condensed Matter

Model	Improvement
SSH Model (Topological)	+61.0%
XY Model	+60.8%
Ferro Ising	+45.1%
Transverse Ising	+42.0%
Heisenberg XXZ	+20.8%
Kitaev Chain	+20.4%
Hubbard Dimer	+14.1%

⚛️ Quantum VQE - Chemistry

Molecule	Improvement
FakeFez H₂	+52.4% (p=0.043)
He Atom	+51.2%
H₂ Molecule	+46.6%
H₃⁺ Chain	+42.0%
LiH Molecule	+41.4%
BeH₂ Molecule	+37.8%

🎯 QAOA (Combinatorial Optimization)

Problem	Improvement	Wins
FakeFez MaxCut	+45.1%	p=0.0003
Vertex Cover	+31.9%	51/60
Max Independent Set	+31.9%	51/60
MaxCut	+21.5%	45/60

💰 Finance (QUBO)

Problem	Improvement
Credit Risk	+52.3%
Portfolio Optimization	+51.7%

💊 Drug Discovery

Task	Improvement	Config
Binding Affinity	+12.2%	AMSGrad + standard

---

📦 Installation

pip install mobiu-q

---

🔧 Configuration

📖 See CONFIGURATION_GUIDE.md for complete details

Which Class to Use?

Use Case	Class	Mode
PyTorch (RL, LLM, Deep Learning)	MobiuOptimizer	Hybrid
Quantum (VQE, QAOA)	MobiuQCore	Cloud
NumPy optimization	MobiuQCore	Cloud

Methods

Method	Best For	Default LR
standard	VQE, Chemistry, Finance	0.01
deep	QAOA, Noisy Hardware	0.1
adaptive	RL, LLM, High-variance	0.0003

Base Optimizers

Optimizer	Best For
Adam	Default, most cases
AdamW	LLM, weight decay
SGD	QAOA
AMSGrad	Drug Discovery
NAdam	Alternative to Adam
Momentum	RL alternative
LAMB	Large batch

Important: Optimizer names are case-sensitive!

---

🆕 MobiuOptimizer (v2.7)

The new MobiuOptimizer auto-detects your optimizer type:

from mobiu_q import MobiuOptimizer

# PyTorch optimizer → Hybrid mode (recommended for RL/LLM)
base_opt = torch.optim.Adam(model.parameters())
opt = MobiuOptimizer(base_opt, method="adaptive")

# NumPy params → Cloud mode (same as MobiuQCore)
params = np.random.randn(10)
opt = MobiuOptimizer(params, method="standard")

How Hybrid Mode Works

┌─────────────────┐     loss/return    ┌─────────────────┐
│  Local PyTorch  │ ──────────────────▶│   Mobiu Cloud   │
│                 │                    │                 │
│  • Gradients    │   adaptive_lr      │  • Soft Algebra │
│  • Weight Update│ ◀──────────────────│  • Super-Eq Δ†  │
│  • Momentum     │                    │  • Trust Ratio  │
└─────────────────┘                    └─────────────────┘

Benefits:

• ✅ PyTorch handles precision & GPU acceleration
• ✅ Cloud provides Soft Algebra intelligence
• ✅ Minimal network overhead (only sends loss value)
• ✅ No momentum state corruption

---

🛠️ Troubleshooting

If optimization is not improving or diverging:

1. Switch Base Optimizer

opt = MobiuQCore(license_key="KEY", base_optimizer="NAdam")
opt = MobiuQCore(license_key="KEY", base_optimizer="Momentum")

2. Switch Method

If This Fails	Try This
standard	adaptive
adaptive	deep
deep	standard

3. Switch Mode (Quantum)

opt = MobiuQCore(license_key="KEY", mode="hardware")

4. Adjust Learning Rate

Scenario	Recommendation
Diverging	Lower LR by 2-5x
No improvement	Increase LR by 2x

---

🔬 How It Works

Mobiu-Q is based on Soft Algebra (ε²=0):

(a, b) × (c, d) = (ad + bc, bd)

Evolution Law:

S_{t+1} = (γ · S_t) · Δ_t + Δ_t

The Super-Equation Δ† detects emergence moments for adaptive scaling.

---

💰 Pricing

Tier	Price	Runs
Free	$0	20 runs/month
Pro	$19/month	Unlimited

Get your key at app.mobiu.ai

---

📊 Summary by Domain

Domain	Best Result	Avg Improvement
RL	+129.7%	~96%
Classical Opt	+75.8%	~56%
Condensed Matter	+61.0%	~38%
Quantum Chemistry	+52.4%	~45%
Finance	+52.3%	~52%
QAOA	+45.1%	~32%
Drug Discovery	+12.2%	+12%

---

🧑‍🔬 Scientific Foundation

• Dr. Moshe Klein – Soft Logic and Soft Numbers
• Prof. Oded Maimon – Tel Aviv University

---

📚 Links

• Website: mobiu.ai
• App: app.mobiu.ai
• PyPI: pypi.org/project/mobiu-q

---

© 2025 Mobiu Technologies. All rights reserved.