mobiu-q 2.9.1

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q v2.9.1

Mobiu-Q wraps your existing optimizer with Soft Algebra and the new Frustration Engine to filter noise, detect stagnation, and improve convergence. Same API, better results.

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🆕 What's New in v2.9.1

Frustration Engine - Client-side adaptive mechanism that:

• Detects when optimization is stuck
• Automatically boosts learning rate 3x
• Achieves +60% improvement over base Soft Algebra on LunarLander

# Frustration Engine activates automatically!
opt = MobiuOptimizer(base_opt, method="adaptive", maximize=True)

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⚡ Quick Start

from mobiu_q import MobiuOptimizer

# PyTorch (RL, LLM, Deep Learning)
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)
opt = MobiuOptimizer(base_opt, license_key="YOUR_KEY", method="adaptive")

# RL with Frustration Engine (maximize=True for rewards)
opt = MobiuOptimizer(base_opt, license_key="YOUR_KEY", method="adaptive", maximize=True)

# Quantum (VQE, QAOA) - pass params instead of optimizer
params = np.random.randn(10)
opt = MobiuOptimizer(params, license_key="YOUR_KEY", method="standard", mode="simulation")

Note: MobiuOptimizer auto-detects PyTorch optimizers vs numpy arrays and uses the appropriate backend.

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🔧 Configuration

Methods

Method	Best For	Default LR
standard	VQE, Chemistry, smooth landscapes	0.01 (sim) / 0.02 (hw)
deep	QAOA, combinatorial, rugged landscapes	0.1
adaptive	RL, LLM, high-variance problems	0.0003

Modes (Quantum only)

Mode	When to Use	Gradient Method
simulation	Clean simulator (Qiskit Aer, PennyLane default)	Finite Difference (2N evals)
hardware	Real quantum hardware, FakeFez, noisy backends	SPSA (2 evals, noise-resilient)

Rule of thumb: If your backend has noise → use hardware. If it's a perfect simulator → use simulation.

New: maximize Parameter (v2.9.0)

# For Loss minimization (default)
opt = MobiuOptimizer(base_opt, maximize=False)

# For Reward maximization (RL)
opt = MobiuOptimizer(base_opt, maximize=True)

A/B Testing Parameter

# For fair comparisons, toggle Soft Algebra:
opt = MobiuOptimizer(base_opt, use_soft_algebra=True)   # Default - SA + Frustration Engine
opt = MobiuOptimizer(base_opt, use_soft_algebra=False)  # Baseline - SA disabled

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📦 Installation

pip install mobiu-q

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🎯 Usage Examples

PyTorch (RL with Frustration Engine)

import torch
from mobiu_q import MobiuOptimizer

LICENSE_KEY = "your-license-key"

policy = PolicyNetwork()
base_opt = torch.optim.Adam(policy.parameters(), lr=0.0003)

opt = MobiuOptimizer(
    base_opt,
    license_key=LICENSE_KEY,
    method="adaptive",
    maximize=True,           # NEW: For RL rewards
    use_soft_algebra=True,   # Enables Frustration Engine
    verbose=True
)

for episode in range(1000):
    reward = run_episode(policy)
    loss = compute_policy_loss(...)
    loss.backward()
    opt.step(reward)  # Frustration Engine auto-detects stagnation
    opt.zero_grad()

opt.end()

PyTorch (Loss Minimization)

opt = MobiuOptimizer(
    base_opt,
    license_key=LICENSE_KEY,
    method="adaptive",
    maximize=False,          # Default: minimize loss
    sync_interval=50,
)

for epoch in range(100):
    loss = criterion(model(x), y)
    loss.backward()
    opt.step(loss.item())
    opt.zero_grad()

opt.end()

Quantum VQE (Simulation)

from mobiu_q import MobiuOptimizer
import numpy as np

params = np.random.randn(10)

opt = MobiuOptimizer(
    params,
    license_key=LICENSE_KEY,
    method="standard",
    mode="simulation",
)

for step in range(100):
    params = opt.step(params, energy_fn)

opt.end()

Standalone Frustration Engine

from mobiu_q import UniversalFrustrationEngine

engine = UniversalFrustrationEngine(base_lr=0.001)

for step in range(1000):
    metric = evaluate()
    factor = engine.get_lr_factor(metric)
    current_lr = base_lr * factor  # 1.0x, 2.0x, or 3.0x
    
    # Use current_lr in your optimizer

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🔑 License Key

Get your key at app.mobiu.ai

# Option 1: Pass directly
opt = MobiuOptimizer(base_opt, license_key="your-key")

# Option 2: Environment variable
export MOBIU_Q_LICENSE_KEY="your-key"

# Option 3: Save to file (one time)
from mobiu_q import save_license_key
save_license_key("your-key")

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🏆 Verified Benchmark Results

All benchmarks use fair A/B testing: Soft Algebra ON vs OFF, same seeds, same conditions.

🆕 Frustration Engine Results (v2.9.0)

Configuration	LunarLander Score	vs Vanilla
Vanilla Adam	-98.3	-
Soft Algebra Only	-70.9	+27.9%
SA + Frustration Engine	-27.6	+71.9%

Frustration Engine adds +60% improvement on top of Soft Algebra!

• Win rate: 5/5 seeds (100%)
• p-value: 0.03125

🎮 Reinforcement Learning

Environment	Improvement	Win Rate	p-value	Cohen's d
LunarLander-v3	+146.9%	93.3%	< 0.000001	+1.50
Atari Breakout	+54.2%	100%	-	-

LunarLander: 30 seeds, 1000 episodes each. Atari: 3 seeds, 200 episodes each.

💰 Portfolio Optimization

Noise Level	Improvement	Win Rate	p-value	Cohen's d
1%	+16.8%	100%	< 0.000001	+0.94
10%	+13.7%	100%	< 0.000001	+0.99
50%	+12.8%	100%	< 0.000001	+0.98

100 seeds per noise level. Sharpe ratio optimization on AAPL, GOOGL, MSFT, AMZN, TSLA.

Overall: 300/300 wins (100%), average improvement +14.5%

⚛️ Quantum VQE on IBM FakeFez

Molecule	Qubits	Improvement	Win Rate
H₂	2	+52.5%	100%
BeH₂	6	+55.1%	100%
LiH	4	+34.5%	100%

🎯 QAOA on IBM FakeFez

Problem	Improvement	p-value
MaxCut	+45.1%	0.0003

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🛠️ Troubleshooting

Not Improving?

1. Try maximize=True: For RL rewards, set maximize=True
2. Switch optimizer: Try NAdam or Momentum (Quantum mode)
3. Switch method: standard ↔ adaptive ↔ deep
4. Adjust LR: Diverging → lower by 2-5x, stuck → raise by 2x
5. Reduce sync_interval: Try sync_interval=1 for more frequent updates

Frustration Engine Not Triggering?

• Check if use_soft_algebra=True (default)
• Engine needs 20+ steps to detect stagnation
• Verify maximize parameter matches your metric

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📖 API Reference

MobiuOptimizer (Universal)

MobiuOptimizer(
    optimizer_or_params,          # torch.optim.Optimizer OR np.ndarray
    license_key: str,
    method: str = "adaptive",     # "standard", "deep", "adaptive"
    mode: str = "simulation",     # "simulation", "hardware"
    use_soft_algebra: bool = True,
    sync_interval: int = 50,      # Cloud sync frequency (PyTorch only)
    maximize: bool = False,       # NEW: True for RL rewards
    verbose: bool = True
)

UniversalFrustrationEngine (NEW in v2.9.0)

UniversalFrustrationEngine(
    base_lr: float,               # Base learning rate
    sensitivity: float = 0.05    # Stagnation sensitivity
)

# Methods:
engine.get_lr_factor(metric)     # Returns 1.0, 2.0, or 3.0
engine.reset()                   # Reset for new run

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🔬 How It Works

Soft Algebra (Klein/Maimon Theory)

SoftNumber multiplication (ε²=0):
(a, b) × (c, d) = (ad + bc, bd)

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

Frustration Engine (v2.9.0)

┌─────────────────────┐
│   Performance       │
│   History (50 steps)│
└─────────┬───────────┘
          │
          ▼
┌─────────────────────┐     Stagnation     ┌─────────────────────┐
│   Stagnation        │ ──── Detected ────▶│   LR Boost (3x)     │
│   Detection         │                    │   for 30 steps      │
└─────────────────────┘                    └─────────────────────┘
          │
          ▼ Normal
┌─────────────────────┐
│   LR Factor = 1.0   │
└─────────────────────┘

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💰 Pricing

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

Get your key at app.mobiu.ai

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🧑‍🔬 Scientific Foundation

Based on Soft Numbers theory developed by Dr. Moshe Klein and Prof. Oded Maimon (Tel Aviv University), as presented in their book on Soft Logic and Soft Numbers.

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📚 Links

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

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