mobiu-q 2.5.4

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q V2.5.4

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

Works across Quantum Computing, Reinforcement Learning, LLM Fine-tuning, Materials Science, and FinTech.

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🚀 What's New in v2.5

• LLM Fine-tuning Support: +23.3% improvement on full fine-tuning, +97% on LoRA
• Materials Science: +98% on Bulk Modulus, +67% on Band Gap prediction
• Noise Robustness: +32.5% more robust to quantum hardware noise
• Multi-Optimizer: Choose from Adam, NAdam, AMSGrad, SGD, Momentum, LAMB

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🏆 Benchmark Results (v2.5)

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

🔬 Materials Science (NEW)

Task	Improvement	p-value	Win Rate
Bulk Modulus (GPa)	+98.3%	<0.001	100%
Band Gap (eV)	+66.8%	<0.001	100%
Formation Energy	+26.9%	<0.001	100%

🤖 LLM Fine-tuning

Task	Improvement	p-value	Win Rate
LoRA r16 + Momentum	+97.6%	<0.001	100%
LoRA r32 + SGD	+90.2%	<0.001	100%
Full Fine-tuning	+23.3%	0.002	100%
GPT-2 Medium (PPL)	+21.2%	<0.001	100%
Soft Prompt Tuning	+18.1%	<0.05	100%

🎮 Reinforcement Learning

Environment	Improvement	p-value	Win Rate
LunarLander-v3	+129.7%	<0.001	96.7%
MuJoCo InvertedPendulum	+118.6%	0.001	100%
Crypto Trading	+10.9% profit	0.005	90%

🧪 Quantum Chemistry (VQE)

Problem	Improvement
XY Model	+60.8%
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	p-value
MaxCut 4-qubit	+27.2%	0.04
MaxCut 5-qubit	+23.7%	0.004
MaxCut p=3	+15.6%	0.008

🛡️ Noise Robustness (IBM FakeBackend)

Metric	Result
Robustness Advantage	+32.5%
Win Rate (all noise levels)	80% (12/15)
IBM FakeFez VQE	+50.9% (p=0.03)

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📦 Installation

pip install mobiu-q

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⚡ Quick Start

1. Materials Science (NEW)

from mobiu_q import MobiuQCore

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="standard",
    base_optimizer="Adam"
)

for epoch in range(100):
    loss = compute_property_loss(model, batch)
    gradient = compute_gradients()
    
    params = opt.step(params, gradient, loss)

opt.end()

2. LoRA Fine-tuning

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="adaptive",
    base_optimizer="Momentum"  # Recommended for LoRA
)

for step in range(1000):
    loss = lora_forward(model, batch)
    gradient = compute_lora_gradients()
    
    params = opt.step(params, gradient, loss)

opt.end()

3. Reinforcement Learning

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="adaptive",
    base_optimizer="Momentum"
)

for episode in range(1000):
    episode_return = run_episode(policy)
    gradient = compute_policy_gradient()
    
    policy_params = opt.step(policy_params, gradient, episode_return)

opt.end()

4. VQE (Quantum Chemistry)

from mobiu_q import MobiuQCore, Demeasurement

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="standard"
)

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

opt.end()

5. QAOA (Noisy Hardware)

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="deep",
    mode="hardware"
)

for step in range(150):
    grad, energy = Demeasurement.spsa(energy_fn, params)
    params = opt.step(params, grad, energy)

opt.end()

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🔧 Configuration

Methods

Method	Best For	Description
standard	VQE, Chemistry, Materials	Trust Ratio + Gradient Warping
deep	QAOA, Noisy Hardware	Super-Equation Δ† for emergence detection
adaptive	RL, LLM, LoRA, Trading	Trust + Emergence + Warping combined

Base Optimizers

Choose from: Adam, Momentum, SGD, NAdam, AMSGrad, LAMB

Important: Optimizer names are case-sensitive!

opt = MobiuQCore(
    license_key="YOUR-KEY",
    method="adaptive",
    base_optimizer="Momentum"  # Best for RL/LLM
)

Modes

Mode	Description
simulation	Clean quantum simulation (default)
hardware	Noisy quantum hardware

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🛠️ Troubleshooting

If optimization is not improving or diverging, try these adjustments:

1. Switch Base Optimizer

Different optimizers work better for different problems:

Problem Type	Recommended Optimizer
LoRA / LLM	Momentum (not SGD)
VQE / Chemistry	Adam
QAOA	NAdam
RL	Momentum
Materials Science	Adam

# If Adam isn't working, try Momentum:
opt = MobiuQCore(license_key="KEY", base_optimizer="Momentum")

# If Momentum isn't working, try NAdam:
opt = MobiuQCore(license_key="KEY", base_optimizer="NAdam")

2. Switch Method

If This Fails	Try This
standard	adaptive
adaptive	deep
deep	standard

# If standard isn't working for your problem:
opt = MobiuQCore(license_key="KEY", method="adaptive")

3. Switch Mode

For quantum problems, if simulation mode isn't working:

# Try hardware mode (more aggressive noise filtering):
opt = MobiuQCore(license_key="KEY", mode="hardware")

4. Adjust Learning Rate

Soft Algebra works best with moderate learning rates:

Scenario	Recommendation
Diverging	Lower LR by 2-5x
No improvement	Increase LR by 2x
LoRA specifically	Use LR=0.01-0.03

5. Common Fixes by Domain

Domain	Common Issue	Fix
LoRA	SGD + high LR diverges	Use Momentum + LR=0.02
Drug Discovery	BCE loss unstable	Use Adam + standard method
Small Batch LLM	High variance	Increase batch size or use deep method
Classification	Cross-entropy issues	Use Adam + lower LR

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🔬 How It Works

Mobiu-Q is based on Soft Algebra, a mathematical framework that extends real numbers with infinitesimal components using nilpotent arithmetic (ε²=0).

Core SoftNumber Multiplication

(a, b) × (c, d) = (ad + bc, bd)

Where:

• a = potential (infinitesimal component)
• b = realization (real component)

Evolution Law

S_{t+1} = (γ · S_t) · Δ_t + Δ_t

This allows gradients to carry both magnitude AND uncertainty information, enabling the optimizer to distinguish real improvement from noise artifacts.

Key Formulas

• Trust Ratio: trust = |real| / (|real| + |soft| + ε)
• Gradient Warping: g_eff = gradient × soft_factor
• Super-Equation Δ†: For emergence detection in rugged landscapes

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💰 Pricing

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

Get your license key at app.mobiu.ai

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📊 Full Benchmark Summary

Domain	Best Result	vs Optimizer
RL (LunarLander)	+129.7%	vs Momentum
RL (MuJoCo)	+118.6%	vs Momentum
Materials (Bulk Modulus)	+98.3%	vs Adam
LoRA (r16 Momentum)	+97.6%	vs Momentum
Materials (Band Gap)	+66.8%	vs Adam
Quantum (XY Model)	+60.8%	vs Adam
Noise Robustness	+32.5%	vs Momentum
QAOA MaxCut	+27.2%	vs NAdam
LLM Full Fine-tune	+23.3%	vs Momentum
Crypto Trading	+10.9%	vs Momentum

Overall Win Rate: 80% across all benchmarks.

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🧑‍🔬 Scientific Foundation

Developed by Mobiu Technologies, based on Soft Algebra theory by:

• Dr. Moshe Klein – Developer of Soft Logic and Soft Numbers
• Prof. Oded Maimon – Tel Aviv University, Industrial Engineering

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📚 Links

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

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📄 License

Proprietary. See LICENSE for details.

© 2025 Mobiu Technologies. All rights reserved.