mobiu-q 3.0.2

Soft Algebra Optimizer for Quantum & Complex Optimization

Mobiu-Q v3.0.2

Soft Algebra for Optimization & Attention

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Overview

Mobiu-Q is a framework built on Soft Algebra (nilpotent ε²=0) that provides:

1. MobiuOptimizer - Stable optimization in noisy environments
2. MobiuAttention 🧪 - O(N) linear attention for long sequences

Both share the same mathematical foundation but serve different purposes.

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Installation

pip install mobiu-q

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Quick Start

MobiuOptimizer (Stable API)

from mobiu_q import MobiuOptimizer
import torch

# Wrap any PyTorch optimizer
model = MyModel()
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)
opt = MobiuOptimizer(base_opt, method="adaptive", use_soft_algebra=True)

for batch in dataloader:
    loss = criterion(model(batch))
    loss.backward()
    opt.step(loss.item())  # Pass loss for Soft Algebra

opt.end()  # Important: release resources

MobiuAttention (🧪 Experimental)

from mobiu_q.experimental import MobiuAttention, MobiuBlock

# Drop-in replacement for nn.MultiheadAttention
attn = MobiuAttention(d_model=512, num_heads=8)
out = attn(x)  # x: [batch, seq, dim]

# Or use complete block
block = MobiuBlock(d_model=512, num_heads=8)
out = block(x)

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MobiuOptimizer

Methods

Method	Use Case	Default LR
standard	Smooth landscapes, chemistry, physics	0.01
deep	Deep circuits, noisy hardware, complex opt	0.1
adaptive	RL, LLM fine-tuning, high-variance problems	0.0003

Benchmarks

Domain	Improvement	Win Rate	p-value
Crypto Trading 🆕	+56% profit	100%	<0.001
LunarLander-v3	+128%	97%	<0.001
MuJoCo InvertedPendulum	+111%	100%	<0.001
VQE H₂ (FakeFez)	+52%	100%	<0.001
QAOA MaxCut	+45%	95%	<0.001

Crypto Trading Details

Tested on synthetic crypto market with regime switching (bull/bear), flash crashes, and high volatility:

Metric	Adam Baseline	Mobiu Optimizer
Profit	-0.9%	+55.9%
Episode Return	-0.17	+0.46

500 episodes × 10 seeds, p < 0.001

Maximize vs Minimize

By default, Mobiu-Q assumes you're minimizing (loss, energy). For RL/Trading where you maximize (reward, profit), set maximize=True:

# Loss minimization (default) - for supervised learning, VQE
opt = MobiuOptimizer(base_opt, method="standard")
opt.step(loss.item())  # Lower is better

# Reward maximization - for RL, trading
opt = MobiuOptimizer(base_opt, method="adaptive", maximize=True)
opt.step(episode_return)  # Higher is better

Use Case	maximize	What to pass to step()
Supervised Learning	False (default)	loss.item()
VQE / QAOA	False (default)	energy
RL (policy gradient)	True	episode_return
Trading	True	profit or sharpe_ratio

Why does this matter? Soft Algebra tracks the "direction of improvement". Passing reward as loss (or vice versa) confuses the optimizer.

A/B Testing

# Test with Soft Algebra
opt_on = MobiuOptimizer(base_opt, use_soft_algebra=True)

# Test without (baseline)
opt_off = MobiuOptimizer(base_opt, use_soft_algebra=False)

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Base Optimizers

Mobiu-Q enhances these base optimizers with Soft Algebra:

Optimizer	Description	Best For
Adam	Adaptive moments, most popular	Default, most cases
AdamW	Adam with decoupled weight decay	LLM, Transformers
NAdam	Adam with Nesterov momentum	Alternative to Adam
AMSGrad	Adam with max(v) for stability	Drug discovery, unstable loss
SGD	Simple gradient descent	QAOA, convex problems
Momentum	SGD with momentum	RL, LLM fine-tuning
LAMB	Layer-wise adaptive scaling	Large batch training

Choosing an Optimizer

PyTorch mode - Choose your optimizer when creating the base optimizer:

import torch
from mobiu_q import MobiuOptimizer

# Using Adam (default, recommended for most cases)
base_opt = torch.optim.Adam(model.parameters(), lr=0.0003)
opt = MobiuOptimizer(base_opt, method="adaptive")

# Using AdamW (recommended for LLM/Transformers)
base_opt = torch.optim.AdamW(model.parameters(), lr=0.0003, weight_decay=0.01)
opt = MobiuOptimizer(base_opt, method="adaptive")

# Using SGD with Momentum (recommended for RL)
base_opt = torch.optim.SGD(model.parameters(), lr=0.02, momentum=0.9)
opt = MobiuOptimizer(base_opt, method="adaptive", maximize=True)

# Using NAdam
base_opt = torch.optim.NAdam(model.parameters(), lr=0.0003)
opt = MobiuOptimizer(base_opt, method="deep")

Quantum mode - Choose your optimizer via the base_optimizer parameter:

from mobiu_q import MobiuOptimizer
import numpy as np

params = np.random.randn(10)

# Using Adam (default)
opt = MobiuOptimizer(params, method="standard")

# Using NAdam
opt = MobiuOptimizer(params, method="standard", base_optimizer="NAdam")

# Using AMSGrad
opt = MobiuOptimizer(params, method="deep", base_optimizer="AMSGrad")

⚠️ Important: In Quantum mode, optimizer names are case-sensitive!

# ✅ Correct
opt = MobiuOptimizer(params, base_optimizer="NAdam")

# ❌ Wrong - will fall back to Adam
opt = MobiuOptimizer(params, base_optimizer="nadam")

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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 or AdamW
VQE / Chemistry	Adam
QAOA	NAdam
RL / Trading	Momentum
Drug Discovery	AMSGrad
Large Batch	LAMB

# PyTorch: If Adam isn't working, try Momentum:
base_opt = torch.optim.SGD(model.parameters(), lr=0.02, momentum=0.9)
opt = MobiuOptimizer(base_opt, method="adaptive")

# Quantum: If Adam isn't working, try NAdam:
opt = MobiuOptimizer(params, base_optimizer="NAdam", method="adaptive")

2. Switch Method

If This Fails	Try This
standard	adaptive
adaptive	deep
deep	standard

# If standard isn't working for your problem:
opt = MobiuOptimizer(base_opt, method="adaptive")

3. Switch Mode (Quantum only)

If This Fails	Try This
simulation	hardware

opt = MobiuOptimizer(params, method="standard", mode="hardware")

4. Adjust Learning Rate

# Try lower LR if diverging
base_opt = torch.optim.Adam(model.parameters(), lr=0.0001)

# Try higher LR if stuck
base_opt = torch.optim.Adam(model.parameters(), lr=0.001)

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 AMSGrad + standard method
Crypto/RL	High variance	Use Momentum + adaptive method
QAOA	Local minima	Use NAdam + deep method

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MobiuAttention 🧪

Why?

Standard Transformer attention is O(N²) in sequence length. MobiuAttention is O(N).

Seq Length	Transformer	MobiuAttention	Speedup
2,048	21s	9s	2.3x
4,096	39s	10s	3.9x
8,192	42s	7s	6.0x
16,384	OOM 💥	5s ✅	∞

Quality (Same as Transformer)

Benchmark	Transformer	MobiuAttention
Shakespeare PPL	12.8	13.5
ListOps Accuracy	81%	82%
Needle-in-Haystack	100%	100%

Usage

from mobiu_q.experimental import MobiuBlock

class LongContextLM(nn.Module):
    def __init__(self, vocab, d=512, h=8, layers=6):
        super().__init__()
        self.embed = nn.Embedding(vocab, d)
        self.blocks = nn.Sequential(*[MobiuBlock(d, h) for _ in range(layers)])
        self.head = nn.Linear(d, vocab)
    
    def forward(self, x):
        return self.head(self.blocks(self.embed(x)))

# Works with 16K+ tokens!
model = LongContextLM(50000)
x = torch.randint(0, 50000, (1, 16384))
out = model(x)  # No OOM!

⚠️ Experimental Status

• Functional and tested
• API may change in future versions
• Feedback welcome!

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How It Works

Soft Algebra

Both optimizer and attention use the nilpotent property ε²=0:

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

This enables tracking both "potential" and "realized" components.

In Optimization

lr_t = base_lr × (1 + soft_component)

Soft Algebra adapts learning rate based on loss landscape curvature.

In Attention

S(t) = γ·S(t-1) + k_t ⊗ v_t  # O(N) state update

Instead of O(N²) pairwise attention, we track state with O(N) complexity.

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License

Free tier: 20 API calls/month (optimizer only) Pro tier: Unlimited - https://app.mobiu.ai

Note: MobiuAttention runs locally, no API calls required.

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Links

• PyPI
• GitHub Issues

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Citation

@software{mobiu_q,
  title={Mobiu-Q: Soft Algebra for Optimization and Attention},
  author={Mobiu Technologies},
  year={2026},
  url={https://github.com/mobiu-ai/mobiu-q}
}