adv-optm 1.1.0

A family of highly efficient, lightweight yet powerful optimizers.

Advanced Optimizers (AIO)

A comprehensive, all-in-one collection of optimization algorithms for deep learning, designed for maximum efficiency, minimal memory footprint, and superior performance across diverse model architectures and training scenarios.

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📦 Installation

pip install adv_optm

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🧠 Core Innovations

This library integrates multiple state-of-the-art optimization techniques validated through extensive research and practical training, with 1-bit compression for optimizer states:

Memory-Efficient Optimization (SMMF-inspired)

• Paper: SMMF: Square-Matricized Momentum Factorization
• Approach: Uses rank-1 non-negative matrix factorization with reconstruction cycle (factor → reconstruct → update → factor)
• Innovation:
  • First moment split into 1-bit sign + absolute value
  • Final storage: four factored vectors + one 1-bit sign state
  • Preserves Adam-like update quality with drastically reduced memory

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⚡ Performance Characteristics

Memory Efficiency (SDXL Model - 6.5GB)

Optimizer	Memory Usage	Description
Adopt_Factored	328 MB	4 small vectors + 1-bit state
Adopt_Factored + AdEMAMix	625 MB	6 small vectors + two 1-bit states
Simplified_AdEMAMix	328 MB	Same as standard factored (no extra state)

Speed Comparison (SDXL, Batch Size 4)

Optimizer	Speed	Notes
Adafactor	~8.5s/it	Baseline
Adopt_Factored	~10s/it	+18% overhead from compression
Adopt_Factored + AdEMAMix	~12s/it	+41% overhead (3 factored states)

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🧪 Available Optimizers

Standard Optimizers (All support factored=True/False)

Optimizer	Description	Best For
Adam_Adv	Advanced Adam implementation	General purpose
Adopt_Adv	Adam-variant with independent beta2	Stable training for small batch size regimes
Prodigy_Adv	Prodigy with D-Adaptation	Adam with automatic LR tuning
Simplified_AdEMAMix	Adam variant with accumulator momentum	Small/large batch training when tuned correctly
Lion_Adv	Advanced Lion implementation	Memory-constrained environments
Prodigy_Lion_Adv	Prodigy + Lion combination	Lion with automatic LR tuning

Feature Matrix

Feature	Adam_Adv	Adopt_Adv	Prodigy_Adv	Simplified_AdEMAMix	Lion_Adv
Factored	✓	✓	✓	✓	✓
AdEMAMix	✓	✓	✓	✗	✗
Simplified_AdEMAMix	✗	✗	✓	✓	✗
OrthoGrad	✓	✓	✓	✓	✓
Grams	✓	✓	✓	✗	✗
Cautious	✓	✓	✓	✗	✓
atan2	✓	✓	✓	✗	✗
Stochastic Rounding	✓	✓	✓	✓	✓
Fused Backward Pass	✓	✓	✓	✓	✓

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⚙️ Key Features & Parameters

Comprehensive Feature Guide

Feature	Description	Recommended Usage	Performance Impact	Theoretical Basis	Compatibility
Factored	Memory-efficient optimization using rank-1 factorization	Enable for large models (>1B params) or limited VRAM	+12-41% time overhead, 1-bit memory usage	SMMF	All optimizers
AdEMAMix	Dual EMA system for momentum	Use for long training runs (10k+ steps)	+1 state memory.	AdEMAMix	Adam/Adopt/Prodigy
Simplified_AdEMAMix	Accumulator-based momentum	Small batch training (≤32)	Same memory as standard, no extra overhead	Schedule-Free Connections	Adam/Prodigy
OrthoGrad	Removes gradient component parallel to weights	Full finetuning without weight decay	+33% time overhead, no memory impact	Grokking at Edge	All optimizers
Stochastic Rounding	Improves precision for BF16 training	BF16 training	Minimal overhead (<5%)	Revisiting BFloat16 Training	All optimizers
atan2	Robust eps replacement + built-in clipping	Use with Adopt or unstable training	No overhead	Adam-atan2	Adam/Adopt/prodigy
Cautious	Update only when the direction align with the gradients	should faster the convergence	No overhead	C-Optim	Adam/Adopt/prodigy
Grams	Update direction from the gradients	should have a stronger effect than cautious	No overhead	Grams	Adam/Adopt/prodigy

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Simplified_AdEMAMix Parameters

Simplified_AdEMAMix replaces standard momentum with an accumulator for better small-large batch performance.

Parameter	Recommended Values	Description
beta1	0.9 (large BS), 0.99-0.9999 (small BS)	Determines memory length of accumulator
alpha	100-10 (small BS), 1-0 (large BS)	Gradient smoothing factor

Alpha Tuning Guide:

Batch Size	Recommended α	Rationale
Small (≤32)	100, 50, 20, 10	Emphasizes recent gradients for quick adaptation
Medium (32-512)	10, 5, 2, 1	Balanced approach
Large (≥512)	1, 0.5, 0	Emphasizes historical gradients for stability

⚠️ Important: Use ~100x smaller learning rate with Simplified_AdEMAMix compared to AdamW (e.g., 1e-6 instead of 1e-4)

📊 Performance Validation

Small Batch Training (SDXL, BS=2, 1.8K steps)

• 🟢 Prodigy_adv (beta1=0.9, d0=1e-5): Final LR=2.9e-4
• 🔵 Prodigy_adv + Simplified_AdEMAMix (beta1=0.99, α=100, d0=1e-7): Final LR=5.8e-6

Results:

• Simplified_AdEMAMix shows faster convergence and better final performance
• D-Adaptation automatically handles aggressive updates (50x smaller LR)
• Generated samples show significantly better quality with Simplified_AdEMAMix

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⚠️ Known Limitations

1. Prodigy_Adv Sensitivity

• Highly sensitive to gradient modifications (Adopt normalization, low-rank factorization)
• May fail to increase learning rate in some LoRA scenarios
• Fix: Disable factorization or set beta1=0

2. Aggressive Learning Rates

• Can destabilize factored first moment
• Recommendation: Check Prodigy learning rate as reference for safe LR threshold

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📚 References

1. SMMF: Square-Matricized Momentum Factorization
2. The AdEMAMix Optimizer: Better, Faster, Older
3. Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants

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