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

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⚙️ 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	✓	✓	✓	✓	✓
Kourkoutas-β	✓	✓	✓	✓	✗

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🛠️ Comprehensive Feature Guide

A. Universal Safe Features

These features work with all optimizers and are generally safe to enable.

Feature	Description	Recommended Usage	Performance Impact	Theoretical Basis	Compatibility
Fused Back Pass	Fuses backward pass; gradients used immediately and memory freed on-the-fly	Memory-constrained environments	Reduces peak memory	Memory optimization	All optimizers
Stochastic Rounding	Replaces nearest rounding with stochastic rounding to preserve small gradient updates in BF16	BF16 training	Minimal overhead (<5%)	Revisiting BFloat16 Training	All optimizers
OrthoGrad	Removes gradient component parallel to weights to reduce overfitting	Full fine-tuning without weight decay	+33% time overhead (BS=4); less at larger BS	Grokking at Edge	All optimizers
Factored	Memory-efficient optimization via rank-1 1-bit factorization of optimizer states	Large models / memory-limited hardware	Adds compression overhead	SMMF	All optimizers

B. Individual Features

Feature	Description	Recommended Usage	Performance Impact	Theoretical Basis	Compatibility
Cautious	Only applies update if gradient direction aligns with momentum direction	Accelerating convergence	No overhead	C-Optim	Adam/Adopt/Prodigy/Lion
Grams	Update direction derived purely from current gradient	When Cautious is insufficient	No overhead	Grams	Adam/Adopt/Prodigy
AdEMAMix	Dual EMA system that retains relevance of gradients over tens of thousands of steps	Long training runs, especially where model forgetting is a concern	+1 state memory	AdEMAMix	Adam/Adopt/Prodigy
Simplified_AdEMAMix	Accumulator-based momentum, single EMA variant of AdEMAMix	All scenarios when tuned correctly	No overhead	Connections	Adam/Adopt/Prodigy
atan2	Robust epsilon replacement with built-in gradient clipping	Use for stable bounded updates (or for Adopt as it needs that)	No overhead	Adam-atan2	Adam/Adopt/Prodigy
Kourkoutas-β	Layer-wise adaptive β₂ based on gradient “sunspike” ratio	Noisy/small/large-batch/high-LR training	No overhead	Kourkoutas-β	Adam/Adopt/Prodigy/Simplified_AdEMAMix

Note: If both Cautious and Grams are enabled, Grams takes precedence and Cautious is disabled.

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🔍 Feature Deep Dives

AdEMAMix

• Adds a slow-decaying second EMA (beta3) that retains gradient memory over tens of thousands of steps.
• Particularly effective for small batch sizes, where Adam’s standard first moment is nearly useless.

Tunable Hyperparameters

Parameter	Default	Tuning Guide
beta3	0.9999	• Runs >120k steps: 0.9999 • Runs ≤120k steps: 0.999
alpha	5	• Reduce to 2–3 if diverging • Increase to strengthen long-term memory

✅ Pro Tip: Set beta1=0 in Adam/Adopt/Prodigy to skip standard EMA entirely and rely solely on AdEMAMix’s slow EMA, ideal for small-batch regimes.

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Simplified_AdEMAMix

• Introduced in Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants (arXiv:2502.02431).
• Replaces Adam’s first moment with a theory-based momentum with emphasize on raw gradient, combining the stability of long memory with responsiveness to recent gradients.
• Key insight: Classical momentum does not accelerate in noisy (small-batch) regimes; this accumulator do.

Tunable Hyperparameters

Parameter	Default	Tuning Guide
beta1	0.99	Controls accumulator memory length: • Small BS: 0.99–0.9999 • Large BS: 0.9
Grad α	100	Most critical parameter: • Inversely scales with batch size • 100–10 for small BS (≤32) • 1–0.1 for large BS (≥512)

⚠️ Critical: Requires ~100x smaller learning rate than AdamW (e.g., 1e-6 vs 1e-4).
For Prodigy_Adv, set initial_d to:

• LoRA: 1e-8
• Full FT: 1e-10
• Embedding: 1e-7

⚠️ Incompatible with: Cautious, Grams, atan2, and standard update clipping.

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atan2

• Replaces eps in Adam-family optimizers with a scale-invariant, bounded update rule.
• Automatically clips updates to [-2, 2], preventing destabilizing jumps.
• Highly recommended for Adopt_Adv, which is prone to instability without clipping.

📚 Reference:

• Paper: https://arxiv.org/abs/2407.05872
• Code: https://github.com/lucidrains/adam-atan2-pytorch

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Kourkoutas-β

Kourkoutas-β introduces a sunspike-driven, layer-wise adaptive second-moment decay (β₂) as an optional enhancement for Adam_Adv, Adopt_Adv, Prodigy_Adv, and Simplified_AdEMAMix.

Instead of using a fixed β₂ (e.g., 0.999 or 0.95), it dynamically modulates β₂ per layer based on a bounded sunspike ratio:

• During gradient bursts → β₂ ↓ toward Lower β₂ → faster reaction
• During calm phases → β₂ ↑ toward The Selected β₂ → stronger smoothing

This is especially effective for noisy training, small batch sizes, and high learning rates, where gradient norms shift abruptly due to noise or aggressive LR schedules.

Pros/Cons

Category	Details
✅ Pros	• Layer-wise adaptation blends benefits of high β₂ (strong smoothing) and low β₂ (fast reaction). • Robust to sudden loss landscape shifts, reacts quickly during gradient bursts, smooths during calm phases. • High tolerance to aggressive learning rates.
⚠️ Cons	• Potentially unstable at the start of training due to unreliable early gradient norms; mitigated by using K-β Warmup Steps.

💡 Best Practice: Set K_warmup_steps equal to your standard LR warmup steps. During warmup, the optimizer uses the static beta2; adaptation begins only after warmup ends.

📚 Reference:

• Paper: Kourkoutas-β: A Sunspike-Driven Adam Optimizer with Desert Flair
• Code: kbeta

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📚 References

1. Revisiting BFloat16 Training
2. SMMF: Square-Matricized Momentum Factorization
3. The AdEMAMix Optimizer
4. Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD
5. Kourkoutas-β: A Sunspike-Driven Adam Optimizer with Desert Flair
6. Scaling Exponents Across Parameterizations and Optimizers