An enhanced 8-bit Adafactor optimizer featuring fused CUDA kernels, log-space block-wise quantization, optional APOLLO low-rank updates, and 4-bit packed first moments, delivering substantially lower optimizer memory while preserving the low-overhead and numerical stability that make Adafactor attractive for training LLMs and diffusion models.

🔥 Key Features

• Log-Space Quantization: Maps the second moment (variance) to the log2 space before 8-bit quantization. This approach accommodates the long-tail distribution of variances, reducing the risk of small second-moment estimates being truncated to zero and improving overall training stability.
• Fused CUDA Kernels: Combines dequantization, EMA updates, Warp-Shuffle reductions, and requantization into single kernels. It utilizes float4 vectorization to optimize memory bandwidth usage.
• Optional 4-bit Packed First Moment: Stores the first moment (beta1) in a physically packed 4-bit format when enabled, providing momentum with minimal additional memory overhead.
• APOLLO Subspace Projection: Opt-in random subspace projection that estimates adaptive gradient scaling in a low-rank space, preventing stale second-moment statistics and potentially improving convergence and generalization.
• Fira Norm-Growth Limiter: Suppresses destructive gradient spikes by regulating the relative increase of update norms. Originally used for the APOLLO path, it is now available for the standard Adafactor path as well. It improves training stability and often allows the safe removal of external gradient clipping.
• Zero CPU-GPU Sync: Eliminates implicit synchronizations (e.g., D2H copies) in the control flow, ensuring the GPU computation pipeline runs without blocking.
• Cross-Platform JIT: Uses Just-In-Time (JIT) compilation for straightforward setup across both Windows and Linux environments.

📊 Performance

• Memory Footprint: Due to Adafactor's factorized second-moment estimation, 8-bit quantization, and optional 4-bit packed first moments, the optimizer typically consumes substantially less memory than AdamW8Bit.
• Training Speed: The fused kernel design and reduced synchronization overhead allow it to achieve step times comparable to other mainstream 8-bit optimizers.
• Quantization Precision: The second moment (variance) in Adafactor is strictly non-negative and spans multiple orders of magnitude. By mapping it to UINT8 in log2 space rather than linear space, the optimizer preserves relative precision for small variances, mitigating the instability often caused by outlier gradients in standard 8-bit quantization.

📦 Installation

This project uses JIT (Just-In-Time) compilation.

Please ensure torch and ninja are installed, and a CUDA compiler (such as MSVC or GCC) is available in your environment.

If CUDA compilation fails, the optimizer will automatically fall back to the pure PyTorch implementation.

From PyPI

pip install -U adafactor8bit

From Source

pip install git+https://github.com/yanfeiwong/adafactor-8bit.git

[!IMPORTANT] First-Time Compilation: The first time you instantiate the optimizer (or run the example script), it will automatically trigger the JIT compilation of the CUDA source code in the background. This may take anywhere from a few seconds to a couple of minutes depending on your system, and the terminal might appear unresponsive. Once compiled, the binary will be cached, and all subsequent runs will be instantaneous.

🚀 Quick Start

Using it is as simple as using a standard PyTorch optimizer.

from adafactor8bit import Adafactor8Bit

optimizer = Adafactor8Bit(model.parameters(), lr=1e-3)

[!TIP] Passing model.parameters() directly works for a quick test. In production, param_groups are recommended to protect sensitive layers (Norms, Biases) from quantization and weight decay. For sparse token embeddings (large vocabularies + small batch sizes), please refer to the Advanced Example to avoid cold-start variance explosion.

from adafactor8bit import Adafactor8Bit

def get_param_groups(model, weight_decay=1e-2):
    decay, no_decay = [], []
    for name, param in model.named_parameters():
        if not param.requires_grad: continue
        
        # Protect 1D tensors, biases, norms, and embeddings
        if param.ndim <= 1 or "bias" in name or "norm" in name or "embed" in name:
            no_decay.append(param)
        else:
            decay.append(param)
            
    return [
        {"params": decay, "weight_decay": weight_decay, "quantize": True},
        {"params": no_decay, "weight_decay": 0.0, "quantize": False}
    ]

model = MyModel().cuda()
optimizer = Adafactor8Bit(
    get_param_groups(model), 
    lr=1e-3, 
    # For continual learning or when using an external LR scheduler
    relative_step=False,     # Disable internal LR scheduling
    beta2=0.999,             # Lock EMA window to prevent "blunting" over steps
)

# Training loop...

🛠️ Advanced Example

Here we demonstrate a hybrid grouping strategy for complex hybrid architectures (e.g., Vision-Language Models, Diffusion UNets) to achieve stable and efficient training.

📌 The following strategies are applied:

Implementation:

from adafactor8bit import Adafactor8Bit

# Define learning rates
lr = 1e-3
lr_emb = 1e-4 # For Embedding layers, we use an Adam-style learning rate

def get_param_groups(model, lr_emb, weight_decay, apollo_rank=256):
    group_1d, group_embed, group_2d, group_nd = [], [], [], []

    for name, param in model.named_parameters():
        if not param.requires_grad: continue
        
        is_1d = param.ndim <= 1 or "bias" in name or "norm" in name
        # Match true Token Embeddings, excluding Position and Time Embeddings
        is_embedding = ("embed" in name.lower() 
                        and "position" not in name.lower() 
                        and "pos_embed" not in name.lower()
                        and "time" not in name.lower())
        
        if is_1d:
            group_1d.append(param)
        elif is_embedding:
            group_embed.append(param)
        elif param.ndim == 2:
            group_2d.append(param)
        else:
            group_nd.append(param)

    return [
        # 1. 1D / Sensitive: FP32, No Weight Decay
        {"params": group_1d, "weight_decay": 0.0, "quantize": False, "apollo_rank": 0},
        
        # 2. Embeddings: Recreating a momentum-free Adam
        {
            "params": group_embed, 
            "weight_decay": 0.0, 
            "quantize": False,
            "apollo_rank": 0,
            "factored": False,         # Enable element-wise variance
            "scale_parameter": False,  # Disable internal RMS scaling
            "d": 1e9,                  # Disable global Trust-Region clipping
            "lr": lr_emb               # Override global learning rate
        },
        
        # 3. 2D Weights: 8-bit quantization, Weight Decay, APOLLO low-rank projection
        {
            "params": group_2d, 
            "weight_decay": weight_decay, 
            "quantize": True, 
            "apollo_rank": apollo_rank,
            "beta1":0.9,               # Remove if minimizing optimizer memory is the priority.
        },
        
        # 4. >2D Weights: 8-bit quantization, Weight Decay, Full-Rank
        {
            "params": group_nd, 
            "weight_decay": weight_decay, 
            "quantize": True, 
            "apollo_rank": 0,
            "beta1":0.9,               # Remove if minimizing optimizer memory is the priority.
            "factored": False          # Disables factorization to preserve spatial structures, enabling finer gradient scaling.
                                       # Note: This increases state memory for >2D weights, depending on your model architecture.
                                       # If VRAM is constrained, reverting to factored=True is a safe alternative.
        },
    ]

model = MyModel().cuda()
optimizer = Adafactor8Bit(
    get_param_groups(model, lr_emb = lr_emb, weight_decay=1e-2, apollo_rank=256), 
    lr=lr, 
    # For continual learning or when using an external LR scheduler
    relative_step=False,              # Disable internal LR scheduling
    beta2=0.999,                      # Lock EMA window to prevent "blunting" over steps
    enable_fira_for_adafactor=True    # Enable Fira Limiter globally; external grad clipping can be safely removed
)

# Training loop...

[!NOTE] For more complete examples, please refer to the examples folder.

⚙️ Advanced Configuration

Continual Learning (beta2 & relative_step)

By default, Adafactor's second-moment decay rate dynamically decays with the training step, and the internal learning rate schedule (relative_step) scales the learning rate accordingly.

For endless fine-tuning or lifelong learning, this often leads to overly small learning rates and "blunted" second-moment estimates. To avoid these issues and keep the optimizer responsive:

• Set relative_step=False to disable the built-in LR schedule (allowing you to use an external scheduler).
• Set beta2=0.999 to lock the EMA window (similar to Adam).

Decoupled Weight Decay (scale_weight_decay=False)

By default, Adafactor's weight decay is coupled with the parameter's RMS scale.

• If you prefer the AdamW-style decoupled weight decay, set scale_weight_decay=False.

Fira Limiter (enable_fira_for_adafactor & fira_margin)

The Norm-Growth Limiter (introduced in the Fira paper) smooths gradient updates by limiting the relative increase of update norms, effectively suppressing destructive loss spikes.

• enable_fira_for_adafactor: Defaults to False. Set to True to enable the limiter for the standard Adafactor path. (Note: It is inherently active in the APOLLO path). When enabled, external gradient clipping (e.g., torch.nn.utils.clip_grad_norm_) can generally be safely removed to simplify the training pipeline.
• fira_margin: Defaults to 0.01. The tolerance margin for norm growth. The limiter activates only when the current update norm grows by more than this margin (e.g., 0.01 means a 1% growth) compared to the previous step.

Full-Rank and Factorized Variance (factored)

By default, Adafactor factorizes the second moment of $\ge$ 2D tensors into row and column statistics (factored=True) to minimize state memory. Setting factored=False switches to full element-wise variance (similar to RMSProp), while still retaining Adafactor's global RMS clipping mechanism (controlled by the d parameter). This configuration can be useful in the following scenarios:

• Convolution Weights (>2D): Setting factored=False maintains independent variance for each spatial position in the convolution kernel, enabling finer per-element gradient scaling.
• Sparse Embeddings: Combining factored=False, scale_parameter=False, d=1e9 and a lower learning rate creates a momentum-free adaptive optimizer. This allows for fine-grained, per-token updates while avoiding cold-token interference or cold-start explosions.

No-Compiler Environments (use_cuda_kernel=False)

If you are in an environment without a CUDA compiler and want to bypass JIT compilation entirely:

• Set use_cuda_kernel=False to fall back to the pure PyTorch implementation.

🌌 APOLLO Low-Rank Subspace Projection

Enable the APOLLO path to compute gradient scaling factors in a memory-efficient low-rank subspace. Compared to Adafactor's standard row/column factorization (which assumes spatial independence), APOLLO uses random subspace projection to capture cross-dimensional covariance information, potentially leading to better generalization while keeping memory overhead extremely low.

• apollo_rank: The target rank for the projection subspace. The default is 0 (disabled).

  • The official APOLLO GitHub repository recommends a rank of 256 for 1B and 7B models.
  • The LLaMA-Factory default is 16.
  • Setting this to 1 (APOLLO-Mini style) pushes VRAM savings to the limit (saves even more VRAM than the Adafactor path). The original APOLLO-Mini relies on the first-moment (beta1) to smooth out projection noise. To replicate this, set beta1=0.9 alongside apollo_rank=1. Without beta1, rank=1 may still work but can exhibit noisier scaling factors, especially at small batch sizes.

• apollo_scale_type: Determines how the scaling factor is applied. 'channel' applies it per channel (Standard APOLLO), while 'tensor' applies it globally (APOLLO-Mini).

• apollo_update_proj_gap: Steps between projection matrix refreshes. Defaults to 200. Setting this too small may cause frequent oscillations due to abrupt basis mutations, while setting it too large might cause the projection space to become stale and fail to track the drift of the gradient manifold.

• apollo_factorize (Experimental): Applies Adafactor's row/column factorization within the low-rank subspace. Mathematically, this leverages the norm-preserving property of random projections to approximate the variance of the primary dimension, while the secondary dimension's variance is estimated across random bases, introducing inherent noise. This dual-compression mechanism drastically reduces optimizer state overhead. Note that for smaller models, the actual VRAM savings might be marginal, and the introduced noise could impact convergence stability. Use with caution.

• Fira Limiter Integration: The APOLLO path automatically applies the Fira Norm-Growth Limiter to the scaled gradients to prevent sudden gradient rises from causing loss spikes. You can adjust its sensitivity using the global fira_margin parameter.

📈 Learning Rate Guide for Beginners

If you are migrating from optimizers like AdamW, Adafactor's learning rate behavior might feel a bit different. This is mainly due to the scale_parameter option.

• scale_parameter=True (default) Because of RMS scaling, a very small lr (e.g., 1e-5) often leads to extremely slow progress. Start with lr=1e-3 and adjust in the range 1e-4–5e-3 if needed.

• scale_parameter=False Disables RMS scaling, making the update scale more similar to AdamW. Use the learning rates you're familiar with for AdamW and tune as usual. (Note: the second moment is still factorized, so behavior is not identical.)

These are safe starting points. Always validate on your own task and batch size.

🎓 Acknowledgements

Thanks to Noam Shazeer and Mitchell Stern for proposing the original Adafactor algorithm in the paper Adafactor: Adaptive Learning Rates with Sublinear Memory Cost.

Thanks to Tim Dettmers for the inspiration from the paper 8-BIT OPTIMIZERS VIA BLOCK-WISE QUANTIZATION and the bitsandbytes library.

Thanks to Hanqing Zhu, Zhenyu Zhang, and the team for proposing the approximated gradient scaling method in the paper APOLLO: SGD-Like Memory, AdamW-level Performance.

Thanks to Xi Chen, Kaituo Feng, and the team for the Norm-Growth Limiter mechanism introduced in Fira: Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?.

Thanks to the PyTorch team for providing the foundational Optimizer implementation and the C++ Extension toolchain.

Thanks to the large language models Qwen, ChatGLM and DeepSeek for valuable technical discussions and code reviews on CUDA low-level optimization and memory safety mechanisms.

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📄 License

The project is released under the MIT License.