Leo Optimizer: A New Neural Network Optimization Scheme Fusing Lion Momentum and Orthogonalization

This article introduces the Leo optimizer, which fuses the Lion momentum mechanism and element-wise orthogonalization technology to enhance neural network training performance while maintaining computational efficiency, providing deep learning practitioners with a faster model convergence experience. Its core advantages include low memory usage, fast convergence, and good generalization ability, making it suitable for scenarios such as large-scale model training.

In deep learning training, the choice of optimizer directly affects the model's convergence speed and final performance. From classic SGD to Adam, and then to recent improved schemes, researchers continue to look for more efficient parameter update strategies. The Leo optimizer was born in this context, fusing the Lion momentum mechanism and orthogonalization technology to provide a faster and more stable training experience.

Inheritance and Improvement of the Lion Momentum Mechanism

Leo is based on the Lion optimizer, and its core features include sign momentum (updating only using gradient signs), dual momentum buffers (interpolating to calculate update directions), and low memory usage (only one momentum state is stored).

Element-wise Orthogonalization Technology

Orthogonalization ensures that parameter update dimensions are independent of each other and avoids redundancy. The implementation of element-wise orthogonalization in Leo includes: 1. Dimension decomposition; 2. Correlation elimination; 3. Direction optimization. This technology can avoid update interference, improve gradient utilization efficiency, and accelerate convergence to better local minima.

Computational Efficiency

• Low memory requirement (single momentum buffer); - Fast computation (efficient sign operations and orthogonalization); - Hardware-friendly (adapts to GPU/TPU parallel architectures).

Convergence Characteristics

• Faster initial convergence; - More stable late-stage training; - Better generalization performance.

Comparison with Mainstream Optimizers

Feature	SGD	Adam	Lion	Leo
Momentum Type	Classic Momentum	Adaptive Moment Estimation	Sign Momentum	Sign + Orthogonalization
Memory Usage	Low	High	Low	Low
Computational Complexity	Low	Medium	Low	Medium
Hyperparameter Sensitivity	High	Medium	Medium	Low
Adaptability to Large-scale Training	Average	Good	Excellent	Excellent

Large-scale Language Model Training

Suitable for large batch sizes, long sequence modeling, and distributed training (reduces communication overhead).

Computer Vision Tasks

Stabilizes deep CNN/Transformer training, transfer learning fine-tuning, and adversarial training for GANs/diffusion models.

Recommendation Systems and Graph Neural Networks

Handles sparse gradients, optimizes graph convolutional networks, and supports online learning for real-time recommendations.

Installation and Configuration

Easy to integrate into existing training workflows without complex configuration.

Hyperparameter Tuning Recommendations

• Learning rate: initial value of 1e-4 to 1e-3 + decay strategy; - Weight decay: appropriate use of regularization; - Momentum coefficient: default settings are good, can be fine-tuned per task.

Combination with Other Technologies

Combine with learning rate scheduling (cosine annealing, warm-up), mixed-precision training (FP16/BF16), and gradient clipping (when training is unstable).

Limitations

• Task dependence: different tasks have different preferences; - Model architecture impact: specific architectures may be more suitable for other optimizers; - Dataset characteristics: distribution and scale affect performance.

Debugging and Monitoring

Pay attention to training loss curves, validation set performance, and gradient statistics.

Future Research Directions

• Adaptive orthogonalization strength; - Multi-scale orthogonalization; - Integration of second-order information or meta-learning methods.

The Leo optimizer provides an efficient and stable training option by fusing Lion's sign momentum and element-wise orthogonalization technology. Its low memory usage, fast convergence, and good generalization characteristics make it a powerful tool for large-scale model training. It is recommended that deep learning practitioners try using it in their projects.