Theoretical Analysis of Sparse Optimization with Reparameterization, Weight Decay, and Adaptive Learning Rate

Researchers introduce ReWA, a novel sparse optimization method combining reparameterization, weight decay, and adaptive learning rates to address instability issues in ℓp regularization. Experiments on CIFAR-10 and ImageNet demonstrate that ReWA achieves superior sparsity compared to ℓ1 regularization while maintaining test accuracy, offering a practical alternative for neural network compression.

Sparse optimization represents a critical challenge in modern machine learning, particularly as neural networks grow increasingly complex and computationally expensive. Traditional ℓp regularization approaches, while theoretically grounded, struggle with optimization instability when 0<p<1 due to unbounded gradients that complicate training dynamics. The ReWA method addresses this fundamental limitation by reformulating the optimization problem through reparameterization, which transforms the landscape in ways that mitigate gradient-related instabilities while maintaining the sparsity-inducing benefits of ℓp regularization.

The approach builds on established optimization techniques but combines them in a novel manner specifically tailored to sparse learning. Weight decay and adaptive learning rates have proven effective in various contexts, yet their synergistic application within a reparameterized framework creates distinct advantages for achieving sparsity without sacrificing model performance. This combination appears to unlock a more stable optimization trajectory than conventional methods.

For practitioners developing efficient neural networks, this work has immediate practical value. Model compression and sparsity reduction directly impact inference speed, memory requirements, and deployment feasibility across edge devices and resource-constrained environments. The experimental validation on standard benchmarks demonstrates that ReWA doesn't merely achieve sparsity through aggressive regularization that trades accuracy for compression—it maintains competitive accuracy metrics while improving sparsity levels beyond ℓ1 regularization baselines.

Future research directions include investigating ReWA's performance across diverse architectures beyond ResNets, examining scalability to larger models, and exploring theoretical convergence guarantees. The work establishes a foundation for more sophisticated sparse optimization methods that could accelerate the deployment of efficient AI systems in production environments.

• →ReWA combines reparameterization, weight decay, and adaptive learning rates to solve sparse optimization instability inherent in ℓp regularization methods.
• →The approach achieves superior sparsity compared to ℓ1 regularization while preserving test accuracy on CIFAR-10 and ImageNet benchmarks.
• →Unbounded gradients in traditional ℓp regularization (0<p<1) create optimization challenges that ReWA's reformulated landscape mitigates effectively.
• →The method has practical implications for neural network compression, model efficiency, and deployment on resource-constrained devices.
• →ReWA's success suggests that optimization landscape transformation through reparameterization can improve performance of sparse learning algorithms.