On the Effectiveness of the z-Transform Method in Quadratic Optimization

arXiv:2507.03404 · cs.LG, math.OC · Submitted 2025-07-04 · Read on arXiv

cs.LG, math.OC

Submitted: 2025-07-04

Updated: 2026-09-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Scaling Laws — 8× in this paper · explained in 4 episodes
• Hilbert Space — 5× in this paper · explained in 2 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Convergence Guarantees — 2× in this paper · explained in 3 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Non-asymptotic Analysis — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes

Sources

• Acceleration by Random Stepsizes: Hedging, Equalization, and the Arcsine Stepsize Schedule
• Strong Convergence of FISTA Iterates under H{\"o}lderian and Quadratic Growth Conditions
• Dimension-adapted Momentum Outscales SGD
• Provable non-accelerations of the heavy-ball method
• Scaling Laws for Gradient Descent and Sign Descent for Linear Bigram Models under Zipf's Law
• A Simplified Analysis of SGD for Linear Regression with Weight Averaging

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks