# Theoretical Framework for Tempered Fractional Gradient Descent: Application to Breast Cancer Classification

arXiv: https://arxiv.org/abs/2504.18849 · HTML: https://mlsanity.com/paper/2504.18849/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Builds on (most cited first, 3 of 3)

- [PSMGD: Periodic Stochastic Multi-Gradient Descent for Fast Multi-Objective Optimization](https://mlsanity.com/paper/2412.10961/) (2024)
- [A Mirror Descent-Based Algorithm for Corruption-Tolerant Distributed Gradient Descent](https://mlsanity.com/paper/2407.14111/) (2024)
- [Fractional-order spike-timing-dependent gradient descent for multi-layer spiking neural networks](https://mlsanity.com/paper/2410.15293/) (2024)

## Abstract (arXiv)

This paper introduces Tempered Fractional Gradient Descent (TFGD), a novel optimization framework that synergizes fractional calculus with exponential tempering to enhance gradient-based learning. Traditional gradient descent methods often suffer from oscillatory updates and slow convergence in high-dimensional, noisy landscapes. TFGD addresses these limitations by incorporating a tempered memory mechanism, where historical gradients are weighted by fractional coefficients |wj| = binomαj and exponentially decayed via a tempering parameter λ. Theoretical analysis establishes TFGD's convergence guarantees: in convex settings, it achieves an O(1/K) rate with alignment coefficient dα,λ = (1 - e-λ)-α, while stochastic variants attain O(1/kα) error decay. The algorithm maintains O(n) time complexity equivalent to SGD, with memory overhead scaling as O(d/λ) for parameter dimension d. Empirical validation on the Breast Cancer Wisconsin dataset demonstrates TFGD's superiority, achieving 98.25% test accuracy (vs. 92.11% for SGD) and 2× faster convergence. The tempered memory mechanism proves particularly effective in medical classification tasks, where feature correlations benefit from stable gradient averaging. These results position TFGD as a robust alternative to conventional optimizers in both theoretical and applied machine learning.