# A Unified Perspective on Optimization in Machine Learning and Neuroscience: From Gradient Descent to Neural Adaptation

arXiv: https://arxiv.org/abs/2510.18812 · HTML: https://mlsanity.com/paper/2510.18812/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 74 of its 234 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 30 of 74)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)

## Abstract (arXiv)

Iterative optimization is central to modern artificial intelligence (AI) and provides a crucial framework for understanding adaptive systems. This review provides a unified perspective on this subject, bridging classic theory with neural network training and biological learning. Although gradient-based methods, powered by the efficient but biologically implausible backpropagation (BP), dominate machine learning, their computational demands can hinder scalability in high-dimensional settings. In contrast, derivative-free or zeroth-order (ZO) optimization feature computationally lighter approaches that rely only on function evaluations and randomness. While generally less sample efficient, recent breakthroughs demonstrate that modern ZO methods can effectively approximate gradients and achieve performance competitive with BP in neural network models. This ZO paradigm is also particularly relevant for biology. Its core principles of random exploration (probing) and feedback-guided adaptation (reinforcing) parallel key mechanisms of biological learning, offering a mathematically principled perspective on how the brain learns. In this review, we begin by categorizing optimization approaches based on the order of derivative information they utilize, ranging from first-, second-, and higher-order gradient-based to ZO methods. We then explore how these methods are adapted to the unique challenges of neural network training and the resulting learning dynamics. Finally, we build upon these insights to view biological learning through an optimization lens, arguing that a ZO paradigm leverages the brain's intrinsic noise as a computational resource. This framework not only illuminates our understanding of natural intelligence but also holds vast implications for neuromorphic hardware, helping us design fast and energy-efficient AI systems that exploit intrinsic hardware noise.