Update to more inclusive 'emerging optimizers' terminology

Author: sbhavani

README.md

@@ -2,33 +2,33 @@
 
 ## Overview
 
-Emerging Optimizers is a research project focused on understanding and optimizing the algorithmic behavior of matrix-based preconditioning optimizers (including Shampoo, SOAP, Muon, etc.) and their implications to performance of GPU systems in LLM training.
+Emerging Optimizers is a research project focused on understanding and optimizing the algorithmic behavior of emerging optimizers (including Shampoo, SOAP, Muon, and others) and their implications to performance of GPU systems in LLM training.
 
 > ⚠️ Note: Emerging-Optimizers is under active development. All APIs are experimental and subject to change. New features, improvements, and documentation updates are released regularly. Your feedback and contributions are welcome, and we encourage you to follow along as new updates roll out.
 
 ## Background
 
-### What are Matrix-Based Preconditioning Optimizers?
+### What are Emerging Optimizers?
 
-Matrix-based preconditioning optimizers use non-diagonal preconditioning of gradients to achieve faster convergence compared to traditional methods like Adam or SGD. Unlike conventional optimizers that treat each parameter independently (diagonal preconditioning), these optimizers leverage the full or blockwise structure of the gradient's second moment statistics through matrix preconditioning.
+Emerging optimizers represent a class of novel optimization algorithms that go beyond traditional first-order methods like Adam or SGD. These include optimizers that use matrix-based (non-diagonal) preconditioning, orthogonalization techniques, and other innovative approaches to achieve faster convergence and improved training efficiency.
 
-**Reference:** [Shampoo: Preconditioned Stochastic Tensor Optimization](https://arxiv.org/abs/1802.09568)
+Examples include Shampoo, which uses Kronecker-factored preconditioning ([arXiv:1802.09568](https://arxiv.org/abs/1802.09568)), and Muon, which uses Newton-Schulz orthogonalization ([arXiv:2502.16982](https://arxiv.org/abs/2502.16982)).
 
 ### Why They Matter
 
-Matrix-based preconditioning optimizers have demonstrated significant practical impact in large-scale language model training. Most notably, they were used to train the **Kimi K2 model** ([arXiv:2507.20534](https://arxiv.org/abs/2507.20534)), showcasing their effectiveness at scale. These optimizers can:
+Emerging optimizers have demonstrated significant practical impact in large-scale language model training. Most notably, **Muon was used to train the Kimi K2 model** ([arXiv:2507.20534](https://arxiv.org/abs/2507.20534)), showcasing the effectiveness of these novel approaches at scale. These optimizers can:
 
 - Achieve faster convergence, reducing the number of training steps required
 - Improve final model quality through better conditioning of the optimization landscape
 - Enable more efficient hyperparameter tuning due to reduced sensitivity to learning rates
 
 ### Optimizers Included
 
-This project focuses on the following matrix-based preconditioning optimizers:
+This project currently includes the following optimizers:
 
-- **Shampoo**: The foundational optimizer using Kronecker-factored preconditioning ([arXiv:1802.09568](https://arxiv.org/abs/1802.09568))
-- **SOAP (Shampoo with Adam in the Preconditioner)**: A variant that combines Shampoo's preconditioning with Adam-style momentum ([arXiv:2409.11321](https://arxiv.org/abs/2409.11321))
-- **Muon**: A momentum-based optimizer using Newton-Schulz orthogonalization for improved stability and convergence in large-scale training ([arXiv:2502.16982](https://arxiv.org/abs/2502.16982))
+- **Shampoo**: Uses Kronecker-factored preconditioning ([arXiv:1802.09568](https://arxiv.org/abs/1802.09568))
+- **SOAP (Shampoo with Adam in the Preconditioner)**: Combines Shampoo's preconditioning with Adam-style momentum ([arXiv:2409.11321](https://arxiv.org/abs/2409.11321))
+- **Muon**: Uses Newton-Schulz orthogonalization for improved stability and convergence in large-scale training ([arXiv:2502.16982](https://arxiv.org/abs/2502.16982))
 
 
 ## Installation