# Green-ELM: Efficient Analytic Learning via High-Dimensional Random Projections

arXiv: https://arxiv.org/abs/2604.15613 · HTML: https://mlsanity.com/paper/2604.15613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Intriguing Properties of Randomly Weighted Networks: Generalizing While Learning Next to Nothing](https://mlsanity.com/paper/1802.00844/) (2018)
- [Robustifying the Deployment of tinyML Models for Autonomous mini-vehicles](https://mlsanity.com/paper/2007.00302/) (2020)
- [A Principle for Global Optimization with Gradients](https://mlsanity.com/paper/2308.09556/) (2023)
- [Mitigating Catastrophic Forgetting in Streaming Generative and Predictive Learning via Stateful Replay](https://mlsanity.com/paper/2511.17936/) (2025)

## Abstract (arXiv)

We present Green-ELM, a non-iterative neural architecture that replaces gradient-based optimization of the output layer with a closed-form analytic solution over a fixed, high-dimensional random feature representation. By projecting input manifolds into a high-dimensional, random feature space (d gg 784), our results show that complex class boundaries can be effectively untangled without the computational overhead of backpropagation. Utilizing the Moore-Penrose pseudoinverse, LU and Cholesky decomposition to solve for the output layer in a single analytic step, Green-ELM achieves a classification accuracy of 98.10% on MNIST (d=4000) and 86.63% on Fashion-MNIST. Furthermore, we experiment with a pre-trained ``frozen-backbone'' based on ResNet-18 to extract high-quality features and show that these one-shot solvers are effective beyond simple datasets. Notably, our baseline CPU configuration on MNIST (d=2000) achieves 97.15% accuracy in 1.5s, representing a 11.6× reduction in reported training time over an SGD baseline while maintaining comparable performance. We observe a near-logarithmic scaling behavior between dimensionality and accuracy, where the accuracy increases approximately logarithmically with hidden dimensionality over the tested range, suggesting that feature-space expansion contributes substantially to performance in these experiments. . This one-shot linear matrix solver approach offers a viable alternative for real-time Edge AI, where the traditional training phase is bypassed in favor of non-iterative manifold representation and readout. Finally, we propose an Empirical Scaling Hypothesis, a framework that models accuracy bounds as a function of high dimensionality and intrinsic dataset complexity.