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

arXiv:2604.15613v4 Announce Type: replace-cross Abstract: 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$\times$ 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.

Abstract: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$\times$ 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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2604.15613 [cs.LG]

(or arXiv:2604.15613v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2604.15613 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

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

Related coverage