HalfNet: Randomized Neural Networks with Learned Subspace Geometry
2026-06-03 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explore a type of neural network called HalfNet, where some weights are set randomly but according to a pattern learned from data, instead of just random values with no structure. They test this on image tasks and find it performs about as well as fully trained networks, but with fewer parameters. Their analysis suggests that the way weights are spread out or arranged (the geometry) matters more than their exact values. They also show that HalfNet's approach can be seen in different ways, like metric learning or kernel methods, not just as a small trick to reduce complexity.
Neural NetworksRandom WeightsLow-Rank FactorizationGeometry of Weight SpaceMultilayer PerceptronsSpectral AnalysisMetric LearningRandom FeaturesKernel Methods
Authors
Ethem Alpaydin
Abstract
Many researchers investigated neural networks with some of their weights fixed to values randomly drawn from a given distribution, e.g., $N(0, I)$. Our proposed HalfNet draws random weights from $N(0, Σ)$, where $Σ$, which defines the geometry of the distribution, has a low-rank factorization that we learn from data. Experiments on MNIST and CIFAR-10 demonstrate that HalfNet can match the performance of fully trained multilayer perceptrons while using substantially fewer parameters. Spectral analysis indicates that much of the predictive power of neural networks lies in the geometry of their weight space rather than in the precise values of individual parameters, and we observe that accuracy scales smoothly with rank. HalfNet is not a neural architecture trick for low-rank structure; it implements a data-dependent random embedding that can also be interpreted through supervised metric learning, or random-feature and kernel perspectives.