Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.05184

Provably Learning Mixtures of Linear Experts

Adrian Candocia·Aamod Varma·Mark Davenport
View original source ↗Read source document ↗Export metadata ↓

Abstract

Mixture-of-Experts (MoE) models are widely deployed in modern machine learning. However, few convergence guarantees exist for gradient-based training of MoEs: the objective is nonconvex, and even simple mixtures trap first-order methods in spurious local optima. We analyze a canonical gated mixture featuring linear experts and a gate induced by Gaussian clusters in the input space, and give, to our knowledge, the first global convergence guarantee for jointly training the gate and the experts of such a model by gradient EM on its likelihood. Given a logarithmic overparameterization relative to the true number of experts $m$, gradient EM converges from randomly initialized gates and least-squares-initialized experts to any prescribed accuracy in polynomially many iterations, under a separation condition on the gate centers. Our analysis establishes a gradient-dominance inequality for the coupled dynamics by decoupling the loss into per-cluster subproblems. Empirical results validate the predicted $m\log m$ phase transition and suggest that the least-squares warm start required by our analysis is not needed in practice: randomly initialized experts perform nearly as well. We also find that leaving the mixing weights unconstrained concentrates routing onto the true number of experts, whereas load-balancing penalties spread it, so that the fitted model can be pruned to a fraction of its width without loss of accuracy.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Adrian Candocia, Aamod Varma, Mark Davenport. 2026-11-03. Provably Learning Mixtures of Linear Experts. https://arxiv.org/abs/2611.05184

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Subspace Node Pruning

Node pruning is the art of removing computational units such as neurons, filters, attention heads, or even entire layers to significantly reduce inference time while retaining network performance. In this work, we show that a broad family of importance measures, from activation-based to Fisher-based, share a common quadratic form. Through a lower-triangular change of basis, this form yields a pruning subspace in which entire nodes can be removed while the impact of the lost units is simultaneously recovered via linear least squares. Furthermore, the importance measures within our subspace are decoupled and additive through an orthogonalization of the layer activations, allowing multi-node pruning within layers without interference between importance scores. Our method, Subspace Node Pruning (SNP), outperforms the compared baselines on VGG-16 and ResNet-50 on ImageNet. On OPT-125M and LLaMA-2 7B, SNP matches the state-of-the-art LLM Surgeon at a 40-shot schedule and outperforms it whenever fewer shots are used, all without any retraining after pruning.

cs.LG↗
arXiv2026

On the growth of the parameters of approximating ReLU neural networks

This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures, e.g., in terms of width or depth of the networks, we are concerned with the asymptotic growth of the parameters of approximating networks. Such results are of interest, e.g., for error analysis or consistency results for neural network training. The main result of our work is that, for a ReLU architecture with state of the art approximation error, the realizing parameters grow at most polynomially. The obtained rate with respect to a normalized network size is compared to existing results and is shown to be superior in most cases, in particular for high dimensional input.

cs.LG↗
arXiv2026

Correlations Are Ruining Your Gradient Descent

Natural gradient descent, and the preconditioned optimizers which have followed from it, correct gradient descent by estimating curvature and applying its inverse to the gradient. For any single layer of a deep neural network, this correction can be shown to approximately separate into two factors: one which accounts for correlations in the gradient signal, and one which accounts for correlations in the data arriving at that layer. Herein we show that this second factor can be expressed as a change of basis rather than of curvature and, considered thus, it can be removed from the optimizer entirely and placed within the network itself. Specifically, we show that, once forward weights are corrected, right-sided natural gradient descent can be implemented in a form which has three exactly equivalent forms: a gradient preconditioner, a decorrelating linear transform in the forward pass, or a set of recurrent dynamics in which all updates are Hebbian and rely only upon locally available signals. The (recurrent) decorrelation method we discover aligns closely with proposed methods for inhibitory learning and homeostatic plasticity in the brain. Notably, our transform requires no matrix inverse, no matrix decomposition, and no information beyond that which is available at an individual synapse. It can therefore be applied in distributed and physically constrained systems, including neuromorphic hardware and nervous systems, where existing preconditioners cannot. We demonstrate its effectiveness empirically in convolutional and residual network models while significantly improving a range of approximate biologically plausible methods for credit assignment.

cs.LG↗