Luxical: High-Speed Lexical-Dense Text Embeddings

Frontier language model quality increasingly hinges on our ability to organize web-scale text corpora for training. Today's dominant tools trade off speed and flexibility: lexical classifiers (e.g., FastText) are fast but limited to producing classification output scores, while the vector-valued outputs of transformer text embedding models flexibly support numerous workflows (e.g., clustering, classification, and retrieval) but are computationally expensive to produce. We introduce Luxical, a library for high-speed "lexical-dense" text embeddings that aims to recover the best properties of both approaches for web-scale text organization. Luxical combines sparse TF--IDF features, a small ReLU network, and a knowledge distillation training regimen to approximate large transformer embedding models at a fraction of their operational cost. In this technical report, we describe the Luxical architecture and training objective and evaluate a concrete Luxical model in two disparate applications: a targeted webcrawl document retrieval test and an end-to-end language model data curation task grounded in text classification. In these tasks we demonstrate speedups ranging from 3x to 100x over varying-sized neural baselines, and comparable to FastText model inference during the data curation task. On these evaluations, the tested Luxical model illustrates favorable compute/quality trade-offs for large-scale text organization, matching the quality of neural baselines. Luxical is available as open-source software at https://github.com/datologyai/luxical.

No Spurious Local Minima in Deep Quadratic Networks

Despite their practical success, a theoretical understanding of the loss landscape of neural networks has proven challenging due to the high-dimensional, non-convex, and highly nonlinear structure of such models. In this paper, we characterize the training landscape of the quadratic loss landscape for neural networks with quadratic activation functions. We prove existence of spurious local minima and saddle points which can be escaped easily with probability one when the number of neurons is greater than or equal to the input dimension and the norm of the training samples is used as a regressor. We prove that deep overparameterized neural networks with quadratic activations benefit from similar nice landscape properties. Our theoretical results are independent of data distribution and fill the existing gap in theory for two-layer quadratic neural networks. Finally, we empirically demonstrate convergence to a global minimum for these problems.