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Erik Schultheis

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preprint2026arXiv

Grid Games: The Power of Multiple Grids for Quantizing Large Language Models

A major recent advance in quantization is given by microscaled 4-bit formats such as NVFP4 and MXFP4, quantizing values into small groups sharing a scale, assuming a fixed floating-point grid. In this paper, we study the following natural extension: assume that, for each group of values, we are free to select the "better" among two or more 4-bit grids marked by one or more bits in the scale value. We formalize the power-of-two-grids (PO2) problem, and provide theoretical results showing that practical small-group formats such as MXFP or NVFP can benefit significantly from PO2 grids, while the advantage vanishes for very large groups. On the practical side, we instantiate several grid families, including 1) PO2(NF4), which pairs the standard NF4 normal grid with a learned grid, 2) MPO2, a grid pair that is fully learned over real weights and activations, 3) PO2(Split87), an explicit-zero asymmetric grid and 4) SFP4, a TensorCore-implementable triple which pairs NVFP4 with two shifted variants. Results for post-training quantization of standard open models and pre-training of Llama-like models show that adaptive grids consistently improve accuracy vs single-grid FP4 under both weight-only and weight+activation. Source code is available at https://github.com/IST-DASLab/GridGames.

preprint2022arXiv

On Missing Labels, Long-tails and Propensities in Extreme Multi-label Classification

The propensity model introduced by Jain et al. 2016 has become a standard approach for dealing with missing and long-tail labels in extreme multi-label classification (XMLC). In this paper, we critically revise this approach showing that despite its theoretical soundness, its application in contemporary XMLC works is debatable. We exhaustively discuss the flaws of the propensity-based approach, and present several recipes, some of them related to solutions used in search engines and recommender systems, that we believe constitute promising alternatives to be followed in XMLC.

preprint2020arXiv

Unbiased Loss Functions for Extreme Classification With Missing Labels

The goal in extreme multi-label classification (XMC) is to tag an instance with a small subset of relevant labels from an extremely large set of possible labels. In addition to the computational burden arising from large number of training instances, features and labels, problems in XMC are faced with two statistical challenges, (i) large number of 'tail-labels' -- those which occur very infrequently, and (ii) missing labels as it is virtually impossible to manually assign every relevant label to an instance. In this work, we derive an unbiased estimator for general formulation of loss functions which decompose over labels, and then infer the forms for commonly used loss functions such as hinge- and squared-hinge-loss and binary cross-entropy loss. We show that the derived unbiased estimators, in the form of appropriate weighting factors, can be easily incorporated in state-of-the-art algorithms for extreme classification, thereby scaling to datasets with hundreds of thousand labels. However, empirically, we find a slightly altered version that gives more relative weight to tail labels to perform even better. We suspect is due to the label imbalance in the dataset, which is not explicitly addressed by our theoretically derived estimator. Minimizing the proposed loss functions leads to significant improvement over existing methods (up to 20% in some cases) on benchmark datasets in XMC.