Convergence for Discrete Parameter Update Schemes

Paul Wilson; Fabio Zanasi; George Constantinides

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arXiv · 2512.04051

Convergence for Discrete Parameter Update Schemes

Paul Wilson·Fabio Zanasi·George Constantinides

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Abstract

Modern deep learning models require immense computational resources, motivating research into low-precision training. Quantised training addresses this by representing training components in low-bit integers, but typically relies on discretising real-valued updates. We introduce an alternative approach where the update rule itself is discrete, avoiding the quantisation of continuous updates by design. We establish convergence guarantees for a general class of such discrete schemes, and present a multinomial update rule as a concrete example, supported by empirical evaluation. This perspective opens new avenues for efficient training, particularly for models with inherently discrete structure.

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Paul Wilson, Fabio Zanasi, George Constantinides. 2025-12-03. Convergence for Discrete Parameter Update Schemes. https://arxiv.org/abs/2512.04051

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