Trinomial Scaling Law Jointly Derives Optimal Batch Size
orvieto_antonio · x · 2026-07-04
Addressing the compute allocation trade-off between more steps and larger batches, the author proposes a trinomial loss law L(N,M,K)= E + A·N⁻ᵅ + B·M⁻ᵝ + C·K⁻ᵞ, where M is the token-based batch size and K is the number of training steps. Unlike previous approaches that fit batch-size laws separately, the batch size here directly factors into the loss law, allowing optimal and critical batch sizes to be derived rather than fitted independently. Since D=MK (total tokens), the law predicts an optimal batch size M ∝ D^(γ/(β+γ)). A link to the paper is included.
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