2026-07-13 04:00 UTCOriginal source2 min readUpdated: 2026-07-13 08:12 UTC

Signed Symmetric Quantization for Few-Bit Integers

This paper introduces signed symmetric quantization for few-bit integers, addressing clipping errors from standard symmetric quantizers while avoiding the runtime penalty of asymmetric quantization. The method places the extra negative value on the dominant outlier tail, achieving better perplexity and accuracy on large language models at no extra inference cost.

SourcearXiv Machine LearningAuthor: Ian Colbert, Eashan Dash, Pablo Monteagudo-Lago, Juan Amboage, Srinidhi N, Giuseppe Franco, Nicholas J. Fraser, Arun Ramachandran

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Key points

Standard symmetric quantizer clips positive outliers due to signed integer alphabet imbalance, causing non-trivial error at low precision.
Signed symmetric quantization retains symmetric runtime benefits without asymmetric overhead by assigning the extra representable value to the dominant-outlier tail.
Theoretical analysis establishes conditional ℓ2 optimality for 88-99% of LLM weight groups at low bit widths.
Empirical validation on Qwen3, Qwen3.5, and Llama3 families shows improved perplexity and few-shot accuracy over standard unsigned symmetric quantization.

Why it matters

This matters because standard symmetric quantizer clips positive outliers due to signed integer alphabet imbalance, causing non-trivial error at low precision.

Technical impact

May affect model selection, inference cost, product capability, and evaluation benchmarks.

This panel is AI-generated and reviewed for accuracy.

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[Submitted on 12 Jun 2026]

Title:Signed Symmetric Quantization for Few-Bit Integers

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Abstract:The signed integer alphabet contains one more negative representable value than positive. Yet, by convention, the standard symmetric integer quantizer fixes its scale to be strictly positive, which assigns this extra representable value to the negative tail and can force clipping of positive outliers. In this work, we show that, at few-bit precision, such clipping is a non-trivial source of quantization error. Asymmetric quantization addresses this problem with a zero point, shifting the grid toward the observed data range; however, this flexibility is well-known to carry a runtime penalty. For example, in this http URL on an AMD EPYC(TM) "Turin" CPU, a 4-bit symmetric format uses up to 9% less memory with up to 2.45$\times$ higher throughput than its asymmetric counterpart. We highlight signed symmetric quantization as a third option that retains the runtime profile of symmetric quantization without the penalty of the asymmetric format: our signed absmax grid places the extra representable value on the dominant-outlier tail through a principled and lightweight sign selection rule while keeping the zero point at zero. Our theoretical analysis offers two main results. First, we establish the signed absmax grid as conditionally bound-optimal on $\ell_2$ quantization error, and show that the condition holds for 88-99% of weight groups across pre-trained large language models (LLMs) at low bit widths. Second, we show that negating the scale of a standard symmetric quantizer is analytically equivalent to a unit zero point shift on the same signed integer alphabet. We empirically validate our proposal on models from the Qwen3, Qwen3.5, and Llama3 families, and observe improvement in perplexity and downstream few-shot accuracy over the standard unsigned symmetric quantizer at no extra inference cost

Subjects:

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

Cite as: arXiv:2607.08779 [cs.LG]

(or arXiv:2607.08779v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.08779

arXiv-issued DOI via DataCite

Submission history

From: Ian Colbert [view email] [v1] Fri, 12 Jun 2026 17:12:59 UTC (211 KB)

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