[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82040-en":3,"doc-seo-82040-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82040,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Signed Symmetric Quantization for Few-Bit Integers","Signed integer quantization uses an alphabet with one extra negative representable value, while the conventional symmetric integer quantizer forces a strictly positive scale. This convention places the extra value on the negative tail and can clip positive outliers, which becomes a meaningful error source at few-bit precision. Asymmetric quantization mitigates this via a zero point but incurs inference overhead. Signed symmetric quantization keeps the zero point at zero by choosing the scale sign to align the dominant outlier tail, retaining symmetric runtime behavior. Theory shows conditional bound-optimality for ℓ2 error and an analytic equivalence to a unit zero-point shift; experiments on Qwen3/Qwen3.5/Llama3 show improved perplexity and few-shot accuracy without extra inference cost.","arXiv :2607 .08779v1 [ cs .LG] 12 Jun 2026  \nSigned Symmetric Quantization for Few-Bit Integers  \nIan ColbertEashan DashPablo Monteagudo-Lago, Juan Amboage, Srinidhi N, Giuseppe Franco, Nicholas J. Fraser, Arun Ramachandran  \nAMD  \nAbstract  \nThe 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 llama .cpp on an AMD EPYC™“Turin” CPU, a 4-bit symmetric format uses up to 9% less memory with up to  \n2.45 × 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 ℓ2 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.  \n1 Introduction  \nFew-bit quantization relies heavily on uniform integer grids uniquely defined by an alphabet, a scale factor, and (optionally) a zero point. A small but often overlooked detail is that the standard signed q-bit alphabet Aq = {−2q−1 ,..., 2q−1 −1} is not symmetric: it contains one more negative value than positive. Yet, by convention, the standard symmetric quantizer takes the scale s to be positive [12, 13, 29], assigning the extra representable value to the negative tail of the data and thereby possibly clipping large positive values. We show in this work that this can become a material source of quantization error at few-bit precision.  \nAsymmetric quantization introduces a zero point to align the grid with the data range, but this flexibility is well-known to carry an inference cost [13, 17, 19] . Kernels must account for the offset, and the corresponding metadata must be stored and loaded. For example, on Llama3 8B, we find that a symmetric 4-bit format uses 9% less memory and provides 2.21 × higher prefill and 2.03 × higher decode throughput than its asymmetric counterpart as measured on an AMD EPYC™ “Turin” CPU (Table 1) . This motivates a narrower question: can we recover the useful endpoint alignment of an asymmetric grid while keeping the inference path operationally symmetric?  \n∗ Equal contribution. Correspondence to: {ian.colbert, [eashan.dash](eashan.dash}@amd.com)[}](eashan.dash}@amd.com)[@amd.com](eashan.dash}@amd.com).  \nPreprint.  \nWe answer this question with signed symmetric quantization, where we choose the sign of the scale to align the dominant outlier in the data with the extra negative representable value in the signed integer alphabet. The resulting sign rule is closed-form, data-free, and metadata-free when scales are already stored as signed real values, as in llama .cpp. Our analyses show that signed symmetric quantization recovers a restricted asymmetric alignment whil","cbCaisb3pvIEY4C7","https://ap.wps.com/l/cbCaisb3pvIEY4C7","pdf",480727,1,16,"English","en",105,"# Introduction\n## Contributions\n## Notation\n# Background and Related Work","[{\"question\":\"Why does conventional signed symmetric quantization create extra error at few-bit precision?\",\"answer\":\"The signed q-bit integer alphabet contains one more negative value than positive, but symmetric quantization fixes the scale to be strictly positive. This misassigns the extra representable value to the negative tail and can clip large positive outliers, becoming a non-trivial quantization error source at low bit widths.\"},{\"question\":\"How does signed symmetric quantization avoid the runtime penalty of asymmetric quantization?\",\"answer\":\"It retains the symmetric deployment path by keeping the zero point at zero and selecting the scale sign with a principled sign-selection rule that aligns the dominant outlier with the extra negative representable value. This approach avoids the offset handling and metadata requirements typical of asymmetric formats.\"},{\"question\":\"What theoretical results does the paper provide for the proposed method?\",\"answer\":\"It proves that the signed absmax grid is conditionally bound-optimal for ℓ2 quantization error and establishes that flipping the scale sign is analytically equivalent to a unit zero-point shift on the same signed integer alphabet.\"}]",1784177753,40,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"signed-symmetric-quantization-for-few-bit-integers","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/signed-symmetric-quantization-for-few-bit-integers/82040/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does conventional signed symmetric quantization create extra error at few-bit precision?","Question",{"text":75,"@type":76},"The signed q-bit integer alphabet contains one more negative value than positive, but symmetric quantization fixes the scale to be strictly positive. This misassigns the extra representable value to the negative tail and can clip large positive outliers, becoming a non-trivial quantization error source at low bit widths.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does signed symmetric quantization avoid the runtime penalty of asymmetric quantization?",{"text":80,"@type":76},"It retains the symmetric deployment path by keeping the zero point at zero and selecting the scale sign with a principled sign-selection rule that aligns the dominant outlier with the extra negative representable value. This approach avoids the offset handling and metadata requirements typical of asymmetric formats.",{"name":82,"@type":73,"acceptedAnswer":83},"What theoretical results does the paper provide for the proposed method?",{"text":84,"@type":76},"It proves that the signed absmax grid is conditionally bound-optimal for ℓ2 quantization error and establishes that flipping the scale sign is analytically equivalent to a unit zero-point shift on the same signed integer alphabet.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":28,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]