Full Extractors: A Cross-Domain Overview

• Full extractors are mechanisms aimed at achieving near-complete extraction coverage within a target domain, whether recovering maximum entropy, processing multimodal documents, or measuring full logical operator sets.
• In randomness extraction, full extractors focus on outputting near-uniform distributions, while in information extraction they consolidate diverse modalities into structured outputs.
• In quantum and logical processing, full extractors enable direct, low-overhead measurement of all logical Pauli operators, reducing compilation complexity and enhancing system efficiency.

Searching arXiv for recent and relevant uses of “full extractor” and related extractor terminology across domains. “Full extractors” is not a single canonical term across arXiv-facing research communities. Instead, it is used in several technically distinct senses that share a common intuition: an extractor is called “full” when it aims to realize nearly complete coverage of a target object, resource, or operation set rather than solving only a restricted subproblem. In randomness-extractor theory, the nearest formal notion is often an extractor whose output is close to the full uniform distribution, or a construction that extracts essentially all available entropy (Berta et al., 2014, Berta et al., 2014, 0901.2120). In web and document information extraction, the phrase is used more operationally for systems that ingest raw artifacts and return structured outputs across the major modalities or fields of interest (Zhou et al., 30 Jul 2025, Mansour et al., 2 Feb 2026, Li et al., 23 Feb 2026). In fault-tolerant quantum coding, a “full extractor” denotes a surgery system able to measure arbitrary logical Pauli operators on a code block (Blue et al., 2 Jun 2026). The term is therefore best treated as a cross-domain label for completeness-oriented extraction architectures rather than a single formally standardized object.

1. Terminological scope and cross-domain meaning

Across the cited literature, “full extractor” has at least three established usages. In randomness extraction, the term is usually not formalized directly, but papers identify nearby notions such as ordinary extractors as condensers with full output entropy, strong extractors, quantum-proof extractors, and decoupling extractors (Berta et al., 2014, Berta et al., 2014, Berta, 2013). In practical information extraction, the term refers to systems that move beyond single-task parsers or sentence-level NER/RE and instead cover raw-document ingestion, multimodal parsing, schema normalization, and often human correction (Zhou et al., 30 Jul 2025, Mansour et al., 2 Feb 2026). In QLDPC logical processing, the term is explicit: a full extractor is a surgery system that can measure every logical Pauli operator on a code block (Blue et al., 2 Jun 2026).

This divergence matters because completeness is domain-relative. In extractor theory, completeness is measured against entropy or output-uniformity targets. In document systems, it is measured against modality and workflow coverage. In logical processing, it is measured against the supported logical observable set. A plausible implication is that “fullness” is best understood as an operational or asymptotic ideal whose exact formalization depends on the ambient object: a weak source, an HTML/ PDF document, or a code block.

The literature also makes clear that “full” rarely means literally everything. Several papers explicitly separate practical broad coverage from absolute completeness. For example, zERExtractor is described as “a near end-to-end, full-paper-oriented extraction framework” rather than a completely solved full-document extractor for all information in enzyme papers (Zhou et al., 30 Jul 2025). AXE is characterized as a “low-cost, DOM-grounded, cross-domain full extractor for textual HTML extraction,” not a universal browser agent or multimodal web system (Mansour et al., 2 Feb 2026). In randomness extraction, even asymptotically optimal entropy thresholds do not automatically imply long outputs or exponentially small error (Li, 2023).

2. Full extractors in randomness-extractor theory

In theoretical computer science and quantum information, the closest formal notion to a “full extractor” is an extractor whose output is close to the full uniform distribution on its output space. The operator-space formulation of extractor theory states this explicitly: an extractor is the special case of a condenser with full output entropy $k'=\log M=m$ (Berta et al., 2014). The classical condition is written as small $\ell^1$-distance between the extractor output and the uniform distribution $\upsilon_M$, and the quantum-proof version upgrades this to independence from quantum side information via a completely bounded norm characterization (Berta et al., 2014).

Spectral extractors provide one of the main sufficient criteria for robustness against quantum side information. “Variations on Classical and Quantum Extractors” shows that every $(k,\epsilon)$ spectral extractor is also a quantum-proof $(k,2\sqrt{\epsilon})$ extractor, and that the fully quantum analogue yields decoupling extractors with the same error degradation (Berta et al., 2014). The paper’s terminology is precise: in the classical-output setting the strengthened notion is “quantum-proof,” while in the fully quantum setting the strongest analogue is “decoupling” (Berta et al., 2014). The 2013 thesis on quantum side information adopts the same conceptual distinction and identifies strong extractors as the closest match if “full” is taken to mean output uniform jointly with the seed (Berta, 2013).

The literature also treats “full extraction” in a quantitative sense: extracting essentially all available entropy. “Invertible Extractors and Wiretap Protocols” gives exact full extraction for some structured source families. For symbol-fixing sources over sufficiently large fields, MDS-code-based linear extractors achieve output length $m=k$ with zero error (0901.2120). For $\mathbb{F}_q$-restricted affine sources over extension fields, Gabidulin/MRD-code constructions also achieve $m=k$ with zero error; the paper explicitly states that these extractors “are able to extract the entire source entropy with zero error” (0901.2120). For ordinary affine sources over $\mathbb{F}_2$, the same paper obtains near-full invertible extraction with output $m=\delta n-O(n^\alpha)$ and error $\ell^1$0, which is close but not exact (0901.2120).

Later work pushes entropy thresholds rather than exact output length. “Two Source Extractors for Asymptotically Optimal Entropy, and (Many) More” gives explicit two-source extractors with asymptotically optimal logarithmic min-entropy threshold $\ell^1$1, via a reduction chain through seeded and seedless non-malleable extractors (Li, 2023). The paper is explicit, however, that this does not yet yield “full extraction” in the strongest seedless sense, because the final two-source extractor at $\ell^1$2 entropy has only constant output and constant error (Li, 2023). Similarly, Li’s improvement over the Chattopadhyay–Zuckerman extractor raises output from one bit to $\ell^1$3 while retaining polylogarithmic entropy, but it remains well short of $\ell^1$4 output (Li, 2015).

A separate line concerns seed cost. “More Efficient Privacy Amplification with Less Random Seeds via Dual Universal Hash Function” constructs explicit linear strong seeded extractors specialized to privacy amplification, with seed length asymptotically $\ell^1$5 and $\ell^1$6 implementation complexity (Hayashi et al., 2013). Here the “full” aspect is not output optimality per se but preservation of strong privacy-amplification guarantees with much smaller public seeds than standard Toeplitz-based practice (Hayashi et al., 2013).

3. Device-independent and quantum-cryptographic full extraction

Device-independent quantum cryptography adds another specialized meaning of full extraction: extracting essentially all private randomness certified by Bell violation, without the usual seeded privacy-amplification overhead. “High-rate and computationally-efficient seedless extractors for device-independent quantum cryptography” proves a deterministic linear seedless extractor in the memoryless DI setting with asymptotic rate

$\ell^1$7

reaching $\ell^1$8 at maximal CHSH violation $\ell^1$9 (Lin et al., 29 May 2026). The paper explicitly interprets this as “the optimal rate of one key bit per singlet” (Lin et al., 29 May 2026).

The extractor here is not generic in the classical complexity-theoretic sense. Its promise is Bell-violation-based rather than min-entropy-based, and the extraction map is a deterministic linear map

$\upsilon_M$0

implemented in $\upsilon_M$1 time (Lin et al., 29 May 2026). The conceptual advance is a truncation-based proof that allows parameter estimation on an asymptotically vanishing fraction of rounds, $\upsilon_M$2, instead of the heavy estimation overhead that made earlier seedless DI extraction inefficient (Lin et al., 29 May 2026).

This DI result is “full” only in the physically certified-resource sense. It does not claim to be a universal extractor for arbitrary weak sources. The paper is explicit that it is a Bell-promised, DI-specific full extraction result, and that the memoryless-device assumption remains essential (Lin et al., 29 May 2026). This distinction mirrors the broader ambiguity of the term across fields: fullness is measured against the relevant resource theory, here the per-round private randomness available from maximal Bell violation.

4. Full extractors as end-to-end document and web information extraction systems

In information extraction, “full extractor” usually denotes workflow breadth rather than an entropy-theoretic property. zERExtractor is a clear example. It ingests raw PDFs, segments them into tables, figures, and textual content, processes each modality with replaceable components, and merges outputs into JSON-backed biochemical records (Zhou et al., 30 Jul 2025). Its architecture is “unified, modular, and extensible,” with “plug-and-play integration” of deep learning models and LLMs as interchangeable components (Zhou et al., 30 Jul 2025). The system covers table recognition, OCR, semantic normalization, molecular image recognition through UniMolRec, LLM-based entity and relation extraction, and an interactive annotation-and-retraining loop (Zhou et al., 30 Jul 2025).

Its benchmark figures support the claim that it is broader than sentence-level or table-only extractors: table recognition accuracy $\upsilon_M$3, molecular image interpretation up to $\upsilon_M$4, and relation extraction accuracy $\upsilon_M$5 on the reported benchmark (Zhou et al., 30 Jul 2025). At the same time, the paper explicitly limits the claim. It supports full-text PDFs, tables, molecular depictions, and associated text, but does not demonstrate comprehensive extraction from arbitrary plots, spectra, non-chemical diagrams, or supplementary materials, nor a single end-to-end raw-paper-to-record metric (Zhou et al., 30 Jul 2025). This suggests that “full extractor” in document IE is typically aspirational and partial: full enough to cover the dominant modalities of the target corpus, not necessarily every information-bearing artifact.

AXE makes the same point in the web-IE setting. It is an end-to-end pipeline from raw HTML plus a user schema to grounded structured outputs, with three stages: preprocessing, AI extraction, and postprocessing via Grounded XPath Resolution (GXR) (Mansour et al., 2 Feb 2026). The preprocessor removes scripts and CSS, applies HTMLRAG lossless cleaning, and uses AutoChunker to produce structural chunks (Mansour et al., 2 Feb 2026). The pruner decomposes chunks into XPath-based mini-chunks and selects only those relevant to the query or schema. The extractor then uses a Qwen3-0.6B model with LoRA adaptors to generate schema-aligned JSON, and GXR grounds generated values back to DOM nodes using token overlap and fuzzy matching (Mansour et al., 2 Feb 2026).

AXE’s empirical case for “fullness” is architectural rather than merely representational. It covers raw HTML ingestion, DOM-aware pruning, schema-conditioned generation, and source-node grounding, and reaches $\upsilon_M$6 F1 on SWDE in the zero-shot setting (Mansour et al., 2 Feb 2026). Yet the paper is careful not to overstate scope: it is HTML-only, primarily textual, and does not handle rendering, browser interaction, or schema induction from scratch (Mansour et al., 2 Feb 2026). The most accurate description given is a “low-cost, DOM-grounded, cross-domain full web structured information extractor for textual HTML pages” (Mansour et al., 2 Feb 2026).

A related but different completeness problem appears in HTML-to-text extraction for LLM pretraining. “Beyond a Single Extractor: Re-thinking HTML-to-Text Extraction for LLM Pretraining” argues that a single fixed extractor gives only one lossy view of the web and that a union over multiple extractors materially increases retained coverage (Li et al., 23 Feb 2026). The reported token yield increases by up to $\upsilon_M$7 for DCLM-Baseline settings while maintaining broad benchmark performance, and extractor choice changes structured-content performance by up to $\upsilon_M$8 percentage points on WikiTQ and $\upsilon_M$9 points on HumanEval-related code evaluations (Li et al., 23 Feb 2026). Although this paper does not use “full extractor” as a label, it sharpens the operational notion: fuller extraction can be achieved by multi-extractor coverage rather than by a single supposedly universal extractor.

5. Full extractors in logical processing for hypergraph product codes

In QLDPC logical processing, “full extractor” is a formal architectural term. “Full Extractors for Logical Processing in Hypergraph Product Codes” defines a full extractor as an ancilla/surgery system capable of measuring all logical Pauli operators on a code block (Blue et al., 2 Jun 2026). This contrasts with partial extractors, which support only a proper subset of logical observables (Blue et al., 2 Jun 2026).

The construction proceeds in three layers. First, the authors build verifiable single-column partial extractors for cyclic HGP codes using graph-based ancilla systems. Then they assemble these into single-basis extractors that can measure arbitrary logical $(k,\epsilon)$0 or arbitrary logical $(k,\epsilon)$1. Finally, they bridge the $(k,\epsilon)$2- and $(k,\epsilon)$3-basis extractors with $(k,\epsilon)$4 additional edges so that arbitrary products of canonical $(k,\epsilon)$5 and $(k,\epsilon)$6 logicals become measurable, yielding a full extractor (Blue et al., 2 Jun 2026). The resulting phenomenological fault-distance theorem is

$(k,\epsilon)$7

where $(k,\epsilon)$8 is the code distance and $(k,\epsilon)$9 the edge connectivity of the single-column extractor graph (Blue et al., 2 Jun 2026).

The practical motivation is elimination of compilation overhead in Pauli-based computation. Prior fixed-connectivity partial-extractor approaches required arbitrary target logical Paulis to be compiled into supported native measurements. The present construction aims for $(k,2\sqrt{\epsilon})$0 compilation overhead by measuring the desired logical Pauli natively (Blue et al., 2 Jun 2026). For the $(k,2\sqrt{\epsilon})$1 code, the paper reports logical measurement error approximately $(k,2\sqrt{\epsilon})$2 at physical error rate $(k,2\sqrt{\epsilon})$3 using $(k,2\sqrt{\epsilon})$4 noisy merged-code rounds, extractor sizes between $(k,2\sqrt{\epsilon})$5 and $(k,2\sqrt{\epsilon})$6 of the base HGP codes, and bounded hardware degree ten after Bell-check splitting (Blue et al., 2 Jun 2026).

Here “full” is unambiguous and finite: the extractor is full if its supported measurement set equals the full logical Pauli group of the block. This is perhaps the clearest example of a domain where the term has an exact operational definition rather than a looser breadth claim.

6. Common design principles, limitations, and persistent gaps

Despite the diversity of meanings, the papers share several recurrent design principles. One is modularity. zERExtractor uses plug-and-play OCR, document analysis, molecular recognition, semantic extraction, and LLM modules (Zhou et al., 30 Jul 2025). AXE separates pruning, generation, and DOM grounding (Mansour et al., 2 Feb 2026). The QLDPC full-extractor construction explicitly assembles many verifiable partial extractors into a single full one (Blue et al., 2 Jun 2026). In randomness extraction, concatenation and composition play a similar role: the privacy-amplification paper concatenates universal and dual-universal components to reduce seed length while preserving strong-extractor guarantees (Hayashi et al., 2013).

A second shared principle is that completeness usually requires a domain-specific intermediate representation. AXE introduces DOM-grounded mini-chunks and the typed schema/JSON target (Mansour et al., 2 Feb 2026). zERExtractor normalizes multimodal outputs into biochemical JSON rows (Zhou et al., 30 Jul 2025). The Coq-extraction literature offers a further analogy: “Extracting functional programs from Coq, in Coq” builds a full extraction pipeline around the typed intermediate language $(k,2\sqrt{\epsilon})$7, turning certified erasure into an end-to-end extraction workflow for Elm, Liquidity, CameLIGO, and a Rust subset (Annenkov et al., 2021). Although that paper is about program extraction rather than “full extractors” as a standalone term, it demonstrates the same systems pattern: a full extractor is often defined by its IR and pipeline, not only by a terminal decoder.

The main limitations are equally consistent. Fullness is often component-wise rather than end-to-end. zERExtractor’s evaluation is split across table recognition, molecular OCR, and relation extraction, with no single raw-paper-to-fully-correct-record metric (Zhou et al., 30 Jul 2025). AXE is strong on textual HTML pages but does not handle rendering or multimodal web signals (Mansour et al., 2 Feb 2026). In randomness extraction, asymptotically optimal entropy thresholds do not imply optimal output length or negligible error; the two-source literature remains explicit about this gap (Li, 2023, Li, 2015). In DI seedless extraction, asymptotic optimality is proved only in the memoryless setting, and finite-size practicality still faces meaningful lower-order penalties (Lin et al., 29 May 2026). In QLDPC logical processing, decoder practicality and extension beyond cyclic HGP families remain open (Blue et al., 2 Jun 2026).

This suggests a common misconception to avoid: a “full extractor” is rarely a claim of total closure of the problem class. It is usually a claim that the dominant operational bottleneck has been crossed. For randomness extractors, that bottleneck may be entropy-loss or seed-length optimality; for IE systems, it may be multimodal document coverage; for QLDPC architectures, it may be arbitrary logical Pauli support without compilation overhead.

7. Conceptual synthesis and outlook

Taken together, the literature supports a general characterization: a full extractor is an extraction mechanism that targets completeness relative to the relevant downstream semantics, rather than merely increasing local accuracy on one subtask. In extractor theory, this means full output entropy or near-total recovery of available entropy under the relevant promise (Berta et al., 2014, 0901.2120). In DI cryptography, it means asymptotically one secret bit per singlet under maximal CHSH violation (Lin et al., 29 May 2026). In document and web IE, it means ingesting raw artifacts and returning structured records across the important modalities, with grounding or correction mechanisms that make the pipeline practically end-to-end (Zhou et al., 30 Jul 2025, Mansour et al., 2 Feb 2026). In hypergraph-product-code processing, it means supporting the full logical Pauli measurement set (Blue et al., 2 Jun 2026).

A plausible implication is that the term will remain polysemous rather than converge to a single definition. The underlying research problems are too different for a uniform formalization, but the common design pressure is stable: reduce the gap between an abstract extraction primitive and a deployable, scope-complete system. Current work points toward several extensions of that agenda. In IE, broader multimodal coverage and stronger document-wide evidence fusion remain open (Zhou et al., 30 Jul 2025, Li et al., 23 Feb 2026). In web extraction, adaptive or learned multi-extractor selection is an obvious next step beyond simple unions (Li et al., 23 Feb 2026). In extractor theory, the open frontier is still simultaneous optimality in threshold, output length, error, and seed cost for broader source classes (Li, 2023, Li, 2015). In DI cryptography, extending high-rate seedless extraction beyond the memoryless model is identified as a central next step (Lin et al., 29 May 2026). In QLDPC logical processing, the challenge is generalizing full-extractor architectures to stronger code families and practical decoders (Blue et al., 2 Jun 2026).

The most defensible encyclopedia-level conclusion is therefore not a single definition, but a taxonomy. “Full extractor” names a family resemblance across fields: extraction systems or constructions that aim to eliminate the dominant incompleteness of prior methods by covering the full output distribution, the full document workflow, or the full logical operation set relevant to a target domain.