Pith. sign in

REVIEW 5 major objections 5 minor 5 cited by

The paper claims that the quality–validity trade-off in structured LLM generation is mostly an artifact of how constraints are enforced, and that a two-step, training-free procedure—first an unconstrained draft, then constrained decoding co

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 03:28 UTC pith:DNOJSZAE

load-bearing objection A simple, plausibly useful draft-then-constrain decoding recipe with consistent accuracy gains, wrapped in a KL story that is neat but not tested where it matters. the 5 major comments →

arxiv 2603.03305 v2 pith:DNOJSZAE submitted 2026-02-08 cs.CL cs.AIcs.LG

The Hidden Cost of Structured Generation in LLMs: Draft-Conditioned Constrained Decoding

Avinash Reddy , Thayne T. Walker , James S. Ide , Amrit Singh Bedi This is my paper
classification cs.CL cs.AIcs.LG MSC 68T5068T07
keywords constrained decodingstructured generationfeasible massKL projectiondraft-conditioned decodingtest-time scalingJSON schemasemantic distortion
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that the familiar trick of constraining an LLM's output token-by-token to force valid JSON or grammar is itself the cause of much of the accuracy loss, and that a simple two-step procedure largely removes that loss. First generate a free-form draft (the semantic plan); then run constrained decoding with the draft in the context, so schema tokens like braces and quotes become probable before masking. The paper analyzes this through a KL-projection lens: the distortion of constrained decoding equals log(1/feasible mass), the probability the model gives to valid next tokens, and draft conditioning raises that mass, lowering the cumulative 'projection tax.' Empirically, across math and logic benchmarks, the method raises strict accuracy by up to 24 percentage points, for instance from 15.2% to 39.0% on a grade-school math benchmark with a 1B model, and lets small model pairs beat much larger single models.

Core claim

The paper's central claim is that the quality–validity trade-off in structured generation is largely an artifact of how constraints are enforced, not an intrinsic cost of the constraints. Standard constrained decoding renormalizes the model's distribution at every token over the valid set; this perturbs the distribution by an amount equal to log(1/α), where α is the probability the model assigns to valid next tokens. Because small models assign little mass to schema tokens like braces and field names, the perturbation compounds into a 'projection tax' that steers decoding toward locally easy but globally wrong trajectories. The paper proposes DCCD: sample an unconstrained draft first, then a

What carries the argument

The central object is the feasible mass α(h_t) — the total probability a model assigns, at a given prefix h_t, to tokens that can still lead to a valid output. Hard constraints work by masking everything outside that set and renormalizing, which the paper shows is exactly a reverse-KL projection onto the valid-token simplex, incurring per-step distortion KL = log(1/α). The key trick is that the feasible mass depends on the conditioning context: appending a draft d changes the distribution to π(·|h_t, d), so a well-chosen draft makes formatting tokens probable and raises α(h_t; d) ≫ α(h_t), reducing the cumulative tax. An optional best-of-K selection scores drafts by their cumulative log feas

Load-bearing premise

The whole benefit rests on the empirical claim that an unconstrained draft makes the schema-forced tokens (braces, quotes, field names) much more probable in the conditioned model; if drafts are unhelpful or adversarial, the reduced KL divergence will not translate into higher accuracy.

What would settle it

Measure α(h_t; d) − α(h_t) on thousands of prefixes drawn from diverse tasks; if increases in feasible mass do not predict strict accuracy gains, the mechanism fails. A sharper test: replace the draft with a fixed, content-free string such as 'Answer in JSON format' — if accuracy improves as much as with a real draft, then the benefit comes from prompt conditioning alone, not from drafting.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Exact structural validity (JSON schema, grammar, tool-call format) can be preserved while largely recovering the accuracy of unconstrained generation.
  • Smaller model pairs (e.g., a 3B draft model plus a 1.5B projector) can match or exceed single-model constrained decoding at much larger scale, improving accuracy per parameter.
  • Test-time compute is better spent sampling several drafts and picking one than sampling many outputs under hard constraints; gains continue past 13 samples.
  • The two-stage recipe is model-agnostic and training-free, so it can be dropped into existing serving pipelines that already use constrained decoding.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the mechanism is right, any task with a hard output syntax—API calls, database queries, executable code, structured summaries—should see the same benefit, not just math and logic benchmarks.
  • A testable refinement: the paper's confidence plots suggest draft conditioning sharpens the answer-slot distribution; one could quantify this as a drop in conditional entropy and use it as a debugging signal.
  • The best-of-K selection rule could be replaced by a verifier or a task-specific judge; the framework is agnostic, so the reported gains may be conservative relative to what an external scorer would add.
  • The load-bearing assumption points to a risk: a wrong draft could mislead the conditioned model, so a safety mechanism (e.g., a draft plausibility filter) may be necessary for deployment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper studies the quality degradation caused by token-level constrained decoding for structured generation. It derives a KL-projection view in which the per-step distortion of masking-with-renormalization equals log(1/α(h_t)), the 'projection tax,' and proposes Draft-Conditioned Constrained Decoding (DCCD): first generate an unconstrained draft, then use the draft as additional context for standard constrained decoding. Optionally, K drafts are sampled and a best-of-K selection is made by cumulative log feasible mass. Experiments on GSM8K, MATH500, GSM-Symbolic, and FOLIO across six model sizes (1B–14B) report consistent strict-accuracy gains over CD, parameter-efficiency advantages for two-model compositions, and improved test-time scaling. The paper also presents a utility-stability bound in Appendix A and selected case studies.

Significance. The KL-projection identities (Eqs. 5–8) are a clean and correct formalization of the distortion induced by token-level constraints, and the proposed method is simple, training-free, and preserves exact structural validity. If the reported gains are robust, DCCD is a practical and low-cost recipe. However, the paper currently overclaims: the abstract and related work assert that DCCD 'matches or approaches unconstrained task accuracy,' yet no unconstrained decoding baseline is reported anywhere. The core mechanism — that draft conditioning increases feasible mass and thereby reduces distortion — is supported only by two selected examples and a case study, not by aggregate measurements. Appendix A's Pinsker bound does not establish that the draft-conditioned reference has high utility. These gaps prevent the central causal claim from being considered established.

major comments (5)
  1. [Abstract; §5.1 Table 2] The abstract and related work state that DCCD 'matches or approaches unconstrained task accuracy,' but no unconstrained decoding baseline appears in Table 2 or anywhere in the experiments. The claim that the quality–validity tradeoff is 'largely an artifact of how constraints are enforced' cannot be evaluated without comparing to a no-masking, no-constraint selection. Please add unconstrained decoding results for the same models and datasets, or remove/qualify this claim.
  2. [§4.1, Eq. (11)] The central mechanism is the assertion π(s_t|h_t,d) ≫ π(s_t|h_t), which is an empirical regularity about the model's conditional distributions, not a consequence of the setup. The paper provides only two selected examples (Figures 2–3) and a case study (Appendix J), but no aggregate measurement of α(h_t;d) vs α(h_t) over the evaluated trajectories. Moreover, the non-verifiable summarization experiments (§5.3, Appendix E) show DCCD beating CD even when no grammar/schema constraint is present, suggesting the gains may come from the extra free-form reasoning pass rather than from increased feasible mass. A control that conditions on a draft but does not use masking, or a content-free draft baseline, is needed to isolate the mechanism.
  3. [Appendix A, Eq. (17)] The Pinsker bound shows that a constrained distribution close to a high-utility reference cannot lose much utility, but it does not establish that the draft-conditioned reference p2(·|x,d) has high utility, nor that DCCD's constrained distribution is closer to a better reference than standard CD is. The paper only instantiates the bound for standard CD with Q=ρ_θ (Eq. 18). Thus the theory does not support the claim that increasing α(·) improves accuracy; that remains an unproven empirical link. Please either prove the required condition or present direct evidence that p2(·|x,d) assigns high probability to valid high-utility outputs.
  4. [§5.1, Table 2] No error bars, seeds, or confidence intervals are reported for any result. Given that some entries are based on small samples (e.g., FOLIO accuracies in single digits, MATH500 subset of 500) and the headline claim is a large improvement on a 1B model, the reader cannot assess whether the differences are statistically stable. Please provide standard errors, multiple seeds, or at least the number of examples per dataset and a statement of decoding hyperparameters (temperature, top-p, K) for each reported number.
  5. [§5.2 A3, Figure 6] The test-time scaling comparison is confounded. For CD, n independently generated structured outputs are majority-voted; for DCCD, n drafts are sampled and then a single constrained projection is run on the selected draft. These procedures use different amounts and types of compute, and the selection rule S(k) is not validated as a proxy for correctness. The claim that DCCD 'scales better with test-time compute' should be tested under matched compute (e.g., n constrained projections for both, or n drafts plus n projections for DCCD), and the best-of-K selection rule should be compared against alternatives such as random draft selection or majority voting over drafts.
minor comments (5)
  1. [Figure 7 caption] The caption refers to 'Llama 3.2 3B Instruct', but Table 1 lists Llama 3.2 1B and no 3B Llama. Please correct the model name or verify which model was used.
  2. [Eq. (8)] The product notation for the trajectory-dependent factor is typeset ambiguously ('QT t=1 alpha(ht)'); please write \prod_{t=1}^T \alpha(h_t) consistently and ensure the denominator matches the text.
  3. [Algorithm 1] The draft sampling procedure (temperature, top-p, max length) and whether K=1 in the main results are not specified. Please state the hyperparameters used for Table 2 and Figure 6.
  4. [Related Work] The interleaved reasoning framework of Banerjee et al. (2025) is discussed but not empirically compared. Consider adding a comparison or at least clarifying why DCCD is a different mechanism from simply doing 'reason then answer'.
  5. [Appendix J.2.3] The Constrained Few-Shot output is truncated in the excerpt ('1/'); please fix the rendering so the reader can see the actual final output and the point about truncation is clear.

Circularity Check

0 steps flagged

No significant circularity: the KL identities are self-contained and no prediction reduces to a fitted parameter or self-citation.

full rationale

The paper's formal core is a set of exact identities: Eq. (5) (KL = log 1/α), Eq. (7) (kL projection characterization), Eq. (8) (sequence-level reweighting), and Eq. (17) (Pinsker utility bound). These follow directly from the definitions of masking, renormalization, and KL divergence; they are not fitted to any result. No parameter is estimated from the benchmark outcomes, and no reported accuracy number is derived by construction from the selected feasible-mass criterion. The best-of-K selection in Algorithm 1 uses cumulative log feasible mass as a designed scoring rule, so it is true by selection that the chosen draft maximizes that score, but the reported strict-accuracy improvements are external measurements, not algebraic consequences of that selection rule, and the main K=1 result does not depend on selection at all. The load-bearing empirical step is Eq. (11)'s assertion that conditioning on a draft materially increases probability of schema-forced tokens; the paper supports this with examples rather than an aggregate test. That is an evidence/completeness concern about the causal mechanism, not a circularity: Eq. (11) is an assumed empirical regularity, not a redefinition of the outcome nor a fitted input disguised as a prediction. There are no load-bearing self-citations, no imported uniqueness theorems, and no ansatz smuggled in via citation. The paper is self-contained against external benchmarks, so the honest finding is no significant circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

No new physical or mechanistic entities are postulated; 'projection tax' is a defined quantity (sum of per-step log-renormalization factors), not an independently evidenced entity. The central claims rest on the empirical draft-conditioning assumption and on the correctness of the constraint oracles.

free parameters (3)
  • K (number of drafts) = 1 (main table); 1–13 (test-time scaling)
    Chosen by hand; main-table K is not explicitly stated; magnitude of gains depends on it.
  • Decoding temperature / sampling mode = not reported
    If CD and DCCD used different sampling settings, comparisons are not apples-to-apples; this is a missing hyperparameter rather than a fitted value.
  • Best-of-K selection rule S(k) = cumulative log feasible mass
    Design choice in Algorithm 1 line 12; not shown to correlate with correctness; alternative rules are mentioned but not compared.
axioms (4)
  • standard math Renormalized distribution q = π·mask/α is the unique reverse-KL projection onto the constrained simplex
    Eq. 7; standard information geometry, used as the starting point of the analysis.
  • domain assumption Draft conditioning increases feasible mass: π(s_t|h_t,d) ≫ π(s_t|h_t) in Eq. (11)
    Empirical premise; this is the core mechanism of DCCD and is not proven.
  • domain assumption The draft-conditioned distribution p2(·|x,d) is a high-utility reference for valid outputs
    Appendix A; the Pinsker bound only transfers utility if the reference distribution already concentrates on correct valid outputs.
  • domain assumption XGrammar masks and dataset schemas exactly match the intended hard constraints and ground-truth evaluation
    Appendix I; the validity of strict accuracy metrics depends on the constraint oracle being a faithful implementation.

pith-pipeline@v1.3.0-alltime-deepseek · 24141 in / 12964 out tokens · 134504 ms · 2026-08-03T03:28:02.731438+00:00 · methodology

0 comments
read the original abstract

Large language models (LLMs) are increasingly used to generate executable outputs, JSON objects, and API calls, where a single syntax error can make the output unusable. Constrained decoding enforces validity token-by-token via masking and renormalization, but it can distort generation when the model assigns low probability mass to valid continuations, pushing decoding toward locally valid yet semantically incorrect trajectories. We propose \emph{Draft-Conditioned Constrained Decoding (DCCD)}, a simple two-step, training-free inference procedure that decouples semantic planning from structural enforcement: an unconstrained draft is generated first, and constrained decoding is then applied, conditioned on this draft, to guarantee validity. We analyze DCCD through a KL-projection view, showing that draft conditioning increases feasible mass and reduces the cumulative "projection tax" induced by hard constraints, with an optional best-of-$K$ draft selection. Across structured reasoning benchmarks, DCCD improves strict structured accuracy by up to +24 percentage points over standard constrained decoding (e.g., 15.2\% to 39.0\% on GSM8K with a 1B model), and enables smaller model pairs to match or exceed much larger constrained baselines, yielding substantial gains in parameter efficiency.

Figures

Figures reproduced from arXiv: 2603.03305 by Amrit Singh Bedi, Avinash Reddy, James S. Ide, Thayne T. Walker.

Figure 1
Figure 1. Figure 1: Our proposed approach, Draft-Conditioned Constrained Decoding (DCCD), yields consistent accuracy improvements over standard constrained decoding (state of the art) across model scales (1B–14B). Purple bars denote baseline constrained decoding accu￾racy, while green segments show the absolute accuracy gain from DCCD. These gains reflect improved response correctness and structure adherence at all model size… view at source ↗
Figure 3
Figure 3. Figure 3: Token-wise confidence distribution for answer tokens in a single example. Constrained decoding spreads probability mass across multiple plausible answer tokens (“6”, “27”, “28”, “6”, “84”, “9”), with the incorrect answer “27” receiving moderate confidence (0.46). DCCD shows a sharp, concentrated distribution with near-perfect confidence (1.0) on the correct token “14”. symbols, etc.). As a result, α(ht) ≪ … view at source ↗
Figure 2
Figure 2. Figure 2: Low feasible mass results in distortion. Across tokens in a toy example, the feasible mass α(ht) under constrained de￾coding is always < 0.53 and is near zero for early tokens. In this setting, the constraint admits only ≈ 1% of the full vocabulary as feasible tokens, forcing strong renormalization and accumulating KL distortion. A toy example. Consider a task whose output must be a single-slot JSON object… view at source ↗
Figure 4
Figure 4. Figure 4: Average performance comparison across all evaluation datasets (GSM8K, GSM Symbolic, Math500, and FOLIO). We compare prompting-based baselines (CP, CF), grammar-based constrained decoding (CD), and our Draft-Conditioned Constrained Decoding (DCCD). Across all model scales, DCCD achieves the best aggregated performance, with the largest relative gains for smaller models where hard constraints induce the stro… view at source ↗
Figure 5
Figure 5. Figure 5: Parameter efficiency (accuracy per billion parameters). For each dataset, we report strict structured accuracy normalized by total parameters for single-model CD and parameter-matched DCCD compositions. DCCD consistently achieves higher accuracy per parameter, with the largest gains in low-capacity regimes. A1: DCCD improves strict structured accuracy across model scales and constraint types [PITH_FULL_IM… view at source ↗
Figure 6
Figure 6. Figure 6: Test-time scaling comparison across GSM8K and MATH500 (averaged over six models, 1.5B-14B parameters). Solid lines: GSM8K; dashed lines: MATH500. Draft-Conditioned Constrained Decoding (blue) shows superior scaling versus Con￾strained Decoding (red), with widening performance gaps as n increases from 1 to 13. accuracy per billion), despite using 39% fewer parameters. This pattern holds consistently across … view at source ↗
Figure 8
Figure 8. Figure 8: Win rate comparison between DCCD and CD on non￾verifiable summarization tasks. LLM as a Judge assessed 256- token TL;DR summaries across three criteria: overall quality, faith￾fulness, and coverage. DCCD consistently outperforms CD with approximately 78–80.5% win rate across all evaluation dimensions, demonstrating the effectiveness of staged inference for reasoning￾intensive generation tasks. Appendix E f… view at source ↗
Figure 9
Figure 9. Figure 9: Token-wise probability distributions across the first 600 token positions for different decoding strategies. Constrained Decoding (top) shows degraded confidence over longer sequences, with probabilities declining from 0.8 initially to 0.35 in later positions. Draft Generation (middle) maintains consistent moderate probabilities throughout without structural constraints. Draft-Conditioned Constrained Decod… view at source ↗
Figure 10
Figure 10. Figure 10: Probability distribution analysis across decoding strategies. (a) Normalized token-level probability distributions show that Draft￾Conditioned Constrained Decoding (DCCD, Stage 2) achieves significantly higher mean probability (0.527) compared to Constrained Decoding (CD, 0.393), indicating improved model confidence. Draft Generation (Stage 1) serves as the intermediate unconstrained reasoning step. (b) C… view at source ↗
Figure 11
Figure 11. Figure 11: Detailed test-time scaling comparison across all six models for GSM8K and MATH500 benchmarks. Each subplot shows the scaling behavior for a specific model, comparing Constrained Decoding(CD) (red) with Draft-Conditioned Constrained Decoding(DCCD) (blue). The consistent gap between methods across model sizes and benchmarks demonstrates the robustness of the DCCD approach. 30 [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 12
Figure 12. Figure 12: DCCD demonstrates consistent superiority across all evaluation criteria with win rates of 78–80.5%. The highest performance on coverage (80.5%) validates our hypothesis that separating reasoning from formatting preserves information density. The low tie rate (2–3%) indicates clear quality differences, while robust performance across diverse prompt categories demonstrates generalizability. These findings c… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Extrapolation Cliff in On-Policy Distillation of Near-Deterministic Structured Outputs

    cs.LG 2026-05 unverdicted novelty 7.0

    On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.

  2. Schema Key Wording as an Instruction Channel in Structured Generation under Constrained Decoding

    cs.CL 2026-04 unverdicted novelty 7.0

    Schema-key wording functions as an implicit instruction channel under constrained decoding, with experiments showing that rephrasing only the keys can substantially change accuracy on math benchmarks while prompt, mod...

  3. LatticeBridge: Rare-Event Sequential Inference for Faithful Structured Sequence Synthesis

    cs.CL 2026-04 conditional novelty 6.0

    A twisted sequential Monte Carlo decoder with surface automata improves exact constraint satisfaction in structured text generation over standard decoding baselines across three benchmarks.

  4. The Format Tax

    cs.CL 2026-04 conditional novelty 6.0

    Structured-output instructions alone impose a large accuracy tax on open-weight LLMs; decoupling freeform reasoning from formatting recovers most of it, while recent closed models largely avoid the tax.

  5. ATLAS-RTC: Closing the Loop on LLM Agent Output with Token-Level Runtime Control

    cs.LG 2026-03 unverdicted novelty 6.0

    ATLAS-RTC raises first-attempt success on structured LLM generation and tool calling by 20-37.8 points through closed-loop token-level interventions.

Reference graph

Works this paper leans on

21 extracted references · 3 linked inside Pith · cited by 5 Pith papers

  1. [1]

    Numerical MathWe evaluate on three math datasets:GSM8K(Cobbe et al., 2021), comprising grade school math word problems requiring multi-step arithmetic reasoning;MATH500(Hendrycks et al., 2021), a subset of 500 problems from the MATH benchmark covering algebra, geometry, and number theory

    2021

  2. [2]

    GSM-Symbolic(Mirzadeh et al., 2024), a symbolic variant of GSM8K designed to test genuine mathematical reasoning rather than pattern matching

    Symbolic Math. GSM-Symbolic(Mirzadeh et al., 2024), a symbolic variant of GSM8K designed to test genuine mathematical reasoning rather than pattern matching

    2024

  3. [3]

    doi: 10.18653/v1/2021.emnlp-main.779

    Association for Computational Linguistics. doi: 10.18653/v1/2021.emnlp-main.779. URL https:// aclanthology.org/2021.emnlp-main.779/ . 1, 2, 3 Suresh, T., Banerjee, D., Ugare, S., Misailovic, S., and Singh, G. Dingo: Constrained inference for diffusion llms.arXiv preprint arXiv:2505.23061, 2025. 2, 3 Tam, Z. R., Wu, C.-K., Tsai, Y .-L., Lin, C.-Y ., Lee, H...

    Pith/arXiv arXiv 2021

  4. [4]

    logical negation of expr1: {not}expr1

  5. [5]

    expr1 implies expr2: expr1 {implies} expr2

  6. [6]

    expr1 if and only if expr2: expr1 {iff} expr2

  7. [7]

    FOLIO(Han et al., 2024), a first-order logic reasoning dataset requiring structured logical formalization

    Logical Reasoning. FOLIO(Han et al., 2024), a first-order logic reasoning dataset requiring structured logical formalization. Given natural language premises and a conclusion, models must produce a formal representation. Outputs are verified using the Prover9 theorem, and accuracy is measured by whether the formalized proof matches the ground truth conclu...

    2024

  8. [8]

    Constrained Prompting(CP): System prompts are carefully engineered to specify the required output structure, including explicit format constraints and examples of valid outputs

  9. [9]

    This below method guarantees format compliance but often sacrifices answer quality:

    Constrained Few-Shot (CF): In addition to format specifications, we providek= 3 in-context examples that demonstrate the expected output structure, following standard few-shot prompting practices. This below method guarantees format compliance but often sacrifices answer quality:

  10. [10]

    At each decoding step, a token mask is constructed from the grammar specification, restricting sampling exclusively to syntactically valid tokens

    Constrained Decoding (CD): We employ grammar-based constrained decoding using XGrammar (Dong et al., 2025) integrated with vLLM. At each decoding step, a token mask is constructed from the grammar specification, restricting sampling exclusively to syntactically valid tokens. This approach guarantees syntactic correctness but directly intervenes in the gen...

    2025

  11. [11]

    4) On the more challenging MATH500 benchmark, the scaling behavior is more gradual, with performance improvements continuing through n=13, though at diminishing rates

    Larger models (Qwen2.5 14B, Llama 3.1 8B, Qwen2.5 7B) demonstrate strong baseline performance with DCCD , approaching or exceeding 90% on GSM8K. 4) On the more challenging MATH500 benchmark, the scaling behavior is more gradual, with performance improvements continuing through n=13, though at diminishing rates. 5) Constrained Decoding exhibits more pronou...

  12. [12]

    The model is informed of the downstream budget to ensure sufficient detail for compression

    Draft Generation:Generate a comprehensive, unconstrained answer focusing on accuracy, coverage, and reasoning. The model is informed of the downstream budget to ensure sufficient detail for compression

  13. [13]

    steps": [

    Constrained Compression:Compress the draft into a faithful summary within the hard budget, prioritizing coverage of core claims, key points, and critical numbers while avoiding fabrications. Hypothesis:Decoupling content generation from constraint satisfaction maintains reasoning quality while achieving structural constraints. Table 3.Evaluation prompt ca...

  14. [14]

    logical conjunction of expr1 and expr2: expr1 {and} expr2

  15. [15]

    logical disjunction of expr1 and expr2: expr1 {or} expr2

  16. [16]

    logical exclusive disjunction of expr1 and expr2: expr1 {xor} expr2

  17. [20]

    logical universal quantification: {forall} x

  18. [21]

    Predicates:

    logical existential quantification: {exists} x These are the ONLY operations in the grammar. Expected output format: Predicates: P(x) ::: description of P Q(x) ::: description of Q Premises: forall x (P(x) implies Q(x)) ::: premise description Conclusion: Q(a) ::: conclusion statement ------ Given the message above, Just write the "Predicates:", "Premises...

  19. [2021]

    and Liu, Q

    6, 13 Hokamp, C. and Liu, Q. Lexically constrained decoding for sequence generation using grid beam search. In Barzi- lay, R. and Kan, M.-Y . (eds.),Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 1535–1546, Vancouver, Canada, July 2017. Association for Compu- tational Linguistics. doi: ...

    Pith/arXiv arXiv 2017

  20. [2023]

    making valid tokens higher-likelihood

    1, 2, 3 Yao, S., Zhao, J., Yu, D., Du, N., Shafran, I., Narasimhan, K. R., and Cao, Y . React: Synergizing reasoning and acting in language models. InThe eleventh international conference on learning representations, 2022. 1 10 Appendix Contents 1 Introduction 1 2 Related Works 2 3 Problem Formulation 3 3.1 Existing Approach: Constrained Decoding . . . . ...

    2022

  21. [2024]

    Accessed: 2024-08-24

    URL https://openai.com/index/int roducing-structured-outputs-in-the-a pi/. Accessed: 2024-08-24. 2, 3 OpenAI. Introducing agent kit, October 2025. URLhttps: //openai.com/index/introducing-agent kit/. Accessed: 2025-10-06. 1 Park, K., Zhou, T., and D’Antoni, L. Flexible and ef- ficient grammar-constrained decoding.arXiv preprint arXiv:2502.05111, 2025. 1, ...

    Pith/arXiv arXiv 2024