{"id":"6169e577-dd59-4b8c-a99e-3f3e1189b50d","arxiv_id":"2606.28354","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Relaxing eventual validity to vanishing error rates in language generation in the limit strictly increases recall under partial revelation by the adversary.","lead":"The paper extends language generation in the limit by allowing learners to produce infinitely many invalid strings if their frequency tends to zero, preserving precision of one. This relaxation can strictly increase recall when an adversary withholds large parts of the target language.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption correctly flags the scoping condition, but because the claim is already restricted to that regime the condition does not constitute a load-bearing flaw in the argument as written. Full-text verification of the proof would still be warranted given the abstract-only review, yet no technical gap is visible from the supplied material.","tokens_in":1692,"tokens_out":254,"duration_ms":26568,"concrete_test":"Extract the formal definition of the 'permanently withholds a large portion' adversary from the paper and the corresponding theorem statement; confirm that the recall comparison is witnessed by an explicit learner construction or proof for at least one such adversary.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim states that the relaxation (precision-1 learners allowing infinitely many hallucinations whose frequency tends to zero) can strictly increase recall when the adversary permanently withholds a large portion of the target language. This is an explicitly conditional existence result rather than a universal claim. The abstract supplies no indication of an internal inconsistency, hidden assumption, or unsupported step within the stated scope; the condition on the adversary is part of the theorem statement, not an unexamined prerequisite.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper extends the language generation in the limit framework by relaxing the validity (precision) constraint to permit infinitely many hallucinations provided their asymptotic frequency tends to zero, thereby preserving precision one. Under this relaxation it proves a conditional existence result: recall can be strictly higher than in the eventually-valid case when the adversary permanently withholds a large portion of the target language. The manuscript also analyzes a continuous relaxation of the novelty constraint that requires only a fixed positive fraction of outputs to be novel, and situates both relaxations within the classic recall-precision trade-off for settings closer to large language models.","tokens_in":1769,"tokens_out":408,"duration_ms":31884,"significance":"If the derivations hold, the work supplies a theoretically grounded relaxation that aligns the formal model more closely with practical language generation, where occasional errors and repetitions are inevitable. The conditional strict-increase result under permanent withholding is a precise, falsifiable statement that clarifies when the precision-recall tension can be mitigated without sacrificing the limit guarantee.","major_comments":[{"comment":"Theorem on relaxed precision (presumably the central result following the definitions of precision-1 learners): the strict increase in recall is shown only under the permanent-withholding adversary; the manuscript should state explicitly whether the construction fails or becomes non-strict when the withheld set is eventually revealed, as this boundary condition is load-bearing for the claimed advantage over eventually-valid learners.","section":null}],"minor_comments":[{"comment":"Notation for the frequency-of-hallucinations limit (e.g., lim freq(hallucinations) = 0) should be introduced with a displayed equation and cross-referenced in the statement of the main theorem to avoid ambiguity with the classic “eventually valid” definition.","section":null},{"comment":"The continuous novelty relaxation is introduced late; a short paragraph in the introduction contrasting the discrete and continuous novelty constraints would improve readability.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed reading and for identifying this important boundary condition in our central result. We address the comment below and will revise the manuscript accordingly.","responses":[{"response":"We agree that the strict-increase result is proved only for the permanent-withholding case. The construction in the proof exploits the fact that the withheld strings are never revealed, allowing the learner to produce them at a vanishing rate without ever being contradicted by the adversary. If the withheld set is eventually revealed, the same learner would eventually be forced to output strings already seen in the enumeration, causing recall to drop to the level achieved by eventually-valid learners; the strict separation therefore disappears. We will add an explicit paragraph after the theorem statement clarifying this boundary condition and noting that the advantage is conditional on permanent partial revelation.","revision_made":"yes","referee_comment":"Theorem on relaxed precision (presumably the central result following the definitions of precision-1 learners): the strict increase in recall is shown only under the permanent-withholding adversary; the manuscript should state explicitly whether the construction fails or becomes non-strict when the withheld set is eventually revealed, as this boundary condition is load-bearing for the claimed advantage over eventually-valid learners."}],"tokens_in":1306,"tokens_out":271,"duration_ms":16886,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this work relaxes the eventual-validity requirement so a learner can output infinitely many errors provided their rate goes to zero, and proves this can give strictly higher recall when the adversary never reveals a large chunk of the target language. They also introduce a continuous relaxation where only a fixed fraction of outputs need to be novel.\n\nThe paper does a solid job recasting the generation problem as an explicit recall-precision trade-off and tying the constraints to settings that feel closer to LLMs. The new precision definition and the existence result under withholding are presented as extensions beyond the cited prior work, and the abstract keeps the claims conditional rather than universal.\n\nThe soft spot is the reliance on permanent withholding; if the adversary eventually reveals everything the strict increase may not hold, which is already flagged in the abstract. The analysis stays abstract, so downstream payoff for actual models remains limited, and the full derivations are not visible here to check for gaps.\n\nThis is for people working in formal language theory who care about adapting identification-in-the-limit ideas to generation. A reader focused on theoretical foundations would find the relaxations useful. It deserves a serious referee because it adds concrete new results inside an established framework without obvious internal contradictions.","headline":"The paper shows that allowing infinitely many hallucinations with frequency tending to zero can strictly increase recall in generation in the limit, but only under permanent adversary withholding.","tokens_in":2228,"tokens_out":325,"would_cite":false,"duration_ms":23731,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Allowing infinitely many hallucinations with vanishing frequency strictly raises recall in language generation in the limit when the adversary withholds part of the language.","keywords":["language generation in the limit","hallucinations","recall-precision trade-off","asymptotic validity","adversarial learning","language identification","large language models"],"falsifier":"A concrete language class and adversary strategy in which every asymptotically valid learner attains higher recall than every eventually valid learner when a fixed fraction of strings is permanently withheld.","tokens_in":2594,"feed_emoji":"","tokens_out":605,"duration_ms":21779,"temperature":0.7,"pith_summary":"The paper reframes language generation in the limit as a recall-precision problem where the learner must output valid novel strings from a target language that an adversary reveals incrementally. It relaxes the usual demand for eventual validity into asymptotic validity: learners may produce infinitely many invalid outputs provided their rate tends to zero, preserving precision of one. Under this relaxation the paper proves that recall can be strictly higher than for eventually valid learners precisely when the adversary permanently withholds a large fraction of the target language. A second relaxation replaces strict novelty with a fixed fractional novelty requirement. The overall goal is to model realistic generation settings in which occasional errors and repetitions occur but remain controlled.","feed_headline":"Infinitely many low-rate hallucinations raise recall in the limit","feed_subtitle":"Asymptotic validity keeps precision at one and strictly improves coverage when the adversary permanently withholds part of the target langua","key_machinery":"Asymptotic validity: the requirement that the frequency of invalid outputs tends to zero rather than that invalid outputs eventually cease.","core_discovery":"In the generation-in-the-limit setting, learners that produce infinitely many invalid strings yet maintain precision one through a vanishing error rate can achieve strictly higher recall than eventually valid learners whenever the adversary permanently withholds a positive fraction of the target language.","pith_inferences":["In practice this suggests that models allowed controlled repetition and rare errors could cover more of an underlying distribution than strictly valid generators.","The advantage is tied to permanent withholding; if the withheld set eventually appears the recall ordering may reverse.","The same asymptotic-precision idea could be applied to other partial-information learning settings beyond formal languages."],"forward_implications":["Precision remains exactly one even though the learner never becomes valid.","The set of languages that can be generated with high recall enlarges under permanent withholding adversaries.","A continuous novelty constraint requiring only a fixed fraction of outputs to be novel still permits positive recall.","Enumeration, novelty, and validity constraints can be traded off while keeping precision one."],"fun_headline_variants":["Infinite hallucinations raise recall with vanishing rate","Vanishing hallucination rate raises recall despite infinite errors","Precision one with infinite hallucinations raises recall","Infinite low rate hallucinations raise recall in the limit"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The adversary must permanently withhold a large portion of the target language; the strict recall gain disappears if the adversary eventually reveals everything.","fun_headline_variants_meta":{"raw":{"variants":["Infinite hallucinations raise recall with vanishing rate","Vanishing hallucination rate raises recall despite infinite errors","Precision one with infinite hallucinations raises recall","Infinite low rate hallucinations raise recall in the limit"]},"model":"grok-4.3","cost_usd":0.008217,"raw_usage":{"total_tokens":3715,"prompt_tokens":641,"num_sources_used":0,"completion_tokens":55,"cost_in_usd_ticks":82174500,"prompt_tokens_details":{"text_tokens":641,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3019,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":641,"tokens_out":55,"duration_ms":29878,"temperature":1.0,"reasoning_tokens":3019,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T10:43:17.626977+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A concrete language class and adversary strategy in which every asymptotically valid learner attains higher recall than every eventually valid learner when a fixed fraction of strings is permanently withheld.","supporting_citations":[],"review_version":1}