{"id":"fdced356-2335-4c5a-a1a2-81b88e38158b","arxiv_id":"2508.09654","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Recall-oriented training losses (TruncR, c-Div with alpha>1, and lambda-PR) make language models more tunable through temperature, improving precision-recall trade-offs beyond NLL plus temperature scaling.","lead":"The paper studies why raising the decode temperature of language models rarely improves diversity (coverage) as expected, and proposes training losses that focus on recall instead. It shows that models trained with these recall-oriented losses can achieve better precision-recall trade-offs under temperature scaling than standard maximum-likelihood training.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposition 4.3's proof is unverifiable: Lemma A.3's key derivative (Eq. 109) is corrupted, so the theoretical basis for the central claim is not established.","rationale":"The reader's weakest assumption focused on the toy model's transferability to real language distributions. I agree that is a concern, but a more immediate and concrete problem is that the proof of the key lemma underpinning Proposition 4.3 is not verifiable as written. The garbled expression in Eq. (109) prevents checking whether h(t) is strictly increasing, so the theoretical 'analysis reveals' claim is unsupported even within the toy setting. This does not overturn the paper's empirical results, which may still be suggestive, but it raises the bar for acceptance: the authors need to provide a clean, correct proof. This is consistent with the reader's CONDITIONAL verdict, so I recommend keeping the verdict unchanged, with the condition now explicitly requiring a verifiable proof of Lemma A.3.","tokens_in":37624,"tokens_out":8343,"duration_ms":94146,"concrete_test":"Independently re-derive h'(t) from Eq. (106) using symbolic differentiation (e.g., SymPy) and evaluate its sign over Lemma A.3's parameter space (0<ϵ<1, 0<ρ<1, 0<b<a, K≤V). If any valid parameters give h'(t)<0, Lemma A.3 and Props. A.4/4.3 are false. Also inspect the arXiv source for Eq. (109); if the corruption is a rendering artifact, the authors should supply a clean, line-by-line derivation of the sign of h(t).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim ('for a model to be effectively tunable through temperature adjustments, it must be trained toward coverage') rests on Proposition 4.3's account of why Recall declines with temperature. That proposition is based on Lemma A.3 and Proposition A.4 in Appendix A.2. In the proof of Lemma A.3, after defining h(t) in Eq. (106), the manuscript derives h'(t) and asserts h is strictly increasing. However, the displayed equation for h'(t) (Eq. 109) contains an extended corrupted string of symbols ('⌟⟨⟨⟪rl⟫l⟩⟩⟪⌟⟪⟨⟨...') instead of a readable algebraic expression. No reader can verify the sign of h'(t) from the text. If h is not strictly increasing, the threshold λ_min^t may not have the claimed monotonicity, and the 'initial increase then decline' of Recall (Prop. 4.3) is not proven even in the toy model. Since the abstract's 'our analysis reveals' is the theoretical justification for changing the loss, the headline claim currently lacks verifiable support. The toy model's uniform-sparse assumption is a separate extrapolation, but the immediate issue is that the proof itself is not checkable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies temperature scaling in language models through a precision-recall (PR) lens. It gives a general sparsity-based upper bound on PR under temperature (Theorem 4.2), then analyzes a toy sparse-uniform model to argue that recall first rises and then falls as temperature increases, so that likelihood-trained models are not effectively tunable for coverage. On the training side, it reinterprets Trunc, GOLD, and TaiLr as precision-oriented losses, proposes recall-oriented variants (TruncR, c-Div with α>1, λ-PR), and reports experiments on code generation, integer multiplication, and open-ended generation showing better PR trade-offs than NLL plus temperature scaling. The central claim is that a model must be trained toward coverage for temperature to be an effective diversity control.","tokens_in":37981,"tokens_out":4225,"duration_ms":49289,"significance":"If the central claim holds, the paper makes a useful conceptual contribution: it reframes the common intuition that temperature increases diversity, showing that coverage of the reference distribution must be trained in. The proposed losses are concrete and the experiments cover several tasks and model scales. Strengths include an explicit PR-curve characterization in a tractable toy model and derivations connecting existing losses to PR-divergences. However, the theoretical load-bearing block (Proposition 4.3) is not verifiable as written, and the empirical support lacks basic statistical safeguards. The paper is potentially significant, but the current version is not yet at the standard for acceptance.","major_comments":[{"comment":"The displayed expression for h'(t) is a corrupted string of symbols, not a readable algebraic formula. Lemma A.3's claim that h is strictly increasing—and hence the monotonicity of λ_min^t and the initial-increase-then-decline of Recall in Proposition 4.3—cannot be checked by the reader. Since Proposition 4.3 is the theoretical basis for the paper's headline claim that temperature tunability requires coverage-oriented training, this is load-bearing. The authors must supply a complete, readable derivation or a machine-checkable proof, and state explicitly which inequalities are used to sign h'.","section":"Appendix A.2, Eq. (109)"},{"comment":"The definition of TruncR in Eq. (16) sets the threshold δ via E_{x∼Q}[1{̄Q_θ(x)≤δ}]=1−Δ, whereas Proposition 5.3 claims that optimizing TruncR maximizes Recall at fixed Precision α=1−Δ. The proof in Appendix B.1 (Lemma B.1 and Proposition B.3) uses instead the quantile condition ∑_{i:Q_i<δ} P_i = 1−Δ, and Algorithm 1 computes δ from samples drawn from the training set (i.e., from P). This mismatch between the main-text definition, the algorithm, and the proof must be resolved. With the E_Q definition, the claimed Precision identity does not follow from the supplied proof.","section":"§5.2, Eq. (16) and Appendix B.1"},{"comment":"The empirical comparisons report single numbers with no error bars, confidence intervals, or multiple seeds. Some differences are small relative to what would be expected from sampling noise (e.g., Table 1: NLL R=8.9 vs. TruncR R=9.3; NLL P=81.4 vs. TruncR P=85.5). Moreover, §6.6 selects the temperature on the test set to exhibit the best PR point for each method, and Figures 6–7 show best-looking sweeps. This makes the claim that the proposed losses achieve a 'substantially better trade-off' difficult to evaluate. The authors should report means and variances over at least a few seeds, and either fix a temperature grid a priori or clearly separate model selection from evaluation.","section":"§6.4–§6.6, Tables 1, 3, 4"},{"comment":"Proposition 4.3 is proven only for a target distribution P that is uniform over K tokens at every position and for a model that deviates at two hand-picked positions. The paper then uses this toy model to interpret real-language results in WritingPrompts and CodeContests (e.g., 'These observations are consistent with the theoretical findings'). This extrapolation is a correctness-risk concern: real conditional distributions are heavy-tailed, not sparse uniform, and the conditions K≪V or Q close to P may not hold. The paper should either provide a direct empirical test of the predicted peak-and-decline (e.g., β_λ vs. temperature at fixed λ for the real tasks) or explicitly limit the theoretical explanation to the toy case and to the integer-multiplication experiment where the behavior is actually observed.","section":"§4 / §6.4"}],"minor_comments":[{"comment":"The sentence 'Further details about ̃Qθ The formal theorem...' is incomplete and should be rewritten.","section":"§4, after Proposition 4.3"},{"comment":"The notation P(X K V) is used in the theorem statement but is not defined; the paper elsewhere uses P(V^L). Please unify notation.","section":"Appendix A.1"},{"comment":"Typos: 'distrbutions' (Appendix A.2), 'proove' (Appendix B.1), and 'the WritingPrompts on MathQA-Python datasets' in Table 3 heading. These should be corrected.","section":"Throughout"},{"comment":"The support-based Precision/Recall of Eq. (4) is a special case of the PR-curve (α_∞, β_0). It would help to state this relation explicitly when introducing Definition 2.2, since the experiments use the PR-curve definitions.","section":"§2.3"}],"recommendation":"major_revision","confidential_remarks":"The corrupted text in Eq. (109) is likely a rendering artifact, but under the reviewing rules I treat it as in-scope; the authors must restore the derivation. The mismatch between Eq. (16) and the appendix proof for TruncR is more than a typo: it affects the formal statement of the proposed method. The empirical weaknesses (no variance, test-set temperature selection) are serious but fixable with additional experiments. I do not see grounds for rejection if these points are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things before reading this closely. First, it is a serious attempt to unify several training losses for language models under a Precision-Recall umbrella, and it introduces two new variants (TruncR and λ-PR) that plausibly push toward Recall. Second, the theoretical core that motivates the whole thing is currently unverifiable: in the proof of Lemma A.3, Eq. (109) is a corrupted string of symbols rather than a derivative. Since Proposition 4.3 — the claim that Recall eventually declines with temperature — rests on this lemma, the central narrative \"temperature fails unless you train for coverage\" is not yet supported by the math.\n\nWhat is genuinely new and useful: the PR-framework reading of Trunc, GOLD, and TaiLr is clean, and the new loss variants are natural and worth experimenting with. The toy-model analysis in Section 4 gives a simple intuition for why high temperature can hurt coverage, and the authors are honest about its scope. The empirical work covers several tasks and models, and the results do show that some Recall-oriented losses can shift the trade-off relative to NLL.\n\nThe soft spots are real. Missing error bars / multiple seeds in Tables 1, 3, and 4 make effect sizes hard to trust. Tuning temperature on the test set is a protocol issue that can inflate reported gains. Defining Recall on code tasks as pass@100 − pass@1 conflates correctness with coverage and deserves validation or at least discussion. The paper also leans heavily on the same group's PR framework and evaluates the new losses with PR-curve-style metrics, so the circularity concern is partly fair. And the uniform-sparse toy distribution is far from the heavy-tailed conditional distributions in real language; the extrapolation is a leap.\n\nMy overall take: the core idea is plausible and the empirical direction is useful, but the paper is not there yet. I would send it to referees — the unification and the new losses are worth discussing — but I would expect substantial revisions, starting with fixing the corrupted equation, adding seeds/error bars, moving temperature selection to a validation split, and validating the pass@k-based recall metric. I would not cite it in my own work until those are fixed.","headline":"Worth taking seriously, but the central proof is unverifiable due to a corrupted equation in Lemma A.3, and the empirics are suggestive rather than conclusive.","tokens_in":38475,"tokens_out":2036,"would_cite":false,"duration_ms":21268,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T50","62B10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Raising decoding temperature does not reliably improve recall unless the language model was trained with a coverage-oriented objective.","keywords":["diversity","temperature scaling","precision-recall","coverage","loss functions","language models","TruncR","c-Div"],"falsifier":"Train a model with a recall-oriented loss such as c-Div with alpha > 1 on a heavy-tailed token distribution with known Zipf exponents, then measure whether recall as a function of temperature still rises-then-falls; if recall monotonically increases or plateaus, the paper's explanation for why temperature fails on likelihood-trained models breaks.","tokens_in":1459,"feed_emoji":"🎛️","tokens_out":1533,"duration_ms":40402,"temperature":0.7,"pith_summary":"This paper tries to establish why turning up the decoding temperature of an autoregressive language model often fails to increase diversity as measured by recall, and what to do about it. The authors argue that a model is only tunable by temperature once it has been trained toward coverage: negative log-likelihood training optimizes precision, so temperature scaling on such a model mostly sharpens or flattens an already narrow distribution. They propose recall-oriented alternatives to standard losses, show these are reweighted NLL losses, and demonstrate empirically that they yield a better precision-recall trade-off than NLL plus temperature tuning. If true, this reframes diversity as a training-objective problem rather than a decoding-time fix.","feed_headline":"One loss change makes temperature tuning actually improve diversity","feed_subtitle":"Likelihood training optimizes precision; recall-oriented losses let decoding temperature boost coverage and give a better trade-off.","key_machinery":"The precision-recall curve with parameter $\\lambda$: for distributions $P$ and $Q$, $\\alpha_\\lambda = \\sum_x \\min(\\lambda P(x), Q(x))$ and $\\beta_\\lambda = \\sum_x \\min(P(x), Q(x)/\\lambda)$, which measures quality versus coverage across thresholds. Temperature is modeled as raising the softmax distribution to power $1/t$ and renormalizing, so the analysis tracks how the curve moves with $t$. The training methods are all reweighted NLL losses: TruncR upweights low-likelihood samples, c-Div weights by $\\bar Q^{1-\\alpha}$ with $\\alpha>1$ for mass-covering behavior, and $\\lambda$-PR targets a chosen point on the PR-curve. A sparsity theorem and a two-position artificial distribution supply the theor","core_discovery":"The paper's central claim is that temperature scaling alone cannot meaningfully improve recall because a likelihood-trained model has not been trained to cover the reference distribution. Using the precision-recall curve of Sajjadi et al., the authors prove a sparsity bound showing that both precision and recall are limited by the support size of the true distribution relative to the vocabulary, and they construct a simplified two-position toy model in which recall first peaks then declines as temperature increases. They then reinterpret three existing losses (Trunc, GOLD, TaiLr) as precision-oriented reweightings of NLL, and introduce recall-oriented counterparts: TruncR, c-Div with alpha g","pith_inferences":["The toy model suggests an untested corollary: on heavy-tailed reference distributions, the temperature at which recall peaks should depend on tail exponents, not just support sparsity; a systematic sweep on Zipfian conditional distributions would sharpen the practical guidance.","The paper's framing implies that decoding-time diversity methods (top-p, KL-guided sampling, and similar) are also trying to recover coverage the training loss never encouraged; the appendix results support treating these as second-best to loss design.","If the mechanism transfers, then alignment or RLHF pipelines that optimize precision may be silently degrading the temperature-tunable diversity of the final model, and adding a recall-oriented loss during the alignment stage could counteract that.","The threshold $\\epsilon_0$ in the appendix predicts a phase change in recall behavior depending on noise level; a direct experiment varying the noise mass outside the support of a controlled reference distribution could test this prediction in a real model."],"forward_implications":["Temperature becomes an effective diversity control only after recall-oriented training; on NLL models, increasing temperature will at best briefly raise recall before degrading it.","Recall-oriented losses such as TruncR, c-Div with $\\alpha>1$, and lambda-PR can be implemented as simple per-token reweightings of the standard NLL objective, making them cheap drop-in alternatives.","In code generation, the pass@1-to-pass@k gap, used as a recall proxy, can be widened by training for coverage rather than by raising temperature at decoding time.","Precision-oriented post-training, such as RL-style fine-tuning, may shrink the range over which temperature tuning can recover recall; the paper's RLEF comparison points in this direction.","The proposed losses can be combined with temperature tuning to reach recall levels that NLL cannot attain at the same precision level."],"supporting_citations":[{"why":"Defines the precision-recall curve and the $\\alpha_\\lambda, \\beta_\\lambda$ quantities that the paper uses as its evaluation and theoretical target.","marker":"Sajjadi et al., 2018"},{"why":"Supplies the support-based definition of precision and recall used for metric computation in the language experiments.","marker":"Kynkäänniemi et al., 2019"},{"why":"Introduces the Trunc loss, the precision-oriented baseline that the paper generalizes into TruncR.","marker":"Kang & Hashimoto, 2020"},{"why":"Introduces GOLD, which the paper unifies as c-Div with $\\alpha=1/2$ and extends to recall-oriented $\\alpha>1$.","marker":"Pang & He, 2021"},{"why":"Introduces TaiLr, the total-variation-based loss that the paper generalizes to lambda-PR.","marker":"Ji et al., 2023"},{"why":"Provides the precision-recall evaluation method for LLMs used on the WritingPrompts task.","marker":"Le Bronnec et al., 2024"},{"why":"Provides the unbiased pass@k estimator used to define precision and recall proxies for code generation and MathQA-Python.","marker":"Chen et al., 2021"}],"fun_headline_variants":["Temperature fails? Swap the loss to boost recall","Why high temperature won't add diversity: the fix","Precision vs recall: the loss that makes temperature work","Train for coverage, then tune temperature for diversity"],"cache_read_input_tokens":40192,"weakest_assumption_plain":"The theoretical mechanism assumes the reference distribution is a sparse uniform distribution over exactly K tokens at every position, while real language distributions are heavy-tailed, so the predicted peak-and-decline of recall with temperature may not transfer.","fun_headline_variants_meta":{"raw":{"variants":["Temperature fails? Swap the loss to boost recall","Why high temperature won't add diversity: the fix","Precision vs recall: the loss that makes temperature work","Train for coverage, then tune temperature for diversity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000954,"raw_usage":{"total_tokens":3854,"prompt_tokens":641,"completion_tokens":3213,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":385,"completion_tokens_details":{"reasoning_tokens":3151}},"tokens_in":385,"tokens_out":3213,"duration_ms":22176,"temperature":1.0,"reasoning_tokens":3151,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T20:55:23.867963+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train a model with a recall-oriented loss such as c-Div with alpha > 1 on a heavy-tailed token distribution with known Zipf exponents, then measure whether recall as a function of temperature still rises-then-falls; if recall monotonically increases or plateaus, the paper's explanation for why temperature fails on likelihood-trained models breaks.","supporting_citations":[],"review_version":1}