Improving Diversity in Language Models: When Temperature Fails, Change the Loss

Alexandre Allauzen; Alexandre Verine; Benjamin Negrevergne; Florian Le Bronnec; Kunhao Zheng; Yann Chevaleyre

REVIEW 4 major objections 4 minor 1 cited by

Improving Diversity in Language Models: When Temperature Fails, Change the Loss

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Raising decoding temperature does not reliably improve recall unless the language model was trained with a coverage-oriented objective.

desk verdict 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. read the letter →

arxiv 2508.09654 v1 pith:UGNUBCGA submitted 2025-08-13 cs.CL cs.LG

Alexandre Verine , Florian Le Bronnec , Kunhao Zheng , Alexandre Allauzen , Yann Chevaleyre , Benjamin Negrevergne This is my paper · ORCID

classification cs.CLcs.LG MSC 68T5062B10

keywords diversitytemperaturescalingprecision-recallcoveragelossfunctionslanguagemodelsTruncRc-Div

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

What carries the argument

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

What would settle it

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.

Watch

Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the 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.

What 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.

The 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.

My 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.

Referee Report

4 major / 4 minor

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.

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 (4)

[Appendix A.2, Eq. (109)] 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'.
[§5.2, Eq. (16) and Appendix B.1] 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.
[§6.4–§6.6, Tables 1, 3, 4] 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.
[§4 / §6.4] 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.

minor comments (4)

[§4, after Proposition 4.3] The sentence 'Further details about ̃Qθ The formal theorem...' is incomplete and should be rewritten.
[Appendix A.1] 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.
[Throughout] Typos: 'distrbutions' (Appendix A.2), 'proove' (Appendix B.1), and 'the WritingPrompts on MathQA-Python datasets' in Table 3 heading. These should be corrected.
[§2.3] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central derivation and proposed losses are not equivalent to their evaluation by construction.

full rationale

I found no circular step that reduces a prediction to its own inputs. Section 4's theoretical claim is derived from an explicit toy model (sparse uniform P; Q specified by a, b, rho, epsilon) using the PR definitions and temperature scaling; it does not assume the conclusion. The proposed losses are not identical to the evaluation metrics: e.g. L^alpha_cDiv = -E[\bar{Q}^{1-alpha} log Q] is a reweighted NLL, while beta_lambda = sum min(P, Q/lambda); the lambda-PR loss is a weighted NLL with an indicator threshold, derived as a lower bound on (alpha_lambda, beta_lambda), not the metric itself. Therefore the empirical recall gains are not true by construction. The self-citations (Verine et al. 2023; Verine 2024; Le Bronnec et al. 2024) supply notation, an elementary identity for the PR divergence, and an evaluation protocol; none is a uniqueness theorem or an unverified premise on which the central claim depends. The cited identity D_lambda = 1/2 sum |lambda P - Q| - 1/2 |lambda - 1| follows directly from Definition 2.2, so it is independent support rather than load-bearing. One verifiability caveat, not a circularity: the proof of Lemma A.3 contains a corrupted displayed expression at Eq. (109) ('⌟⟨⟨⟪rl⟫l⟩⟩⟪⌟...'), so the monotonicity of h(t) cannot be checked as printed; this is an omitted/unverifiable proof step but does not make the derivation circular.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The paper's central claims rest on a small number of explicit modeling assumptions: sparsity of the true language distribution, a toy sparse-uniform distribution used to prove temperature effects, a gamma-proxy approximation for the conditional target distribution, and a pass@k-based proxy for recall in code tasks. The training methods add hand-chosen hyperparameters (alpha, lambda, gamma, Delta) and the evaluation adds test-set temperature selection. No fundamentally new physical or architectural entities are introduced.

free parameters (6)

Temperature t during evaluation = tuned on test set, e.g., t=1.6 for NLL in Table 4a, t=1.0 for c-Div
Chosen after test evaluation to maximize Recall or Precision at a fixed counterpart; a post-hoc free parameter in the comparison.
alpha in c-Div = 1.3-1.4 in tables
Hyperparameter of the Tsallis alpha-divergence loss; selected per task/model, no sensitivity analysis shown.
lambda in lambda-PR = 0.1, 0.5, 0.9 in tables
Target point on PR-curve; chosen per task, no principled selection rule.
gamma in lambda-PR and TaiLr = 1e-5 to 1e-7
Proxy-mixture coefficient; chosen by hand.
Delta for Trunc/TruncR = 0.25 on WritingPrompts, 0.1 on MathQA
Truncation quantile; chosen by hand.
Toy distribution parameters (a, rho, epsilon) = e.g., a/rho=1.45, epsilon=0.15, rho=0.5 in Figures 2, 9, 10
Hand-picked toy distribution parameters used to prove recall declines with temperature; the result depends on these choices.

assumptions (5)

standard math Probability distributions are over finite sequence space V^L and temperature scaling follows the power 1/t normalization (Eq. 3).
Foundation for all PR computations and temperature analysis.
domain assumption The true language distribution P is sparse: |Supp(P)|/V^L << 1.
Used in Theorem 4.2 and empirically 'estimated' via top-p token counts in Section 6.3; the theorem's conclusions about hardness follow from sparsity, and the paper's interpretation assumes this sparsity.
ad hoc to paper The gamma-proxy distribution (Definition 5.1, from Ji et al. 2023) approximates the conditional target P<l for deriving lambda-PR and TaiLr losses.
Required to turn the PR-divergence into a trainable loss; not independently verified in the paper.
domain assumption pass@100 - pass@1 is a valid proxy for Recall in code tasks.
Used in Section 6.1 and Algorithm 5; the paper provides no justification that a difference of pass rates estimates coverage of the reference distribution.
domain assumption The support of P can be estimated by the number of top-p tokens from a reference model.
Section 6.3 treats Llama3.1's top-p counts as an upper bound on true support size; this assumes the reference model's calibration.

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Cite this review

Pith. "Pith review of Improving Diversity in Language Models: When Temperature Fails, Change the Loss." pith.science (2026). https://pith.science/paper/UGNUBCGA

@misc{pith2026250809654,
  author       = {Pith},
  title        = {Pith review of: Improving Diversity in Language Models: When Temperature Fails, Change the Loss},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UGNUBCGA}},
  note         = {Machine review of arXiv:2508.09654}
}

read the original abstract

Increasing diversity in language models is a challenging yet essential objective. A common approach is to raise the decoding temperature. In this work, we investigate this approach through a simplistic yet common case to provide insights into why decreasing temperature can improve quality (Precision), while increasing it often fails to boost coverage (Recall). Our analysis reveals that for a model to be effectively tunable through temperature adjustments, it must be trained toward coverage. To address this, we propose rethinking loss functions in language models by leveraging the Precision-Recall framework. Our results demonstrate that this approach achieves a substantially better trade-off between Precision and Recall than merely combining negative log-likelihood training with temperature scaling. These findings offer a pathway toward more versatile and robust language modeling techniques.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Quality-constrained Entropy Maximization Policy Optimization for LLM Diversity
cs.CL 2026-02 conditional novelty 4.0 of 10

Quality-constrained entropy maximization yields simple DPO-like objectives that increase LLM output diversity while preserving or slightly improving quality, with theoretical guarantees under tuned temperature conditions.

Reference graph

Works this paper leans on

11 extracted references · 9 canonical work pages · cited by 1 Pith paper

[1]

(57) In this regime, that is, for large values of λ, αλ reflects the model’s quality, as it converges to Precision whenλ→+∞

For λ≥ a(1− ϵ)/ρ, we have: αλ(P∥Qθ)= 1 K K ∑ i cl(1− ϵ)= (1− ϵ) K ∑ i cl ρK = 1− ϵ. (57) In this regime, that is, for large values of λ, αλ reflects the model’s quality, as it converges to Precision whenλ→+∞

work page
[2]

(59) We will denote µ= ρ/(1− ρ) in the following, and since ρK a ρK +(1− ρ)K b ρK = 1, we have: b 1− ρ ρ = 1− a

For b(1− ϵ)/ρ≤ λ< a(1− ϵ)/ρ, we have: αλ(P∥Qθ)= 1 K ρK ∑ l=1 λ+ 1 K K ∑ l=ρK b(1− ϵ)/ρ (58) = ρλ+ b(1− ϵ) 1− ρ ρ . (59) We will denote µ= ρ/(1− ρ) in the following, and since ρK a ρK +(1− ρ)K b ρK = 1, we have: b 1− ρ ρ = 1− a. (60) Thus, we have: αλ(P∥Qθ)= ρλ+(1− ϵ)(1− a) (61) 17 When Temperature Fails, Change the Loss

work page
[3]

(63) In that regime, Recall is maximal since the model generates all tokens

For λ< b(1− ϵ)/ρ, we have: αλ(P∥Qθ)= 1 K K ∑ l=1 λ= λ, (62) and therefore: βλ(P∥Qθ)= 1. (63) In that regime, Recall is maximal since the model generates all tokens. PR-Curve for Tempered distributions. • Tempered distribution Qt θ: To simplify the notation, we define the inverse temperature τ = 1/t and set µ= ρ/(1− ρ). We define the tempered distribution ...

work page
[9]

For λ≥ λt max, we have: min(λ, 1 (1− ρ)µτ cτ l (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ ) = 1 (1− ρ)µτ cτ l (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ . Therefore: αλ(P∥Qt θ)= 1 K K ∑ l cτ l ρaτ +(1− ρ)bτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ (81) = 1 K (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ K ∑ l cτ l ρaτ +(1− ρ)bτ (82) = (1− ϵ)τ (1− ϵ)τ +(V /K− 1...

work page
[10]

(87) We can note that: αλ(P∥Qt θ)= ρλ+(1− ρ)λt min

For λ∈ [λt min, λt max], we have: αλ(P∥Qt θ)= ρK ∑ l=1 λ K + K ∑ l=ρK 1 (1− ρ)K (1− a)τ (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ (85) = ρλ+ (1− ρ)K (1− ρ)K (1− a)τ (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ (86) = ρλ+ (1− a)τ (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ . (87) We can note that: αλ(P∥Qt θ)= ρλ+(1− ρ)λt min. (88) In ...

work page
[11]

(90) This concludes the proof

For λ≤ λt min, we have: αλ(P∥Qt θ)= K ∑ l=1 1 K λ= λ and thus βλ(P∥Qt θ)= 1. (90) This concludes the proof. Analysis of the PR-Curve. To analyze the behavior of the PR-curve, we study the dependence of the expression (1− a)τ (1− a)τ + µ1−τ aτ ⋅ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ , (91) on the temperature parameter t. We first introduce the function: fγ,ν(τ)...

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URL https://aclanthology.org/2024. acl-long.616/. Li, Y ., Choi, D., Chung, J., Kushman, N., Schrittwieser, J., Leblond, R., Eccles, T., Keeling, J., Gimeno, F., Lago, A. D., Hubert, T., Choy, P., d’Autume, C. d. M., Babuschkin, I., Chen, X., Huang, P.-S., Welbl, J., Gowal, S., Cherepanov, A., Molloy, J., Mankowitz, D. J., Rob- son, E. S., Kohli, P., Frei...

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URL https://proceedings.neurips. cc/paper_files/paper/2023/hash/ 67159f1c0cab15dd34c76a5dd830a389-Abstract-Conference. html. Verine, A., Pydi, M. S., Negrevergne, B., and Cheva- leyre, Y . Optimal Budgeted Rejection Sampling for Generative Models. Proceedings of The 27th Inter...

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

(57) In this regime, that is, for large values of λ, αλ reflects the model’s quality, as it converges to Precision whenλ→+∞

For λ≥ a(1− ϵ)/ρ, we have: αλ(P∥Qθ)= 1 K K ∑ i cl(1− ϵ)= (1− ϵ) K ∑ i cl ρK = 1− ϵ. (57) In this regime, that is, for large values of λ, αλ reflects the model’s quality, as it converges to Precision whenλ→+∞

work page

[2] [2]

(59) We will denote µ= ρ/(1− ρ) in the following, and since ρK a ρK +(1− ρ)K b ρK = 1, we have: b 1− ρ ρ = 1− a

For b(1− ϵ)/ρ≤ λ< a(1− ϵ)/ρ, we have: αλ(P∥Qθ)= 1 K ρK ∑ l=1 λ+ 1 K K ∑ l=ρK b(1− ϵ)/ρ (58) = ρλ+ b(1− ϵ) 1− ρ ρ . (59) We will denote µ= ρ/(1− ρ) in the following, and since ρK a ρK +(1− ρ)K b ρK = 1, we have: b 1− ρ ρ = 1− a. (60) Thus, we have: αλ(P∥Qθ)= ρλ+(1− ϵ)(1− a) (61) 17 When Temperature Fails, Change the Loss

work page

[3] [3]

(63) In that regime, Recall is maximal since the model generates all tokens

For λ< b(1− ϵ)/ρ, we have: αλ(P∥Qθ)= 1 K K ∑ l=1 λ= λ, (62) and therefore: βλ(P∥Qθ)= 1. (63) In that regime, Recall is maximal since the model generates all tokens. PR-Curve for Tempered distributions. • Tempered distribution Qt θ: To simplify the notation, we define the inverse temperature τ = 1/t and set µ= ρ/(1− ρ). We define the tempered distribution ...

work page

[4] [9]

For λ≥ λt max, we have: min(λ, 1 (1− ρ)µτ cτ l (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ ) = 1 (1− ρ)µτ cτ l (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ . Therefore: αλ(P∥Qt θ)= 1 K K ∑ l cτ l ρaτ +(1− ρ)bτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ (81) = 1 K (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ K ∑ l cτ l ρaτ +(1− ρ)bτ (82) = (1− ϵ)τ (1− ϵ)τ +(V /K− 1...

work page

[5] [10]

(87) We can note that: αλ(P∥Qt θ)= ρλ+(1− ρ)λt min

For λ∈ [λt min, λt max], we have: αλ(P∥Qt θ)= ρK ∑ l=1 λ K + K ∑ l=ρK 1 (1− ρ)K (1− a)τ (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ (85) = ρλ+ (1− ρ)K (1− ρ)K (1− a)τ (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ (86) = ρλ+ (1− a)τ (1− a)τ + µ1−τ aτ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ . (87) We can note that: αλ(P∥Qt θ)= ρλ+(1− ρ)λt min. (88) In ...

work page

[6] [11]

(90) This concludes the proof

For λ≤ λt min, we have: αλ(P∥Qt θ)= K ∑ l=1 1 K λ= λ and thus βλ(P∥Qt θ)= 1. (90) This concludes the proof. Analysis of the PR-Curve. To analyze the behavior of the PR-curve, we study the dependence of the expression (1− a)τ (1− a)τ + µ1−τ aτ ⋅ (1− ϵ)τ (1− ϵ)τ +(V /K− 1)1−τ ϵτ , (91) on the temperature parameter t. We first introduce the function: fγ,ν(τ)...

work page 2023

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acl-long.616/

URL https://aclanthology.org/2024. acl-long.616/. Li, Y ., Choi, D., Chung, J., Kushman, N., Schrittwieser, J., Leblond, R., Eccles, T., Keeling, J., Gimeno, F., Lago, A. D., Hubert, T., Choy, P., d’Autume, C. d. M., Babuschkin, I., Chen, X., Huang, P.-S., Welbl, J., Gowal, S., Cherepanov, A., Molloy, J., Mankowitz, D. J., Rob- son, E. S., Kohli, P., Frei...

arXiv 2024

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Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models

URL https://aclanthology.org/2024. acl-long.841/. Grover, A., Dhar, M., and Ermon, S. Flow-GAN: Com- bining Maximum Likelihood and Adversarial Learning in Generative Models, January 2018. URL http:// arxiv.org/abs/1705.08868. arXiv:1705.08868 [cs, stat]. Holtzman, A., Buys, J., Du, L., Forbes, M., and Choi, Y . The curious case of neural text degeneration...

work page Pith review arXiv 2024