arxiv: 2602.20816 · v3 · submitted 2026-02-24 · 💻 cs.CL · cs.LG

Recognition: no theorem link

Don't Ignore the Tail: Decoupling top-K Probabilities for Efficient Language Model Distillation

Sayantan Dasgupta , Trevor Cohn , Timothy Baldwin

Authors on Pith no claims yet

Pith reviewed 2026-05-15 20:07 UTC · model grok-4.3

classification 💻 cs.CL cs.LG

keywords distillationdivergenceteachermodelprobabilitiescontributiondatasetsdistribution

0 comments

The pith

Decoupling the top-K probabilities from the tail in the distillation loss reduces mode dominance and boosts tail contribution in language models.

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

The standard KL divergence in language model distillation is dominated by the teacher's most probable next tokens, reducing the influence of rarer but useful predictions. This paper introduces a tail-aware divergence that decouples the top-K high-probability terms from the lower-probability tail while keeping the same computational cost. By downweighting the modes, the student receives a stronger signal from the distribution's tail. Experiments across pre-training and supervised distillation tasks show this yields competitive performance on decoder models without requiring large-scale compute.

Core claim

The proposed method modifies the KL divergence by decoupling the contribution of the teacher's top-K predicted probabilities from the lower-probability predictions. This reduces the impact of the teacher modes and increases the contribution of the tail of the distribution, leading to effective distillation of decoder language models in both pre-training and supervised settings at standard computational cost.

What carries the argument

The decoupled tail-aware divergence, which separates the top-K component from the tail component in the loss calculation to balance their contributions.

Load-bearing premise

Emphasizing the tail via decoupling provides a net positive learning signal without losing essential information from the high-probability modes.

What would settle it

Training two students with identical setups except for the loss (standard KL vs decoupled), and finding that the decoupled version underperforms on metrics that reward accurate tail probability estimation, such as perplexity on rare token sequences.

Figures

Figures reproduced from arXiv: 2602.20816 by Sayantan Dasgupta, Timothy Baldwin, Trevor Cohn.

**Figure 1.** Figure 1: KL divergence on the validation set of Regmix for vanilla KD vs. TAD. The x axis shows training progress in terms of the number of tokens, and the y axis shows held-out KL between the student and teacher. is the kth maximum of all the token probabilities for a vocabulary V, we can split the KL divergence between the top-K and the rest as, DKL P T ∥PS =DKL p T ∥p S pT ∈{ ∗ p T k }K k=1 + α T KDKL p˜ T … view at source ↗

**Figure 2.** Figure 2: Tail probability mass (α T K) against K for different teachers in the first, and the Next Token vs. Mode mismatch rate in percentage in the second plot, measured on the validation set of Regmix (see Section 3.2) the teacher, with larger teachers having lower mismatch rates ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

The core learning signal used in language model distillation is the standard Kullback-Leibler (KL) divergence between the student and teacher distributions. Traditional KL divergence tends to be dominated by the next tokens with the highest probabilities, i.e., the teacher's modes, thereby diminishing the influence of less probable yet potentially informative components of the output distribution. We propose a new tail-aware divergence that decouples the contribution of the teacher model's top-K predicted probabilities from that of lower-probability predictions, while maintaining the same computational profile as the KL Divergence. Our decoupled approach reduces the impact of the teacher modes and, consequently, increases the contribution of the tail of the distribution. Experimental results demonstrate that our modified distillation method yields competitive performance in both pre-training and supervised distillation of decoder models across various datasets. Furthermore, the distillation process is efficient and can be performed with a modest academic budget for large datasets, eliminating the need for industry-scale computing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper offers a lightweight split of the KL loss into top-K and tail terms to push distillation toward rarer tokens, but without the explicit equation or controls it's unclear if the tail actually gains gradient weight.

read the letter

The core move is to decouple the teacher's top-K probabilities from the remaining mass inside the distillation objective, so the student is less dominated by the modes and gets a stronger signal from the tail. This keeps the same computational cost as ordinary KL, which is the practical selling point for decoder-model distillation at scale. If the implementation works as described, it could be a cheap way to improve smaller models in pre-training or supervised settings without new hardware demands. The abstract claims competitive results across datasets, and the efficiency angle is believable for academic budgets. That said, the exact loss formula is not shown, so it is hard to tell whether the tail term is renormalized or up-weighted relative to standard KL. If the change is just a mask without rescaling, the tail probabilities stay small and their gradients may not increase much, which matches the stress-test concern. There are also no details on baselines, K ablations, statistical tests, or how the split is applied during pre-training versus fine-tuning. The work is aimed at people already running distillation pipelines who want a minimal change with possible upside. It is coherent on its own terms and shows honest engagement with the standard KL setup, so it deserves a serious referee to check the math and the experiments. I would send it for review but flag the need for the full derivation and tighter controls in the first round.

Referee Report

3 major / 2 minor

Summary. The paper proposes a tail-aware divergence for language model distillation that decouples the teacher model's top-K probabilities from the lower-probability tail. This modification to standard KL divergence is claimed to reduce mode dominance and increase the relative contribution of the tail while preserving the same computational profile. Experiments reportedly show competitive performance for both pre-training and supervised distillation of decoder models across datasets, achievable with modest academic compute budgets.

Significance. If the decoupling demonstrably amplifies tail gradients without discarding critical mode information, the method could offer a lightweight, parameter-light (only K) improvement to distillation that better utilizes the full teacher distribution. The efficiency claim for large datasets with academic resources is a practical strength worth verifying.

major comments (3)

[Method] Method section (likely §3): The abstract claims the decoupled divergence 'increases the contribution of the tail' relative to KL, but without the explicit loss equation it is impossible to confirm whether top-K separation includes renormalization of the tail mass or a multiplicative reweighting; absent this, the tail probabilities remain small and their gradients may not grow, as noted in the stress-test concern.
[Experiments] Experiments section (likely §4): The abstract reports 'competitive performance' but provides no details on baselines, statistical significance, ablation on K, or exact loss formulation; without these, the central claim that decoupling yields a net positive learning signal cannot be assessed from the given text.
[§3.1] §3.1 or equivalent: The decoupling is presented as an independent modification to KL with no circularity, yet the weakest assumption—that emphasizing the tail provides a net positive without losing mode information—requires a concrete gradient comparison or toy example to show the tail term is effectively up-weighted.

minor comments (2)

[Abstract] Abstract: Mention the specific datasets and model sizes used to support the 'competitive performance' claim for concreteness.
[Method] Notation: Clarify whether K is the sole free parameter and how it is chosen across experiments.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We agree that the manuscript would benefit from greater mathematical clarity and experimental detail. We address each major comment below and will incorporate the requested changes in the revised version.

read point-by-point responses

Referee: [Method] Method section (likely §3): The abstract claims the decoupled divergence 'increases the contribution of the tail' relative to KL, but without the explicit loss equation it is impossible to confirm whether top-K separation includes renormalization of the tail mass or a multiplicative reweighting; absent this, the tail probabilities remain small and their gradients may not grow, as noted in the stress-test concern.

Authors: We thank the referee for this observation. The current manuscript describes the decoupling at a high level but does not include the explicit loss equation. In the revision we will add the precise formulation in Section 3: the top-K mass is isolated, the remaining tail is renormalized to sum to one, and the loss is the sum of a standard KL term on the top-K and a scaled KL term on the renormalized tail. This renormalization directly amplifies tail gradients. We will also include a short gradient derivation and a stress-test example to confirm the effect. revision: yes
Referee: [Experiments] Experiments section (likely §4): The abstract reports 'competitive performance' but provides no details on baselines, statistical significance, ablation on K, or exact loss formulation; without these, the central claim that decoupling yields a net positive learning signal cannot be assessed from the given text.

Authors: We agree that the experimental section is currently underspecified. In the revised manuscript we will expand Section 4 to report: (i) the full set of baselines (standard KL, temperature-scaled KL, and other recent divergences), (ii) mean and standard deviation over three random seeds with paired t-test p-values, (iii) an ablation table varying K from 5 to 100, and (iv) the exact loss equation with implementation pseudocode. These additions will allow direct assessment of the net learning signal. revision: yes
Referee: [§3.1] §3.1 or equivalent: The decoupling is presented as an independent modification to KL with no circularity, yet the weakest assumption—that emphasizing the tail provides a net positive without losing mode information—requires a concrete gradient comparison or toy example to show the tail term is effectively up-weighted.

Authors: We accept this critique. The manuscript currently relies on the high-level claim without supporting derivation. In the revision we will insert a new subsection (or appendix) containing (a) a side-by-side gradient comparison between standard KL and the decoupled loss, and (b) a small-vocabulary toy example (vocabulary size 8) that numerically demonstrates higher relative gradients on tail tokens while the top-K modes remain fully represented. This will make the net-positive assumption explicit and verifiable. revision: yes

Circularity Check

0 steps flagged

No circularity: independent modification to KL with no self-referential derivation

full rationale

The paper proposes a new tail-aware divergence by decoupling top-K teacher probabilities from the tail, presented as a direct conceptual change to standard KL that preserves its computational profile. No equations, derivations, or self-citations are exhibited in the provided text that reduce the new loss to a fitted quantity defined by the same data or to a prior result by the same authors. The central claim rests on the explicit decoupling step rather than any loop back to inputs, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the tail carries useful signal worth up-weighting and that K can be chosen without introducing new fitted parameters beyond standard distillation hyperparameters.

free parameters (1)

K
Top-K cutoff used to split the divergence; treated as a tunable hyperparameter whose value affects the balance between modes and tail.

axioms (1)

domain assumption The lower-probability tail of the teacher distribution contains informative components that improve student learning when emphasized.
Invoked to justify why reducing mode dominance helps distillation performance.

pith-pipeline@v0.9.0 · 5461 in / 1161 out tokens · 20280 ms · 2026-05-15T20:07:34.181288+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 15 internal anchors

[1]

Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone

Abdin, M., Aneja, J., Awadalla, H., Awadallah, A., Awan, A. A., Bach, N., Bahree, A., Bakhtiari, A., Bao, J., Behl, H., et al. Phi-3 technical report: A highly capable lan- guage model locally on your phone.arXiv preprint arXiv:2404.14219,

work page internal anchor Pith review Pith/arXiv arXiv
[2]

D., McAleer, S., Jiang, A

Azerbayev, Z., Schoelkopf, H., Paster, K., Santos, M. D., McAleer, S., Jiang, A. Q., Deng, J., Biderman, S., and Welleck, S. Llemma: An open language model for math- ematics.arXiv preprint arXiv:2310.10631,

work page arXiv
[3]

Training Verifiers to Solve Math Word Problems

Cobbe, K., Kosaraju, V ., Bavarian, M., Chen, M., Jun, H., Kaiser, L., Plappert, M., Tworek, J., Hilton, J., Nakano, R., Hesse, C., and Schulman, J. Training verifiers to solve math word problems.arXiv preprint arXiv:2110.14168,

work page internal anchor Pith review Pith/arXiv arXiv
[4]

The Pile: An 800GB Dataset of Diverse Text for Language Modeling

Gao, L., Biderman, S., Black, S., Golding, L., Hoppe, T., Foster, C., Phang, J., He, H., Thite, A., Nabeshima, N., et al. The pile: An 800gb dataset of diverse text for language modeling.arXiv preprint arXiv:2101.00027,

work page internal anchor Pith review Pith/arXiv arXiv
[5]

Distilling the knowl- edge in a neural network

Hinton, G., Vinyals, O., and Dean, J. Distilling the knowl- edge in a neural network. InNIPS 2014 Deep Learn- ing Workshop,

work page 2014
[6]

Distilling the Knowledge in a Neural Network

doi: 10.48550/ARXIV .1503.02531. URLhttps://arxiv.org/abs/1503.02531. 9 Don’t Ignore the Tail: Decoupling top-KProbabilities for Efficient Language Model Distillation Iwana, B. K., Kuroki, R., and Uchida, S. Explaining con- volutional neural networks using softmax gradient layer- wise relevance propagation. In2019 IEEE/CVF Inter- national Conference on Co...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv
[7]

Sequence-Level Knowledge Distillation

Kim, Y . and Rush, A. M. Sequence-level knowledge distil- lation.arXiv preprint arXiv:1606.07947,

work page internal anchor Pith review Pith/arXiv arXiv
[8]

Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980,

work page internal anchor Pith review Pith/arXiv arXiv
[9]

Rho-1: Not all tokens are what you need.arXiv preprint arXiv:2404.07965,

Lin, Z., Gou, Z., Gong, Y ., Liu, X., Shen, Y ., Xu, R., Lin, C., Yang, Y ., Jiao, J., Duan, N., et al. Rho-1: Not all tokens are what you need.arXiv preprint arXiv:2404.07965,

work page arXiv
[10]

Full-ece: A metric for token-level calibration on large language models.arXiv preprint arXiv:2406.11345, 2024a

Liu, H., Zhang, Y ., Wang, B., Chen, W., and Hu, X. Full-ece: A metric for token-level calibration on large language models.arXiv preprint arXiv:2406.11345, 2024a. Liu, Q., Zheng, X., Muennighoff, N., Zeng, G., Dou, L., Pang, T., Jiang, J., and Lin, M. Regmix: Data mixture as regression for language model pre-training.arXiv preprint arXiv:2407.01492, 2024...

work page arXiv
[11]

Orca-math: Unlocking the potential of slms in grade school math.arXiv preprint arXiv:2402.14830,

Mitra, A., Khanpour, H., Rosset, C., and Awadallah, A. Orca-math: Unlocking the potential of slms in grade school math.arXiv preprint arXiv:2402.14830,

work page arXiv
[12]

T., Joshi, R., Chochowski, M., Patwary, M., Shoeybi, M., Catanzaro, B., Kautz, J., and Molchanov, P

Muralidharan, S., Sreenivas, S. T., Joshi, R., Chochowski, M., Patwary, M., Shoeybi, M., Catanzaro, B., Kautz, J., and Molchanov, P. Compact language models via pruning and knowledge distillation.arXiv preprint arXiv:2407.14679,

work page arXiv
[13]

D., Azerbayev, Z., and Ba, J

Paster, K., Santos, M. D., Azerbayev, Z., and Ba, J. Open- webmath: An open dataset of high-quality mathematical web text.arXiv preprint arXiv:2310.06786,

work page arXiv
[15]

DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter

URL http:// arxiv.org/abs/1910.01108. Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347,

work page internal anchor Pith review Pith/arXiv arXiv 1910
[16]

and Rush, A

Shleifer, S. and Rush, A. M. Pre-trained summarization distillation.arXiv preprint arXiv:2010.13002,

work page arXiv 2010
[17]

Multilingual translation with extensible multilingual pretraining and finetuning.arXiv preprint arXiv:2008.00401,

Tang, Y ., Tran, C., Li, X., Chen, P.-J., Goyal, N., Chaudhary, V ., Gu, J., and Fan, A. Multilingual translation with extensible multilingual pretraining and finetuning.arXiv preprint arXiv:2008.00401,

work page arXiv 2008
[18]

Galactica: A Large Language Model for Science

Taylor, R., Kardas, M., Cucurull, G., Scialom, T., Hartshorn, A., Saravia, E., Poulton, A., Kerkez, V ., and Stojnic, R. Galactica: A large language model for science.arXiv preprint arXiv:2211.09085,

work page internal anchor Pith review Pith/arXiv arXiv
[19]

Gemma 2: Improving Open Language Models at a Practical Size

Team, G., Riviere, M., Pathak, S., Sessa, P. G., Hardin, C., Bhupatiraju, S., Hussenot, L., Mesnard, T., Shahri- ari, B., Ramé, A., et al. Gemma 2: Improving open language models at a practical size.arXiv preprint arXiv:2408.00118,

work page internal anchor Pith review Pith/arXiv arXiv
[20]

Llama 2: Open Foundation and Fine-Tuned Chat Models

10 Don’t Ignore the Tail: Decoupling top-KProbabilities for Efficient Language Model Distillation Touvron, H., Martin, L., Stone, K., Albert, P., Almahairi, A., Babaei, Y ., Bashlykov, N., Batra, S., Bhargava, P., Bhosale, S., et al. Llama 2: Open foundation and fine- tuned chat models.arXiv preprint arXiv:2307.09288,

work page internal anchor Pith review Pith/arXiv arXiv
[22]

HuggingFace's Transformers: State-of-the-art Natural Language Processing

URL http://arxiv.org/ abs/1910.03771. Wu, C., Wu, F., and Huang, Y . One teacher is enough? pre- trained language model distillation from multiple teach- ers. InFindings of the Association for Computational Linguistics: ACL-IJCNLP 2021, pp. 4408–4413,

work page internal anchor Pith review Pith/arXiv arXiv 1910
[23]

Yang, A., Yang, B., Zhang, B., Hui, B., Zheng, B., Yu, B., Li, C., Liu, D., Huang, F., Wei, H., et al. Qwen2. 5 technical report.arXiv preprint arXiv:2412.15115,

work page internal anchor Pith review Pith/arXiv arXiv
[24]

MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models

Yu, L., Jiang, W., Shi, H., Yu, J., Liu, Z., Zhang, Y ., Kwok, J. T., Li, Z., Weller, A., and Liu, W. Metamath: Boot- strap your own mathematical questions for large language models.arXiv preprint arXiv:2309.12284,

work page internal anchor Pith review Pith/arXiv arXiv
[25]

TinyLlama: An Open-Source Small Language Model

Zhang, P., Zeng, G., Wang, T., and Lu, W. Tinyllama: An open-source small language model.arXiv preprint arXiv:2401.02385,

work page internal anchor Pith review Pith/arXiv arXiv
[26]

OPT: Open Pre-trained Transformer Language Models

Zhang, S., Roller, S., Goyal, N., Artetxe, M., Chen, M., Chen, S., Dewan, C., Diab, M., Li, X., Lin, X. V ., et al. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068,

work page internal anchor Pith review Pith/arXiv arXiv
[27]

Derivation of the Gradient Here we present an elaborated derivation of the gradients

A. Derivation of the Gradient Here we present an elaborated derivation of the gradients. The derivations follow the material in the appendix of An- shumann et al. (2025). If pi = exp(z i)/P|V| i=1 exp(zi) is the softmax probability for a logit zi for a vocabulary V, then the gradient ofp k is (from (Iwana et al., 2019)): ∂pj ∂zi =p j 1[i=j] −p i (7) Now, ...

work page 2025
[28]

The architectures of the students of Qwen 1.5−1.8 B are kept the same as in the MiniPLM paper (Gu et al., 2025)

All students have approx- imately 1B active parameters, except for the 0.5B student of Qwen, which has approximately 475M active parameters. The architectures of the students of Qwen 1.5−1.8 B are kept the same as in the MiniPLM paper (Gu et al., 2025). The experiments are divided into two major parts: pre- training distillation from scratch, and continue...

work page 2025
[29]

B.1. Cost of Supervised Distillation We conduct a comparative cost analysis of GPU hours re- quired to produce state-of-the-art mathematical reasoning, starting with foundational models such as TinyLlama-1.1B and Llama2-7B. Models like Llemma or Rho-1 are trained using industrial resources. Rho-1 is trained for approxi- mately 10 hours on a 32-GPU H100 st...

work page 2024