arxiv: 2604.20216 · v1 · submitted 2026-04-22 · 💻 cs.CL

Recognition: unknown

Text-to-Distribution Prediction with Quantile Tokens and Neighbor Context

Yilun Zhu , Yuan Zhuang , Nikhita Vedula , Dushyanta Dhyani , Shaoyuan Xu , Moyan Li , Mohsen Bayati , Bryan Wang

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Shervin Malmasi

Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:54 UTC · model grok-4.3

classification 💻 cs.CL

keywords distributional regressionquantile regressionlarge language modelstext regressionretrieval augmentationconditional distributionsquantile tokensneighbor context

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The pith

Dedicated quantile tokens inserted into LLM inputs create direct pathways for predicting full conditional distributions from text.

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

Standard LLM regression predicts single points or relies on indirect shared representations that limit accuracy for full distributions. This work inserts specialized quantile tokens directly into the input sequence so self-attention can link each quantile output straight to the text input without bottlenecks. It further retrieves semantically similar neighbor examples and their observed quantile values to supply local empirical evidence. Experiments across model sizes show these additions cut mean absolute percentage error by roughly four points while halving prediction-interval width, with the largest gains on smaller or harder datasets. The paper also analyzes quantile loss functions to show which objectives each one optimizes.

Core claim

Quantile Token Regression inserts dedicated quantile tokens into the input sequence to form direct input-output pathways through self-attention for each quantile, then augments those tokens with retrieved neighbor instances and their empirical distributions to ground predictions locally; this produces sharper and more accurate conditional distributions than baseline methods that lack such direct pathways or local grounding.

What carries the argument

Quantile Token Regression, which places dedicated quantile tokens in the input sequence to enable direct self-attention pathways to quantile outputs and augments them with retrieved neighbor empirical distributions.

If this is right

Prediction intervals become roughly twice as narrow while maintaining coverage.
Mean absolute percentage error drops by approximately four points on average.
Gains are largest on smaller and more challenging datasets.
Distributions become substantially sharper and more accurate when local neighbor evidence is added.
Theoretical clarification shows which quantile loss functions optimize specific distributional properties.

Where Pith is reading between the lines

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

The method may extend naturally to other sequence-to-distribution tasks such as time-series forecasting.
Retrieval of neighbors could be replaced by learned memory modules if similar empirical distributions can be synthesized on the fly.
Direct quantile pathways may reduce the need for post-hoc calibration in uncertainty-aware LLM applications.

Load-bearing premise

Dedicated quantile tokens create direct attention pathways without new representational bottlenecks, and retrieved neighbors supply relevant empirical distributions that improve rather than bias the target prediction.

What would settle it

An experiment on a new text-regression dataset in which the quantile-token-plus-neighbor method fails to produce at least a four-point MAPE reduction and at least a twofold narrowing of prediction intervals relative to standard baselines would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.20216 by Bryan Wang, Dushyanta Dhyani, Mohsen Bayati, Moyan Li, Nikhita Vedula, Shaoyuan Xu, Shervin Malmasi, Yilun Zhu, Yuan Zhuang.

**Figure 1.** Figure 1: Overview of our approach. Left: Input includes query text and retrieved neighbors with their full empirical distributions (as quantiles). Center: The baseline (Vedula et al., 2025) uses only query text without neighbors and computes all quantiles from a shared hidden state via separate linear heads. Our Quantile Token approach augments the input with neighbors and inserts dedicated ⟨Qτ ⟩ tokens that attend… view at source ↗

**Figure 2.** Figure 2: Quantile tokens enable specialized representations and direct input-output pathways for each quantile [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

read the original abstract

Many applications of LLM-based text regression require predicting a full conditional distribution rather than a single point value. We study distributional regression under empirical-quantile supervision, where each input is paired with multiple observed quantile outcomes, and the target distribution is represented by a dense grid of quantiles. We address two key limitations of current approaches: the lack of local grounding for distribution estimates, and the reliance on shared representations that create an indirect bottleneck between inputs and quantile outputs. In this paper, we introduce Quantile Token Regression, which, to our knowledge, is the first work to insert dedicated quantile tokens into the input sequence, enabling direct input-output pathways for each quantile through self-attention. We further augment these quantile tokens with retrieval, incorporating semantically similar neighbor instances and their empirical distributions to ground predictions with local evidence from similar instances. We also provide the first theoretical analysis of loss functions for quantile regression, clarifying which distributional objectives each optimizes. Experiments on the Inside Airbnb and StackSample benchmark datasets with LLMs ranging from 1.7B to 14B parameters show that quantile tokens with neighbors consistently outperform baselines (~4 points lower MAPE and 2x narrower prediction intervals), with especially large gains on smaller and more challenging datasets where quantile tokens produce substantially sharper and more accurate distributions.

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

Quantile tokens plus neighbor retrieval produce measurable gains on two regression benchmarks, but the direct-pathway claim does not survive the shared-layer architecture and the experiments need more transparency on baselines and significance.

read the letter

The paper's main move is to insert dedicated quantile tokens into the input sequence and to retrieve semantically similar neighbors along with their empirical distributions. This combination is tested on Inside Airbnb and StackSample with models from 1.7B to 14B parameters. The reported outcome is roughly 4 points lower MAPE and roughly twice narrower prediction intervals, with the largest improvements on the smaller and harder subsets. The authors also supply an analysis of which quantile loss functions optimize which distributional properties. Those two elements—the token insertion plus the neighbor grounding—are the concrete additions, and the loss discussion is a useful clarification that many papers skip. The experiments cover a reasonable range of model sizes and show the pattern holds across them. That is the part worth noting. The central architectural claim does not hold up. Every token, quantile or not, still receives the same layer norms, attention, and feed-forward transformations, so the quantile tokens do not create direct input-output pathways that bypass shared representations; they simply add more positions whose final states are later read out. The neighbor component carries its own risk: on the small datasets where the gains are said to be largest, retrieved neighbors can introduce selection bias rather than pure local evidence. The abstract and summary give no details on baseline implementations, hyperparameter matching, exact data splits, or statistical testing, which leaves the size of the improvement hard to judge. This work is aimed at people doing uncertainty-aware regression from text rather than at general language modeling. A reader who needs full conditional distributions instead of point estimates will find a practical recipe and some loss-function guidance. The paper shows clear engagement with the quantile-regression literature and ships concrete experiments, so it deserves a serious referee. Reviewers can press on the mechanism description and the missing experimental controls. I would send it to peer review.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes Quantile Token Regression for LLM-based text-to-distribution prediction. It inserts dedicated quantile tokens into the input sequence to create direct self-attention pathways from inputs to quantile outputs, augments these with retrieval of semantically similar neighbor instances and their empirical distributions for local grounding, and provides a theoretical analysis of quantile loss functions. Experiments on the Inside Airbnb and StackSample datasets using LLMs from 1.7B to 14B parameters report consistent outperformance over baselines, with approximately 4 points lower MAPE and 2x narrower prediction intervals, and especially large gains on smaller and more challenging datasets.

Significance. If the empirical gains hold under rigorous verification and the direct-pathway mechanism is clarified, the work could meaningfully advance distributional regression with LLMs by addressing local evidence and representational issues. The theoretical analysis of loss functions is a potential strength if it offers new insights beyond existing quantile regression literature. The focus on smaller datasets where gains are largest is practically relevant, though the introduction of new architectural components (quantile tokens and neighbor retrieval) rather than parameter-free derivations limits axiomatic generality.

major comments (3)

[§3] §3 (Quantile Token Regression description): The claim that dedicated quantile tokens 'enable direct input-output pathways for each quantile through self-attention' that avoid the indirect bottleneck of shared representations is not obviously correct. In a standard decoder-only transformer, quantile tokens still receive identical layer-norm, multi-head attention, and FFN transformations as all other tokens; their final hidden states remain nonlinear functions of the full input sequence via shared weights. If a shared output projection or loss head is applied afterward, the pathway is not demonstrably more direct than standard multi-output heads.
[Experiments] Experiments section (results on Inside Airbnb and StackSample): The reported gains (~4 points lower MAPE, 2x narrower intervals, larger on small datasets) are central to the contribution, yet the abstract and results lack details on baseline implementations (e.g., how standard quantile regression heads or retrieval-augmented models were reproduced), statistical significance tests, hyperparameter search protocols, or precise train/validation/test splits. Without these, the outperformance claims and the assertion of 'especially large gains' on smaller datasets cannot be fully assessed for robustness.
[Method and Experiments] Neighbor context retrieval component (method and results): The paper asserts that retrieved neighbors supply relevant empirical distributions yielding sharper predictions, but on smaller datasets this risks injecting selection bias or reducing diversity. The claim of 'especially large gains' precisely where such bias would be most harmful requires explicit analysis or ablation showing that neighbor retrieval improves rather than harms calibration and sharpness on low-data regimes.

minor comments (2)

[Abstract and Introduction] The abstract and introduction repeatedly use 'to our knowledge, is the first' for both the quantile token insertion and the theoretical loss analysis; these novelty claims should be supported by a more exhaustive literature comparison in the related work section.
[Figures and Tables] Figure captions and tables reporting MAPE and interval widths should explicitly state the number of runs, random seeds, and confidence intervals to allow readers to gauge variability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below with clarifications and revisions to the manuscript.

read point-by-point responses

Referee: [§3] §3 (Quantile Token Regression description): The claim that dedicated quantile tokens 'enable direct input-output pathways for each quantile through self-attention' that avoid the indirect bottleneck of shared representations is not obviously correct. In a standard decoder-only transformer, quantile tokens still receive identical layer-norm, multi-head attention, and FFN transformations as all other tokens; their final hidden states remain nonlinear functions of the full input sequence via shared weights. If a shared output projection or loss head is applied afterward, the pathway is not demonstrably more direct than standard multi-output heads.

Authors: We agree that the referee's observation is technically accurate: all tokens, including the quantile tokens, pass through the same shared transformer layers and weights. The intended distinction is that each quantile token is a separate, dedicated embedding whose final hidden state is produced by attending specifically from its own position to the input tokens, allowing quantile-specific attention patterns before any shared output projection. This differs from a conventional multi-output head that derives all quantiles from a single pooled representation. We have revised §3 to remove the phrasing 'direct input-output pathways' and replaced it with a more precise description of 'per-quantile attention pathways,' added a clarifying diagram, and acknowledged the shared-layer limitation explicitly. revision: yes
Referee: [Experiments] Experiments section (results on Inside Airbnb and StackSample): The reported gains (~4 points lower MAPE, 2x narrower intervals, larger on small datasets) are central to the contribution, yet the abstract and results lack details on baseline implementations (e.g., how standard quantile regression heads or retrieval-augmented models were reproduced), statistical significance tests, hyperparameter search protocols, or precise train/validation/test splits. Without these, the outperformance claims and the assertion of 'especially large gains' on smaller datasets cannot be fully assessed for robustness.

Authors: The referee correctly identifies insufficient experimental documentation. We have expanded the Experiments section and added an appendix with: (i) full baseline implementation details, including the exact architecture of the added quantile regression heads and how retrieval-augmented baselines were reproduced; (ii) statistical significance results (paired t-tests and Wilcoxon signed-rank tests with p-values); (iii) the hyperparameter search protocol, ranges, and final selected values; and (iv) the precise train/validation/test splits with instance counts. These additions allow direct assessment of the reported gains and the larger improvements on smaller datasets. revision: yes
Referee: [Method and Experiments] Neighbor context retrieval component (method and results): The paper asserts that retrieved neighbors supply relevant empirical distributions yielding sharper predictions, but on smaller datasets this risks injecting selection bias or reducing diversity. The claim of 'especially large gains' precisely where such bias would be most harmful requires explicit analysis or ablation showing that neighbor retrieval improves rather than harms calibration and sharpness on low-data regimes.

Authors: We acknowledge the risk of selection bias in low-data regimes and the need for explicit verification. We have added ablation experiments that remove the neighbor retrieval component and evaluate performance across training-set sizes down to the smallest subsets. The results show that neighbor retrieval still improves both MAPE and interval sharpness while preserving calibration (empirical coverage remains close to nominal) and does not reduce distributional diversity (measured via entropy). A short discussion of semantic similarity filtering to mitigate bias has been included. These ablations are now reported in the Experiments section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in claimed derivation

full rationale

The paper presents a new architectural method (quantile tokens inserted into the input sequence plus neighbor retrieval) and reports empirical results on external benchmarks, without any equations or derivations that reduce the claimed performance gains to quantities defined by the same fitted parameters or evaluation data. The theoretical analysis of quantile loss functions is described as novel and clarifying rather than self-referential. No self-citation chains, self-definitional constructs, or fitted-input-as-prediction patterns appear in the provided text or abstract. The central claims rest on introduced components and experimental comparisons, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The approach rests on standard transformer assumptions plus two new design choices whose value is demonstrated only empirically.

axioms (2)

domain assumption Self-attention mechanisms can form effective direct pathways between input text and per-quantile output tokens without representational bottlenecks.
Invoked in the design of quantile token regression to justify inserting tokens into the input sequence.
domain assumption Semantically similar retrieved neighbors supply empirical distributions that improve rather than contaminate the target conditional distribution estimate.
Core premise of the neighbor-context augmentation.

invented entities (2)

Quantile tokens no independent evidence
purpose: Dedicated tokens placed in the input sequence to allow direct attention-based prediction of each quantile.
New architectural element introduced to address the indirect bottleneck limitation.
Neighbor context retrieval no independent evidence
purpose: Mechanism to incorporate semantically similar instances and their observed distributions as local grounding evidence.
Augmentation technique proposed to provide local evidence for distribution estimates.

pith-pipeline@v0.9.0 · 5557 in / 1548 out tokens · 48456 ms · 2026-05-10T00:54:45.565651+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

45 extracted references · 12 canonical work pages · 3 internal anchors

[1]

Aho and Jeffrey D

Alfred V. Aho and Jeffrey D. Ullman , title =. 1972

1972
[2]

Publications Manual , year = "1983", publisher =

1983
[3]

Chandra and Dexter C

Ashok K. Chandra and Dexter C. Kozen and Larry J. Stockmeyer , year = "1981", title =. doi:10.1145/322234.322243

work page doi:10.1145/322234.322243 1981
[4]

Scalable training of

Andrew, Galen and Gao, Jianfeng , booktitle=. Scalable training of
[5]

Dan Gusfield , title =. 1997

1997
[6]

Tetreault , title =

Mohammad Sadegh Rasooli and Joel R. Tetreault , title =. Computing Research Repository , volume =. 2015 , url =

2015
[7]

A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data , Volume =

Ando, Rie Kubota and Zhang, Tong , Issn =. A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data , Volume =. Journal of Machine Learning Research , Month = dec, Numpages =
[8]

2025 , eprint=

LLP: LLM-based Product Pricing in E-commerce , author=. 2025 , eprint=

2025
[9]

and Bayati, Mohsen and Malmasi, Shervin

Vedula, Nikhita and Dhyani, Dushyanta and Jalali, Laleh and Oreshkin, Boris N. and Bayati, Mohsen and Malmasi, Shervin. Quantile Regression with Large Language Models for Price Prediction. Findings of the Association for Computational Linguistics: ACL 2025. 2025. doi:10.18653/v1/2025.findings-acl.641

work page doi:10.18653/v1/2025.findings-acl.641 2025
[10]

1978 , journal =

Regression Quantiles , author =. 1978 , journal =

1978
[11]

Proceedings of the 41st International Conference on Machine Learning , articleno =

Das, Abhimanyu and Kong, Weihao and Sen, Rajat and Zhou, Yichen , title =. Proceedings of the 41st International Conference on Machine Learning , articleno =. 2024 , publisher =

2024
[12]

Proceedings of the 38th International Conference on Neural Information Processing Systems , articleno =

Wang, Yuxuan and Wu, Haixu and Dong, Jiaxiang and Qin, Guo and Zhang, Haoran and Liu, Yong and Qiu, Yunzhong and Wang, Jianmin and Long, Mingsheng , title =. Proceedings of the 38th International Conference on Neural Information Processing Systems , articleno =. 2024 , isbn =

2024
[13]

Proceedings of the 36th International Conference on Neural Information Processing Systems , articleno =

Garg, Shivam and Tsipras, Dimitris and Liang, Percy and Valiant, Gregory , title =. Proceedings of the 36th International Conference on Neural Information Processing Systems , articleno =. 2022 , isbn =

2022
[14]

2024 , eprint=

From Words to Numbers: Your Large Language Model Is Secretly A Capable Regressor When Given In-Context Examples , author=. 2024 , eprint=

2024
[15]

Non-Linear Text Regression with a Deep Convolutional Neural Network

Bitvai, Zsolt and Cohn, Trevor. Non-Linear Text Regression with a Deep Convolutional Neural Network. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 2: Short Papers). 2015. doi:10.3115/v1/P15-2030

work page doi:10.3115/v1/p15-2030 2015
[16]

2025 , note =

Get the Data , howpublished =. 2025 , note =

2025
[17]

StackSample: 10\ year =
[18]

What is the license for the content I post? , year =
[19]

Advances in Neural Information Processing Systems , volume=

Large Language Models Are Zero-Shot Time Series Forecasters , author=. Advances in Neural Information Processing Systems , volume=
[20]

Regression with Large Language Models for Materials and Molecular Property Prediction

Regression with Large Language Models for Materials and Molecular Property Prediction , author=. arXiv preprint arXiv:2409.06080 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[21]

and Mak, Ho-Yin , title =

Arora, Siddharth and Taylor, James W. and Mak, Ho-Yin , title =. Manufacturing & Service Operations Management , volume =. 2023 , doi =

2023
[22]

Econometrics and Statistics , volume=

Rage Against the Mean--A Review of Distributional Regression Approaches , author=. Econometrics and Statistics , volume=. 2023 , publisher=

2023
[23]

2021 , address =

Imperial, Joseph Marvin , booktitle =. 2021 , address =. doi:10.26615/978-954-452-072-4_069 , url =

work page doi:10.26615/978-954-452-072-4_069 2021
[24]

Understanding

Eric Tang and Bangding Yang and Xingyou Song , journal=. Understanding. 2025 , url=

2025
[25]

Xingyou Song and Oscar Li and Chansoo Lee and Bangding Yang and Daiyi Peng and Sagi Perel and Yutian Chen , title =. Trans. Mach. Learn. Res. , volume =. 2024 , url =

2024
[26]

Proceedings of ICLR , year=

Better Autoregressive Regression with LLMs via Regression-Aware Fine-Tuning , author=. Proceedings of ICLR , year=
[27]

2025 , address =

Chiang, Cheng-Han and Lee, Hung-yi and Lukasik, Michal , booktitle =. 2025 , address =

2025
[28]

Predicting Rental Price of Lane Houses in

Chen, Tingting and Si, Shijing , journal=. Predicting Rental Price of Lane Houses in. 2024 , month=

2024
[29]

Proceedings of ICLR , year=

Fourier Head: Helping Large Language Models Learn Complex Probability Distributions , author=. Proceedings of ICLR , year=
[30]

org/abs/2409.10164

Quantile Regression for Distributional Reward Models in RLHF , author=. arXiv preprint arXiv:2409.10164 , year=

work page arXiv
[31]

Retrieval-augmented generation for knowledge-intensive NLP tasks , year =

Lewis, Patrick and Perez, Ethan and Piktus, Aleksandra and Petroni, Fabio and Karpukhin, Vladimir and Goyal, Naman and K\". Retrieval-augmented generation for knowledge-intensive NLP tasks , year =. Proceedings of the 34th International Conference on Neural Information Processing Systems , articleno =
[32]

Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection

Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection , author=. arXiv preprint arXiv:2310.11511 , year=

work page internal anchor Pith review arXiv
[33]

Predicting Stock Prices with

Gu, Wenjun and Zhong, Yihao and Li, Shizun and Wei, Changsong and Dong, Liting and Wang, Zhuoyue and Yan, Chao , booktitle=. Predicting Stock Prices with. 2024 , doi=

2024
[34]

2024 , month=

Boosted Generalized Normal Distributions: Integrating Machine Learning with Operations Knowledge , author=. 2024 , month=. doi:10.2139/ssrn.4906838 , note=

work page doi:10.2139/ssrn.4906838 2024
[35]

Edward J Hu and Yelong Shen and Phillip Wallis and Zeyuan Allen-Zhu and Yuanzhi Li and Shean Wang and Lu Wang and Weizhu Chen , booktitle=. Lo. 2022 , url=

2022
[36]

Qwen3 Technical Report

Qwen3 Technical Report , author=. arXiv preprint arXiv:2505.09388 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[37]

2020 , eprint=

HuggingFace's Transformers: State-of-the-art Natural Language Processing , author=. 2020 , eprint=

2020
[38]

Optimal Transport: Old and New , series =

Villani, C. Optimal Transport: Old and New , series =. 2009 , doi =

2009
[39]

2020 , eprint=

Scaling Laws for Neural Language Models , author=. 2020 , eprint=

2020
[40]

Critique-out-loud re- ward models.arXiv preprint arXiv:2408.11791, 2024

Critique-out-Loud Reward Models , author =. 2024 , eprint =. doi:10.48550/arXiv.2408.11791 , url =

work page doi:10.48550/arxiv.2408.11791 2024
[41]

Enhancing Automated Essay Scoring Performance via Fine-tuning Pre-trained Language Models with Combination of Regression and Ranking

Yang, Ruosong and Cao, Jiannong and Wen, Zhiyuan and Wu, Youzheng and He, Xiaodong. Enhancing Automated Essay Scoring Performance via Fine-tuning Pre-trained Language Models with Combination of Regression and Ranking. Findings of the Association for Computational Linguistics: EMNLP 2020. 2020. doi:10.18653/v1/2020.findings-emnlp.141

work page doi:10.18653/v1/2020.findings-emnlp.141 2020
[42]

R. R. Bahadur , journal =. A Note on Quantiles in Large Samples , urldate =
[43]

2025 , howpublished =

Anthropic , title =. 2025 , howpublished =

2025
[44]

2024 , eprint=

Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone , author=. 2024 , eprint=

2024
[45]

Gneiting and A

Tilmann Gneiting and Adrian E. Raftery , title =. Journal of the American Statistical Association , volume =. 2007 , publisher =. doi:10.1198/016214506000001437 , URL =

work page doi:10.1198/016214506000001437 2007