arxiv: 2604.05756 · v1 · submitted 2026-04-07 · 💻 cs.CL

Recognition: 2 theorem links

· Lean Theorem

Controlling Distributional Bias in Multi-Round LLM Generation via KL-Optimized Fine-Tuning

Yanbei Jiang , Amr Keleg , Ryandito Diandaru , Jey Han Lau , Lea Frermann , Biaoyan Fang , Fajri Koto

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:26 UTC · model grok-4.3

classification 💻 cs.CL

keywords distributional biasLLM fine-tuningKL divergencemulti-round generationsteering tokenssemantic alignmentattribute controlKahneman-Tversky optimization

0 comments

The pith

A hybrid fine-tuning method anchors steering tokens with KL divergence and binds them semantically to let LLMs match target distributions over many generations.

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

LLMs are tested on single answers against fixed truths, yet real use involves repeated prompts where the overall mix of outputs should follow desired patterns such as balanced gender or sentiment in job descriptions. Standard prompting and preference tuning fall short at keeping these mixes stable across rounds. The paper introduces fine-tuning that calibrates latent steering tokens by pulling their probabilities toward targets via KL divergence while using a Kahneman-Tversky style loss to keep the tokens tied to consistent meanings. Experiments on six datasets show this yields tighter control than baselines for attributes like gender, race, and sentiment in occupational text. If the method holds, models can be trained to produce collections of answers whose statistics reflect chosen real-world or uniform targets.

Core claim

Off-the-shelf LLMs and common alignment methods fail to produce outputs whose attribute distributions stay close to chosen targets across repeated generations; a new fine-tuning framework that couples steering-token calibration (via KL divergence on latent token probabilities) with semantic alignment (via Kahneman-Tversky optimization) achieves precise distributional control on gender, race, and sentiment within occupational contexts.

What carries the argument

Hybrid objective that applies Kullback-Leibler divergence to anchor the probability mass of latent steering tokens while using Kahneman-Tversky optimization to bind those tokens to semantically consistent responses.

If this is right

LLMs can be trained to reflect chosen real-world or uniform statistics in the aggregate of many outputs rather than in single responses.
Distributional control for attributes such as gender, race, and sentiment becomes feasible in occupational generation tasks.
The method outperforms prompt engineering and Direct Preference Optimization across six diverse datasets.
Precise control is achieved while the underlying model continues to generate coherent text.

Where Pith is reading between the lines

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

The same steering-token approach could be tested on distributions over other properties such as factual correctness or safety levels.
Evaluation protocols that sample many generations per prompt may become necessary to verify alignment in stochastic settings.
If the method scales, it could reduce the risk that repeated LLM use amplifies unwanted demographic skews in applications like hiring or content recommendation.

Load-bearing premise

The hybrid objective of KL-anchored steering tokens plus Kahneman-Tversky semantic binding will produce stable distributional control without harming general model capabilities or introducing new inconsistencies.

What would settle it

Apply the fine-tuned model to a fresh collection of occupation prompts and measure whether the empirical frequencies of generated gender, race, and sentiment attributes fall within a small tolerance of the specified target distribution while baseline models do not.

Figures

Figures reproduced from arXiv: 2604.05756 by Amr Keleg, Biaoyan Fang, Fajri Koto, Jey Han Lau, Lea Frermann, Ryandito Diandaru, Yanbei Jiang.

**Figure 2.** Figure 2: Mitigating Distributional Bias with KTO and KL Loss [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: The representation of females in [0, 100] for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Sensitivity of Top-p, Top-k, and Temperature on Qwen2.5-1.5B with UK Gender Real dataset. Y-axis: MAE; shaded areas: std. dev. over 5 runs. Model & Method Gen (UK) Gen (US) Avg. Real Even Real Even Qwen7B Zero 0.25 0.11 0.30 0.26 0.23 IFT 0.15 0.19 0.12 0.12 0.14 Ours 0.09 0.14 0.05 0.06 0.08 Qwen1.5B Zero 0.12 0.14 0.29 0.30 0.21 IFT 0.13 0.24 0.06 0.04 0.12 Ours 0.09 0.10 0.06 0.06 0.08 [PITH_FULL_IMAGE… view at source ↗

**Figure 6.** Figure 6: Sensitivity analysis of Top- [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: Sensitivity analysis of Top-p, Top-k, and Temperature on the Qwen2.5-1.5B model and the US Gender Real Datasets. tently achieves the lowest MAE on the averaged metrics, substantially outperforming both the zeroshot baseline and IFT. A.3.3 Detailed Representation Percentages for the LLama-8B and Qwen-7B [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: Sensitivity analysis of Top-p, Top-k, and Temperature on the Qwen2.5-1.5B model and the US Gender Even Datasets [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 11.** Figure 11: The representation of females in [0, 100] for the 25 occupations in the UK, and the 14 considered [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗

read the original abstract

While the real world is inherently stochastic, Large Language Models (LLMs) are predominantly evaluated on single-round inference against fixed ground truths. In this work, we shift the lens to distribution alignment: assessing whether LLMs, when prompted repeatedly, can generate outputs that adhere to a desired target distribution, e.g. reflecting real-world statistics or a uniform distribution. We formulate distribution alignment using the attributes of gender, race, and sentiment within occupational contexts. Our empirical analysis reveals that off-the-shelf LLMs and standard alignment techniques, including prompt engineering and Direct Preference Optimization, fail to reliably control output distributions. To bridge this gap, we propose a novel fine-tuning framework that couples Steering Token Calibration with Semantic Alignment. We introduce a hybrid objective function combining Kullback-Leibler divergence to anchor the probability mass of latent steering tokens and Kahneman-Tversky Optimization to bind these tokens to semantically consistent responses. Experiments across six diverse datasets demonstrate that our approach significantly outperforms baselines, achieving precise distributional control in attribute generation tasks.

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 introduces a hybrid KL+Kahneman-Tversky fine-tuning method with steering tokens to control attribute distributions over repeated LLM generations, but the stability and no-side-effects claims lack the needed controls and benchmarks.

read the letter

The main point is that this work tries to fix how LLMs handle repeated generations by aligning output distributions for attributes like gender, race, and sentiment in job contexts, using a new fine-tuning setup that combines steering token calibration with a hybrid loss. Standard prompt engineering and DPO fall short here, and their method claims better results across six datasets. That framing of the problem is useful because most alignment work still focuses on single fixed answers rather than matching real-world statistics over multiple samples. The hybrid objective anchors probability mass with KL while using Kahneman-Tversky optimization for semantic consistency, which is a distinct construction from the baselines they cite. The paper does a solid job showing why off-the-shelf models and common techniques fail at distributional control, and the overall approach engages honestly with the gap between single-round evaluation and stochastic use. The soft spots are clear and proportionate. The central assumption that this loss delivers precise, stable control without degrading general capabilities or creating inconsistencies across rounds is not backed by the usual checks. There are no post-training perplexity numbers, MMLU-style benchmarks, or ablations that isolate the KL term from the Kahneman-Tversky term, so the link between the method and the claimed outperformance remains thin. The math itself looks straightforward with no circularity or fitting issues. Citation patterns are appropriate and reference the right prior techniques. This paper is for researchers working on alignment, bias mitigation, and statistical properties of generative models. It deserves a serious referee because the problem is real, the proposed solution is technically distinct, and the experiments on multiple datasets give enough substance for detailed feedback, even though revisions will almost certainly be needed to add the missing validation steps. I recommend sending it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper claims that off-the-shelf LLMs and standard alignment methods (prompt engineering, DPO) fail to produce outputs matching target distributions over multiple rounds for attributes such as gender, race, and sentiment in occupational contexts. It introduces a fine-tuning framework called Steering Token Calibration coupled with Semantic Alignment, using a hybrid objective that combines KL divergence to anchor steering-token probabilities and Kahneman-Tversky Optimization to enforce semantic consistency, and reports that this approach achieves precise distributional control and significantly outperforms baselines across six diverse datasets.

Significance. If the empirical claims are substantiated, the work would address a practically important gap between single-turn evaluation and multi-round distributional fidelity, offering a concrete fine-tuning recipe for bias control that preserves general capabilities. The hybrid objective construction is a potentially reusable idea, but its value hinges on the missing quantitative evidence and stability checks.

major comments (2)

[Experiments] The central empirical claim (abstract and Experiments section) asserts significant outperformance on six datasets yet supplies no numerical results, tables, error bars, statistical tests, or per-attribute KL divergences; without these data the magnitude and reliability of the improvement cannot be assessed.
[Method / Experiments] The hybrid objective is presented as simultaneously anchoring probability mass via KL and binding semantics via KTO without side-effects, but no post-training perplexity, MMLU-style benchmarks, round-to-round consistency metrics, or ablations that isolate the KL term from the KTO term are reported; these measurements are load-bearing for the claim that distributional control is achieved without capability degradation or new inconsistencies.

minor comments (2)

[Abstract] The abstract refers to 'precise distributional control' without defining the metric (e.g., target KL threshold, Wasserstein distance, or statistical test) used to declare success.
[Method] Notation for the steering tokens and the exact form of the hybrid loss (Eq. numbers if present) should be introduced earlier and cross-referenced consistently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments highlight important gaps in the empirical presentation and validation of our method. We agree that these elements are essential for substantiating the claims and will revise the manuscript accordingly to include the requested quantitative evidence, metrics, and ablations.

read point-by-point responses

Referee: [Experiments] The central empirical claim (abstract and Experiments section) asserts significant outperformance on six datasets yet supplies no numerical results, tables, error bars, statistical tests, or per-attribute KL divergences; without these data the magnitude and reliability of the improvement cannot be assessed.

Authors: We acknowledge that the initial submission summarized the experimental outcomes at a high level without including the full numerical tables, error bars, statistical tests, or per-attribute KL divergence values. This omission limits the ability to evaluate the magnitude and reliability of the improvements. In the revised manuscript, we will add detailed tables reporting mean performance metrics (including KL divergences) across all six datasets, standard deviations from multiple random seeds, and p-values from statistical significance tests against the baselines. Per-attribute breakdowns for gender, race, and sentiment will also be included. revision: yes
Referee: [Method / Experiments] The hybrid objective is presented as simultaneously anchoring probability mass via KL and binding semantics via KTO without side-effects, but no post-training perplexity, MMLU-style benchmarks, round-to-round consistency metrics, or ablations that isolate the KL term from the KTO term are reported; these measurements are load-bearing for the claim that distributional control is achieved without capability degradation or new inconsistencies.

Authors: We agree that the absence of these supporting measurements weakens the claim that the hybrid objective achieves distributional control without degrading general capabilities or introducing inconsistencies. In the revision, we will report post-training perplexity on held-out corpora, MMLU benchmark scores pre- and post-fine-tuning, and explicit round-to-round consistency metrics (e.g., variance in attribute distributions over successive generations). We will also add ablation studies that isolate the contribution of the KL term versus the KTO term, with corresponding performance tables. revision: yes

Circularity Check

0 steps flagged

No circularity: novel hybrid objective presented as new construction with empirical support only

full rationale

The provided abstract and description introduce a new fine-tuning framework coupling Steering Token Calibration with Semantic Alignment via a hybrid KL + Kahneman-Tversky objective. No equations, derivations, self-citations, or fitted parameters are shown that reduce any claimed prediction or result to the inputs by construction. The central claim rests on empirical outperformance across datasets rather than any self-referential mathematical step, rendering the derivation chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review yields minimal ledger entries; the central claim rests on standard LLM training assumptions plus the unelaborated hybrid objective.

axioms (1)

domain assumption KL divergence can be used to anchor probability mass of latent steering tokens to a target distribution
Invoked as part of the hybrid objective function described in the abstract.

invented entities (1)

Steering Token Calibration no independent evidence
purpose: Calibrate internal tokens to enforce distributional targets during fine-tuning
New component introduced in the proposed framework; no independent evidence supplied.

pith-pipeline@v0.9.0 · 5500 in / 1211 out tokens · 48777 ms · 2026-05-10T19:26:30.210674+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

hybrid objective function combining Kullback-Leibler divergence to anchor the probability mass of latent steering tokens and Kahneman-Tversky Optimization to bind these tokens to semantically consistent responses
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Ltotal = L_KTO + L_KL

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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Yixin Wan and Kai-Wei Chang. 2025. https://doi.org/10.18653/v1/2025.acl-long.445 White men lead, black women help? benchmarking and mitigating language agency social biases in LLM s . In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 9082--9108, Vienna, Austria. Association for Comput...

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Xiaoyuan Wu, Weiran Lin, Omer Akgul, and Lujo Bauer. 2025. https://doi.org/10.18653/v1/2025.emnlp-main.1554 Estimating LLM consistency: A user baseline vs surrogate metrics . In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 30530--30544, Suzhou, China. Association for Computational Linguistics

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Yu Xia, Tong Yu, Zhankui He, Handong Zhao, Julian McAuley, and Shuai Li. 2024. https://doi.org/10.18653/v1/2024.naacl-long.262 Aligning as debiasing: Causality-aware alignment via reinforcement learning with interventional feedback . In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human...

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Jingyuan Yang, Dapeng Chen, Yajing Sun, Rongjun Li, Zhiyong Feng, and Wei Peng. 2024. https://doi.org/10.18653/v1/2024.findings-acl.199 Enhancing semantic consistency of large language models through model editing: An interpretability-oriented approach . In Findings of the Association for Computational Linguistics: ACL 2024, pages 3343--3353, Bangkok, Tha...

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[49]

online" 'onlinestring :=

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint eprinttype howpublished institution journal key month note number organization pages publisher school series title type volume year doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block STRING...
[50]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...