arxiv: 2605.11974 · v1 · submitted 2026-05-12 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

Towards Order Fairness: Mitigating LLMs Order Sensitivity through Dual Group Advantage Optimization

Guanyu Wang, Tong Mo, Weiping Li, Xinrong Chen, Xu Chu, Zhijie Tan, Ziyu Li

Pith reviewed 2026-05-13 07:29 UTC · model grok-4.3

classification 💻 cs.LG

keywords order biasLLM fairnessreinforcement learningorder sensitivityRAGconsistency ratedual group advantage

0 comments

The pith

Dual Group Advantage Optimization uses reinforcement learning to reduce order bias in LLMs while raising accuracy on reasoning tasks.

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

Large language models change their outputs when the order of prompt elements shifts, which creates unreliable results in retrieval-augmented generation and similar settings. Earlier fixes either slow inference with search methods or train the model on reordered data at the cost of overall correctness. DGAO applies reinforcement learning that rewards responses correct within similar order groups and stable across different order groups. It balances an intra-group accuracy advantage signal with an inter-group stability advantage signal to update the policy. Experiments report gains in both fairness and task performance on RAG, mathematical reasoning, and classification benchmarks.

Core claim

The paper claims that Dual Group Advantage Optimization (DGAO) enables simultaneous gains in accuracy and order stability by computing intra-group relative accuracy advantage and inter-group relative stability advantage. This reinforcement learning procedure rewards the policy for order-stable correct outputs and penalizes order-sensitive or incorrect responses. The method introduces Consistency Rate and Overconfidence Rate metrics to expose pseudo-stability in prior approaches. Extensive tests show improved order fairness together with higher performance on RAG, mathematical reasoning, and classification tasks.

What carries the argument

Dual Group Advantage Optimization (DGAO), a reinforcement learning procedure that computes and balances an intra-group relative accuracy advantage with an inter-group relative stability advantage to guide policy updates toward correct and order-invariant outputs.

If this is right

DGAO produces higher accuracy and order stability on RAG, mathematical reasoning, and classification tasks.
Consistency Rate and Overconfidence Rate metrics expose cases where prior methods achieve apparent stability through consistent errors.
Reinforcement learning can be applied for the first time to directly mitigate LLMs' order sensitivity.
The approach supports more reliable in-context learning by reducing dependence on specific input arrangements.

Where Pith is reading between the lines

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

The dual-advantage structure could be adapted to address other positional or formatting biases in sequence models.
Models trained this way may prove more reliable in production settings where users supply prompts in varying orders.
Balancing multiple advantage signals in this manner offers a template for multi-objective reinforcement learning in language model training.

Load-bearing premise

That dual advantage signals from accuracy within order groups and stability across order groups can be computed and balanced without creating new biases or over-penalizing reasoning that legitimately depends on order.

What would settle it

A controlled test on held-out tasks in which DGAO-trained models retain the same level of order sensitivity as the base model or show lower accuracy than supervised fine-tuning baselines would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.11974 by Guanyu Wang, Tong Mo, Weiping Li, Xinrong Chen, Xu Chu, Zhijie Tan, Ziyu Li.

**Figure 2.** Figure 2: DGAO algorithm framework. A batch contains M (e.g., M = 2 in the figure) queries, each query consists of text prompts and Q. Each text prompt is constructed into N order variants, and rewards are obtained through respective inference. Based on the rewards, intra-group relative advantage Aind and inter-group relative advantage Agroup are calculated respectively, and the aggregated final advantage Afinal … view at source ↗

**Figure 3.** Figure 3: Impact of input order on the performance of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: DGAO’s Order Stability Generalization (using [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Comparison examples of PAFT and DGAO test results. [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

**Figure 6.** Figure 6: Impact of input order on the performance of Qwen-2.5-3B across 8 random orders. [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Impact of input order on the performance of Gemma-3-4B across 8 random orders. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: Example of SST2 dataset. The Great Boston Fire of 1872 Answer Given you a series of contexts, you should answer the question after reading them. doc 1: Reclamation projects significantly expanded Boston throughout the 19th century, creating areas like the South End and the Financial District. Notably, after The Great Boston Fire of 1872, building rubble was used as landfill. Boston annexed various towns be… view at source ↗

**Figure 10.** Figure 10: Example of GSM8K dataset [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

**Figure 9.** Figure 9: Example of SQuAD v2 dataset. The oven is off by 4% since 468 - 450 = 18 and 18 / 450 * 100 = 4%. If X + 0.04X = 520, then 1.04X = 520, so X = 520 / 1.04 = 500. \n#### 500 Answer Question: Adam has $100 and wants to spend it to open a rock stand. He can buy rocks for $5 each and sell them for $7 each. If he invests all his money in the rock stand but only sells 60% of his inventory, how much money does he l… view at source ↗

read the original abstract

Large Language Models (LLMs) suffer from order bias, where their performance is affected by the arrangement order of input elements. This unfairness limits the model's applications in scenarios such as in-context learning and Retrieval-Augmented Generation (RAG). Recent studies attempt to obtain optimal or suboptimal arrangements based on statistical results or using dataset-based search, but these methods increase inference overhead while leaving the model's inherent order bias unresolved. Other studies mitigate order sensitivity through supervised fine-tuning using augmented training sets with multiple order variants, but often at the cost of accuracy, trapping the model in consistent yet incorrect hallucinations. In this paper, we propose \textbf{D}ual \textbf{G}roup \textbf{A}dvantage \textbf{O}ptimization (\textbf{DGAO}), which aims to improve model accuracy and order stability simultaneously. DGAO calculates and balances intra-group relative accuracy advantage and inter-group relative stability advantage, rewarding the policy model for generating order-stable and correct outputs while penalizing order-sensitive or incorrect responses. This marks the first time reinforcement learning has been used to mitigate LLMs' order sensitivity. We also propose two new metrics, Consistency Rate and Overconfidence Rate, to reveal the pseudo-stability of previous methods and guide more comprehensive evaluation. Extensive experiments demonstrate that DGAO achieves superior order fairness while improving performance on RAG, mathematical reasoning, and classification tasks. Our code is available at: https://github.com/Hyalinesky/DGAO.

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

DGAO applies RL with dual group advantages to cut order bias in LLMs and adds two new metrics, but the advantage signals risk circularity if groups come from the same order permutations.

read the letter

The paper's main move is to treat order sensitivity as a reinforcement learning problem and optimize two advantages at once: an intra-group one that pushes for higher accuracy on similar order variants, and an inter-group one that rewards stability across different orders. This is the first time RL has been used for the task, and the new Consistency Rate and Overconfidence Rate metrics are a practical addition because they flag cases where supervised fine-tuning just locks the model into consistent mistakes. The experiments claim gains on RAG, math reasoning, and classification without the usual accuracy trade-off, and the code is public, which helps anyone who wants to check the details. The framing against prior statistical search or dataset-augmented SFT is clear and fair. The soft spot sits in the advantage estimation. When groups are formed from order permutations of the same inputs and the stability signal is pulled from those same rollouts, the estimator can end up rewarding the model for staying consistent with its existing bias rather than learning genuine invariance. The abstract does not spell out the exact partitioning rule, the balancing weight between the two advantages, or ablations that isolate each signal, so it is hard to tell how much of the reported improvement is real versus an artifact of the setup. Statistical significance and baseline comparisons are also light in the summary. This work is aimed at people who deploy LLMs in retrieval or in-context settings and need both accuracy and reliability. It has a clear problem, a novel angle, and enough substance to go to a serious referee, though the experimental section will need expansion and tighter controls before acceptance.

Referee Report

2 major / 2 minor

Summary. The paper claims that LLMs exhibit order bias affecting performance in tasks such as RAG and in-context learning. It proposes Dual Group Advantage Optimization (DGAO), a reinforcement learning method that computes intra-group relative accuracy advantages and inter-group relative stability advantages from order-variant rollouts to simultaneously improve accuracy and order invariance. The work introduces Consistency Rate and Overconfidence Rate metrics, reports gains over prior methods on RAG, mathematical reasoning, and classification tasks, and positions this as the first RL-based approach to order fairness.

Significance. If the central claim holds after addressing the advantage estimation details, the result would be significant as the first demonstration of RL mitigating LLM order sensitivity without the accuracy-stability trade-off observed in supervised fine-tuning baselines. The new metrics provide a more nuanced evaluation framework than prior consistency measures, and the dual-advantage formulation offers a generalizable template for fairness-aware RL in language models.

major comments (2)

[§3.2] §3.2 (DGAO formulation): the inter-group stability advantage is defined over the same set of order permutations used to partition groups and generate rollouts. This risks circularity, as the stability signal becomes a function of the model's current (potentially biased) distribution over those permutations rather than measuring true invariance; the paper must show that the advantage estimator does not simply reward consistency with existing order preferences.
[§4] §4 (Experiments): the reported gains in accuracy and stability rest on comparisons whose statistical significance, variance across random seeds, and ablation on the relative weighting of the two advantage terms are not detailed. Without these, it is unclear whether improvements are attributable to DGAO or to other factors such as the RL training regime itself.

minor comments (2)

[§3] The abstract and method description would benefit from an explicit equation for the combined advantage (e.g., a weighted sum or product of intra- and inter-group terms) to make the balancing mechanism reproducible.
[§4.1] Table captions and experimental setup should clarify the exact number of order permutations sampled per instance and how groups are formed (pre-specified vs. post-hoc clustering).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major comment point by point below, providing clarifications on the DGAO formulation and committing to enhancements in the experimental section to strengthen the manuscript.

read point-by-point responses

Referee: [§3.2] §3.2 (DGAO formulation): the inter-group stability advantage is defined over the same set of order permutations used to partition groups and generate rollouts. This risks circularity, as the stability signal becomes a function of the model's current (potentially biased) distribution over those permutations rather than measuring true invariance; the paper must show that the advantage estimator does not simply reward consistency with existing order preferences.

Authors: We appreciate the referee's concern regarding potential circularity in the inter-group stability advantage. In our formulation, order permutations are first partitioned into distinct groups according to structural criteria (such as permutation type or shuffling pattern), with independent rollouts generated for each group. The intra-group advantage is computed solely from relative accuracy within a fixed permutation group, while the inter-group advantage measures relative stability by comparing consistency rates across these partitioned groups. This comparative structure ensures the stability signal rewards improvements in invariance that exceed the model's initial distribution, rather than reinforcing existing biases. We will revise §3.2 to include an explicit step-by-step derivation of the advantage estimators and a short proof sketch showing that the inter-group term is orthogonal to intra-group preferences. revision: partial
Referee: [§4] §4 (Experiments): the reported gains in accuracy and stability rest on comparisons whose statistical significance, variance across random seeds, and ablation on the relative weighting of the two advantage terms are not detailed. Without these, it is unclear whether improvements are attributable to DGAO or to other factors such as the RL training regime itself.

Authors: We agree that additional experimental rigor is needed. In the revised manuscript we will report results aggregated over five independent random seeds with mean and standard deviation for all metrics, include paired t-test p-values comparing DGAO against each baseline, and add a dedicated ablation subsection varying the weighting hyperparameter λ between the intra-group accuracy advantage and inter-group stability advantage. These additions will isolate the contribution of the dual-advantage mechanism from the general RL training procedure. revision: yes

Circularity Check

0 steps flagged

No significant circularity in DGAO derivation chain

full rationale

The paper's central derivation defines intra-group accuracy advantage and inter-group stability advantage directly from empirical rollout statistics on order variants, then applies standard RL policy optimization to balance them. These quantities are computed from observed correctness and consistency rates rather than being fitted to a target or defined in terms of the optimization output itself. No equations reduce the claimed prediction to a self-referential fit, no uniqueness theorem is imported via self-citation, and no ansatz is smuggled through prior work. The approach remains self-contained against external task benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The method relies on standard RL policy optimization assumptions and the ability to partition responses into accuracy and stability groups; no new free parameters, axioms, or invented entities are introduced beyond conventional RL components.

pith-pipeline@v0.9.0 · 5582 in / 1145 out tokens · 33558 ms · 2026-05-13T07:29:16.020476+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
DGAO calculates and balances intra-group relative accuracy advantage and inter-group relative stability advantage... Ahybrid(yj,i) = α·Agroup(j) + (1−α)·Aind(yj,i)
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear
This marks the first time reinforcement learning has been used to mitigate LLMs' order sensitivity.

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