arxiv: 2604.08723 · v1 · submitted 2026-04-09 · 💻 cs.CL · cs.AI

Recognition: unknown

Decomposing the Delta: What Do Models Actually Learn from Preference Pairs?

Chia-Hsuan Lee , Mingyang Zhou , Renkun Ni , Zelei Cheng , Sihui Dai , Supriyo Chakraborty , Shixiong Zhang , Sambit Sahu

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William Campbell

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:17 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords preference optimizationreasoning modelsquality deltadata filteringLLM judgeDPOalignmentout-of-domain generalization

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The pith

Larger capability differences between models in preference pairs drive better reasoning gains after optimization.

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

The paper investigates what properties of preference data help improve reasoning performance in language models trained with preference optimization. It distinguishes generator-level delta, the capability gap between the models creating the chosen and rejected responses, from sample-level delta, the quality difference within each pair as rated by an LLM judge. Experiments show that bigger generator-level deltas lead to stronger improvements on out-of-domain reasoning tasks, and that selecting pairs with large sample-level deltas allows effective training with fewer examples. This matters for practitioners because it provides a concrete strategy for building preference datasets that yield more reliable gains in model reasoning abilities.

Core claim

Decomposing quality differences in preference pairs reveals that generator-level delta, defined as the difference in capability between the models generating the chosen and rejected reasoning traces, steadily improves out-of-domain reasoning performance when increased. Sample-level delta, measured via LLM-as-a-judge ratings of quality across reasoning dimensions, can be used to filter data for more efficient training. The authors conclude that maximizing generator-level delta during data construction and exploiting sample-level delta for example selection forms a recipe for better reasoning through preference optimization.

What carries the argument

The generator-level delta and sample-level delta in preference pairs; the former isolates the effect of using stronger versus weaker generators for responses, while the latter quantifies judged quality gaps within pairs to guide data selection.

Load-bearing premise

The LLM-as-a-judge ratings accurately reflect true differences in reasoning quality that causally drive the measured performance changes, rather than being artifacts of the judge model or other data generation factors.

What would settle it

Replicate the data filtering experiment using human annotators to score the sample-level quality differences and verify whether the data efficiency gains persist or disappear.

Figures

Figures reproduced from arXiv: 2604.08723 by Chia-Hsuan Lee, Mingyang Zhou, Renkun Ni, Sambit Sahu, Shixiong Zhang, Sihui Dai, Supriyo Chakraborty, William Campbell, Zelei Cheng.

**Figure 1.** Figure 1: The relevant performance gain against base model (Nemotron-8B) over math-reasoning easy and math-Reasoning hard evaluation sets after SFT and DPO fine-tuning on responses from the weak model (S1) and the strong model (DeepseekR1) To investigate the scaling properties of delta learning, we establish a controlled setup by fixing the model used to generate rejected responses (s1-3B) while scaling the capab… view at source ↗

**Figure 2.** Figure 2: Scaling law of delta learning for reasoning tasks. Chosen models are ordered by [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Nemotron-8B DPO performance on all correctness combinations (chosen [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Scaling performance across quality dimensions for S1-32B vs. S1-3B. We show accuracy as a function of the top-k pairs with highest quality difference measured by each quality dimension (with 16.5k representing the full set of preference pairs). Performance is evaluated on in-domain (easy and hard math) and out-of-domain (STEM) tasks. The dotted grey line represents the base model performance without DPO. s… view at source ↗

**Figure 5.** Figure 5: Overlap between data in datasets formed by top 1000, 2500, and 5000 deltas in [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗

read the original abstract

Preference optimization methods such as DPO and KTO are widely used for aligning language models, yet little is understood about what properties of preference data drive downstream reasoning gains. We ask: what aspects of a preference pair improve a reasoning model's performance on general reasoning tasks? We investigate two distinct notions of quality delta in preference data: generator-level delta, arising from the differences in capability between models that generate chosen and rejected reasoning traces, and sample-level delta, arising from differences in judged quality differences within an individual preference pair. To study generator-level delta, we vary the generator's scale and model family, and to study sample-level delta, we employ an LLM-as-a-judge to rate the quality of generated traces along multiple reasoning-quality dimensions. We find that increasing generator-level delta steadily improves performance on out-of-domain reasoning tasks and filtering data by sample-level delta can enable more data-efficient training. Our results suggest a twofold recipe for improving reasoning performance through preference optimization: maximize generator-level delta when constructing preference pairs and exploit sample-level delta to select the most informative training examples.

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 splits preference data quality into generator capability gaps and within-pair judge gaps, then links both to better out-of-domain reasoning, but the causal isolation is still loose.

read the letter

The main thing to know is that bigger capability differences between the models generating the chosen and rejected traces, plus filtering pairs by how much an LLM judge prefers one over the other, appear to improve reasoning performance after preference tuning. They report steady gains on out-of-domain tasks from scaling the generator gap and more data-efficient training when keeping only high sample-level delta pairs. That twofold recipe is the practical takeaway they want readers to take away.

Referee Report

3 major / 2 minor

Summary. The paper investigates what properties of preference data drive downstream reasoning gains in language models aligned via methods such as DPO and KTO. It decomposes quality differences in preference pairs into generator-level delta (capability gaps between models producing chosen vs. rejected reasoning traces) and sample-level delta (within-pair quality gaps rated by an LLM judge along reasoning dimensions). Experiments vary generator scale and family to study the former and apply LLM-as-a-judge filtering for the latter, claiming that larger generator-level deltas steadily improve OOD reasoning performance while high sample-level delta pairs enable more data-efficient training.

Significance. If the causal claims hold after addressing confounds, the work supplies a concrete, actionable recipe for preference data construction that could improve both effectiveness and efficiency of reasoning alignment. The explicit separation of generator- and sample-level effects offers a reusable lens for diagnosing preference optimization, with potential to guide dataset curation beyond current ad-hoc practices.

major comments (3)

[§4, §5.1] §4 (Experimental Setup) and §5.1 (Generator-level Delta Results): The reported performance gains when increasing generator scale/family are not accompanied by controls for total compute, prompt templates, or sampling hyperparameters; without these, the steady OOD improvement cannot be attributed specifically to generator-level delta rather than higher-quality chosen responses overall.
[§5.2] §5.2 (Sample-level Delta Filtering): Filtering by LLM-judge ratings is presented as improving data efficiency, yet no human validation, inter-rater agreement, or correlation with downstream task metrics is reported; this leaves open whether the delta tracks reasoning quality or proxies for length, style, or token diversity.
[§5] §5 (Results): No statistical significance tests, confidence intervals, or multiple-run variance are provided for the key trends, and no baseline comparisons (e.g., random pair selection or standard DPO data) are shown, weakening support for the twofold recipe as the operative driver.

minor comments (2)

[§3] §3 (Delta Definitions): Formalize the two deltas with explicit equations or pseudocode to clarify how they are computed from generator outputs and judge scores.
[Tables/Figures] Tables and figures: Ensure all axes, legends, and abbreviations (e.g., model family names) are fully defined in captions for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments that highlight opportunities to strengthen causal attribution, validation, and statistical support. We respond point-by-point to the major comments and indicate revisions where the manuscript will be updated.

read point-by-point responses

Referee: [§4, §5.1] §4 (Experimental Setup) and §5.1 (Generator-level Delta Results): The reported performance gains when increasing generator scale/family are not accompanied by controls for total compute, prompt templates, or sampling hyperparameters; without these, the steady OOD improvement cannot be attributed specifically to generator-level delta rather than higher-quality chosen responses overall.

Authors: We held prompt templates and sampling hyperparameters (temperature, top-p, max new tokens) fixed across all generators and families. Total compute necessarily differs with scale, as this is intrinsic to the generator-level delta variable under investigation. We will revise §4 to state these controls explicitly and add a limitations paragraph clarifying that chosen-response quality improves with scale by design, yet the consistent OOD gains across families support the delta as the operative factor. Where feasible, we will include a same-family compute-matched ablation. revision: partial
Referee: [§5.2] §5.2 (Sample-level Delta Filtering): Filtering by LLM-judge ratings is presented as improving data efficiency, yet no human validation, inter-rater agreement, or correlation with downstream task metrics is reported; this leaves open whether the delta tracks reasoning quality or proxies for length, style, or token diversity.

Authors: We employed a structured rubric with GPT-4o scoring reasoning traces on logical correctness, coherence, and error avoidance. We will add to the revision: inter-rater agreement across multiple LLM judges, Pearson correlation between sample-level delta and downstream accuracy gains, and a length/style-matched subset analysis. These additions will show that high-delta pairs capture genuine reasoning differences beyond superficial proxies. revision: yes
Referee: [§5] §5 (Results): No statistical significance tests, confidence intervals, or multiple-run variance are provided for the key trends, and no baseline comparisons (e.g., random pair selection or standard DPO data) are shown, weakening support for the twofold recipe as the operative driver.

Authors: We will revise §5 to report results averaged over three random seeds with 95% bootstrap confidence intervals on OOD metrics. We will also add baseline comparisons: (i) random selection of equal-sized pairs and (ii) DPO on the full unfiltered set. These will demonstrate that sample-level delta filtering improves data efficiency beyond random or unfiltered baselines. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical investigation without derivations or self-referential predictions

full rationale

The paper conducts an empirical study by generating preference pairs from models of varying scales and families, rating traces with an LLM-as-a-judge on reasoning dimensions, and measuring downstream performance after preference optimization. No equations, mathematical derivations, or predictions that reduce to fitted inputs by construction appear in the provided text. The twofold recipe is presented as a summary of observed experimental outcomes rather than a logical reduction. Any self-citations (e.g., to DPO or KTO) serve as background methods and are not load-bearing for the central claims, which rest on controlled variations and external evaluation. The work is self-contained against its own benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the reliability of LLM-as-judge ratings for reasoning quality and on the assumption that performance changes are attributable to the measured deltas. No free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption LLM-as-a-judge ratings along reasoning-quality dimensions provide a valid proxy for sample-level delta
Invoked to quantify within-pair quality differences used for filtering

pith-pipeline@v0.9.0 · 5515 in / 1183 out tokens · 43332 ms · 2026-05-10T17:17:03.469798+00:00 · methodology

discussion (0)

Reference graph

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{category name}

A Additional Experimental Setup Details A.1 Trace Quality Judge Setup Details This section details the prompt architecture and scoring rubric used for GPT-OSS-120b ratings of reasoning trace quality. A.1.1 Comprehensive Evaluation Rubric The following table defines the dimensions across the two primary categories:Logicand Brevity. A.1.2 System Prompt and ...

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