Paper Citation Record · LEDGER

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning

As of 20 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2506.15706.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.15706 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:29:35.826782Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

13 of 13 outbound references displayed

verified exact0
verified fuzzy0
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c61dd3a6-0f87-4fba-bed9-78da6f6c6430 · outbound

This paper cites Qwen Technical Report.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Qwen Technical Report

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.069984Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9ad4ebe-4bfa-4155-a22e-7471c5277dd7 · outbound

This paper cites ORPO: Monolithic Preference Optimization without Reference Model.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning ORPO: Monolithic Preference Optimization without Reference Model

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.631728Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d4f9a7d-1972-40c9-b23c-eae567766c12 · outbound

This paper cites MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.957668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 946a8099-ad50-43ce-ada0-929c11b49985 · outbound

This paper cites Orca-Math: Unlocking the potential of SLMs in Grade School Math.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Orca-Math: Unlocking the potential of SLMs in Grade School Math

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:35.252687Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d94a3e4-526c-4e4e-a214-63c1098c235c · outbound

This paper cites LLaMA: Open and Efficient Foundation Language Models.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning LLaMA: Open and Efficient Foundation Language Models

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:35.566083Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b4612a2-3425-4484-9dae-1f571c030c6a · outbound

This paper cites MathPile: A Billion-Token-Scale Pretraining Corpus for Math.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning MathPile: A Billion-Token-Scale Pretraining Corpus for Math

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:35.680196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6560daf-019a-4a7a-85c5-15fd3c253c84 · outbound

This paper cites Automatic Chain of Thought Prompting in Large Language Models.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Automatic Chain of Thought Prompting in Large Language Models

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:35.826782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a397e16-b92e-468e-8660-2dbfc3d1c1e6 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Training Verifiers to Solve Math Word Problems

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.220523Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ada7517d-270b-424d-bb77-6823d4c674a6 · outbound

This paper cites MathScale: Scaling Instruction Tuning for Mathematical Reasoning.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning MathScale: Scaling Instruction Tuning for Mathematical Reasoning

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:35.374285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afa863ba-4dbf-4806-9fc1-8135714b49ef · outbound

This paper cites KTO: Model Alignment as Prospect Theoretic Optimization.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning KTO: Model Alignment as Prospect Theoretic Optimization

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.363833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b40b769e-4c06-48e5-9d9d-e10fc34fc93c · outbound

This paper cites Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.795071Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83c80812-fb4f-4f46-8b67-046aef42f866 · outbound

This paper cites Measuring Mathematical Problem Solving With the MATH Dataset.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Measuring Mathematical Problem Solving With the MATH Dataset

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:34.481780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 930ec7a3-8608-4099-8aa6-f78e94c68117 · outbound

This paper cites Improve Mathematical Reasoning in Language Models by Automated Process Supervision.

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning Improve Mathematical Reasoning in Language Models by Automated Process Supervision

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:35.084817Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.