# Hierarchical Process Reward Models are Symbolic Vision Learners

arXiv: https://arxiv.org/abs/2512.03126 · HTML: https://mlsanity.com/paper/2512.03126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Diffusion and multimodal model alignment](https://mlsanity.com/alignment/diffusion-and-multimodal-model-alignment/)

## Builds on (most cited first, 23 of 23)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [LLaMA-Adapter V2: Parameter-Efficient Visual Instruction Model](https://mlsanity.com/paper/2304.15010/) (2023)
- [DeepSeek-VL2: Mixture-of-Experts Vision-Language Models for Advanced Multimodal Understanding](https://mlsanity.com/paper/2412.10302/) (2024)
- [SPHINX: The Joint Mixing of Weights, Tasks, and Visual Embeddings for Multi-modal Large Language Models](https://mlsanity.com/paper/2311.07575/) (2023)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [ImageBind-LLM: Multi-modality Instruction Tuning](https://mlsanity.com/paper/2309.03905/) (2023)
- [VisualPRM: An Effective Process Reward Model for Multimodal Reasoning](https://mlsanity.com/paper/2503.10291/) (2025)
- [SPHINX-X: Scaling Data and Parameters for a Family of Multi-modal Large Language Models](https://mlsanity.com/paper/2402.05935/) (2024)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [MultiMath: Bridging Visual and Mathematical Reasoning for Large Language Models](https://mlsanity.com/paper/2409.00147/) (2024)
- [Plot2Code: A Comprehensive Benchmark for Evaluating Multi-modal Large Language Models in Code Generation from Scientific Plots](https://mlsanity.com/paper/2405.07990/) (2024)
- [PlotGen: Multi-Agent LLM-based Scientific Data Visualization via Multimodal Feedback](https://mlsanity.com/paper/2502.00988/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [VisCodex: Unified Multimodal Code Generation via Merging Vision and Coding Models](https://mlsanity.com/paper/2508.09945/) (2025)
- [Training Vision-Language Process Reward Models for Test-Time Scaling in Multimodal Reasoning: Key Insights and Lessons Learned](https://mlsanity.com/paper/2509.23250/) (2025)
- [GroundedPRM: Tree-Guided and Fidelity-Aware Process Reward Modeling for Step-Level Reasoning](https://mlsanity.com/paper/2510.14942/) (2025)
- [VisioMath: Benchmarking Figure-based Mathematical Reasoning in LMMs](https://mlsanity.com/paper/2506.06727/) (2025)

## Abstract (arXiv)

Symbolic computer vision represents diagrams through explicit logical rules and structured representations, enabling interpretable understanding in machine vision. This requires fundamentally different learning paradigms from pixel-based visual models. Symbolic visual learners parse diagrams into geometric primitives-points, lines, and shapes-whereas pixel-based learners operate on textures and colors. We propose a novel self-supervised symbolic auto-encoder that encodes diagrams into structured primitives and their interrelationships within the latent space, and decodes them through our executable engine to reconstruct the input diagrams. Central to this architecture is Symbolic Hierarchical Process Reward Modeling, which applies hierarchical step-level parsing rewards to enforce point-on-line, line-on-shape, and shape-on-relation consistency. Since vanilla reinforcement learning exhibits poor exploration in the policy space during diagram reconstruction; we thus introduce stabilization mechanisms to balance exploration and exploitation. We fine-tune our symbolic encoder on downstream tasks, developing a neuro-symbolic system that integrates the reasoning capabilities of neural networks with the interpretability of symbolic models through reasoning-grounded visual rewards. Evaluations across reconstruction, perception, and reasoning tasks demonstrate the effectiveness of our approach: achieving a 98.2% reduction in MSE for geometric diagram reconstruction, surpassing GPT-4o by 0.6% with a 7B model on chart reconstruction, and improving by +13% on the MathGlance perception benchmark, and by +3% on MathVerse and GeoQA reasoning benchmarks.