# Scaling Unverifiable Rewards: A Case Study on Visual Insights

arXiv: https://arxiv.org/abs/2512.22650 · HTML: https://mlsanity.com/paper/2512.22650/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 27 Dec 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 16 of 16)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [HypoBench: Towards Systematic and Principled Benchmarking for Hypothesis Generation](https://mlsanity.com/paper/2504.11524/) (2025)
- [Two Heads are Better Than One: Test-time Scaling of Multi-agent Collaborative Reasoning](https://mlsanity.com/paper/2504.09772/) (2025)
- [LEVA: Using Large Language Models to Enhance Visual Analytics](https://mlsanity.com/paper/2403.05816/) (2024)
- [AgentTTS: Large Language Model Agent for Test-time Compute-optimal Scaling Strategy in Complex Tasks](https://mlsanity.com/paper/2508.00890/) (2025)
- [ChartInsighter: An Approach for Mitigating Hallucination in Time-series Chart Summary Generation with A Benchmark Dataset](https://mlsanity.com/paper/2501.09349/) (2025)
- [What are Data Insights to Professional Visualization Users?](https://mlsanity.com/paper/2008.13057/) (2020)
- [A2P-Vis: an Analyzer-to-Presenter Agentic Pipeline for Visual Insights Generation and Reporting](https://mlsanity.com/paper/2512.22101/) (2025)
- [Characterizing the Quality of Insight by Interactions: A Case Study](https://mlsanity.com/paper/2010.05723/) (2020)

## Built on by (most cited first, 1 of 1)

- [SanSi: A Looped Typed Decision Model for System 1.5 Thinking](https://mlsanity.com/paper/2610.07730/) (2026)

## Abstract (arXiv)

Large Language Model (LLM) agents can increasingly automate complex reasoning through Test-Time Scaling (TTS), iterative refinement guided by reward signals. However, many real-world tasks involve multi-stage pipeline whose final outcomes lack verifiable rewards or sufficient data to train robust reward models, making judge-based refinement prone to accumulate error over stages. We propose Selective TTS, a process-based refinement framework that scales inference across different stages in multi-agent pipeline, instead of repeated refinement over time by prior work. By distributing compute across stages and pruning low-quality branches early using process-specific judges, Selective TTS mitigates the judge drift and stabilizes refinement. Grounded in the data science pipeline, we build an end-to-end multi-agent pipeline for generating visually insightful charts and report of given dataset, and design a reliable LLM-based judge model, aligned with human experts (Kendall's τ=0.55). Our proposed selective TTS then improves insight quality under a fixed compute budget, increasing mean scores from 61.64 to 65.86 while reducing variance. We hope our findings serve as the first step toward to scaling complex, open-ended tasks with unverifiable rewards, such as scientific discovery and story generation.