# AlgBench: To What Extent Do Large Reasoning Models Understand Algorithms?

arXiv: https://arxiv.org/abs/2601.04996 · HTML: https://mlsanity.com/paper/2601.04996/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [GPT4Graph: Can Large Language Models Understand Graph Structured Data ? An Empirical Evaluation and Benchmarking](https://mlsanity.com/paper/2305.15066/) (2023)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [KoLA: Carefully Benchmarking World Knowledge of Large Language Models](https://mlsanity.com/paper/2306.09296/) (2023)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [LeetCodeDataset: A Temporal Dataset for Robust Evaluation and Efficient Training of Code LLMs](https://mlsanity.com/paper/2504.14655/) (2025)
- [LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?](https://mlsanity.com/paper/2506.11928/) (2025)
- [The CLRS-Text Algorithmic Reasoning Language Benchmark](https://mlsanity.com/paper/2406.04229/) (2024)
- [ProBench: Benchmarking Large Language Models in Competitive Programming](https://mlsanity.com/paper/2502.20868/) (2025)
- [GraCoRe: Benchmarking Graph Comprehension and Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2407.02936/) (2024)
- [UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2501.13766/) (2025)

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

- [CP-Agent: A Calibrated Risk-Controlled Agent for Feedback-Driven Competitive Programming](https://mlsanity.com/paper/2605.24693/) (2026)

## Abstract (arXiv)

Reasoning ability has become a central focus in the advancement of Large Reasoning Models (LRMs). Although notable progress has been achieved on several reasoning benchmarks such as MATH500 and LiveCodeBench, existing benchmarks for algorithmic reasoning remain limited, failing to answer a critical question: Do LRMs truly master algorithmic reasoning? To answer this question, we propose AlgBench, an expert-curated benchmark that evaluates LRMs under an algorithm-centric paradigm. AlgBench consists of over 3,000 original problems spanning 27 algorithms, constructed by ACM algorithmic experts and organized under a comprehensive taxonomy, including Euclidean-structured, non-Euclidean-structured, non-optimized, local-optimized, global-optimized, and heuristic-optimized categories. Empirical evaluations on leading LRMs (e.g., Gemini-3-Pro, DeepSeek-v3.2-Speciale and GPT-o3) reveal substantial performance heterogeneity: while models perform well on non-optimized tasks (up to 92%), accuracy drops sharply to around 49% on globally optimized algorithms such as dynamic programming. Further analysis uncovers strategic over-shifts, wherein models prematurely abandon correct algorithmic designs due to necessary low-entropy tokens. These findings expose fundamental limitations of problem-centric reinforcement learning and highlight the necessity of an algorithm-centric training paradigm for robust algorithmic reasoning.