# Dual-Density Inference for Efficient Language Model Reasoning

arXiv: https://arxiv.org/abs/2512.15358 · HTML: https://mlsanity.com/paper/2512.15358/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## 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, 17 of 17)

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- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [T2: An Adaptive Test-Time Scaling Strategy for Contextual Question Answering](https://mlsanity.com/paper/2505.17427/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) have shown impressive capabilities in complex reasoning tasks. However, current approaches employ uniform language density for both intermediate reasoning and final answers, leading to computational inefficiency. Our observation found that reasoning process serves a computational function for the model itself, while answering serves a communicative function for human understanding. This distinction enables the use of compressed, symbol-rich language for intermediate computations while maintaining human-readable final explanations. To address this inefficiency, we present Denser: underlineDual-dunderlineensity infunderlineerence, a novel framework that optimizes information density separately for reasoning and answering phases. Our framework implements this through three components: a query processing module that analyzes input problems, a high-density compressed reasoning mechanism for efficient intermediate computations, and an answer generation component that translates compressed reasoning into human-readable solutions. Experimental evaluation across multiple reasoning question answering benchmarks demonstrates that Denser reduces token consumption by up to 62% compared to standard Chain-of-Thought methods while preserving or improving accuracy. These efficiency gains are particularly significant for complex multi-step reasoning problems where traditional methods generate extensive explanations.