# Semantic Density Effect (SDE): Maximizing Information Per Token Improves LLM Accuracy

arXiv: https://arxiv.org/abs/2604.17659 · HTML: https://mlsanity.com/paper/2604.17659/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 4 references that are in the map.
- First posted on arXiv 19 Apr 2026.

## Builds on (most cited first, 1 of 1)

- [Re-Reading Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.06275/) (2023)

## Abstract (arXiv)

We introduce the Semantic Density Effect (SDE): the empirical finding that prompts carrying higher semantic information per token consistently produce more accurate, focused, and less hallucinated outputs across all major LLM families. SDE is defined as the ratio of semantically loaded tokens to total prompt tokens, adjusted for redundancy and concreteness. Unlike prior prompt optimization techniques that add tokens (Chain of Thought), duplicate the prompt (Prompt Repetition), or reorder components (Instruction Placement Effect), SDE improves performance by removing or replacing low-information tokens while preserving or sharpening the semantic signal. Evaluated across five frontier models and seven benchmarks, ultra-dense prompts (SDE > 0.80) outperform diluted counterparts by an average of +8.4 percentage points with 0 additional tokens and 0 latency overhead. Combined with Instruction Placement Effect (IPE), the gain reaches +11.7 percentage points