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

TL;DR

The paper introduces the Semantic Density Effect (SDE), showing that prompts with higher semantic information per token lead to more accurate and focused outputs across various large language models.

Contribution

It defines SDE as a measure of semantic content per token and demonstrates that optimizing for higher SDE improves LLM performance without extra tokens or latency.

Findings

Ultra-dense prompts (SDE > 0.80) outperform diluted prompts by +8.4 percentage points.

Combining SDE with Instruction Placement Effect yields a +11.7 percentage point improvement.

SDE outperforms prior prompt optimization techniques by removing low-information tokens.

Abstract

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