# The First Drop of Ink: Nonlinear Impact of Distracting Information in Long-Context Reasoning

arXiv: https://arxiv.org/abs/2605.10828 · HTML: https://mlsanity.com/paper/2605.10828/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- Retrieval-augmented generation / [RAG robustness and adaptive retrieval](https://mlsanity.com/rag/rag-robustness-and-adaptive-retrieval/)
- LLM agents and tool use / [Agent memory systems](https://mlsanity.com/agents/agent-memory-systems/)

## Builds on (most cited first, 9 of 9)

- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [∞Bench: Extending Long Context Evaluation Beyond 100K Tokens](https://mlsanity.com/paper/2402.13718/) (2024)
- [Agentic Retrieval-Augmented Generation: A Survey on Agentic RAG](https://mlsanity.com/paper/2501.09136/) (2025)
- [From Web Search towards Agentic Deep Research: Incentivizing Search with Reasoning Agents](https://mlsanity.com/paper/2506.18959/) (2025)
- [Lost in the Noise: How Reasoning Models Fail with Contextual Distractors](https://mlsanity.com/paper/2601.07226/) (2026)
- [Hidden in the Haystack: Smaller Needles are More Difficult for LLMs to Find](https://mlsanity.com/paper/2505.18148/) (2025)
- [A Controllable Examination for Long-Context Language Models](https://mlsanity.com/paper/2506.02921/) (2025)
- [Learning to Focus: Focal Attention for Selective and Scalable Transformers](https://mlsanity.com/paper/2511.06818/) (2025)

## Abstract (arXiv)

As large language models are increasingly deployed in retrieval-augmented generation and agentic systems that accumulate extensive context, understanding how distracting information affects long-context performance becomes critical. Prior work shows that semantically relevant yet misleading documents degrade performance, but the quantitative relationship between the proportion of distractors and performance remains unstudied. In this work, we systematically vary the hard-distractor proportion in fixed-length contexts, revealing a striking nonlinear pattern: as the proportion of hard distractors increases, performance drops sharply within the first small fraction, while the remainder of the range yields only marginal additional decline. We term this ''The First Drop of Ink'' effect, analogous to how a single drop of ink contaminates water. Our theoretical and empirical analyses grounded in attention mechanics show that hard distractors capture disproportionate attention even at small proportions, with diminishing marginal impact as their proportion grows. Controlled experiments further show that filtering gains mainly come from context-length reduction rather than distractor removal; substantial recovery requires reducing the hard-distractor proportion to near zero, highlighting the importance of upstream retrieval precision.