# Hallucinations as Orthogonal Noise: Inference-Time Manifold Alignment via Dynamic Contextual Orthogonalization

arXiv: https://arxiv.org/abs/2606.03022 · HTML: https://mlsanity.com/paper/2606.03022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 2 Jun 2026.

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

- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Entity-Based Knowledge Conflicts in Question Answering](https://mlsanity.com/paper/2109.05052/) (2021)
- [Trusting Your Evidence: Hallucinate Less with Context-aware Decoding](https://mlsanity.com/paper/2305.14739/) (2023)
- [Retrieval Head Mechanistically Explains Long-Context Factuality](https://mlsanity.com/paper/2404.15574/) (2024)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [FactKB: Generalizable Factuality Evaluation using Language Models Enhanced with Factual Knowledge](https://mlsanity.com/paper/2305.08281/) (2023)
- [In-Context Sharpness as Alerts: An Inner Representation Perspective for Hallucination Mitigation](https://mlsanity.com/paper/2403.01548/) (2024)
- [Mechanistic Understanding and Mitigation of Language Model Non-Factual Hallucinations](https://mlsanity.com/paper/2403.18167/) (2024)
- [The Benefits of Bad Advice: Autocontrastive Decoding across Model Layers](https://mlsanity.com/paper/2305.01628/) (2023)
- [DeCoRe: Decoding by Contrasting Retrieval Heads to Mitigate Hallucinations](https://mlsanity.com/paper/2410.18860/) (2024)
- [52B to 1T: Lessons Learned via Tele-FLM Series](https://mlsanity.com/paper/2407.02783/) (2024)
- [Mosaic Pruning: A Hierarchical Framework for Generalizable Pruning of Mixture-of-Experts Models](https://mlsanity.com/paper/2511.19822/) (2025)
- [MR-UIE: Multi-Perspective Reasoning with Reinforcement Learning for Universal Information Extraction](https://mlsanity.com/paper/2509.09082/) (2025)
- [Making Every Head Count: Sparse Attention Without the Speed-Performance Trade-off](https://mlsanity.com/paper/2511.09596/) (2025)

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

- [Multi-Objective Exploration and Preference Optimization via Mutual Information](https://mlsanity.com/paper/2607.01392/) (2026)

## Abstract (arXiv)

Hallucination in Large Language Models (LLMs), characterized by the generation of content inconsistent with contextual facts or logical constraints -- remains a persistent challenge for reliable deployment. In this work, we address this issue through a geometric framework rooted in the linear representation hypothesis. We propose that hallucinations manifest as orthogonal noise relative to the semantic manifold of the residual stream. Specifically, we hypothesize that while attention heads ideally propagate information congruent with the context subspace, hallucinations arise when specific heads introduce components orthogonal to this subspace, disrupting the coherence of the latent representation. Based on this formulation, we introduce Dynamic Contextual Orthogonalization (DCO), an inference-time intervention method. DCO utilizes the input residual stream as a dynamic context anchor to perform orthogonal decomposition on attention head outputs. To distinguish between context-aligned semantic updates and divergent noise, DCO employs a layer-wise Z-score suppression mechanism that selectively attenuates outlier orthogonal components based on statistical distributions. Evaluations on Llama-3-8B and 70B across benchmarks such as XSum, NQ-Swap, and IFEval demonstrate that DCO achieves superior contextual faithfulness compared to state-of-the-art intervention baselines. Furthermore, DCO maintains high performance on knowledge-intensive tasks like TriviaQA and TruthfulQA, effectively mitigating the trade-off between hallucination suppression and parametric knowledge retention often observed in existing methods. Our findings validate the geometric interpretation of hallucinations and establish DCO as a computationally efficient approach for enforcing manifold alignment.Our code is available at https://github.com/Harry-Miral/DCO