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

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

Resonant Context Anchoring: Decoupling Attention Routing and Signal Gain at Inference Time

Large Language Models (LLMs) frequently exhibit "contextual disregard" when faced with input evidence that conflicts with their internal parametric memory, leading to persistent factual hallucinations. Existing mitigation strategies primarily rely on suppressing specific neuron activations or employing computationally expensive contrastive decoding mechanisms, which often result in increased perplexity or significantly elevated inference latency. To address these limitations, we propose Resonant Context Anchoring (RCA), a lightweight inference-time intervention method grounded in the perspective of residual stream signal dynamics. RCA aims to resolve the signal attenuation of external evidence during its propagation through deep networks. The core mechanism involves the orthogonal decoupling of routing logic and information magnitude within the self-attention module. By utilizing raw pre-softmax attention scores as an instantaneous metric of semantic alignment, we construct a dynamic gain field via non-linear rectification to selectively amplify the norms of value vectors corresponding to context tokens, without altering the attention probability distribution. This mechanism effectively elevates the signal-to-noise ratio (SNR) of input evidence within the residual stream mixture, thereby robustly anchoring the generation trajectory to the truthful context during inference. Extensive experiments on the Llama-3 model series demonstrate that RCA significantly improves contextual faithfulness across multiple factual consistency and strong knowledge-conflict tasks, effectively suppressing parametric hallucinations. Furthermore, results confirm that as a training-free and computationally negligible plug-and-play module, RCA achieves a Pareto improvement in faithfulness and fluency while maintaining the model's general language understanding capabilities.