WavePhaseNet: A DFT-Based Method for Constructing Semantic Conceptual Hierarchy Structures (SCHS)

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

Calculating semantic textual similarity is a foundational task in natural language processing. Current large language models (LLMs) based methods typically rely on extracting last-layer hidden states with fixed dimensions to compute similarity for every text pairs. We argue that this paradigm is suffer from two limitations: (i) The last hidden layer encodes more general knowledge rather than just semantic knowledge, making it suboptimal for semantic similarity computation; (ii) The hidden layer dimensions of LLMs are generally very large, which introduces some redundancy and noise for representing semantics. In this work, we propose DySem, a novel training-free framework that investigates more semantic-related internal components of LLMs via multilingual consensus, and shifts away from static representation spaces in favor of dynamic, sample-specific semantic dimensions by constructing text-dependent joint semantic set and computes similarity over this shared dimensional subset. Extensive experiments across various LLMs show that our method consistently outperforms recent baselines while maintaining lower dimensions for similarity calculation. The code is released at https://github.com/szu-tera/DySem.

We introduce CAROL (Chain-based Adaptive Reconfiguration Over Lattices), a probabilistic framework for test-time hallucination reduction in large language models. Rather than relying on token-level uncertainty, CAROL defines a semantic uncertainty measure based on the consistency between generated responses and a trusted context, inducing a string-submodular objective over a lattice of textual sequences. This formulation enables hallucination mitigation to be cast as a Markov chain accept-reject process with provable convergence and near-optimality guarantees, allowing the model to iteratively refine outputs toward semantic consistency. By operating at the level of meaning, CAROL unifies hallucination detection and mitigation within a single framework. Empirical results on question answering and multi-agent reasoning benchmarks show that CAROL significantly reduces hallucinations and improves reliability and interpretability compared to likelihood-based and retrieval-augmented baselines, while maintaining competitive computational efficiency.