Orthogonality
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Hallucinations as Orthogonal Noise: Inference-Time Manifold Alignment via Dynamic Contextual Orthogonalization
Announce Type: new Abstract: 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.
Embedding linear codes over Z4 into self-orthogonal codes
Announce Type: new Abstract: The purpose of this paper is to investigate the self-orthogonal embedding problem for linear codes over Z4. We propose several tight bounds on the length of the shortest self-orthogonal embedding over Z4, and determine the exact shortest self-orthogonal embedding length under specific conditions. As an example satisfying these conditions, we establish the exact length of the shortest self-orthogonal embedding for the quaternary Preparata codes.
On solving symmetric multi-type orthogonal non-negative matrix tri-factorization problem
arXiv:2606.08291v1 Announce Type: new Abstract: We study the symmetric multi-type orthogonal non-negative matrix tri-factorization problem, where several symmetric non-negative matrices are simultaneously approximated by factors of the form $GS_{i}G^{\top}$, with a shared non-negative and orthogonal factor $G$. This model is motivated by clustering and network analysis, where non-negativity improves interpretability and orthogonality gives a natural assignment-type structure to the latent...
OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality
arXiv:2606.08783v1 Announce Type: cross Abstract: Orthogonalized momentum updates, as used in Muon-style optimizers, have recently shown strong empirical stability in large-scale deep learning. However, existing orthogonalized methods are typically paired with constant or open-loop magnitude rules, and therefore do not explicitly calibrate their update magnitudes from the observed optimization trajectory.
POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation
arXiv:2603.05500v2 Announce Type: replace Abstract: Efficient and stable training of large language models (LLMs) remains a core challenge in modern machine learning systems. To address this challenge, Reparameterized Orthogonal Equivalence Training (POET), a spectrum-preserving framework that optimizes each weight matrix through orthogonal equivalence transformation, has been proposed. Although POET provides strong training stability, its original implementation incurs high memory...
Faster algorithms for k-Orthogonal Vectors in low dimension
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A Note on Stability for Orthogonalized Matrix Momentum with Client Sampling
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Signed Spiking Neuron Enabled by an Orthogonal-Easy-Axis Magnetic Tunnel Junction
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Multifidelity Proper Orthogonal Decomposition
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OrthoPhys: Physically Plausible Video Generation with Orthogonal-View Geometry Guidance
Announce Type: replace Abstract: Recent progress in video generation has led to substantial improvements in visual fidelity, yet ensuring physically consistent motion remains a fundamental challenge. Intuitively, this limitation can be attributed to the fact that real-world object motion unfolds in three-dimensional space, while video observations provide only partial, view-dependent projections of such dynamics. To address these issues, we propose OrthoPhys, a two-stage framework that...