GeoSteer introduces a geometry-aware, optimization-based approach to norm-preserving activation steering in large language models. By formulating steering as a Riemannian optimization problem, it updates activations through a sequence of small geodesic steps guided by a learned nonlinear objective, avoiding fixed steering directions. Experiments on TruthfulQA, RealToxicityPrompts, and UltraFeedback show that GeoSteer consistently outperforms existing activation steering baselines, offering smoother, more stable, and more consistent steering behavior.
By Xuan Cuong Ngo, Hao Vo, Ngan Le
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
By Tushar Das
arXiv:2603. 10718v3 Announce Type: replace Abstract: Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE.
By Zichen Zhong, Haoliang Sun, Yukun Zhao, Yongshun Gong, Yilong Yin
arXiv:2609.10305v1 Announce Type: new
Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transfor...
By Fang Li
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
By Szczepan Konior, Alexandre Quemy, Przemys{\l}aw Klocek, Gr\'egoire Cattan, Bart{\l}omiej Sobieski
arXiv:2609.05575v1 Announce Type: new
Abstract: Understanding how concepts are encoded in the internal representations of machine learning models is a central problem in mechanistic interpretability,...
By Yiming Tang, Harshvardhan Saini, Samyak Jha, Huaming Chen, Xufeng Duan, Dianbo Liu