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arXiv AI

Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering

arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.

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arXiv Machine Learning
Sep 11

GEOSTEER: Geodesic Optimization for Activation Steering in Large Language Models

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
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arXiv Machine Learning
Sep 7

Nested Inductive Bias Framework for SPD Manifold Learning

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
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arXiv Machine Learning
Jun 18

Riemannian MeanFlow for One-Step Generation on Manifolds

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
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arXiv Machine Learning
Sep 14

Geometric-to-Semantic Spherical Transfer Learning for Cortical Sulci Labeling

The paper introduces a Geometric-to-Semantic Spherical Transfer Learning framework for labeling cortical sulci on brain surfaces. It first pre‑trains a spherical encoder on ~30,000 unlabeled UK Biobank subjects using only curvature and depth, then injects sulcal fundi lines as a soft‑initialized Topological Prior Injector to bridge the geometric‑semantic gap. Experiments show the method surpasses fully supervised baselines, achieving a mean Dice score of 0.77 and delivering the largest gains on variable and tertiary sulci.

By Saeb Tounsi, Jo\"el Chavas, Pietro Gori, Vincent Frouin, Denis Rivi\`ere, Jean-Fran\c{c}ois Mangin
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