RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
By Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung
arXiv:2607. 05436v1 Announce Type: new Abstract: The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers?
By Bing Cheng, Yi-Shuai Niu, Howell Tong, Shing-Tung Yau
arXiv:2512. 18471v2 Announce Type: replace Abstract: Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference.
By Xin Li
arXiv:2606. 03022v1 Announce Type: cross 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.
By Mingkuan Zhao, Wentao Hu, Tianchen Huang, Yuheng Min, Suquan Chen, Yide Gao, Yanbo Zhai, Shuangyong Song, Xuelong Li
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
HoloAegis is a minimally parametric topological inference framework that uses frozen representations to map text onto the unit sphere and makes decisions via Gibbs‑Boltzmann free‑energy differences over pre‑computed anchor centroids. On a frozen three‑benchmark protocol, it matches WildGuard‑7B on toxicity, outperforms it on harmful behaviors, but underperforms on oversafety detection, while ShieldGemma‑2B fails on indirect harms. The study demonstrates that geometric guardrails can substitute for LLM judges in some cases and must defer to them in others, with anchor banks reducing score variance and boundary displacement.
By Tak Ho Alex Li, Kaijie Liu, Lik-Hang Lee, Kin Chung Ho, Ping Shum, Michael K. Ng
arXiv:2608. 08485v1 Announce Type: new Abstract: Current LLM safety guardrails face a fundamental tension: fine-tuning distorts pre-trained representations while generative judges incur prohibitive inference costs.
By Tak Ho Alex Li, Kaijie Liu, Lik-Hang Lee, Kin Chung Ho, Ping Shum, Michael K. Ng
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.
By Narmeen Oozeer, Shivam Raval, Philip Quirke, Manikandan Ravikiran, Jeff Phillips, Shriyash Upadhyay, Amirali Abdullah
arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
By Ronald Katende
arXiv:2608. 09385v1 Announce Type: cross Abstract: Generative AI models are primarily designed to imitate the data distribution, an objective that neither corrects diversity lost by a learned generator nor defines how generation should extend beyond the diversity of the data itself.
By Hossein Goli, Farzan Farnia, Amin Gohari
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. 17146v1 Announce Type: cross Abstract: We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle $\calE = \calM \times \R^d$.
By Zhihua Liang