arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.
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?
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.
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.
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.
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.
arXiv:2511. 02496v2 Announce Type: replace Abstract: We study latent geometry as an explicit component of representation quality in data-scarce learning.
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.
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 $\calE = \calM \times \R^d$.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2508. 04227v3 Announce Type: replace-cross Abstract: Vision-language models (VLMs), spanning predictive architectures to generative Multimodal Large Language Models (MLLMs), have revolutionized artificial intelligence through powerful cross-modal alignment and zero-shot generalization.
arXiv:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.