The paper presents a statistical framework for Mixture-of-Experts (MoE) models, treating them as localized aggregation systems. It derives oracle risk bounds that separate approximation, expert‑learning, and router‑estimation errors for both dense and sparse routing with evolving experts. The authors also analyze how sparse Top‑K routing balances computational cost with performance, interpret gating geometrically, and explain how shared experts can capture common predictive structure while allowing routed experts to focus on local residuals.
By Siyuan He, Bokai Yang, Jie Hu, Ziwen Gao, Yuhong Yang
arXiv:2605. 17232v5 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology.
By Kelvin Kan, Xingjian Li, Benjamin J. Zhang, Tuhin Sahai, Stanley Osher, Markos A. Katsoulakis
arXiv:2607. 20540v1 Announce Type: cross Abstract: How should a diffusion model decide which noise levels to train on, and how much?
By Luca Ambrogioni, Giulio Franzese, Alberto Foresti, Gabriel Raya, Bac Nguyen, Georgios Batzolis, Yuhta Takida, Naoki Murata, Chieh-Hsin Lai, Yuki Mitsufuji
The paper investigates how routing decisions in sparse mixture-of-experts (MoE) models evolve across layers. By aligning router control subspaces with generalized orthogonal Procrustes analysis, the authors find that a single linear transition can predict routing states across depth with substantial accuracy, revealing a shared geometric structure. They further demonstrate that these canonical states preserve expert selection better than generic hidden representations and improve next‑step routing predictions, reducing negative log‑likelihood by up to 15.7% on OLMoE and 6.2% on Phi.
By Kirill Labzin, Stepan Kulibaba, Artem Dzhalilov, Artem Gorokhov
The paper studies how to choose sampling schedules for tau‑leaping in masked discrete diffusion models. By deriving an exact integral representation of the factorization error ε_fact in terms of a dependence density ρ, the authors develop estimators and recursive equations that identify the unique optimal schedule under a monotonicity condition. In the large‑scale limit, they provide explicit characterizations of the optimal smooth schedule and show that while optimizing smooth schedules can improve constants, it does not change the N/K scaling unless the dependence density degenerates, in which case asymptotic improvements are possible.
By Cecilia Secchi, Giacomo Zanella
arXiv:2505.20817v3 Announce Type: replace-cross
Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
By Taha El Bakkali El Kadi, Savelii Chezhegov, Aleksandr Beznosikov, Samuel Horv\'ath, Eduard Gorbunov
arXiv:2512. 23075v5 Announce Type: replace-cross Abstract: Policy gradient methods for Large Language Models optimize a policy $\pi_\theta$ via a surrogate objective computed from samples of a rollout policy $\pi_{\text{roll}}$.
By Yingru Li, Jiacai Liu, Jiawei Xu, Yuxuan Tong, Ziniu Li, Qian Liu, Baoxiang Wang
arXiv:2606. 01509v1 Announce Type: cross Abstract: Mixture-of-Experts (MoE) models scale by activating only a small subset of experts per token.
By Heng Zhao, Zilei Shao, Guy Van den Broeck, Zhe Zeng
arXiv:2607. 10592v1 Announce Type: new Abstract: Many geometric statistics and manifold learning pipelines routinely produce observations -- such as tangent vectors or local frames -- whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space.
By Swagatam Das, Vaclav Snasel
arXiv:2607. 28670v1 Announce Type: new Abstract: A stochastic Gumbel-Top-$K$ router defines, for every token of a mixture-of-experts (MoE) model, a \emph{routing law}: a distribution over ordered expert lists and mixture weights.
By Richard Yi Da Xu
arXiv:2609.39497v1 Announce Type: cross
Abstract: Randomized smoothing certifies the probability of a fixed output event as the center of Gaussian noise moves. Feasibility or confidence filtering rep...
By Syed Izhan Khilji, Alireza Furutanpey, Schahram Dustdar
The paper studies how to allocate a fixed computational budget across the denoising steps of diffusion models to improve sample quality at deployment. It shows that the expected benefit of evaluating multiple candidates at a step can be decomposed into a step‑specific sensitivity and a universal sample‑size factor, and that the optimal allocation follows a water‑filling structure. Experiments demonstrate that this allocation achieves the same quality as a uniform strategy while reducing function evaluations by 20–50%.
By Yuan Cao, Yifu Tang, Hangqi Li, Zeyu Zheng