The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.
By Mark Kozdoba, Shie Mannor
The paper challenges the common assumption that the successor measure in reinforcement learning is approximately low-rank, showing instead that a low-rank structure emerges in a shifted successor measure that ignores initial transitions. It provides finite-sample guarantees for estimating this low-rank approximation, introduces Type II Poincaré inequalities to bound spectral recoverability, and links the necessary shift to the decay of high-order singular values and local mixing properties. Experiments confirm that shifting the successor measure improves goal-conditioned RL performance.
By Bastien Dubail, Stefan Stojanovic, Alexandre Prouti\`ere
arXiv:2607. 19855v1 Announce Type: new Abstract: Adversarial robustness is commonly evaluated with predefined attack ensembles, such as AutoAttack, at a single perturbation budget $\varepsilon$ and on a selective choice of perturbation norms.
By Luca Scionis, Luca Melis, Maura Pintor, Fabio Brau, Ambra Demontis, Giorgio Fumera, Fabio Roli, Battista Biggio
arXiv:2610.23343v1 Announce Type: new
Abstract: Low-rank adaptation (LoRA) has become the standard method for parameter-efficient fine-tuning of large pretrained models, yet theoretical explanations...
By Long Nguyen-Chi, Quynh Nguyen, Thanh Nguyen-Cung, Binh T. Nguyen
The paper presents the first provably efficient offline reinforcement learning algorithms for risk-sensitive settings using optimized certainty equivalents (OCE). It introduces two formulations—dynamic-OCE, applying OCE at each step, and static-OCE, applying a single OCE to cumulative rewards—and develops pessimistic value-iteration methods with tight sublinear suboptimality bounds in tabular and linear function approximation settings. The authors also establish minimax lower bounds, characterizing the fundamental limits of offline risk-sensitive RL.
By Hanzhen Wang, Boxiang Lyu, Zhongxiang Dai, Siyang Gao, Dake Zhang, Shuang Qiu
arXiv:2609.32002v2 Announce Type: replace
Abstract: The rank $r$ in LoRA is widely treated as a capacity control: a smaller rank is assumed to yield a simpler model that generalizes better. We show t...
By Babak Barazandeh
arXiv:2607. 08971v1 Announce Type: new Abstract: The stochastic linear bandit, where actions are represented as vectors and rewards are linear, is a central paradigm for sequential decision making.
By Gautam Dasarathy, Vineet Gattani, Lalit Jain
The paper introduces REP-PD-TEG, a representation‑learning algorithm for low‑rank continuous‑state constrained Markov Decision Processes (CMDPs) that achieves optimal ≥O(√K) regret in the soft cumulative‑violation setting while maintaining a ≥O(K^{3/4}) sample bound when exploratory actions are penalised. For the stricter hard cumulative‑violation scenario, REP-PD-H-TEG is proposed, which uses a bonus‑corrected lower‑confidence utility certificate and a stabilized dual search to guarantee both regret and hard‑violation bounds. Together, these methods provide the first theoretically guaranteed representation‑learning framework for low‑rank continuous‑state CMDPs with both soft and hard violation controls.
By Chenhao Zhou, Chao Zhang, Wensong Bai, Hanbin Zhao, Hui Qian
The paper introduces a deterministic Simulated Oracle Direction (SOD) framework that enables escaping spurious local minima in non‑convex low‑rank matrix sensing without explicit tensor lifting. By projecting over‑parameterized escape directions back into the original parameter space, the method guarantees a strict decrease in objective value from existing local minima. Experiments show reliable escape from local minima and convergence to global optima with minimal computational overhead compared to explicit over‑parameterization.
By Tianqi Shen, Jinji Yang, Junze He, Kunhan Gao, Zeyu Zheng, Ziye Ma
arXiv:2607. 06643v1 Announce Type: cross Abstract: Backdoor attacks severely threaten large-scale AI models.
By Issam Seddik, Sami Souihi, Mohamed Tamaazousti, Sara Tucci Piergiovanni
The paper addresses the limitations of spectral dimension reduction for dynamical systems composed of weakly interacting components, where standard rank‑based methods either require exponentially many modes or omit entire components (a phenomenon termed linear masking). It proposes scoring the σ‑algebra generated by coordinates instead of individual modes, using a χ²‑divergence criterion that guarantees an embedding with twice the intrinsic dimension captures the full operator spectrum. Experiments on benchmark systems show that this algebraic approach recovers masked components and enables accurate prediction from few labels, outperforming traditional rank‑based and VAMP methods.
arXiv:2606. 00002v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) decision engines routinely output nominally optimal plans for high-stakes industrial systems.
By Yi-Xiang Hu