arXiv AI
Dynamical low-rank equilibrium computation for stochastic games between advanced persistent threats and moving target defense
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arXiv Machine Learning
Aug 20
Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems
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.
arXiv Machine Learning
Aug 31
Shift Before You Learn: Enabling Low-Rank Representations in Reinforcement Learning
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.
arXiv Machine Learning
Jul 23
Adversarial Frontiers: Minimum-Norm Attack Ensembles for Robustness Evaluation
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.
arXiv Machine Learning
Oct 19
How Finite-Rank Bottlenecks Shape the Low-Rank Adaptation Landscape
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...
arXiv AI
Oct 16
Provably Efficient Risk-Sensitive Offline Reinforcement Learning via Optimized Certainty Equivalents
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.
arXiv AI
Oct 21
What Does the Rank Buy? A Spectral and Distributional Analysis of Low-Rank Adaptation
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...