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A unified abstract regularity lemma
Combinatorics [Submitted on 4 Jun 2026] Title:A unified abstract regularity lemma View PDF HTML (experimental)Abstract:The goal of this short note is to prove a unified abstract regularity lemma which recovers Szemerédi's graph regularity lemma, Green's arithmetic regularity lemma, and a regularity lemma for Boolean functions as direct corollaries. Current browse context: math.
A high-order regularization of the non-linear shallow water equations with weakly singular shock waves and its approximation by finite volume methods
arXiv:2606.01200v1 Announce Type: cross Abstract: Considered herein is a high-order regularization of the nonlinear shallow water equations within the framework of water wave theory. The regularized system is Galilean invariant and its solutions maintain an energy level that closely matches that of the nonlinear shallow water equations.
VISReg: Variance-Invariance-Sketching Regularization for JEPA training
Announce Type: new Abstract: Self-supervised learning methods prevent embedding collapse via modeling heuristics or explicit regularization of the embedding space. Among the latter, VICReg decomposes regularization into variance and covariance objectives, offering flexibility and interpretability. However, covariance captures only second-order statistics -- encouraging decorrelation but failing to enforce the full distributional shape needed for stable training.
RADE: Random Add-Drop Edge as a Regularizer
arXiv:2606.00757v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) suffer from overfitting and over-squashing of long-range information. Stochastic graph augmentations (e.g., edge deletion) regularize training against overfitting but can introduce train-inference misalignment and do not improve over-squashing. In contrast, rewiring methods improve connectivity to mitigate over-squashing, but are not designed to regularize training.
CAREF: Calibration-Aware Regularization for Explanation Faithfulness Without Rationale Supervision
Announce Type: replace Abstract: We introduce CAREF, a parameter-efficient fine-tuning framework that jointly optimizes predictive accuracy and explanation faithfulness via calibration-aware regularization. At its core, CAREF couples entropy-based calibration with token-level sparsity control through a single unified loss, the Calibration-Aware Regularization for Explanation Faithfulness (LSCED), without requiring rationale supervision. Evaluated on four NLE benchmarks (COS-E, ECQA, ComVE,...
Counting Hamiltonian Paths in 3-Regular Planar Graphs
Combinatorics [Submitted on 5 Jun 2026] Title:Counting Hamiltonian Paths in 3-Regular Planar Graphs View PDF HTML (experimental)Abstract:We introduce two infinite families of 3-regular planar graphs. Both families are conceptual adversaries to the Pohl-Warnsdorf algorithm for finding Hamiltonians.
Implicit Regularization for Multi-label Feature Selection
arXiv:2411.11436v2 Announce Type: replace Abstract: In this paper, we address the problem of feature selection in the context of multi-label learning, by using a new estimator based on implicit regularization and label embedding. Unlike the sparse feature selection methods that use a penalized estimator with explicit regularization terms such as $l_{2,1}$-norm, MCP or SCAD, we propose a simple alternative method via Hadamard product parameterization. In order to guide the feature selection...
Building Generalization Into Behavior Generation Via Adaptive Compositions of Regularities
arXiv:2605.31110v1 Announce Type: new Abstract: Generalization in robotics requires prior knowledge about how the world is structured, yet this structure changes from one situation to the next. This paper investigates the proposition that generalization arises from adaptively composing regularities -- predictable relationships within the robot-environment system -- into situation-appropriate structures for behavior generation. We examine this proposition by analyzing the mechanism in AICON...
Global Convergence of Wasserstein Policy Gradient for Entropy-Regularized Reinforcement Learning
Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions. For the entropy-regularized RL objective, WPG evolves each state-conditional policy by transporting it along the action gradient of the soft Q-function together with a Langevin-type diffusion. Despite its appeal for continuous-control problems, its global convergence properties remain poorly...
Just 90 minutes of one regular exercise per week could lower early death risk, study finds
Just 90 minutes of one regular exercise per week could lower early death risk, study finds A major long-term study has found that one particular exercise is linked to lower mortality rates and could make a significant difference to your health New research reveals that just 90 minutes to two hours of weight training weekly could substantially cut the risk of premature death, a major long-term study has found. The findings, published in the British Journal of Sports Medicine, show that...