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2,653 papers
This work considers the setting where $D$ is a linear differential operator and analyzes a physics-informed kernel estimator combining value observations and differential observations to derive physically consistent rates in a stronger norm that jointly controls the errors in $\hat u$ and $D\hat u$.
This paper derives explicit Wasserstein stability bounds that quantify the effect of relative graph perturbations on the generated distributions and introduces a principled framework for designing stable graph filters that preserve the smoothing behavior of graph heat diffusion, while boosting structural stability.
This paper provides a self-contained proof of the rank of the pathlifting Jacobian of a DAG ReLU network by performing an induction on the network's number of hidden nodes. In fact, the induction is elementary, and the key recipe is to consider the skeleton matrix of the network, a sparse matrix encoding the network pa...
This paper introduces the technique of "persistence of memory" to greatly extend and improve the random subspace methods, and establishes to the knowledge the first theoretical analysis of classical SSD methods for sparse functions.
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We study the convergence of Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known up to a normalisation constant. By combining Wasserstein transport with Fisher-Rao birth-death dynamics, WFR flows balance exploration and selection. These flows have been recognised as a promising...
A new single-loop algorithmic framework for smooth nonconvex--concave minimax optimization and a lower bound of $\Omega(L^2D_Y\Delta_\phi\varepsilon^{-3})$ for optimization stationarity over projected zero-respecting first-order methods is established.
Manifold-Based Clustering (MBC) is proposed, which returns an explicit bracket interval to quantify the underlying data uncertainty, and suggests that ambiguity in cluster number is often intrinsic, and should be quantified rather than resolved.
It is proved that a family of such deletion sets of cardinality \(q\) has size at most \(\exp(8k+2q)\).
METALICA, which implements Metadynamics on a pretrained diffusion model via Replica Exchange, is introduced, which implements Metadynamics on a pretrained diffusion model via Replica Exchange and accumulates a bias potential along a Collective Variable, repels new samples from previous ones through biased sampling, and...
In an important recent work, Blanc (2026) gave an algorithm for robustly learning Boolean concept classes with respect to a fixed distribution that outputs a (randomized) classifier achieving the optimal error of $\eta + \varepsilon$ where $\eta$ is the noise rate. In contrast, it is well known that deterministic hypot...
Deep spline superposition networks face a tension between approximation order and stability across depth. We study approximation under a hard layerwise Lipschitz budget, and organise it around two quantities: the factorisation stability complexity of a given deep factorisation, and the budget-compatible approximation c...
These are the first non-asymptotic R\'enyi-divergence tracking bounds for Langevin dynamics with discrete target updates for Langevin diffusion and Langevin Monte Carlo.
MIT Statistics and Data Science Center Director Alexander (Sasha) Rakhlin shares important considerations for departments and institutions.
MIT Statistics and Data Science Center Director Alexander (Sasha) Rakhlin shares important considerations for departments and institutions.
MIT Statistics and Data Science Center Director Alexander (Sasha) Rakhlin shares important considerations for departments and institutions.
By rethinking how large cloud computing systems operate, Associate Professor Christina Delimitrou seeks to make data centers more energy efficient.
As director, Bourg has focused on digital access, open and equitable scholarly publishing, and expanded support for data-intensive research.
Jennifer Neville did not want to go into computer science—but that’s exactly where she landed. Neville discusses the starts and stops that led to her professional sweet spot and her work identifying “surprising failures” making it hard for AI to handle complexity. The post What AI gets wrong and what failure teaches us appeared first on Microsoft Research.
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