Related papers: Temporal Anchoring in Deepening Embedding Spaces: …
Concurrent multiscale damage models are often used to quantify the impacts of manufacturing-induced micro porosity on the damage response of macroscopic metallic components. However, these models are challenged by major numerical issues…
Unsupervised video object segmentation has often been tackled by methods based on recurrent neural networks and optical flow. Despite their complexity, these kinds of approaches tend to favour short-term temporal dependencies and are thus…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
We study the hardmax limit of self-attention dynamics for token embeddings obtained in the zero-temperature ($\beta\to+\infty$) regime, and relate it to the finite-$\beta$ setting. In this limit, the update rule can be viewed as a…
Embeddings play an important role in end-to-end solutions for multi-modal language processing problems. Although there has been some effort to understand the properties of single-modality embedding spaces, particularly that of text, their…
We prove that an $\mathbb{R}$-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions $\mathbb{R}\to[0,1]$ if its fixed point set can be topologically embedded in the unit interval. This is a refinement…
We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carath\'eodory distance. Hence we obtain…
We study the closure of the convex hull of a compact set in a complete CAT(0) space. First we give characterization results in terms of compact sets and the closure of their convex hulls for locally compact CAT(0) spaces that are either…
Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation…
In this paper, we propose to learn temporal embeddings of video frames for complex video analysis. Large quantities of unlabeled video data can be easily obtained from the Internet. These videos possess the implicit weak label that they are…
In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both…
Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
We observe that embeddings into random metrics can be fruitfully used to study the $L_1$-embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new…
In this paper, we show empirical evidence on how to construct the optimal feature selection or input representation used by the input layer of a feedforward neural network for the propose of forecasting spatial-temporal signals. The…
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…
As a fundamental backbone for video generation, diffusion models are challenged by low inference speed due to the sequential nature of denoising. Previous methods speed up the models by caching and reusing model outputs at uniformly…