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We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes…
We describe a generalization of the concept of a pc presentation that applies to groups with a nontrivial solvable radical. Such a representation can be much more efficient in terms of memory use and even of arithmetic, than permuattion and…
A new family of Gaussian-type SIGMA basis sets, termed reduced SIGMA basis sets, is introduced and preliminarily tested. Sharing the same composition as Dunning basis sets, they enhance performance by reducing linear dependencies in large…
Token merging can effectively accelerate various vision systems by processing groups of similar tokens only once and sharing the results across them. However, existing token grouping methods are often ad hoc and random, disregarding the…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
We propose a new approach to interactive image segmentation based on some properties of a family of quadratic optimization problems related to dominant sets, a well-known graph-theoretic notion of a cluster which generalizes the concept of…
We show that pre-trained Generative Adversarial Networks (GANs) such as StyleGAN and BigGAN can be used as a latent bank to improve the performance of image super-resolution. While most existing perceptual-oriented approaches attempt to…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
Video Large Language Models (Video LLMs) achieve strong performance on video understanding tasks but suffer from high inference costs due to the large number of visual tokens. We propose KiToke, a training-free, query-agnostic token…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
We provide a method for counting number fields of fixed Galois group ordered by arbitrary inertial invariants using analytic techniques from the study of multiple Dirichlet series. We prove unconditional results for infinitely many new…
This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm. This transformation may be used to generate new labeled data{}sets from existent ones. It is more flexible that Kleinberg…
This paper provides norm-based generalization bounds for the Transformer architecture that do not depend on the input sequence length. We employ a covering number based approach to prove our bounds. We use three novel covering number bounds…
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.
We study stochastic mixed integer programs with both first-stage and recourse decisions involving mixed integer variables. A new family of Lagrangian cuts, termed ``ReLU Lagrangian cuts," is introduced by reformulating the nonanticipativity…
RGB-based imitation learning requires many demonstrations to generalize to unseen objects or scenes, motivating research into intermediate representations to improve generalization for robotic manipulation. Visual foundation models enable…
Search applications often display shortened sentences which must contain certain query terms and must fit within the space constraints of a user interface. This work introduces a new transition-based sentence compression technique developed…
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an algorithm for a family of plane curves whose…