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The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…
Model parameter synchronization across GPUs introduces high overheads for data-parallel training at scale. Existing parameter synchronization protocols cannot effectively leverage available network resources in the face of ever increasing…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are…
The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Let $\mathcal{P}$ be a subset of primes and for each prime $p\in \mathcal{P}$, consider a subset $\mathcal{L}_p$ of $\mathbb{Z}/p\mathbb{Z}$. We provide restriction estimates with integers $\leq N$ sifted by…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive…
The Cayley table representation of a group uses $\mathcal{O}(n^2)$ words for a group of order $n$ and answers multiplication queries in time $\mathcal{O}(1)$. It is interesting to ask if there is a $o(n^2)$ space representation of groups…
In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By combining generalized theta generating functions with a…
Matrix Lie groups provide a language for describing motion in such fields as robotics, computer vision, and graphics. When using these tools, we are often faced with turning infinite-series expressions into more compact finite series (e.g.,…
In this paper, we extend our prior research named DKIC and propose the perceptual-oriented learned image compression method, PO-DKIC. Specifically, DKIC adopts a dynamic kernel-based dynamic residual block group to enhance the transform…
We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to…
The article suggests a description of a system of tables with a set of special lists absorbing a semantics of data and reflects a fullness of data. It shows how their parallel processing can be constructed based on the descriptions. The…
We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than $\mathtt{A}_{n}$, these are the first explicit asymptotically sharp such bounds. The…
Adapting language models to new data distributions by simple finetuning is challenging. This is due to the rigidity of their subword tokenizers, which typically remain unchanged during adaptation. This inflexibility often leads to…