Related papers: Evolution: A Unified Formula for Feature Operators…
The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…
This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…
By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
We present a new approach to modeling visual attributes. Prior work casts attributes in a similar role as objects, learning a latent representation where properties (e.g., sliced) are recognized by classifiers much in the way objects (e.g.,…
Fine-tuning pre-trained language models, particularly large language models, demands extensive computing resources and can result in varying performance outcomes across different domains and datasets. This paper examines the approach of…
One of the roots of evolutionary computation was the idea of Turing about unorganized machines. The goal of this work is the development of foundations for evolutionary computations, connecting Turing's ideas and the contemporary state of…
Feature transformation aims to reconstruct the feature space of raw features to enhance the performance of downstream models. However, the exponential growth in the combinations of features and operations poses a challenge, making it…
Feature interaction selection is a fundamental problem in commercial recommender systems. Most approaches equally enumerate all features and interactions by the same pre-defined operation under expert guidance. Their recommendation is…
Recent studies show that ensemble methods enhance the stability and robustness of unsupervised learning. These approaches are successfully utilized to construct multiple clustering and combine them into a one representative consensus…
Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We…
Recent state-of-the-art methods for point cloud processing are based on the notion of point convolution, for which several approaches have been proposed. In this paper, inspired by discrete convolution in image processing, we provide a…
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
Large kernels make standard convolutional neural networks (CNNs) great again over transformer architectures in various vision tasks. Nonetheless, recent studies meticulously designed around increasing kernel size have shown diminishing…
The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…
Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for analyzing systems…
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…