Related papers: Machine-Learning Kronecker Coefficients
We consider learning a predictor which is non-discriminatory with respect to a "protected attribute" according to the notion of "equalized odds" proposed by Hardt et al. [2016]. We study the problem of learning such a non-discriminatory…
We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition…
Graph learning, or network inference, is a prominent problem in graph signal processing (GSP). GSP generalizes the Fourier transform to non-Euclidean domains, and graph learning is pivotal to applying GSP when these domains are unknown.…
Neural network training is typically viewed as gradient descent on a loss surface. We propose a fundamentally different perspective: learning is a structure-preserving transformation (a functor L) between the space of network parameters…
The Krohn-Rhodes Theorem proves that a finite semigroup divides a wreath product of groups and aperiodic semigroups. Krohn-Rhodes complexity equals the minimal number of groups that are needed. Determining an algorithm to compute complexity…
Let $A$ be a finite-dimensional algebra over an algebraically closed field $\Bbbk$. For any finite-dimensional $A$-module $M$ we give a general formula that computes the indecomposable decomposition of $M$ without decomposing it, for which…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…
We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of…
Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…
This study proposes a cyclic-shift logistic sparse Kronecker product decomposition (SKPD) model for high-dimensional tensor data, enhancing the SKPD framework with a cyclic-shift mechanism for binary classification. The method enables…
Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic…
It is generally well understood that predictive classification and compression are intrinsically related concepts in information theory. Indeed, many deep learning methods are explained as learning a kind of compression, and that better…
We present a computational approach to studying the structure of the representation ring of the symmetric group in dimension six. The Kronecker coefficients and all power formulae of irreducible representations of $S_6$ are computed using…
A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for Kronecker coefficients, which are multiplicities of the decomposition of the tensor product of two \S_r-irreducibles into irreducibles.…
In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…
Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…