Related papers: Invariant polynomials and machine learning
Building upon works of Hironaka, Bierstone-Milman, Villamayor and Wlodarczyk, we give an a priori estimate for the complexity of the simplified Hironaka algorithm. As a consequence of this result, we show that there exists canonical…
Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric…
In many classification problems a classifier should be robust to small variations in the input vector. This is a desired property not only for particular transformations, such as translation and rotation in image classification problems,…
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…
Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…
This paper is the confluence of two streams of ideas in the literature on generating numerical invariants, namely: (1) template-based methods, and (2) recurrence-based methods. A template-based method begins with a template that contains…
Negative binomial regression is essential for analyzing over-dispersed count data in in comparative studies, but parameter estimation becomes computationally challenging in large screens requiring millions of comparisons. We investigate…
Many machine learning techniques rely on minimizing the covariance between output feature dimensions to extract minimally redundant representations from data. However, these methods do not eliminate all dependencies/redundancies, as…
We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…
This work presents the first statistical performance guarantees for group-invariant generative models. Many real data, such as images and molecules, are invariant to certain group symmetries, which can be taken advantage of to learn more…
Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time, where variational autoencoders, a specialized type of neural network, enable the Bayesian estimation of model…
Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training…
The decremented learning algorithms are required in machine learning, to prune redundant nodes and remove obsolete inline training samples. In this paper, an efficient decremented learning algorithm to prune redundant nodes is deduced from…
In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts…
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…
In machine learning, the use of an artificial neural network is the mainstream approach. Such a network consists of layers of neurons. These neurons are of the same type characterized by the two features: (1) an inner product of an input…
In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural…