Related papers: Algebraic Machine Learning
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this…
In the algorithm selection research, the discussion surrounding algorithm features has been significantly overshadowed by the emphasis on problem features. Although a few empirical studies have yielded evidence regarding the effectiveness…
The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Energy minimization methods are a classical tool in a multitude of computer vision applications. While they are interpretable and well-studied, their regularity assumptions are difficult to design by hand. Deep learning techniques on the…
We study the characterisation of efficient and non-efficient families of Grover's algorithms according to the majorization principle. We develop a geometrical interpretation based on the parameters that appears on these algorithms. Using…
Data subset selection from a large number of training instances has been a successful approach toward efficient and cost-effective machine learning. However, models trained on a smaller subset may show poor generalization ability. In this…
In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
Designing bounded-memory algorithms is becoming increasingly important nowadays. Previous works studying bounded-memory algorithms focused on proving impossibility results, while the design of bounded-memory algorithms was left relatively…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…
In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This…