Related papers: Generation of Two-Layer Monotonic Functions

For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…

A fundamental aspect of behaviour is the ability to encode salient features of experience in memory and use these memories, in combination with current sensory information, to predict the best action for each situation such that long-term…

To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…

In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…

The synthesis of a metasurface exhibiting a specific set of desired scattering properties is a time-consuming and resource-demanding process, which conventionally relies on many cycles of full-wave simulations. It requires an experienced…

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…

A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The…

A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of…

We show that the problem of counting the number of $n$-variable unate functions reduces to the problem of counting the number of $n$-variable monotone functions. Using recently obtained results on $n$-variable monotone functions, we obtain…

Key to multitask learning is exploiting relationships between different tasks to improve prediction performance. If the relations are linear, regularization approaches can be used successfully. However, in practice assuming the tasks to be…

Heralded by the initial success in speech recognition and image classification, learning-based approaches with neural networks, commonly referred to as deep learning, have spread across various fields. A primitive form of a neural network…

Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information…

The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…

One of the challenges of open-ended learning in robots is the need to autonomously discover goals and learn skills to achieve them. However, when in lifelong learning settings, it is always desirable to generate sub-goals with their…

Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy…