This paper extends Bayesian probability theory by developing a multidimensional space of events (MDSE) theory that accounts for mutual influences between events and hypotheses sets. While traditional Bayesian approaches assume conditional independence between certain variables, real-world systems often exhibit complex interdependencies that limit classical model applicability. Building on established probabilistic foundations, our approach introduces a mathematical formalism for modeling these complex relationships. We developed the MDSE theory through rigorous mathematical derivation and validated it using three complementary methodologies: analytical proofs, computational simulations, and case studies drawn from diverse domains. Results demonstrate that MDSE successfully models complex dependencies with 15-20% improved prediction accuracy compared to standard Bayesian methods when applied to datasets with high interdimensionality. This theory particularly excels in scenarios with over 50 interrelated variables, where traditional methods show exponential computational complexity growth while MDSE maintains polynomial scaling. Our findings indicate that MDSE provides a viable mathematical foundation for extending Bayesian reasoning to complex systems while maintaining computational tractability. This approach offers practical applications in engineering challenges including risk assessment, resource optimization, and forecasting problems where multiple interdependent factors must be simultaneously considered.

The latent space of image generative models is a multi-dimensional space of compressed hidden visual knowledge. Its entity captivates computer scientists, digital artists, and media scholars alike. Latent space has become an aesthetic category in AI art, inspiring artistic techniques such as the latent space walk, exemplified by the works of Mario Klingemann and others. It is also viewed as cultural snapshots, encoding rich representations of our visual world. This paper proposes a double view of the latent space, as a multi-dimensional archive of culture and as a multi-dimensional space of potentiality. The paper discusses disentanglement as a method to elucidate the double nature of the space and as an interpretative direction to exploit its organization in human terms. The paper compares the role of disentanglement as potentiality to that of conditioning, as imagination, and confronts this interpretation with the philosophy of Deleuzian potentiality and Hume's imagination. Lastly, this paper notes the difference between traditional generative models and recent architectures.

In the real world, as the complexity of optimization problems continues to increase, there is an urgent need to research more efficient optimization methods. Current optimization algorithms excel in solving problems with a fixed number of dimensions. However, their efficiency in searching dynamic multi-dimensional spaces is unsatisfactory. In response to the challenge of cross-dimensional search in multi-dimensional spaces with varying numbers of dimensions, this study proposes a new optimization algorithm-Dynamic Dimension Wrapping (DDW) algorithm. Firstly, by utilizing the Dynamic Time Warping (DTW) algorithm and Euclidean distance, a mapping relationship between different time series across dimensions is established, thus creating a fitness function suitable for dimensionally dynamic multi-dimensional space. Additionally, DDW introduces a novel, more efficient cross-dimensional search mechanism for dynamic multidimensional spaces. Finally, through comparative tests with 31 optimization algorithms in dynamic multidimensional space search, the results demonstrate that DDW exhibits outstanding search efficiency and provides search results closest to the actual optimal solution.

Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a univariate signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. Our multidimensional space reconstruction method from an arbitrary received signal is proven to be agnostic vis-a-vis the encoding-decoding scheme, computation model, programming language, formal theory, the computable (or semi-computable) method of approximation to algorithmic complexity, and any arbitrarily chosen (computable) probability measure of the events. The method derives from the principles of an approach to Artificial General Intelligence capable of building a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We argue that this optimal and universal method of decoding non-random data has applications to signal processing, causal deconvolution, topological and geometric properties encoding, cryptography, and bio- and technosignature detection.

We introduce a univariate signal deconvolution method based on the principles of an approach to Artificial General Intelligence in order to build a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We investigate how non-random data may encode information about the physical properties, such as dimensions and length scales of the space in which a signal or message may have been originally encoded, embedded, or generated. Our multidimensional space reconstruction method is based on information theory and algorithmic probability, so that it is proven to be agnostic vis-a-vis the arbitrarily chosen encoding-decoding scheme, computable or semi-computable method of approximation to algorithmic complexity, and computational model. The results presented in this paper are useful for applications in coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. We argue that this method has the potential to be of great value in cryptography, signal processing, causal deconvolution, life and technosignature detection.

How similar are bears and bulls? If you ask a biologist, she might say that they are pretty similar, since they are both four-legged mammals found in North America. However, if you ask an economist, he might say they are polar opposites, since they are used to describe distinct stock market conditions. The unique way in which individuals organize their semantic knowledge, or general information gained through life experiences, could cause two people to judge the similarity between two animals in very different ways. Scientists have been trying to understand the structure of semantic knowledge for a long time, in large part because it may lead to deeper insights about human behavior.

To tackle climate change, scientists and advocates have called for a bevy of actions that include reducing fossil fuel use, electrifying transportation, reforming agriculture, and mopping up excess carbon dioxide from the atmosphere. But many of these challenges will be insurmountable without behind-the-scenes breakthroughs in materials science. Today's materials lack key properties needed for scalable climate-friendly technologies. Batteries, for example, require improved materials that can yield higher energy densities and longer discharge times. Without such improvements, commercial batteries won't be able to power mass-market electric vehicles and support a renewable-powered grid.

Welcome to the second stepping stone of Supervised Machine Learning. Again, this chapter is divided into two parts. Part 2 (here) we take on small coding exercise challenge. If you haven't read the Naive Bayes, I would suggest you to read it thorough here. A Support Vector Machine (SVM) is a discriminative classifier formally defined by a separating hyperplane.

PARIS – Designers of machine translation tools still mostly rely on dictionaries to make a foreign language understandable. But now there is a new way: numbers. Facebook researchers say rendering words into figures and exploiting mathematical similarities between languages is a promising avenue -- even if a universal communicator as seen in "Star Trek" remains a distant dream. Powerful automatic translation is a big priority for internet giants. Allowing as many people as possible worldwide to communicate is not just an altruistic goal, but also good business.

The following paper presents a method of comparing two sets of vectors. The method can be applied in all tasks, where it is necessary to measure the closeness of two objects presented as sets of vectors. It may be applicable when we compare the meanings of two sentences as part of the problem of paraphrasing. This is the problem of measuring semantic similarity of two sentences (group of words). The existing methods are not sensible for the word order or syntactic connections in the considered sentences. The method appears to be advantageous because it neither presents a group of words as one scalar value, nor does it try to show the closeness through an aggregation vector, which is mean for the set of vectors. Instead of that we measure the cosine of the angle as the mean for the first group vectors projections (the context) on one side and each vector of the second group on the other side. The similarity of two sentences defined by these means does not lose any semantic characteristics and takes account of the words traits. The method was verified on the comparison of sentence pairs in Russian.