Related papers: Real Analytic Machines and Degrees

Boltzmann Machines (BMs) are graphical models with interconnected binary units, employed for the unsupervised modeling of data distributions. When trained on real data, BMs show the tendency to behave like critical systems, displaying a…

Attention-based encoder-decoder architectures such as Listen, Attend, and Spell (LAS), subsume the acoustic, pronunciation and language model components of a traditional automatic speech recognition (ASR) system into a single neural…

Binary determination of the presence of objects is one of the problems where humans perform extraordinarily better than computer vision systems, in terms of both speed and preciseness. One of the possible reasons is that humans can skip…

We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…

This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their…

Quasi-separable matrices are a class of rank-structured matriceswidely used in numerical linear algebra and of growing interestin computer algebra, with applications in e.g. the linearization ofpolynomial matrices. Various representation…

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs…

This note is a survey of various results on the capabilities of unique hard attention transformers encoders (UHATs) to recognize formal languages. We distinguish between masked vs. non-masked, finite vs. infinite image and general vs.…

A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…

Recent advancements in Large Reasoning Models (LRMs), such as OpenAI's o1/o3 and DeepSeek-R1, have demonstrated remarkable performance in specialized reasoning tasks through human-like deliberative thinking and long chain-of-thought…

Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from…

This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical sets, namely blow-spherical equivalence and we receive several…

Large Language Models (LLMs) are increasingly used as autonomous agents in complex, long-horizon applications, where effective memory is critical for sustained performance. Yet existing memory benchmarks are largely dialogue-centric, while…

We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to…

We examine the relation of BSS-reducibility on subsets of the real numbers. The question was asked recently (and anonymously) whether it is possible for the halting problem H in BSS-computation to be BSS-reducible to a countable set.…