Related papers: On Machine Learning Knowledge Representation In Th…

We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…

We consider Representation Misdirection (RM), a class of large language model (LLM) unlearning methods that achieve forgetting by redirecting the forget-representations, that is, latent representations of forget-samples, toward a target…

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…

We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…

We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the…

A consistent description of images on the disk and of their transformations is given as elements of a vector space and of an operators algebra. The vector space of images on the disk $\mathbb{D}$ is the Hilbert space $L^2(\mathbb{D})$ that…

The machine learning (ML) techniques to predict unitarity (UNI) and bounded from below (BFB) constraints in multi-scalar models is employed. The effectiveness of this approach is demonstrated by applying it to the two and three Higgs…

There is an increasing interest in Quantum Machine Learning (QML) models, how they work and for which applications they could be useful. There have been many different proposals on how classical data can be encoded and what circuit…

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…

In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but…

Knowledge distillation is typically conducted by training a small model (the student) to mimic a large and cumbersome model (the teacher). The idea is to compress the knowledge from the teacher by using its output probabilities as…

We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the…

The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…

A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…

Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn…

The quantum measurement problem considered for the model of measuring system (MS) consist of measured state S (particle), detector D and information processing device (observer) $O$ interacting with S,D. For 'external' observer $O'$ MS…

Modeling has become a widespread, useful tool in mathematics applied to diverse fields, from physics to economics to biomedicine. Practitioners of modeling may use algebraic or differential equations, to the elements of which they attribute…

In this paper, we push forward the idea of machine learning systems whose operators can be modified and fine-tuned for each problem. This allows us to propose a learning paradigm where users can write (or adapt) their operators, according…

Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform…