Related papers: The Memory Function Formalism: A Review
We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate…
Despite the success of neural models in solving reasoning tasks, their compositional generalization capabilities remain unclear. In this work, we propose a new setting of the structured explanation generation task to facilitate…
We propose an epistemic approach to formalizing statistical properties of machine learning. Specifically, we introduce a formal model for supervised learning based on a Kripke model where each possible world corresponds to a possible…
We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a Generalized Langevin Equation (GLE) for a general interacting many-body system. The resulting…
The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled…
Rote learning is a memorization technique based on repetition. Many researchers argue that rote learning hinders generalization because it encourages verbatim memorization rather than deeper understanding. This concern extends even to…
In [Phys. Rev. Lett. 127, 023001 (2021)] a reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting many-fermion systems. Here, we develop a solid foundation for this…
Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations…
The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of Kronecker product and what we have termed the `bra-flipper' operator.…
A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…
Deficits in working memory, which includes both the ability to learn and to retain information short-term, are a hallmark of many cognitive disorders. Our study analyzes data from a neuroscience experiment on animal subjects, where…
Reinforcement learning tasks are typically specified as Markov decision processes. This formalism has been highly successful, though specifications often couple the dynamics of the environment and the learning objective. This lack of…
The pre-trained foundation models (PFMs) have become essential for facilitating large-scale multimodal learning. Researchers have effectively employed the ``pre-train, prompt, and predict'' paradigm through prompt learning to induce…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
The formally exact framework of equilibrium Density Functional Theory (DFT) is capable of simultaneously and consistently describing thermodynamic and structural properties of interacting many-body systems in arbitrary external potentials.…
Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM…
Dynamic Fault Trees (DFTs) is a widely used failure modeling technique that allows capturing the dynamic failure characteristics of systems in a very effective manner. Simulation and model checking have been traditionally used for the…
In this paper we provide a simplified semantics for the logic KD45(G), i.e. the many-valued G\"odel counterpart of the classical modal logic KD45. More precisely, we characterize KD45(G) as the set of valid formulae of the class of…
We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the…
We present a numerical method to compute the approximation of the memory functions in the generalized Langevin models for collective dynamics of macromolecules. We first derive the exact expressions of the memory functions, obtained from…