相关论文: Information Geometry of Bounded Rationality: Entro…

We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…

Bounded rationality investigates utility-optimizing decision-makers with limited information-processing power. In particular, information theoretic bounded rationality models formalize resource constraints abstractly in terms of relative…

Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that…

This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…

We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…

We generalize the information lattice, originally defined for one-dimensional open-boundary chains, to characterize quantum many-body states in higher-dimensional geometries. In one dimension, the information lattice provides a position-…

We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…

It is here proposed a geometric approach for the problem of describing entropy in a quantum system. We make use of an extension of tensor calculus called morphogenetic calculus. By using such formalism we express the entropy of a quantum…

We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…

Formalizations of quantum information theory in category theory and type theory, for the design of verifiable quantum programming languages, need to express its two fundamental characteristics: (1) parameterized linearity and (2) metricity.…

Modified dispersion relations (MDRs) arise in many quantum-gravity approaches, often in non-polynomial or non-analytic form beyond the reach of effective field theory (EFT). Logarithmic, exponential and trigonometric MDRs appear in causal…

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…

Probabilistic graphical models with frustration exhibit rugged energy landscapes that trap iterative optimization dynamics. These landscapes are shaped not only by local interactions, but crucially also by the global loop structure of the…

We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes…

Modern machine learning relies on a collection of empirically successful but theoretically heterogeneous regularization techniques, such as weight decay, dropout, and exponential moving averages. At the same time, the rapidly increasing…

Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…

This presentation's Part 3 studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational…

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…

Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…

In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…