相关论文: The Manifold of the Absolute: Religious Perenniali…

In this paper, we investigate the latent geometry of generative diffusion models under the manifold hypothesis. For this purpose, we analyze the spectrum of eigenvalues (and singular values) of the Jacobian of the score function, whose…

The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century there have been remarkable advances in the development of theory for this diversification, and the theory's success…

We describe a set of novel methods for efficiently sampling high-dimensional parameter spaces of physical theories defined at high energies, but constrained by experimental measurements made at lower energies. Often, theoretical models such…

'Capsule' models try to explicitly represent the poses of objects, enforcing a linear relationship between an object's pose and that of its constituent parts. This modelling assumption should lead to robustness to viewpoint changes since…

This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…

This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…

Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…

Estimating causal effects from observational data (at either an individual -- or a population -- level) is critical for making many types of decisions. One approach to address this task is to learn decomposed representations of the…

Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the…

As recent generative models can generate photo-realistic images, people seek to understand the mechanism behind the generation process. Interpretable generation process is beneficial to various image editing applications. In this work, we…

A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through…

Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that…

Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…

We show that the number of gods in a universe must equal the Euler characteristics of its underlying manifold. By incorporating the classical cosmological argument for creation, this result builds a bridge between theology and physics and…

Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…

Generative machine learning has emerged as a powerful tool for design representation and exploration. However, its application is often constrained by the need for large datasets of existing designs and the lack of interpretability about…

This work initiates the systematic study of explicit distributions that are indistinguishable from a single exponential-size combinatorial object. In this we extend the work of Goldreich, Goldwasser and Nussboim (SICOMP 2010) that focused…

Generative concept representations have three major advantages over discriminative ones: they can represent uncertainty, they support integration of learning and reasoning, and they are good for unsupervised and semi-supervised learning. We…

We develop a novel probabilistic generative model based on the variational autoencoder approach. Notable aspects of our architecture are: a novel way of specifying the latent variables prior, and the introduction of an ordinality enforcing…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…