Related papers: Einstein Fields: A Neural Perspective To Computati…

Neural implicit shape representations are an emerging paradigm that offers many potential benefits over conventional discrete representations, including memory efficiency at a high spatial resolution. Generalizing across shapes with such…

This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Reconstructing neural radiance fields with explicit volumetric representations, demonstrated by Plenoxels, has shown remarkable advantages on training and rendering efficiency, while grid-based representations typically induce considerable…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…

Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are…

Inversion of gravity data is an important method for investigating subsurface density variations relevant to mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here…

Advances in neural operators have introduced discretization invariant surrogate models for PDEs on general geometries, yet many approaches struggle to encode local geometric structure and variable domains efficiently. We introduce enf2enf,…

This paper introduces Multidimensional Task Learning (MTL), a unified mathematical framework based on Generalized Einstein MLPs (GE-MLPs) that operate directly on tensors via the Einstein product. We argue that current computer vision task…

Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on…

Implicit Neural Representations (INRs) have emerged as a paradigm in knowledge representation, offering exceptional flexibility and performance across a diverse range of applications. INRs leverage multilayer perceptrons (MLPs) to model…

The widespread use of Deep Neural Networks (DNNs) has recently resulted in their application to challenging scientific visualization tasks. While advanced DNNs demonstrate impressive generalization abilities, understanding factors like…

Every emission of radiation in gravity also includes a nonwavelike component that leaves a permanent change in proper distances of the spacetime it travels through. This phenomenon is known as gravitational displacement memory. Building up…

Weight Space Learning (WSL), which frames neural network weights as a data modality, is an emerging field with potential for tasks like meta-learning or transfer learning. Particularly, Implicit Neural Representations (INRs) provide a…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., a part unified with fixtures).…

We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…