Related papers: Metriplector: From Field Theory to Neural Architec…

The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…

Understanding the internal representations and decision mechanisms of deep neural networks remains a critical open challenge. While existing interpretability methods often identify influential input regions, they may not elucidate how a…

This study harnesses the embodied intelligence of mechanical metamaterials to sense and process environmental vibrations with minimal digital computation. Using physical reservoir computing (PRC), we turn the metamaterial and its nonlinear…

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…

We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…

A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…

In a physical neural system, backpropagation is faced with a number of obstacles including: the need for labeled data, the violation of the locality learning principle, the need for symmetric connections, and the lack of modularity.…

Implicit neural field generating signed distance field representations (SDFs) of 3D shapes have shown remarkable progress in 3D shape reconstruction and generation. We introduce a new paradigm for neural field representations of 3D scenes;…

The human brain is a dynamical system whose extremely complex sensor-driven neural processes give rise to conceptual, logical cognition. Understanding the interplay between nonlinear neural dynamics and concept-level cognition remains a…

This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…

Many complex physical systems admit natural decomposition into an exactly solvable component and a perturbative correction. Rather than training neural networks to learn complete trajectories from scratch, we introduce Neural Network…

In this paper, we present a new framework for addressing the nonlinear Landau collision operator in terms of particle-in-cell methods. We employ the underlying metriplectic structure of the collision operator and, using a macro particle…

We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…

We consider problems in sequential decision making with natural multi-level structure, where sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure has remained a…

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on…

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional activation functions. Our proposed architecture, SPDER, is a simple…

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

How does the neocortex learn and develop the foundations of all our high-level cognitive abilities? We present a comprehensive framework spanning biological, computational, and cognitive levels, with a clear theoretical continuity between…

The mnesor theory is the adaptation of vectors to artificial intelligence. The scalar field is replaced by a lattice. Addition becomes idempotent and multiplication is interpreted as a selection operation. We also show that mnesors can be…

Neural networks are trained by choosing an architecture and training the parameters. The choice of architecture is often by trial and error or with Neural Architecture Search (NAS) methods. While NAS provides some automation, it often…