Related papers: How Do Transformers "Do" Physics? Investigating th…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
Transformers have significantly advanced the field of natural language processing, but comprehending their internal mechanisms remains a challenge. In this paper, we introduce a novel geometric perspective that elucidates the inner…
Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile…
The states of a planar oscillator are separated to a vibrational mode, containing a zero-point energy, and a rotational mode without the zero-point energy, but having a conserved angular momentum. On the basis of the analysis of properties…
Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…
We discuss various continuous and discrete symmetries of the supersymmetric simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show their relevance in the context of mathematics of differential geometry. We show the…
Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for…
We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form from the observation of a single solution trajectory. We perform extensive evaluations on two…
If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative…
Model transformations operate on models conforming to precisely defined metamodels. Consequently, it often seems relatively easy to chain them: the output of a transformation may be given as input to a second one if metamodels match.…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
Understanding Transformer-based models has attracted significant attention, as they lie at the heart of recent technological advances across machine learning. While most interpretability methods rely on running models over inputs, recent…
Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…
Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…
Transformers have significantly impacted domains like natural language processing, computer vision, and robotics, where they improve performance compared to other neural networks. This survey explores how transformers are used in…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Precise modelling of a signal in processes with multiple observables, exhibiting a complex dependency on the underlying parameters, is often a difficult and challenging task. Predicting the results of experimental measurements in…
A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius $R.$ When hard…
Simulators are a critical component of modern robotics research. Strategies for both perception and decision making can be studied in simulation first before deployed to real world systems, saving on time and costs. Despite significant…
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to…