Related papers: How Do Transformers "Do" Physics? Investigating th…
Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of…
Interpretability methods aim to understand the algorithm implemented by a trained model (e.g., a Transofmer) by examining various aspects of the model, such as the weight matrices or the attention patterns. In this work, through a…
Linear probes and sparse autoencoders consistently recover meaningful structure from transformer representations -- yet why should such simple methods succeed in deep, nonlinear systems? We show this is not merely an empirical regularity…
Highly accurate time-series vibration prediction is an important research issue for electric vehicles (EVs). EVs often experience vibrations when driving on rough terrains, known as torsional resonance. This resonance, caused by the…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
Self-oscillation is a phenomenon studied across many scientific disciplines, including the engineering of efficient heat engines and electric generators. We investigate the single electron shuttle, a model nano-scale system that exhibits a…
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. Keywords: Weil representation,…
Transformers serve as the foundational architecture for large language and video generation models, such as GPT, BERT, SORA and their successors. Empirical studies have demonstrated that real-world data and learning tasks exhibit…
Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to…
The torsional oscillator is the chief instrument for investigating supersolidity in solid 4He. These oscillators can be sensitive to the elastic properties of the solid helium, which show anomalies over the same range of temperature in…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions…
The work fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally. For the work both the transient and stationary state fluctuation theorems hold. The…
We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that…
Simulating the transient effects occurring in superconducting accelerator magnet circuits requires including the mutual electro-thermo-dynamic interaction among the circuit elements, such as power converters, magnets, and protection…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Transformers have demonstrated remarkable success across various applications. However, the success of transformers have not been understood in theory. In this work, we give a case study of how transformers can be trained to learn a classic…