Related papers: Path Integral Solution for Dissipative Generative …
We analyze the relation between CP-divisibility and the lack of information backflow for an arbitrary -- not necessarily invertible -- dynamical map. It is well known that CP-divisibility always implies lack of information backflow.…
We develop a semiclassical method for the determination of the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N, based on the 1/N-expansion and the quantum-classical correspondence. The…
Many technologies emerging from quantum information science heavily rely upon the generation and manipulation of entangled quantum states. Here, we propose and demonstrate a new class of quantum interference phenomena that arise when states…
Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
Have you ever thought that you can be an intelligent painter? This means that you can paint a picture with a few expected objects in mind, or with a desirable scene. This is different from normal inpainting approaches for which the location…
Generating non-Gaussian states and converting them into traveling wavepackets is crucial yet challenging for scalable, fault-tolerant quantum computing. We present a hardware-efficient approach that simultaneously achieves both tasks by…
In slowly driven classical systems, work is a stochastic quantity and its probability distribution is known to satisfy the work fluctuation-dissipation relation, which states that the mean and variance of the dissipated work are linearly…
A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Transformer based language models exhibit intelligent behaviors such as understanding natural language, recognizing patterns, acquiring knowledge, reasoning, planning, reflecting and using tools. This paper explores how their underlying…
The response of dissipative systems to multi-chromatic fields exhibits generic properties which follow from the discrete time-translation symmetry of each driving component. We derive these properties and illustrate them with paradigmatic…
A class of dissipative dynamical systems evolving on smooth constraint hypersurfaces endowed with degenerate induced bilinear forms is studied. The intrinsic evolution is generated by constraint--preserving vector fields on manifolds whose…
Semantic image inpainting is a challenging task where large missing regions have to be filled based on the available visual data. Existing methods which extract information from only a single image generally produce unsatisfactory results…
Most generative models of audio directly generate samples in one of two domains: time or frequency. While sufficient to express any signal, these representations are inefficient, as they do not utilize existing knowledge of how sound is…
Discrete diffusion models offer a flexible, controllable approach to structured sequence generation, yet they still lag behind causal language models in expressive power. A key limitation lies in their reliance on the Markovian assumption,…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…
Representing nonlinear dynamical systems using the Koopman Operator and its spectrum has distinct advantages in terms of linear interpretability of the model as well as in analysis and control synthesis through the use of well-studied…