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Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data…
We introduce and motivate generative modeling as a central task for machine learning and provide a critical view of the algorithms which have been proposed for solving this task. We overview how generative modeling can be defined…
Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…
Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…
Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the…
Learning a good distance measure for distance-based classification in time series leads to significant performance improvement in many tasks. Specifically, it is critical to effectively deal with variations and temporal dependencies in time…
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…
Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension,…
Generative models based on latent variables, such as generative adversarial networks (GANs) and variational auto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields. However, many data such as…
Continuous-time Markov chains have been successful in modelling systems across numerous fields, with currents being fundamental entities that describe the flows of energy, particles, individuals, chemical species, information, or other…
Generative adversarial network (GAN) has achieved impressive success on cross-domain generation, but it faces difficulty in cross-modal generation due to the lack of a common distribution between heterogeneous data. Most existing methods of…
Generative AI (GenAI) has revolutionized data-driven modeling by enabling the synthesis of high-dimensional data across various applications, including image generation, language modeling, biomedical signal processing, and anomaly…
Let $M$ be a closed manifold and $\alpha : \pi_1(M)\to U_n$ a representation. We give a purely $K$-theoretic description of the associated element $[\alpha]$ in the $K$-theory of $M$ with $\R/\Z$-coefficients. To that end, it is convenient…
We deliver the realistic ab initio lattice investigations of $K \overline{K}$ scattering. In the Asqtad-improved staggered dynamical fermion formulation, we carefully measure $K\overline{K}$ four-point function in the $I=0$ channel by…
Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…
Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability…
Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…
An open secret in contemporary machine learning is that many models work beautifully on standard benchmarks but fail to generalize outside the lab. This has been attributed to biased training data, which provide poor coverage over real…
Gradient Descent (GD) and its variants are the primary tool for enabling efficient training of recurrent dynamical systems such as Recurrent Neural Networks (RNNs), Neural ODEs and Gated Recurrent units (GRUs). The dynamics that are formed…
In this paper, we present a novel localized Generative Adversarial Net (GAN) to learn on the manifold of real data. Compared with the classic GAN that {\em globally} parameterizes a manifold, the Localized GAN (LGAN) uses local coordinate…