The rapid progress in generative models has resulted in impressive leaps in generation quality, blurring the lines between synthetic and real data. Web-scale datasets are now prone to the inevitable contamination by synthetic data, directly impacting the training of future generated models. Already, some theoretical results on self-consuming generative models (a.k.a., iterative retraining) have emerged in the literature, showcasing that either model collapse or stability could be possible depending on the fraction of generated data used at each retraining step. However, in practice, synthetic data is often subject to human feedback and curated by users before being used and uploaded online. For instance, many interfaces of popular text-to-image generative models, such as Stable Diffusion or Midjourney, produce several variations of an image for a given query which can eventually be curated by the users. In this paper, we theoretically study the impact of data curation on iterated retraining of generative models and show that it can be seen as an implicit preference optimization mechanism.

The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude characteristics observed in individual source signals. On the other hand, many existing non-Gaussian amplitude distributions derived from hyperspherical models achieve good empirical fit due to their power-law structures, while they do not explicitly account for the complex-plane geometry inherent in complex-valued observations. In this paper, we propose a new probabilistic model for complex-valued random variables, which can be interpreted as a power-weighted noncentral complex Gaussian distribution. Unlike conventional hyperspherical amplitude models, the proposed model is formulated directly on the complex plane and preserves the geometric structure of complex-valued observations while retaining a higher-dimensional interpretation. The model introduces a nonlinear phase diffusion through a single shape parameter, enabling continuous control of the distributional geometry from arc-shaped diffusion along the phase direction to concentration of probability mass toward the origin. We formulate the proposed distribution and analyze the statistical properties of the induced amplitude distribution. The derived amplitude and power distributions provide a unified framework encompassing several widely used distributions in signal modeling, including the Rice, Nakagami, and gamma distributions. Experimental results on speech power spectra demonstrate that the proposed model consistently outperforms conventional distributions in terms of log-likelihood.

Stochastic gradient methods have been a widespread practice in machine learning.

This problem involves identifying a density function that accurately represents the distribution of a given dataset.

DNN pruning is an approach for deep model compression, which aimsateliminating someparameters withtolerable performance degradation.

So far the community has considered`2 as the underlying distance.

This simple intuition makes Bayesian methods appealing approaches for transfer in RL, and many previous works have been proposed in this direction.

In many sequential tasks, a model needs to remember relevant events from the distant past to make correct predictions. Unfortunately, a straightforward application ofgradient based training requires intermediate computations tobestored for every element of a sequence. This requires to store prohibitively large intermediate data ifasequence consists ofthousands oreven millions elements, and asaresult, makeslearning ofverylong-term dependencies infeasible.

Reinforcement Learning (RL) has achievedimpressiveprogress inrecent years, such asresults in Atari [24] and Go [28] in which RL agents even perform better than human beings.

Reinforcement learning (RL) [1] studies the problem of learning in sequential decision-making problems where the dynamics of the environment is unknown, but can be learnt by performing actions andobserving their outcome inanonline fashion. Asample-efficient RLagent must trade off the explorationneeded to collect information about the environment, and theexploitation of the experience gathered so far to gain as much reward as possible.