The paper introduces a control‑theoretic framework for evolutionary clustering using quasi‑stationary Mean Field Games. Each cluster is modeled as a probability density whose dynamics follow a Fokker–Planck equation, while a stationary Hamilton–Jacobi equation determines the velocity field. In a Gaussian specialization, affine dynamics replicate the mean and covariance trajectories of the classical Expectation–Maximization algorithm, and the authors propose causal and non‑causal time‑averaged log‑likelihood objectives to enhance temporal coherence, along with a fully density‑based numerical implementation for non‑Gaussian components. The method is evaluated on synthetic and real time‑dependent datasets, compared to snapshot Expectation–Maximization, temporally smoothed observations, and an evolutionary k‑means baseline.
arXiv:2608. 08770v1 Announce Type: cross Abstract: Diffusion models are increasingly used as controllable samplers, whose generations can be steered at inference time according to a chosen reward function.
arXiv:2602. 01564v2 Announce Type: replace Abstract: We study the mean-field Langevin descent-ascent (MFL-DA), a coupled optimization dynamics on the space of probability measures for entropically regularized two-player zero-sum games, together with its associated interacting particle system.
arXiv:2512.05926v2 Announce Type: replace Abstract: We consider the fundamental problem of balanced $k$-means clustering. In particular, we introduce an optimal transport approach to alternating mini...
arXiv:2609. 06947v1 Announce Type: new Abstract: Flow matching, together with classifier-free guidance (CFG), is widely used in generative modeling, yet much of the theoretical understanding remains distribution-wise.
arXiv:2606. 17523v1 Announce Type: cross Abstract: Information-Geometric Optimization (IGO) provides a unified framework for black-box optimization by interpreting the adaptation of a search distribution as a natural gradient update.
The paper introduces federated soft clustering for devices in a federated learning network, each fitting a personalized Gaussian mixture model. It proposes Generalized Total Variation Minimization (GTVMin) to couple local maximum likelihood problems via a graph regularizer that penalizes discrepancies between connected nodes’ models. Three discrepancy measures are compared: a squared Euclidean distance requiring component matching, a Monte‑Carlo approximated Kullback‑Leibler divergence, and a closed‑form maximum mean discrepancy; all are optimized with synchronous projected gradient updates, with a convergence guarantee for the smooth MMD instance.
arXiv:2605. 30190v2 Announce Type: replace Abstract: Diffusion-based planning has achieved strong results in single-agent offline reinforcement learning, yet scaling to many-agent systems remains intractable due to the curse of dimensionality in the joint trajectory space.
The paper presents a mean‑field framework for studying multi‑agent Q‑learning in networked populations, where agents update stateless Q‑values on a fixed graph while the average behavior of the population feeds back to modify the payoff matrix. A deterministic transport equation for the distribution of Q‑values is derived and coupled with a discrete update for the environmental state, and the model is validated against Monte Carlo simulations on several random graph topologies. Results show that the mean‑field system captures macroscopic cooperation dynamics, that environmental feedback reshapes action‑value ordering, and that the timescale of environmental response critically influences learning outcomes.
Diffusion models are increasingly used as controllable samplers, whose generations can be steered at inference time according to a chosen reward function. While such rewards are typically defined on individual samples, for many applications it is desirable to steer according to distribution-level rewards, for example to calibrate with population-level information or to encourage diversity.
The paper presents a variational learning framework that simultaneously infers non‑parametric interaction kernels and environmental or intra‑agent forces in collective dynamics. It extends existing methods to handle both interaction and environmental components, validating the approach on benchmark models such as synchronization, alignment, and attraction‑repulsion systems. A model‑selection procedure is also introduced to identify the best explanatory framework from trajectory data, enabling direct recovery of mechanistic interaction mechanisms.
arXiv:2407. 04521v3 Announce Type: replace-cross Abstract: This paper studies the continuous-time q-learning in mean-field jump-diffusion models in a setting where the environment simulator does not provide direct access to the population distribution.
The paper studies finite‑horizon minimum‑energy steering of inertial swarms under stochastic disturbances, focusing on mean‑field models with Cucker–Smale alignment or Morse attraction–repulsion interactions. It formulates the problem as a Schr"odinger bridge, deriving nonlinear, time‑symmetric optimality systems and proposing nested fixed‑point schemes for numerical solution. Numerical experiments demonstrate that the optimal corrective drift can either exploit or counteract the natural interaction forces, depending on their alignment with the steering objective.