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We study the interplay between repulsive interaction and an almost staggered on-site potential in one-dimension. Specifically, we address the Harper model for spinless fermions with nearest-neighbor repulsion, close to half-filling. Using…

Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle…

Although robotic applications increasingly demand versatile and dynamic object handling, most existing techniques are predominantly focused on grasp-based manipulation, limiting their applicability in non-prehensile tasks. To address this…

We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…

Guided or controlled data generation with diffusion models\blfootnote{Partial preliminary results of this work appeared in International Conference on Machine Learning 2025 \citep{li2025provable}.} has become a cornerstone of modern…

Continual learning methods are known to suffer from catastrophic forgetting, a phenomenon that is particularly hard to counter for methods that do not store exemplars of previous tasks. Therefore, to reduce potential drift in the feature…

Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…

Federated Learning (FL) is a privacy-constrained decentralized machine learning paradigm in which clients enable collaborative training without compromising private data. However, how to learn a robust global model in the data-heterogeneous…

Federated Learning (FL) enables decentralized model training across clients without sharing raw data, but its performance degrades under real-world data heterogeneity. Existing methods often fail to address distribution shift across clients…

Feature Transformation (FT) crafts new features from original ones via mathematical operations to enhance dataset expressiveness for downstream models. However, existing FT methods exhibit critical limitations: discrete search struggles…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Learning-based methods excel at robot motion generation but remain limited in contact-rich physical interaction. Impedance control provides stable and safe contact behavior but requires task-specific tuning of stiffness and damping…

The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

Density Functional Theory (DFT) allows for predicting all the chemical and physical properties of molecular systems from first principles by finding an approximate solution to the many-body Schr\"odinger equation. However, the cost of these…

The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more…

In Federated Learning (FL), a number of clients or devices collaborate to train a model without sharing their data. Models are optimized locally at each client and further communicated to a central hub for aggregation. While FL is an…

Denosing diffusion model, as a generative model, has received a lot of attention in the field of image generation recently, thanks to its powerful generation capability. However, diffusion models have not yet received sufficient research in…

Drift in machine learning refers to the phenomenon where the statistical properties of data or context, in which the model operates, change over time leading to a decrease in its performance. Therefore, maintaining a constant monitoring…

Federated and Continual Learning have emerged as potential paradigms for the robust and privacy-aware use of Deep Learning in dynamic environments. However, Client Drift and Catastrophic Forgetting are fundamental obstacles to guaranteeing…