Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical power and interpretability. We develop a geometric decomposition framework offering two strategies for partitioning inference problems into regional analyses on data-derived Riemannian graphs. Gradient flow decomposition uses path-monotonicity-validated discrete Morse theory to partition samples into gradient flow cells where outcomes exhibit monotonic behavior. Co-monotonicity decomposition utilizes vertex-level coefficients that provide context-dependent versions of the classical Pearson correlation: these coefficients measure edge-based directional concordance between outcome and features, or between feature pairs, defining embeddings of samples into association space. These embeddings induce Riemannian k-NN graphs on which biclustering identifies co-monotonicity cells (coherent regions) and feature modules. This extends naturally to multi-modal integration across multiple feature sets. Both strategies apply independently or jointly, with Bayesian posterior sampling providing credible intervals.

To unveil the hidden mechanisms under LM's incapability to learn long-tail domain-specific knowledge, we investigate the behaviors of a GPT on the Wikipedia dataset.

We propose a novel and efficient search algorithm which finds initial centers that can be used subsequently for the local search algorithm.

Clustering is a fundamental task in data science with wide-ranging applications.

Recent works have demonstrated that the sample complexity of gradient-based learning of single index models, i.e. functions that depend on a 1-dimensional

Transformers have achieved great success in recent years. Interestingly, transformers have shown particularly strong in-context learning capability - even without fine-tuning, they are still able to solve unseen tasks well purely based on task-specific prompts.

So they have difficulty handling unconstrained images with varying illumination and transient occluders.

Approaches based on point processes provide a principled statistical framework for modeling neural spiking activity.

However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo.