Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research, variations of MCMC remain the default approach to sampling despite slow convergence. Auxiliary neural models can learn to speed up MCMC, but the overhead for training the extra model can be prohibitive. We propose a fundamentally different approach to this problem via a new Hamiltonian dynamics with a non-Newtonian momentum. In contrast to MCMC approaches like Hamiltonian Monte Carlo, no stochastic step is required. Instead, the proposed deterministic dynamics in an extended state space exactly sample the target distribution, specified by an energy function, under an assumption of ergodicity. Alternatively, the dynamics can be interpreted as a normalizing flow that samples a specified energy model without training. The proposed Energy Sampling Hamiltonian (ESH) dynamics have a simple form that can be solved with existing ODE solvers, but we derive a specialized solver that exhibits much better performance.

Mapping neuroanatomy, in the pursuit of linking hypothesized computational models consistent with observed functions to the actual physical structures, is a long-standing fundamental problem in neuroscience. One primary interest is in mapping the network structure of neural circuits by identifying the morphology of each neuron and the locations of synaptic connections between neurons, a field called connectomics.

Multi-modal behavior cloning faces significant challenges due to mode averaging and mode collapse, where traditional models fail to capture diverse input-output mappings. This problem is critical in applications like robotics, where modeling multiple valid actions ensures both performance and safety. We propose EBGAN-MDN, a framework that integrates energy-based models, Mixture Density Networks (MDNs), and adversarial training. By leveraging a modified InfoNCE loss and an energy-enforced MDN loss, EBGAN-MDN effectively addresses these challenges. Experiments on synthetic and robotic benchmarks demonstrate superior performance, establishing EBGAN-MDN as a effective and efficient solution for multi-modal learning tasks.

We thank all the reviewers for providing valuable feedback. In what follows, we address specific questions. The main motivation is computational. We will discuss this motivation in Section 2.1. Q2 (R2): Metrics or experiments to assess whether the model is overfitting or memorizing the dataset.

We propose a method for test-time adaptation of pretrained depth completion models. Depth completion models, trained on some ``source'' data, often predict erroneous outputs when transferred to ``target'' data captured in novel environmental conditions due to a covariate shift. The crux of our method lies in quantifying the likelihood of depth predictions belonging to the source data distribution. The challenge is in the lack of access to out-of-distribution (target) data prior to deployment. Hence, rather than making assumptions regarding the target distribution, we utilize adversarial perturbations as a mechanism to explore the data space. This enables us to train an energy model that scores local regions of depth predictions as in- or out-of-distribution. We update the parameters of pretrained depth completion models at test time to minimize energy, effectively aligning test-time predictions to those of the source distribution. We call our method ``Energy-based Test-time Adaptation'', or ETA for short. We evaluate our method across three indoor and three outdoor datasets, where ETA improve over the previous state-of-the-art method by an average of 6.94% for outdoors and 10.23% for indoors. Project Page: https://fuzzythecat.github.io/eta.

We first introduce Equivari-ant Stein V ariational Gradient Descent algorithm - an equivariant sampling method based on Stein's identity for sampling from densities with symmetries.

There are two types of deep generative models: explicit and implicit.