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Diffusion models have been widely studied for removing unsafe content learned during pre-training. Existing methods require expensive supervised data, either unsafe-text paired with safe-image groundtruth or negative/positive image pairs,…
The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept…
We derive novel low-temperature asymptotics for the spectrum of the infinitesimal generator of the overdamped Langevin dynamics. The novelty is that this operator is endowed with homogeneous Dirichlet conditions at the boundary of a domain…
The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of parametric partial differential equations (PDE). DeepONets have…
Generative models for 3D molecular conformations must respect Euclidean symmetries and concentrate probability mass on thermodynamically favorable, mechanically stable structures. However, E(3)-equivariant diffusion models often reproduce…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
This paper provides a new tauberian approach to the study of quantitative time asymptotics of collisionless transport semigroups with general diffuse boundary operators. We obtain an (almost) optimal algebraic rate of convergence to…
Artificial neural networks, one of the most successful approaches to supervised learning, were originally inspired by their biological counterparts. However, the most successful learning algorithm for artificial neural networks,…
We present a computational method for open-loop minimum-norm control synthesis for fixed-endpoint transfer of bilinear ensemble systems that are indexed by two continuously varying parameters. We suppose that one ensemble parameter scales…
Quantum neural networks (QNNs) provide expressive probabilistic models by leveraging quantum superposition and entanglement, yet their practical training remains challenging due to highly oscillatory loss landscapes and noise inherent to…
Diffusion models currently dominate the field of data-driven image synthesis with their unparalleled scaling to large datasets. In this paper, we identify and rectify several causes for uneven and ineffective training in the popular ADM…
The scaling hypothesis motivates the expansion of models past trillions of parameters as a path towards better performance. Recent significant developments, such as GPT-3, have been driven by this conjecture. However, as models scale-up,…
Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…
Recently, motivated by the outstanding achievements of diffusion models, the diffusion process has been employed to strengthen representation learning in recommendation systems. Most diffusion-based recommendation models typically utilize…
We present an experimental realization of a biased optical periodic potential in the low friction limit. The noise-induced bistability between locked (torsional) and running (spinning) states in the rotational motion of a nanodumbbell is…
Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a…