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Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
When manipulating a novel object with complex dynamics, a state representation is not always available, for example for deformable objects. Learning both a representation and dynamics from observations requires large amounts of data. We…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
Continual Pre-training (CPT) serves as a fundamental approach for adapting foundation models to domain-specific applications. Scaling laws for pre-training define a power-law relationship between dataset size and the test loss of an LLM.…
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian…
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical…
Neural processes (NPs) aim to stochastically complete unseen data points based on a given context dataset. NPs essentially leverage a given dataset as a context representation to derive a suitable identifier for a novel task. To improve the…
We map categorical variables in a function approximation problem into Euclidean spaces, which are the entity embeddings of the categorical variables. The mapping is learned by a neural network during the standard supervised training…
Machine learning has gained widespread attention as a powerful tool to identify structure in complex, high-dimensional data. However, these techniques are ostensibly inapplicable for experimental systems where data is scarce or expensive to…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small…
Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…
Effective planning in model-based reinforcement learning (MBRL) and model-predictive control (MPC) relies on the accuracy of the learned dynamics model. In many instances of MBRL and MPC, this model is assumed to be stationary and is…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…