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This study explores the learnability of memory-less and memory-augmented RNNs, which are theoretically equivalent to Pushdown Automata. Empirical results show that these models often fail to generalize on longer sequences, relying more on…
We leverage probabilistic models of neural representations to investigate how residual networks fit classes. To this end, we estimate class-conditional density models for representations learned by deep ResNets. We then use these models to…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
The availability of precise and accurate simulation is a limiting factor for interpreting and forecasting data in many fields of science and engineering. Often, one or more distinct simulation software applications are developed, each with…
More often than not in benchmark supervised ML, tabular data is flat, i.e. consists of a single $m \times d$ (rows, columns) file, but cases abound in the real world where observations are described by a set of tables with structural…
Car-following behavior modeling is critical for understanding traffic flow dynamics and developing high-fidelity microscopic simulation models. Most existing impulse-response car-following models prioritize computational efficiency and…
Using the properties of differential flatness, a controllable system, such as a quadcoper model, may be transformed into a linear equivalent system via a coordinate change and an input mapping. This is a straightforward advantage for the…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…
Self-driving vehicles plan around both static and dynamic objects, applying predictive models of behavior to estimate future locations of the objects in the environment. However, future behavior is inherently uncertain, and models of motion…
Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…
When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…
Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to…
We propose a soft gradient boosting framework for sequential regression that embeds a learnable linear feature transform within the boosting procedure. At each boosting iteration, we train a soft decision tree and learn a linear input…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
Many complex physical systems admit natural decomposition into an exactly solvable component and a perturbative correction. Rather than training neural networks to learn complete trajectories from scratch, we introduce Neural Network…
Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…