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The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Handwritten mathematical expression recognition is a challenging problem due to the complicated two-dimensional structures, ambiguous handwriting input and variant scales of handwritten math symbols. To settle this problem, we utilize the…
Representation learning becomes especially important for complex systems with multimodal data sources such as cameras or sensors. Recent advances in reinforcement learning and optimal control make it possible to design control algorithms on…
In existing task and motion planning (TAMP) research, it is a common assumption that experts manually specify the state space for task-level planning. A well-developed state space enables the desirable distribution of limited computational…
In this paper we propose a deep neural network model with an encoder-decoder architecture that translates images of math formulas into their LaTeX markup sequences. The encoder is a convolutional neural network (CNN) that transforms images…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based…
We study the evolution of latent space in fine-tuned NLP models. Different from the commonly used probing-framework, we opt for an unsupervised method to analyze representations. More specifically, we discover latent concepts in the…
Neural implicit representations have shown substantial improvements in efficiently storing 3D data, when compared to conventional formats. However, the focus of existing work has mainly been on storage and subsequent reconstruction. In this…
End-to-end learning is emerging as a powerful paradigm for robotic manipulation, but its effectiveness is limited by data scarcity and the heterogeneity of action spaces across robot embodiments. In particular, diverse action spaces across…
Multi-modal large language models (MLLMs) have rapidly advanced in visual tasks, yet their spatial understanding remains limited to single images, leaving them ill-suited for physical-world applications that require multi-frame reasoning.…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
Recent progress in Multi-modal Large Language Models (MLLMs) has enabled step-by-step multi-modal mathematical reasoning by performing visual operations based on the textual instructions. A promising approach uses code as an intermediate…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…
Effective human-robot interaction, such as in robot learning from human demonstration, requires the learning agent to be able to ground abstract concepts (such as those contained within instructions) in a corresponding high-dimensional…
Driving in the dynamic, multi-agent, and complex urban environment is a difficult task requiring a complex decision policy. The learning of such a policy requires a state representation that can encode the entire environment. Mid-level…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
Machine learning models built on training data with multiple modalities can reveal new insights that are not accessible through unimodal datasets. For example, cardiac magnetic resonance images (MRIs) and electrocardiograms (ECGs) are both…