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Purpose: Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…
Deep latent variable models have achieved significant empirical successes in model-based reinforcement learning (RL) due to their expressiveness in modeling complex transition dynamics. On the other hand, it remains unclear theoretically…
An effective approach to solving long-horizon tasks in robotics domains with continuous state and action spaces is bilevel planning, wherein a high-level search over an abstraction of an environment is used to guide low-level…
Understanding and mapping a new environment are core abilities of any autonomously navigating agent. While classical robotics usually estimates maps in a stand-alone manner with SLAM variants, which maintain a topological or metric…
Numerical simulations are commonly used to understand the parameter dependence of given spatio-temporal phenomena. Sampling a multi-dimensional parameter space and running the respective simulations leads to an ensemble of a large number of…
A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…
Latent reasoning has been recently proposed as a reasoning paradigm and performs multi-step reasoning through generating steps in the latent space instead of the textual space. This paradigm enables reasoning beyond discrete language tokens…
We consider an operator-based latent Markov representation of a stochastic nonlinear dynamical system, where the stochastic evolution of the latent state embedded in a reproducing kernel Hilbert space is described with the corresponding…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Explainability of deep neural networks is one of the most challenging and interesting problems in the field. In this study, we investigate the topic focusing on the interpretability of deep learning-based registration methods. In…
Human learning relies on specialization -- distinct cognitive mechanisms working together to enable rapid learning. In contrast, most modern neural networks rely on a single mechanism: gradient descent over an objective function. This…
The state of the art on many NLP tasks is currently achieved by large pre-trained language models, which require a considerable amount of computation. We explore a setting where many different predictions are made on a single piece of text.…
In this paper, a robust multiscale neural network is proposed to recognize handwritten mathematical expressions and output LaTeX sequences, which can effectively and correctly focus on where each step of output should be concerned and has a…
A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where…
In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to…
A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
In this paper, we derive a novel method as a generalization over LCEs such as E2C. The method develops the idea of learning a locally linear state space, by adding a multi-step prediction, thus allowing for more explicit control over the…