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Implicit neural representation (INR) is a popular approach for arbitrary-scale image super-resolution (SR), as a key component of INR, position encoding improves its representation ability. Motivated by position encoding, we propose…

This work presents a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by combining Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The methodology targets the efficient…

We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework provides a flexible mapping from the algebraic specification of a domain to an…

Fine-tuning large language models is essential for task-specific adaptation, yet it remains computationally prohibitive. Parameter-Efficient Fine-Tuning (PEFT) methods have emerged as a solution, but current approaches typically ignore the…

Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of…

We introduce a Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in two spatial variables. PIEs are an algebraic state-space representation of infinite-dimensional systems and have been used to model 1D…

Vision Transformers have achieved remarkable success in computer vision, but their common use of learnable one-dimensional positional encodings weakens the inherent two-dimensional spatial structure of images after patch flattening.…

Currently, a prevalent approach for enhancing Vision-Language Models (VLMs) performance is to encode both the high-resolution version and the thumbnail of an image simultaneously. While effective, this method generates a large number of…

Learning the hierarchical structure of data in vision-language models is a significant challenge. Previous works have attempted to address this challenge by employing entailment learning. However, these approaches fail to model the…

Multimodal time series forecasting is foundational in various fields, such as utilizing satellite imagery and numerical data for predicting typhoons in climate science. However, existing multimodal approaches primarily focus on utilizing…

Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based…

The roto-translation group SE2 has been of active interest in image analysis due to methods that lift the image data to multi-orientation representations defined on this Lie group. This has led to impactful applications of…

Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…

Learning the intrinsic dimensionality of subjective perceptual spaces such as taste, smell, or aesthetics from ordinal data is a challenging problem. We introduce LORE (Low Rank Ordinal Embedding), a scalable framework that jointly learns…

Large vision-language models (LVLMs) are typically trained using autoregressive language modeling objectives, which align visual representations with linguistic space. While effective for multimodal reasoning, this alignment can weaken…

Classification trees continue to be widely adopted in machine learning applications due to their inherently interpretable nature and scalability. We propose a rolling subtree lookahead algorithm that combines the relative scalability of the…

Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction…

In autonomous driving applications, accurate and efficient road surface reconstruction is paramount. This paper introduces RoMe, a novel framework designed for the robust reconstruction of large-scale road surfaces. Leveraging a unique mesh…

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…

This paper primarily focuses on evaluating and benchmarking the robustness of visual representations in the context of object assembly tasks. Specifically, it investigates the alignment and insertion of objects with geometrical extrusions…