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The increased interest in deep learning applications, and their hard-to-detect biases result in the need to validate and explain complex models. However, current explanation methods are limited as far as both the explanation of the…

Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…

The treatment of equality as a type in type theory gives rise to an interesting type-theoretic structure known as `identity type'. The idea is that, given terms $a,b$ of a type $A$, one may form the type $Id_{A}(a,b)$, whose elements are…

Spatial transcriptomics (ST) profiles gene expression across a tissue section while preserving the spatial coordinates. Because current ST technologies typically profile two-dimensional tissue slices, integrating and aligning slices from…

In transformer architectures, position encoding primarily provides a sense of sequence for input tokens. While the original transformer paper's method has shown satisfactory results in general language processing tasks, there have been new…

In our work, we propose to represent HTM as a set of flat models, or layers, and a set of topical hierarchies, or edges. We suggest several quality measures for edges of hierarchical models, resembling those proposed for flat models. We…

Engineered lattices in condensed matter physics, such as cold atom optical lattices or photonic crystals, can have fundamentally different properties from naturally-occurring electronic crystals. Here, we report a novel type of artificial…

The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous)…

In this work, we investigate an important task named instruction-following text embedding, which generates dynamic text embeddings that adapt to user instructions, highlighting specific attributes of text. Despite recent advancements,…

Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…

Sparse autoencoders (SAEs) have emerged as powerful techniques for interpretability of large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there…

An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…

Manifolds are complex topological spaces that can be used to represent datasets of real-world measurements. Visualizing such manifolds can help with illustrating their topological characteristics (e.g., curvature) and providing insights…

Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…

Every Transformer architecture dedicates enormous capacity to learning rich representations in semantic embedding space -- yet the rotation manifold acted upon by Rotary Positional Embeddings (RoPE) has been treated as a fixed, hand-crafted…

The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…

Robotic manipulation in unstructured environments requires the generation of robust and long-horizon trajectory-level policy with conditions of perceptual observations and benefits from the advantages of SE(3)-equivariant diffusion models…

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…

Autoencoders have been widely used for dimensional reduction and feature extraction. Various types of autoencoders have been proposed by introducing regularization terms. Most of these regularizations improve representation learning by…

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…