Related papers: Transport of Algebraic Structure to Latent Embeddi…

Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…

Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…

Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…

Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily…

In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that…

We present a deep learning approach for learning the joint semantic embeddings of images and captions in a Euclidean space, such that the semantic similarity is approximated by the L2 distances in the embedding space. For that, we introduce…

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to…

Autoregressive language models (LMs) generate one token at a time, yet human reasoning operates over higher-level abstractions - sentences, propositions, and concepts. This contrast raises a central question- Can LMs likewise learn to…

Despite the well-developed cut-edge representation learning for language, most language representation models usually focus on specific level of linguistic unit, which cause great inconvenience when being confronted with handling multiple…

Autoregressive language models have demonstrated a remarkable ability to extract latent structure from text. The embeddings from large language models have been shown to capture aspects of the syntax and semantics of language. But what…

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…

We present a scalable framework for cross-embodiment humanoid robot control by learning a shared latent representation that unifies motion across humans and diverse humanoid platforms, including single-arm, dual-arm, and legged humanoid…

Deep metric learning is often used to learn an embedding function that captures the semantic differences within a dataset. A key factor in many problem domains is how this embedding generalizes to new classes of data. In observing many…

Transformer architectures are typically described in algorithmic and statistical terms, leaving their internal mechanics without a familiar structural language for researchers trained in physical theories. To bridge this gap, we develop a…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…

Current 3D-aware pretraining methods for embodied perception and manipulation are largely built on differentiable rendering frameworks, producing either fully implicit neural fields or fully explicit geometric primitives. Implicit…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient…

Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse…

We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…