Related papers: Directional Non-Commutative Monoidal Structures fo…

We introduce a novel framework consisting of a class of algebraic structures that generalize one-dimensional monoidal systems into higher dimensions by defining per-axis composition operators subject to non-commutativity and a global…

We present an empirical validation of the directional non-commutative monoidal embedding framework recently introduced in prior work~\cite{Godavarti2025monoidal}. This framework defines learnable compositional embeddings using distinct…

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…

Network embedding has proved extremely useful in a variety of network analysis tasks such as node classification, link prediction, and network visualization. Almost all the existing network embedding methods learn to map the node IDs to…

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

Recent disentangled representation learning (DRL) methods heavily rely on factor specific strategies-either learning objectives for attributes or model architectures for objects-to embed inductive biases. Such divergent approaches result in…

Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding…

Multimodal retrieval, which seeks to retrieve relevant content across modalities such as text or image, supports applications from AI search to contents production. Despite the success of separate-encoder approaches like CLIP align…

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…

Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…

A hallmark of human intelligence is the ability to construct self-contained chunks of knowledge and reuse them in novel combinations for solving different problems. Learning such compositional structures has been a challenge for artificial…

From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…

In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks. We leverage the theory of algebraic signal processing to model convolutional non commutative architectures, and we derive…

In this article we further the study of non-commutative motives. Our main result is the construction of a symmetric monoidal structure on the localizing motivator Mot of dg categories. As an application, we obtain : (1) a computation of the…

This paper studies visual search using structured queries. The structure is in the form of a 2D composition that encodes the position and the category of the objects. The transformation of the position and the category of the objects leads…

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary.…

Multi-head, key-value attention is the backbone of the widely successful Transformer model and its variants. This attention mechanism uses multiple parallel key-value attention blocks (called heads), each performing two fundamental…

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…