Related papers: Internalizing Tools as Morphisms in Graded Transfo…
Given a cartesian closed category $\mathcal{V}$, we introduce an internal category of elements $\int_\mathcal{C} F$ associated to a $\mathcal{V}$-functor $F\colon \mathcal{C}^{\mathrm{op}}\to \mathcal{V}$. When $\mathcal{V}$ is extensive,…
We give a general, direct and explicit construction of lower-bounded generalized twisted modules satisfying a universal property for a grading-restricted vertex (super)algebra $V$ associated to an automorphism $g$ of $V$. In particular,…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
Self-Organizing Maps (SOMs) provide topology-preserving projections of high-dimensional data, yet their use as generative models remains largely unexplored. We show that the activation pattern of a SOM -- the squared distances to its…
A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…
Modular exponentiation is crucial to number theory and cryptography, yet remains largely unexplored from a mechanistic interpretability standpoint. We train a 4-layer encoder-decoder Transformer model to perform this operation and…
Recursive architectures such as Tiny Recursive Models (TRMs) perform implicit reasoning through iterative latent computation, yet the geometric structure of these reasoning trajectories remains poorly understood. We investigate the…
When humans perform contact-rich manipulation tasks, customized tools are often necessary to simplify the task. For instance, we use various utensils for handling food, such as knives, forks and spoons. Similarly, robots may benefit from…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
Enabling robots to learn long-horizon manipulation tasks from a handful of demonstrations remains a central challenge in robotics. Existing neuro-symbolic approaches often rely on hand-crafted symbolic abstractions, semantically labeled…
Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…
Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. Due to the witnessed efficiency in solving bi-level programs, gradient-based methods have gained popularity in the machine…
Implicit Neural Representations (INRs) have emerged and shown their benefits over discrete representations in recent years. However, fitting an INR to the given observations usually requires optimization with gradient descent from scratch,…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded by two coupled channels-drift and diffusion-whose algebraic…
Vision-language-action (VLA) models have shown strong potential for generalist robot manipulation, yet they remain limited by insufficient spatial reasoning, particularly in determining where to interact in complex visual scenes. While…
Disentangled representations can be useful in many downstream tasks, help to make deep learning models more interpretable, and allow for control over features of synthetically generated images that can be useful in training other models…
This work in the field of developmental cognitive robotics aims to devise a new domain bridging between reinforcement learning and imitation learning, with a model of the intrinsic motivation for learning agents to learn with guidance from…
We build on theoretical foundations of tool-mediated learning, tool design, and human computer interaction to develop a framework for implicit scaffolding in learning environments. Implicit scaffolding employs affordances, constraints,…
Neural-symbolic approaches have recently gained popularity to inject prior knowledge into a learner without requiring it to induce this knowledge from data. These approaches can potentially learn competitive solutions with a significant…