Related papers: A 2-adjunction between representations and preorde…
In this paper, the 2-category $\mathfrak{Rep}_{{\bf 2Mat}_{\mathbb{C}}}(\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces…
Recent recommender system advancements have focused on developing sequence-based and graph-based approaches. Both approaches proved useful in modeling intricate relationships within behavioral data, leading to promising outcomes in…
In this paper we provide explicit dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and…
We define locally wide finitary 2-categories by relaxing the definition of finitary 2-categories to allow infinitely many objects and isomorphism classes of 1-morphisms and infinite dimensional hom-spaces of 2-morphisms. After defining…
Most efforts in interpretability in deep learning have focused on (1) extracting explanations of a specific downstream task in relation to the input features and (2) imposing constraints on the model, often at the expense of predictive…
Understanding convergent learning -- the degree to which independently trained neural systems -- whether multiple artificial networks or brains and models -- arrive at similar internal representations -- is crucial for both neuroscience and…
Image-text multimodal representation learning aligns data across modalities and enables important medical applications, e.g., image classification, visual grounding, and cross-modal retrieval. In this work, we establish a connection between…
Transformers can generate predictions in two approaches: 1. auto-regressively by conditioning each sequence element on the previous ones, or 2. directly produce an output sequences in parallel. While research has mostly explored upon this…
In this paper we introduce a description of ordered groupoids as a particular type of double categories. This enables us to turn Lawson's correspondence between ordered groupoids and left-cancellative categories into a biequivalence. We use…
A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…
Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…
Classical planning representation languages based on first-order logic have preliminarily been used to model and solve robotic task planning problems. Wider adoption of these representation languages, however, is hindered by the limitations…
Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…
We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated. In particular, we modify the…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
In this paper we study a new class of transformations on the set of all Hilbert space effects. This consists of the bijective maps which preserve the order and zero product in both directions. The main result of the paper gives a complete…
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…
The paper proposes a novel technique for representing templates and instances of concept classes. A template representation refers to the generic representation that captures the characteristics of an entire class. The proposed technique…