Related papers: Optimal quadratic binding for relational reasoning…
This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian…
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
In recent years, there has been growing attention to interpretable machine learning models which can give explanatory insights on their behaviour. Thanks to their interpretability, decision trees have been intensively studied for…
This paper describes a process for combining patterns and features, to guide a search process and make predictions. It is based on the functionality that a human brain might have, which is a highly distributed network of simple neuronal…
A notable property of word embeddings is that word relationships can exist as linear substructures in the embedding space. For example, $\textit{gender}$ corresponds to $\vec{\textit{woman}} - \vec{\textit{man}}$ and $\vec{\textit{queen}} -…
Collecting data, extracting value, and combining insights from relational and context-rich multi-modal sources in data processing pipelines presents a challenge for traditional relational DBMS. While relational operators allow declarative…
Relational representation learning has lately received an increase in interest due to its flexibility in modeling a variety of systems like interacting particles, materials and industrial projects for, e.g., the design of spacecraft. A…
Deep learning has recently led to great successes in tasks such as image recognition (e.g Krizhevsky et al., 2012). However, deep networks are still outmatched by the power and versatility of the brain, perhaps in part due to the richer…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
Unveiling visual semantics from neural signals such as EEG, MEG, and fMRI remains a fundamental challenge due to subject variability and the entangled nature of visual features. Existing approaches primarily align neural activity directly…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten-p norm, etc. They usually need many iterations to converge. Moreover, only the low-rank property of matrices is…
Vector representations obtained from word embedding are the source of many groundbreaking advances in natural language processing. They yield word representations that are capable of capturing semantics and analogies of words within a text…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
This paper presents a spike-based model which employs neurons with functionally distinct dendritic compartments for classifying high dimensional binary patterns. The synaptic inputs arriving on each dendritic subunit are nonlinearly…
The brain encodes spacial structure through a combinatorial code of neural activity. Experiments suggest such codes correspond to convex areas of the subject's environment. We present an intrinsic condition that implies a neural code may…