Related papers: Generalized Composition via Nerves: Models and Alg…
Compositionality is a cognitive mechanism that allows humans to systematically combine known concepts in novel ways. This study demonstrates how artificial neural agents acquire and utilize compositional generalization to describe…
Compositional learning, mastering the ability to combine basic concepts and construct more intricate ones, is crucial for human cognition, especially in human language comprehension and visual perception. This notion is tightly connected to…
Humans are remarkably flexible when understanding new sentences that include combinations of concepts they have never encountered before. Recent work has shown that while deep networks can mimic some human language abilities when presented…
Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…
Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…
Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with…
Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…
The most natural notion of a simplicial nerve for a (weak) bicategory was given by Duskin, who showed that a simplicial set is isomorphic to the nerve of a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and only if it…
The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit…
We study the problem of learning how to predict attribute-object compositions from images, and its generalization to unseen compositions missing from the training data. To the best of our knowledge, this is a first large-scale study of this…
A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on…
The main objectives of this paper are to give general proofs of the following two facts: A. For an operad $\oo$ in $\ab$, let $A$ be a simplicial $\oo$-algebra such that $A_m$ is the $\oo$-subalgebra generated by $(\sum_{i = 0}^{m}…
Compositional Generalization (CG) embodies the ability to comprehend novel combinations of familiar concepts, representing a significant cognitive leap in human intellectual advancement. Despite its critical importance, the deep neural…
In "Object generators, relaxed sets, and a foundation for mathematics", we introduced ``object generators'', a logical environment much more general than set theory. Inside this we found a `relaxed' version of set theory. That paper is…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
We propose a new framework that generalizes the parameters of neural network models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the space of complex numbers. A typical example is the space of continuous functions on a…
The visual world around us can be described as a structured set of objects and their associated relations. An image of a room may be conjured given only the description of the underlying objects and their associated relations. While there…