Related papers: A Compositional Framework for Passive Linear Netwo…
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples,…
This dissertation explores the integration of learning and analogy-making through the development of a computer program, called Analogator, that learns to make analogies by example. By "seeing" many different analogy problems, along with…
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
Motivated by deep learning regimes with multiple interacting yet distinct model components, we introduce learning diagrams, graphical depictions of training setups that capture parameterized learning as data rather than code. A learning…
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…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
We look at the internal structure of neural networks which is usually treated as a black box. The easiest and the most comprehensible thing to do is to look at a binary classification and try to understand the approach a neural network…
Monolithic neural networks that make use of a single set of weights to learn useful representations for downstream tasks explicitly dismiss the compositional nature of data generation processes. This characteristic exists in data where…
Monads play an important role in both the syntax and semantics of modern functional programming languages. The problem of combining them has been of profound interest at least since the 90s, and different approaches have been employed to…
We consider the category of linear relations over an arbitrary commutative ring, and identify it as a subcategory of the category of Kronecker representations. We observe that this subcategory forms a definable, faithful and hereditary…
Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to…
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
A new model of bosonic strings is considered. An action of the model is the sum of the standard string action and a term describing an interaction of a metric with a linear (affine) connection. The Lagrangian of this interaction is an…
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
This paper proposes a new classification model called logistic circuits. On MNIST and Fashion datasets, our learning algorithm outperforms neural networks that have an order of magnitude more parameters. Yet, logistic circuits have a…
Cerebellar-like networks, in which input activity patterns are separated by projection to a much higher-dimensional space before classification, are a recurring neurobiological motif, present in the cerebellum, dentate gyrus, insect…
The category of strict polynomial functors inherits an internal tensor product from the category of divided powers. To investigate this monoidal structure, we consider the category of representations of the symmetric group which admits a…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…