Related papers: Failure Modes for Structural Highness Notions
A description is an entity that can be interpreted as true or false of an object, and using feature structures as descriptions accrues several computational benefits. In this paper, I create an explicit interpretation of a typed feature…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
A large body of research in machine learning is concerned with supervised learning from examples. The examples are typically represented as vectors in a multi-dimensional feature space (also known as attribute-value descriptions). A teacher…
Despite several (accepted) standards, core notions typically employed in information technology or system engineering architectures lack the precise and exact foundations encountered in logic, algebra, and other branches of mathematics. In…
There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles.…
This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I,…
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…
A good feature representation is a determinant factor to achieve high performance for many machine learning algorithms in terms of classification. This is especially true for techniques that do not build complex internal representations of…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often…
To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be…
Suppose we are given a computably enumerable object arise from algorithmic randomness or computable analysis. We are interested in the strength of oracles which can compute an object that approximates this c.e. object. It turns out that,…
This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or fuzzy, attributes…
We examine the degree structure $\mathbf{ER}$ of equivalence relations on $\omega$ under computable reducibility. We examine when pairs of degrees have a join. In particular, we show that sufficiently incomparable pairs of degrees do not…
It is well known that the R, the set of real numbers, is an abstract set, where almost all its elements cannot be described in any finite language. We investigate possible approaches to what might be called an epi-constructionist approach…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news", innovation, and others, are highly dependent on the structure of the social network on which they occur. However, questions on why most social…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…