Related papers: A proof challenge: multiple alignment and informat…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data…
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles…
Different machine learning models can represent the same underlying concept in different ways. This variability is particularly valuable for in-the-wild multimodal retrieval, where the objective is to identify the corresponding…
We present a theoretical framework that extends classical information theory to finite and structured systems by redefining redundancy as a fundamental property of information organization rather than inefficiency. In this framework,…
Quantum information theory and quantum computing are theoritical basis of quantum computers. Thanks to entanglement, quantum mechanical systems are provisioned to realize many information processing problems faster than classical…
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are: (a) being atomic, i.e. not being…
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a…
This paper argues that the operations of a 'Universal Turing Machine' (UTM) and equivalent mechanisms such as the 'Post Canonical System' (PCS) - which are widely accepted as definitions of the concept of `computing' - may be interpreted as…
The POPLMARK Challenge comprises a set of problems intended to measure the strength of reasoning systems in the realm of mechanizing programming language meta-theory at the time the challenge was enunciated. Included in the collection is…
Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…