20 papers · ranked by Valyu relevance
Przemysław Chojecki
We study the special role of mathematics and coding inside the moduli space M of psychometric batteries for AI agents. Building on the AAI framework of [[1]] and GVU dynamics from [[2]], we define the Mathematics Fiber Mmath and show that, when paired with formal proof kernels (e.g. Lean, Coq), GVU flows on this fiber…
Sudan, Madhu
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting codes that depend on relatively simple elements of applied algebra. While the…
Angelos Gkekas, Nikos A. Mitsiou, Ioannis Souldatos, George K. Karagiannidis
—This work studies the problem of constructing capacity-achieving codes from an algorithmic perspective. Specifically, we prove that there exists a Turing machine which, given a discrete memoryless channel p Y | X , a target rate R less than the channel capacity Cpp Y | X q, and an error tolerance ϵ ą 0, outputs a…
Eduardo Y. Sakabe, Felipe S. Abrahão, Alexandre Simões, Esther Colombini + 3 more
Understanding and controlling the complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based loss functions and statistical metrics, these measures often fail to capture deeper, causally…
Giulio Ruffini, Ming Li
The regulator theorem states that, under certain conditions, any optimal controller must embody a model of the system it regulates, grounding the idea that controllers embed, explicitly or implicitly, internal models of the controlled. This principle underpins neuroscience and predictive brain theories like the…
Tristan Simas
—Single-Source Coherence Theorem. We prove that among all possible degrees of freedom (DOF = number of independent encoding locations), exactly one value (DOF = 1) guarantees coherence. DOF = 0 fails (no fact encoded). DOF ≥ 2 fails (permits explicit construction of inconsistency). Only DOF = 1 satisfies both…
Lihong Cao
The human brain encodes a virtually infinite repertoire of semantic concepts using a finite number of neurons, a feat that defies the capacity limits of classical attractor networks. While “Concept Cells” in the medial temporal lobe (MTL) exhibit extreme sparsity, the information-theoretic principles governing their…
Anina Gruica, Benjamin Jany, Alberto Ravagnani
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of weight distribution that captures the code’s locality. Using a duality result analogous to a MacWilliams identity, we then derive an LP-type…
Neri Merhav, Chi Wan Sung
We derive a few extended versions of the Kraft inequality for information lossless finite-state encoders. The main basic contribution is in defining a notion of a Kraft matrix and in establishing the fact that a necessary condition for information losslessness of a finite-state encoder is that none of the eigenvalues…
Zheng Yang, Xiaofang Wang, Shuguang Lu, Jia Wang + 2 more
Ultra-reliable and low-latency communication (URLLC) is one of the key requirements in future wireless communications. In practical URLLC scenarios, an enhanced mobile broadband (eMBB) message together with an URLLC message are simultaneously encoded as codewords and transmitted over the same channels. Traditionally…
Willie K. Harrison, Truman Welling, Andrew Swain, Morteza Shoushtari + 1 more
Physical-layer security can aid in establishing secure telecommunication networks including cellular, Internet of Things, and telemetry networks, among others. Channel sounding techniques and/or telemetry systems for reporting channel conditions, coupled with superior wiretap code design are necessary to implement such…
Søren Riis
Term Coding asks: given a finite system of term identities Γ in v variables, how large can its solution set be on an n–element alphabet, when we are free to choose the interpretations of the function symbols? This turns familiar existence problems for quasigroups, designs, and related objects into quantitative extremal…
Lucas Waite, Nuh Aydin
This paper investigates the relationship between coding theory and extremal combinatorics by representing codes in general metric spaces as independent sets in proximity graphs. We provide a generalized framework for the Gilbert-Varshamov (GV) bound applicable to codes over any finite metric space and explore the…
Don Yin
Among individuals with equivalent Alzheimer’s pathology, cognitive outcomes can diverge by decades, a phenomenon termed cognitive reserve that remains descriptive after thirty years of research. We propose that the ∼10^9^-to-10 bits/s gap between sensory input and behavioral output functions as error-correcting…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
Kees Schouhamer Immink, Jos H. Weber, Tuan Thanh Nguyen, Kui Cai + 2 more
The design of low-complexity and efficient constrained codes has been a major research item for many years. This paper reports on a versatile method named concatenated constrained codes for designing efficient fixed-length constrained codes with small complexity. A concatenated constrained code comprises two (or more)…
Hongyang Liu, Wei Yan
For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this interval, the optimal code length for the symbol equals $k$. Furthermore, for infinite…
Fatih Dinc, Marta Blanco-Pozo, David Klindt, Francisco Acosta + 8 more
Many neural recordings have revealed low-dimensional sets of behaviorally relevant variables encoded within large-scale neural activity patterns. However, dimensionality reduction analyses alone cannot yield causal explanations for how networks stably implement computations that are resilient to the substantial…
Boggavarapu Kiran
Biological inheritance can be treated as a class of catalytic templating reactions in which a daughter molecule, generated by a kinetic kernel acting on a parent template, is itself a substrate for the next round of the same catalysis. We give the physicochemical conditions under which such a reaction can support…
Tuomo Kiiskinen, Oscar Kivinen, Manuel A Rivas
The central problem of biology is the origin of biological organization. We show, using information theory, that an organism does not contain enough organism-specific information to specify its own fully functioning microscopic organization. The organized machinery of life is therefore not the execution of a fully…