A post-Shannon issue on structured coding, geometric neural constraints, quantum foundations, and archival precursor papers.
In this preliminary AI note, we present a unified perspective on structured source coding (SSC) and structured channel coding (SCC), forming a cohesive framework that extends classical Shannon theory. The central thesis is that atypical and error events possess internal geometric structure that can...
Classical source coding treats the atypical set as a monolithic error event, achieving reliable compression at rates approaching the source entropy \(H(X)\). We develop a structured extension in which the atypical set \(B_^{(n)}\) is partitioned into \(k\) clusters under a Hamming-distance metric....
In this preliminary AI note, we introduce Structured Channel Coding, merging the vanishing-clustering framework of structured source coding with the two-phase variable-delay Gaussian-feedback reliability scheme for infinite-bandwidth peak-power-constrained AWGN channels. The monolithic...
Quantum Bayesianism (QBism), as articulated most prominently by Mermin, Fuchs, and Schack, reframes quantum theory as a user-centered framework in which probabilities represent an agent's personal degrees of belief about the outcomes of interventions. While QBism successfully dissolves several...
We establish a bridge between incidence geometry and neurobiological structure by showing that the classical joints problem provides a strict upper bound on the branching complexity of neural arbors. We refine this connection using bounded-degree incidence graphs, demonstrating that pruning,...
In this paper, the authors report a way to use concepts from statistical learning to gain an advantage in terms of error exponents while communicating over a discrete memoryless channel. The study utilizes the simulation capability of the scientific computing package MATLAB to show that the...
In this paper, the authors provide a weak decoding version of the traditional source coding theorem of Claude Shannon. The central bound that is obtained is {{} \[ >_{}(2^{-n(H(X)+)}) \] where \[ ={(k)}{n(H(X)+)} \] and $k$ is the number of unsupervised learning classes formed out of the...
In this paper the authors extend [1] and provide more details of how the brain may act like a quantum computer. In particular, positing the difference between voltages on two axons as the environment for ions undergoing spatial superposition, we argue that evolution in the presence of metric...
In this brief paper, the authors study the tuning curves of starburst amacrine cells (SACs) and introduce a quantity called the irresolution or ambiguity of a SAC. They show that the rate of data generated by a starburst amacrine cell is inversely proportional to its irresolution. This is done by...