3 citations · 4 across the 13 of their papers we have counts for
14 papers
What Must Survive? Exact Task-Information--State Frontiers Under Partial Task Revelation
Ronald Katende
A state may need to be compressed before its exact downstream task is known. For a finite family of linear task operators $\{T_u\}_{u\in\U}$, we characterize exactly how much state…
Contextual Fraction Beyond Satisfiability: Pure NAE Completeness, Exact Orbit Packings, and Width Barriers
Ronald Katende
The contextual fraction measures how much globally consistent probability can be packed beneath prescribed local event probabilities. We study the quantitative regime in which supp…
Contextual Fraction on Permutation Gain Graphs: Exact Algorithms, Query Lower Bounds, and Dynamic Maintenance
Ronald Katende
For an explicitly represented finite empirical model, deciding whether the contextual fraction is strictly below one is NP-complete, while the standard exact linear program has one…
Interpretive Efficiency: Information-Geometric Foundations of Data Usefulness
Ronald Katende
Interpretability is central to trustworthy machine learning, yet existing metrics rarely quantify how effectively data support an interpretive representation. We propose Interpreti…
Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
Ronald Katende
We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (ϕ), we define (Q_{β,γ}(ϕ)=I(ϕ(X);Y)-β\mathcal C(ϕ)-γd_{\mathrm{…
Structured Variational -Decomposition for Accurate and Stable Low-Rank Approximation
Ronald Katende
We introduce the -decomposition, a non-orthogonal matrix factorization of the form , where , , and…
Counterfactual Operator Relevance for PDE Discovery: Screening, Pruning, and Identifiability
Ronald Katende
We study operator relevance in data-driven partial differential equation (PDE) discovery. Sparse residual methods can select terms that improve residual fit, but residual contribut…
Decentralized Neural Networks for Robust and Scalable Eigenvalue Computation
Ronald Katende
This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challe…
Symmetry-Enriched Learning: A Category-Theoretic Framework for Robust Machine Learning Models
Ronald Katende
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hy…
A Nonlinear Generalization of the Bauer-Fike Theorem and Novel Iterative Methods for Solving Nonlinear Eigenvalue Problems
Ronald Katende
Nonlinear eigenvalue problems (NEPs) present significant challenges due to their inherent complexity and the limitations of traditional linear eigenvalue theory. This paper address…
Cross-Country Comparative Analysis of Climate Resilience and Localized Mapping in Data-Sparse Regions
Ronald Katende
Climate resilience across sectors varies significantly in low-income countries (LICs), with agriculture being the most vulnerable to climate change. Existing studies typically focu…
Optimizing Neural Network Performance and Interpretability with Diophantine Equation Encoding
Ronald Katende
This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and de…
Topological Eigenvalue Theorems for Tensor Analysis in Multi-Modal Data Fusion
Ronald Katende
This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion, leveraging topological invariants such as Betti numbers. Traditional…
Core-Conditioned Regularized Matrix Tri-Factorization for High-Dimensional Structured Systems
Ronald Katende
This paper studies a regularized matrix tri-factorization \(A\approx PDQ\), where \(P\) and \(Q\) are side factors and \(D\) is a central core whose conditioning can be explicitly…