6 papers
Unit-Consistent (UC) Adjoint for GSD and Backprop in Deep Learning Applications
Jeffrey Uhlmann
Deep neural networks constructed from linear maps and positively homogeneous nonlinearities (e.g., ReLU) possess a fundamental gauge symmetry: the network function is invariant to…
Graded Projection Recursion (GPR): Corrections, Obstructions, and Conservative Approximate Matrix Multiplication
Jeffrey Uhlmann
Earlier versions proposed Graded Projection Recursion (GPR) as a deterministic packed-recursion framework for model-honest near-quadratic dense matrix multiplication. This revised…
The Fourth State: Signed-Zero Ternary for Stable LLM Quantization (and More)
Jeffrey Uhlmann
Quantization is usually regarded as a means to trade quality of performance for reduced compute requirements, i.e., as a suboptimal approximation. However, if examined in terms of…
Is Arrow's Dictator a Drinker?
Jeffrey Uhlmann
We critique the formulation of Arrow's no-dictator condition to show that it does not correspond to the accepted informal/intuitive interpretation. This has implications for the th…
A Note on the Incompleteness of Gödel's Incompleteness Theorems
Jeffrey Uhlmann
In this note we observe that automated theorem provers (ATPs) that recursively enumerate theorems in a particular way will fail to identify some valid theorems for a reason that is…
A Cautionary Example Relating to the Interpretation of Numerical Results
Jeffrey Uhlmann
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometr…