59 citations · 224 across the 22 of their papers we have counts for
25 papers
Solomonoff Induction and Singular Integrals
Will Troiani, Daniel Murfet
The Solomonoff distribution assigns an a priori probability to a finite binary string by summing over all programs whose output begins with , weighting a program of leng…
Linear Logic and the Hilbert Scheme
William Troiani, Daniel Murfet
We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logi…
Linear Logic and Quantum Error Correcting Codes
Daniel Murfet, William Troiani
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-eliminat…
The Local Learning Coefficient: A Singularity-Aware Complexity Measure
Edmund Lau, Zach Furman, George Wang +2
The Local Learning Coefficient (LLC) is introduced as a novel complexity measure for deep neural networks (DNNs). Recognizing the limitations of traditional complexity measures, th…
Elimination and cut-elimination in multiplicative linear logic
Daniel Murfet, William Troiani
We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination…
Geometry of Program Synthesis
James Clift, Daniel Murfet, James Wallbridge
We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases…