7 papers
Interpretability for Turing Machines
Billy Snikkers, Rumi Salazar, Daniel Murfet +1
We show that susceptibilities, an interpretability technique developed for neural networks, can identify the presence of algorithmic structure in Turing machines by probing the loc…
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…
Programs as Singularities
Daniel Murfet, Will Troiani
We develop a correspondence between the structure of Turing machines and the structure of singularities of real analytic functions, based on connecting the Ehrhard-Regnier derivati…
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…
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…
Gentzen-Mints-Zucker duality
Daniel Murfet, William Troiani
The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrati…