Oskar Eriksson | Searcharxiv

arXiv2026

A Graded Modal Dependent Type Theory with Erasure, Formalized

We present a graded modal type theory, a dependent type theory with grades that can be used to enforce various properties of the code. The theory has $Π$-types, weak and strong $Σ$-types, natural numbers, an empty type, and a universe, and we also extend the theory with weak and strong unit types and graded $Σ$-types. The theory is parameterized by a modality structure, a kind of partially ordered semiring, whose elements (grades) are used to track the usage of variables in terms and types. Different modalities are possible. We focus mainly on quantitative properties, in particular erasure: with the erasure modality one can mark function arguments as erasable. The theory is fully formalized in Agda. The formalization, which uses a syntactic Kripke logical relation at its core and is based on earlier work, establishes major meta-theoretic properties such as subject reduction, consistency, normalization, and decidability of definitional equality. We also prove a substitution theorem for grade assignment, and preservation of grades under reduction. Furthermore we study an extraction function that translates terms to an untyped $λ$-calculus and removes erasable content, in particular function arguments with the "erasable" grade. For a certain class of modalities we prove that extraction is sound, in the sense that programs of natural number type have the same value before and after extraction. Soundness of extraction holds also for open programs, as long as all variables in the context are erasable, the context is consistent, and erased matches are not allowed for weak $Σ$-types.

cs.LO↗

arXiv2022

Robust automated radiation therapy treatment planning using scenario-specific dose prediction and robust dose mimicking

Purpose: We present a framework for robust automated treatment planning using machine learning, comprising scenario-specific dose prediction and robust dose mimicking. Methods: The scenario dose prediction pipeline is divided into the prediction of nominal dose from input image and the prediction of scenario dose from nominal dose, each using a deep learning model with U-net architecture. By using a specially developed dose-volume histogram-based loss function, the predicted scenario doses are ensured sufficient target coverage despite the possibility of the training data being non-robust. Deliverable plans may then be created by solving a robust dose mimicking problem with the predictions as scenario-specific reference doses. Results: Numerical experiments are performed using a dataset of 52 intensity-modulated proton therapy plans for prostate patients. We show that the predicted scenario doses resemble their respective ground truth well, in particular while having target coverage comparable to that of the nominal scenario. The deliverable plans produced by the subsequent robust dose mimicking were showed to be robust against the same scenario set considered for prediction. Conclusions: We demonstrate the feasibility and merits of the proposed methodology for incorporating robustness into automated treatment planning algorithms.

physics.med-ph↗