Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Interpretability”

Interpretability

Alexandre Borovik, Ali Nesin · 1994

Abstract We need very little from model theory: just two concepts, and no real results, not even the compactness theorem. The concepts, definability and interpretability, are dealt with in this chapter and the next. The algebraist who has gi en no thought to formal languages will need to look carefully at the material of this section as well as its first few applications subsequently. The motivation comes from algebraic geometry over algebraically closed fields, where definable sets in the technical sense turn out to be the Zariski constructible sets (Zariski open subsets of algebraic varieties) in affine space. The notion of the dimension of an irreducible variety extends to a notion of dimension for constructible sets with little change in its properties, though it becomes somewhat harder to define irreducibility and impossible to define connectivity in this context.

Cited by 0

Interpretability

Henrica C. W. de Vet, Caroline B. Terwee, Lidwine B. Mokkink et al. · Cambridge University Press eBooks · 2011

After addressing the development of measurement instruments in Chapters 3 and 4 and evaluating measurement properties (i.e. reliability, validity and responsiveness) in Chapters 5–7, it is time to pay attention to the interpretability of the scores when applying the measurement instruments. For well-known instruments, such as blood pressure measurements and the Apgar score, the interpretability will cause no problems, but for new or lesser known instruments this may be challenging. This particularly applies to the scores for multi-item measurement instruments, the meaning of which is not immediately clear. For example, in a randomized trial on back pain carried out in the United Kingdom, the effectiveness of exercise therapy and manipulation was compared with usual care in 1334 patients with low back pain. The researchers used the Roland–Morris Disability Questionnaire (RDQ) to assess functional disability (UK BEAM trial team, 2004). The RDQ has a 0–24-point scale, with a score of 0 indicating no disability, and 24 indicating very severe disability. The mean baseline score for the patients with low back pain was 9.0. In the group who received usual care, the mean RDQ value decreased to 6.8 after 3 months, resulting in an average improvement of 2.2 points. This gives rise to the following questions: What does a mean value of 9.0 points on the 0–24 RDQ scale mean? In addition, is an improvement of 2.2 points meaningful for the patients? The primary focus of this chapter is on the interpretability of scores and change scores on a measurement instrument. In other words, the aim is to learn more about the measurement instrument, and not about the disease under study.

Cited by 10

Materializing Interpretability

Jesse Josua Benjamin, Claudia Müller-Birn · 2019

Interpretability has become a key objective in the research, development and implementation of machine learning algorithms. However, existing notions of interpretability may not be conducive to how meaning emerges in algorithmic systems that employ ML algorithms. In this provocation, we suggest that hermeneutic analysis can be used to probe assumptions in interpretability. First, we propose three levels of interpretability that may be analyzed: formality, achievability, and linearity. Second, we discuss how the three levels have surfaced in prior work, in which we conducted an explicitation interview with a developer to understand decision-making in an algorithmic system implementation. Third, we suggest that design practice may be needed to move beyond analytic deconstruction, and showcase two design projects that exemplify possible strategies. In concluding, we suggest how the proposed approach may be taken up in future work and point to research avenues.

Cited by 6

Interpretability formalized

Joosten, Joost Johannes · Data Archiving and Networked Services (DANS) · 2004

The dissertation is in the first place a treatment of mathematical interpretations. Interpretations themselves will be studied, but also shall they be used to study formal theories.
\n
\n 
\nInterpretations, when used in comparing theories, tell us, in a natural way, something about proof-strength of formal theories. Roughly, an interpretation j of a theory T into a theory S is a structure-preserving map, mapping axioms of T to theorems of S. Structure-preserving means that the map should com-mute with proof constructions and with logical connectives. For example, the constraints on the map should exclude the possibility that we simply map all axioms of T to some tautology of S, say 1 = 1. The notion of interpretahil- ity that is studied in the thesis, is the notion of relativized interpretability as studied by Tarski et al. in [TMR53].
\n
\n 
\nIn the thesis, only interpretations between first order theories of some mini-mal strength will be considered. As said before, interpretations will be used to study theories, but also shall they be the subject of our study. In the latter case, the emphasis lies on the structural behavior of interpretahility. This behavior is manifested in so-called interpretability logics. The dissertation is organised in three parts. 
\n
\nPart one 
\n
\n
\nIn the first part we introduce the notion of interpretability, and relate it to other important meta-mathematical notions. This results in the well-known Orey-Hajék characterizations of interpretability. Central notions in these characterizations are consistency statements, definable cuts and II1-conservativity.
\n
\n Interpretability, being a purely syntactical notion, is formalized, and also the formalizations take place in a completely formalized setting. For every implication in the characterizations, we will carefully spell out the conditions on the meta-theory. The characterizations get an especially elegant form when formulated in terms of category theory.
\n
\n 
\nAt the end of the first part we will focus on interpretahility logics. In es-pecially, we shall be interested in a modal characterization of IL(All), the interpretability logic of all reasonable arithmetical theories. We present a new principle R for this logic and prove its arithmetical validity. This correctness is proved in two different ways. We present two modal systems corresponding to these different proof methods. We see that all principles in IL(All), known so far, are provable in both modal systems, again, giving rise to two different soundness proofs.
\n
\n Part two 
\n
\n
\nIn the section part of the thesis we fully concentrate on the modal semantics for interpretability logics. A central question is the modal completeness of interpretability logics. We give completeness proofs for the logics IL, ILM, ILM0, ILW and ILW*. The completeness proofs for ILM0 and for ILW* can he seen as first proofs. We also expose some applications of completeness proofs.
\n
\n 
\nWe try to develop a uniform format for completeness proofs for interpretability logics. However, there still has to be done more work and research in this direction. A step in the good direction is undoubtedly where we introduce full labels and develop some general theory of these labels.
\n
\n 
\nIn the last chapter of the second part we prove ILP0W* to be modally incomplete. In this proof, the principle R plays a central role.
\n
\nPart three
\n
\n
\nIn the third and final part of the thesis, we shall study Primitive Recursive Arithmetic (PRA). We shall especially pay some attention to its relation to IΣ1. We shall give two proofs of Parsons' theorem. One proof is of a model-theoretic nature and gives us some insight in provable closure properties of the provably total recursive functions. 
\n
\n
\nPRA and IΣ1 are known to be equi-consistent over PRA. However, IΣ1 prove the consistency of PRA on a definable cut. We give two proofs of this theorem. 
\n
\n
\nAn important problem is the modal characterization of IL(PRA), the interpretability logic of PRA. We calculate a frame condition for Beklemishev's principle. We also show that Beklemishev's principle is at least as strong as Zambella's principle. 
\n
\n
\nWe give a characterization of the closed fragment of the interpretahility logic of PRA with a constant for IΣ1. Also, we develop a method for calculating up-perbounds on IL(PRA) (and on interpretahility logics in general) and provide such an upperhound. The calculation proceeds by restricting the possibly substitutions in Solovay's completeness proof. 
\nThe encore of the thesis deals with modal semantics for the closed fragment of Japapridze's logic GLP. We give a small variant of Ignatiev's model, a model of 'depth ε0'. The model is submitted to a purely modal analysis without further reference to arithmetical ingredients. 
\n
\nReferences 
\n
\n[TMR53] A. Tarski, A. Mostowski, and R. Robinson. Undecidable theories. North-Holland, Amsterdam, 1953.

Cited by 3Open access

Model interpretability.

Stefano van Gogh (13569844), Subhadip Mukherjee (13569847), Jinqiu Xu (2833439) et al. · Figshare · 2022

<p>Due to the local linearity of a bias-free network, it is possible to visualize how the denoising happens by computing the Jacobian of the network with respect to the input image [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0272963#pone.0272963.ref045" target="_blank">45</a>]. A small image patch is shown for computational reasons. From left to right, we plot the noisy input patch, its denoised counterpart with two pixels highlighted in red. The third and fourth image show how strongly each pixel is weighted to denoise the two pixels highlighted in red.</p>

Cited by 0Open access

Feasible interpretability

Rineke Verbrugge · 1993

Abstract Abstract In PA, or even in 1.Δ.o+ EXP, we can define the concept of feasible interpretability. Informally stated, U feasibly interprets V iff: for some interpretation, U proves the interpretations of all axioms of V by proofs with Giidel numbers of length polynomial in the length of the Gödel numbers of those axioms.

Cited by 24

Interpretability analysis.

Michela C. Massi (14599915), Nicola R. Franco (14599918), Andrea Manzoni (9449680) et al. · Figshare · 2023

<p>(A) Absolute frequency of the generative rules in the training data, limited to the positive class. (B) Interactions selected by <i>hi</i>PRS with <i>K</i> = 10 and corresponding <i>β</i> coefficients. (C) Coefficients of the glinternet model with 3 interaction terms: main effects are in gray, interactions in yellow. (D) Lists of SNPs selected by SVM-Behravan during its five internal cross validations, cf. Benchmark Algorithms in the Materials and Methods Section. Note: reported results are limited to one simulation among the 30 randomly generated datasets.</p>

Cited by 0Open access

Measuring Interpretability: An Investigation of Domain Independent Interpretability

Prateek Goel, Rosina O. Weber · 2025

Interpretability and explainability share the connotation of characterizing information that artificial intelligence (AI) models can provide for humans. They differ in that interpretability refers to information produced from inherent properties of AI models whereas explainability refers to what humans absorb from said information. Previous work suggests that information that may be used in lieu of explainability be evaluated for computational quality before it is made available for human studies to evaluate explainability. Measurement is a precondition for evaluation, therefore this paper investigates approaches proposed to measure aspects relevant for interpretability of the information that AI models produce. The goal is to evaluate, from a computational perspective, the quality of information models provide. The benefit of such evaluations would be the ability to provide valuable feedback to improve their quality. The resulting information could then be offered for user studies in different domains and applications. To validate interpretability, we rely on two concepts that reflect consensual notions, namely, those that compare models such as deep learning is less interpretable than decision trees and that the number of features is inversely proportional to interpretability.

Cited by 0

Iconicity, ambiguity, interpretability

Elżbieta Tabakowska · Iconicity in language and literature · 2017

The paper argues that diagrammatic iconicity can be used in discourse as a means to elicit “covert” meanings of expressions, by evoking associations with other expressions that differ in meaning but are built according to the same structural schemas. The more strongly entrenched the expression thus evoked (proverbs being a case in point), the higher the probability that the association will be recognized and the “covert” meaning brought to the fore. It is claimed that interpretability of expressions that involve diagrammatically iconic associations is a matter of degree and that it can be measured along scales based on pragmatic parameters of the contexts of discourse.

Cited by 1

GAMLSS and interpretability

Marmolejo-Ramos, Fernando · Figshare · 2022

This folder contains files that further examine the interpretation of a GAMLSS model

Cited by 0Open access