Davide La Torre

Background. Clinicians influence whether Internet-delivered and artificial intelligence (AI)-enabled interventions reach routine care. Since late 2022, web-based large language models (LLMs) have widened clinicians’ exposure to AI.Objective. To describe differences in physicians’ attitudes toward clinical AI between 2022 and 2026, a period of widespread LLM diffusion, and to examine correlates of trust in AI clinical decisions.Methods. Repeated cross-sectional comparison of two open web surveys of physicians in Italy, conducted in 2022 before the release of ChatGPT (N=500) and in 2026 (N=500), using the same eight-item attitude scale. Each item was compared between waves using mean differences and standardized effect sizes with false-discovery-rate correction. Correlates of trust in AI clinical decisions in 2026 were examined with ordinal logistic regression.Results. After correction, five of the eight items were higher in 2026, but most differences were small. The largest were for ease of use (+0.59 points; d=0.58), utility (d=0.37) and peer encouragement (d=0.29). Perceived trustworthiness did not differ (d=0.05), and perceived safety and transparency were slightly lower (d=−0.13). The composite score was 3.46 in 2022 and 3.66 in 2026. In 2026, 80.2% of respondents had used AI tools in clinical practice, but only 4.0% had received formal training and 81.4% reported low familiarity. Trust in AI clinical decisions was low (mean 2.95 out of 5) and was most strongly associated with perceived trustworthiness (adjusted odds ratio 1.94 per standard deviation, 95% CI 1.54-2.45). Governance expectations were near-unanimous (mean 4.59).Conclusions. During the diffusion of LLMs, physicians’ attitudes toward clinical AI were modestly more favorable, while trust in AI decisions remained limited, formal training rare and governance expectations high. Clinician training and accountability structures are plausible targets for implementing AI-enabled Internet interventions.

BackgroundPhysician trust is the rate-limiting step in the clinical translation of artificial intelligence (AI). The public diffusion of large language models (LLMs) since late 2022 may have reshaped that trust at scale, yet longitudinal evidence outside Anglophone health systems remains scarce.ObjectiveTo quantify the magnitude, structure and determinants of change in Italian physicians’ attitudes toward clinical AI between 2022 and 2026, and to identify the levers that now govern acceptance and decision-level trust.MethodsRepeated cross-sectional study comparing a 2022 national baseline (N=500, fielded before the public release of ChatGPT) with a 2026 national cohort (N=500), both administered an identical validated eight-factor Attitude-toward-AI scale. Reporting follows STROBE and CHERRIES. The prespecified analytic plan combined reliability and dimensionality testing; standardized effect sizes with 95% confidence intervals; Benjamini-Hochberg false-discovery control; random-effects pooling with bootstrap and minimum-effect corroboration; heteroskedasticity-consistent regression with two variance decompositions; proportional-odds ordinal models; and silhouette-validated clustering.ResultsThe scale was highly reliable (α=0.87; ω=0.90). All eight dimensions increased (Benjamini-Hochberg P<0.001); the composite rose from 3.46 to 4.23 (+22.2%), with a pooled standardized mean difference of 0.74 (95% CI 0.46-1.02) exceeding a small-effect benchmark (P<0.001). Gains concentrated in peer encouragement (d=1.35), self-rated competence and ease of use. Trustworthiness dominated acceptance and multiplied the odds of trusting AI clinical decisions more than fivefold per standard deviation (aOR 5.31, 95% CI 3.57-7.90). Universal AI use coexisted with low self-rated familiarity (440/500, 88.0%) and minimal formal training (20/500, 4.0%); 367/500 (73.4%) simultaneously embraced AI, demanded accountability and retained professional concern.ConclusionsTrust in clinical AI has risen sharply and broadly, but now outpaces competence and remains contingent on governance. Workforce capability-building and institutional accountability, not further advocacy, are the decisive levers for safe and sustainable deployment.

We develop a mathematical framework that transplants the classical Collage Theorem, andits generalization to coercive fixed-point operators, into the setting of neural operators (NOs)acting between infinite-dimensional function spaces. Given observations f of an unknown system, the inverse problem is to identify parameters θ such that the learned operator Tθ maps acandidate element ¯u close to f. We introduce a learnable collage bound: an explicit, computable estimate ∥¯u - u∗∥ ≤ C(θ) ∥f -Tθ¯u∥+∆(θ) in which both the stability constant C(θ) and the residual floor ∆(θ) are determined by the network weights and degrade gracefully under approximation error. After recalling the background on complete metric spaces, Banach fixed-point theory, and the classical Generalized Collage Theorem, we establish a uniform Lipschitz estimate for neural operator families satisfying a spectral-norm weight condition, a rigorous coercivity certificate based on the symmetric part of the Jacobian, and two forms of the Neural Operator Generalized Collage Theorem: one that inherits coercivity from the true forward map and one that certifies coercivity of the learned operator directly. We then introduce a training criterion, the Collage Loss, whose minimization drives down the collage residual while keeping the stability constant bounded, and we prove a consistency result for the resulting inverse problem estimator. We further analyze the quantitative behaviour of the framework: the reconstruction error inherits the forward approximation rate of the architecture, any low-loss parameter carries a certified coercivity floor that insulates the bound from the non-convexity of training, and a covering of the admissible set transfers empirical residuals into a uniform error estimate. Nine numerical examples illustrate the framework: a linear deconvolution problem with fully explicit constants, a Picard-operator inverse problem for an ordinary differential equation, a cautionary exampleon the backward heat equation in which coercivity fails, a Volterra integral problem in which the learnable bound is verified across a family of candidates, three further examples confirming the predicted spectral convergence rate, the stability of the certified coercivity under stochastic gradient training, and the covering-based control of the off-sample error, a physics-informed neural network in which the collage distance is precisely the PDE residual and coercivity follows from ellipticity, and a digit-classification problem that lies outside the coercive regime and delineates the boundary of the framework. The analysis exposes a fundamental tension between approximation capacity and the uniformity of the coercivity constant required by the collage bound, and we discuss how the condition number of he learned operator governs both quantities.

The classical Collage Theorem of Barnsley gives a quantitative estimate for approximatinga target set by the attractor of an iterated function system (IFS) in a complete metric space,resting on the Hausdorff metric, metric contractivity, and Banach’s fixed point theorem. Wedevelop a generalization of this theory to topological spaces carrying no metric. After recall-ing the background, we introduce orbit-contractivity as the primitive notion of contraction and relate it, through the Bessaga–Meyers metrization theorems, to classical metric contractivity. Working with the Vietoris topology on the hyperspace of compact sets, we prove existence and uniqueness of IFS attractors on compact Hausdorff spaces, and establish a Topological Collage Theorem in which forward-invariant open neighbourhoods replace ε-balls. We then develop a Uniform Collage Theorem with quantitative entourage bounds in complete Hausdorff uniform spaces that recovers Barnsley’s estimate as a special case, and we record the correspondence between attractors and the fixed points of the Hutchinson functor in the language of coalgebras.A dimension discussion introduces a topological spectral radius for the IFS maps and relatescovering dimension to a topological Moran equation. We treat the locally compact case through the one-point compactification, and we give a careful account of the non-Hausdorff setting, where sobriety replaces Hausdorff separation and the lower Vietoris (Scott) topology governs the hyperspace of closed sets. Several worked examples in genuinely non-metrizable spaces — the Alexandroff double circle, the long line, the co-countable topology, and the Zariski setting — illustrate the theory, and a final discussion examines what orbit-contractivity forces on the fundamental group of an attractor.