Pierpaolo Vivo

Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo

We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud of data points is obtained via a double-stochastic process, where the sample is obtained from a Gaussian distribution whose variance is itself a random parameter sampled from a scalar distribution $\varrho$. As a result, our analysis covers a large family of data distributions, including the case of power-law-tailed distributions with no covariance, and allows us to test recent "Gaussian universality" claims. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and we analytically characterise the separability transition.

Silvia Bartolucci, Pierpaolo Vivo

Quantifying the workplace productivity effects of Generative Artificial Intelligence is now central to economics, management, and public policy. The deployment of AI tools in customer service, writing, software development, and consulting operations has been reported to generate large per-task productivity gains, typically measured as tasks completed per worker-hour or reductions in mean handle time. We argue that such mean-based metrics can misrepresent AI's effects in workflows where tasks accumulate and compete for scarce human attention. AI assistance can generate a deceptive productivity signature: average completion times fall because AI tools typically supply a fast first draft, yet workflow-level performance deteriorates when a subset of AI errors escapes review and returns as costly downstream rework. We call this divergence between mean task speed and system-level delay the variance wedge. Depending on the operational parameters, the most time-efficient way to complete a workflow may undergo a transition between two task-processing regimes, a fully AI-assisted and a fully manual one. We formalize the mechanism as a queueing model and derive two main implications analytically. First, under congestion, reviewers rationally raise the risk threshold for checking AI outputs, reducing scrutiny precisely when it would matter the most. Second, AI assistance can stabilize an overloaded workflow only when (i) the fraction of tasks handled by AI exceeds a critical threshold, and (ii) the human attention required for review and expected rework is lower than the attention for manual completion, a requirement substantially more stringent than faster draft generation. These results suggest that AI deployment should be evaluated not only by average task speed, but by its overall effects on congestion, rework, and the robustness of human oversight under load.

Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica method from statistical physics, we analytically compute the typical value of the top eigenvalue, the top eigenvector component density, and the overlap between the signal vector and the top eigenvector. The solution is given in terms of recursive distributional equations for auxiliary probability density functions which can be efficiently solved using a population dynamics algorithm. Specialising the noise matrix to Poissonian and Random Regular degree distributions, the critical signal strength is analytically identified at which a transition happens for the recovery of the signal via the top eigenvector, thus generalising the celebrated BBP transition to the sparse noise case. In the large-connectivity limit, known results for dense noise are recovered. Analytical results are in agreement with numerical diagonalisation of large matrices.