2 citations · 4 across the 8 of their papers we have counts for
10 papers
Sharp Higher Integrability Theory, Part I: The -norm of the Beurling--Ahlfors transform
Andrea Agazzi, Kari Astala, Giuseppe Bruno +18
We confirm a conjecture posed by T. Iwaniec in 1982: the norm of the Beurling--Ahlfors transform is if , and if .
Quantitative Diffusive Limits for Singular Nonlocal Transport
Andrea Agazzi, Giuseppe Bruno, Federico Pasqualotto +1
We study the nonlocal continuity equation \[ \partial_tμ_b =\operatorname{div}\!\left( μ_b\nabla\log\bigl((I-b^2Δ)^{-1}μ_b\bigr) \right) \] on a closed connected Riemannian manifol…
Morrey's problem in and
Andrea Agazzi, Giuseppe Bruno, André Guerra +1
We find an explicit rank-one convex non-quasiconvex integrand in : to falsify the quasiconvexity inequality, we exhibit a map …
Quasiconvexity for the Dacorogna--Marcellini Energy
Giuseppe Bruno, Federico Pasqualotto
We prove that the planar Dacorogna--Marcellini energy is quasiconvex exactly when it is rank-one convex, i.e. if and only if .…
Scaling Limits of Long-Context Transformers
Giuseppe Bruno, Shi Chen, Zhengjiang Lin +2
We study the long-context limit of softmax self-attention with a fixed query and a random context of i.i.d. keys on the sphere, viewing the inverse temperature as the sca…
Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
Andrea Agazzi, Giuseppe Bruno, Eloy Mosig García +2
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time st…
A multiscale analysis of mean-field transformers in the moderate interaction regime
Giuseppe Bruno, Federico Pasqualotto, Andrea Agazzi
In this paper, we study the evolution of tokens through the depth of encoder-only transformer models at inference time by modeling them as a system of particles interacting in a me…
Securities Transaction Settlement Optimization on superconducting quantum devices
Francesco Martini, Daniele Lizzio Bosco, Carlo Barbanera +7
We describe a quantum variational algorithm for securities transactions settlement optimization, based on a novel mathematical formalization of the problem that includes the most r…
Emergence of meta-stable clustering in mean-field transformer models
Giuseppe Bruno, Federico Pasqualotto, Andrea Agazzi
We model the evolution of tokens within a deep stack of Transformer layers as a continuous-time flow on the unit sphere, governed by a mean-field interacting particle system, build…
The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks
Andrea Bonfanti, Giuseppe Bruno, Cristina Cipriani
The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the cas…