arXiv subjects

Lorenzo Tiberi

Publications and source records attributed to Lorenzo Tiberi.

6 recordsLinked to original sources

arXiv2026

Connecting $t$-channel Dark Matter Models to the Standard Model Effective Field Theory

We investigate the connection between simplified dark matter models featuring a $t$-channel scalar mediator and the Standard Model Effective Field Theory (SMEFT). We focus on scenarios with fermionic dark matter interacting with leptons, under the assumption of Minimal Flavor Violation. The dimension-six SMEFT Wilson coefficients are computed in the Warsaw basis at one loop, with the aid of Matchete. Assuming a compressed mass spectrum for the dark matter and the mediator, we incorporate coannihilations, Sommerfeld enhancement, and bound-state effects in the relic density calculation. We then analyze the interplay between the dark matter energy density, global SMEFT fits, and direct detection constraints. Our results show that SMEFT bounds, though loop-suppressed, can meaningfully constrain the parameter space for $m_χ\gtrsim 0.5$ TeV and $\mathcal{O}(1)$ portal couplings.

hep-ph↗

arXiv2026

Is the Standard Model Effective Field Theory Enough for Higgs Pair Production?

We study Higgs-boson pair production in the Standard Model Effective Field Theory (SMEFT) up to dimension six and in the Higgs Effective Field Theory (HEFT) at leading order in the effective theory expansion, and assess which description is appropriate in concrete UV scenarios. Motivated by "Loryon"-inspired models, we compare the Higgs pair production cross sections predicted by the full models to their SMEFT and HEFT counterparts. We identify regimes in which the two EFTs provide comparable descriptions, and clarify the limits required for their couplings to match. We also find that, for parts of parameter space in some of these models, HEFT can reproduce Higgs pair production more accurately than SMEFT, highlighting di-Higgs measurements as a potential probe of non-linear electroweak dynamics.

hep-ph↗

arXiv2024

Dissecting the Interplay of Attention Paths in a Statistical Mechanics Theory of Transformers

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable. We develop a statistical mechanics theory of Bayesian learning in this model, deriving exact equations for the network's predictor statistics under the finite-width thermodynamic limit, i.e., $N,P\rightarrow\infty$, $P/N=\mathcal{O}(1)$, where $N$ is the network width and $P$ is the number of training examples. Our theory shows that the predictor statistics are expressed as a sum of independent kernels, each one pairing different 'attention paths', defined as information pathways through different attention heads across layers. The kernels are weighted according to a 'task-relevant kernel combination' mechanism that aligns the total kernel with the task labels. As a consequence, this interplay between attention paths enhances generalization performance. Experiments confirm our findings on both synthetic and real-world sequence classification tasks. Finally, our theory explicitly relates the kernel combination mechanism to properties of the learned weights, allowing for a qualitative transfer of its insights to models trained via gradient descent. As an illustration, we demonstrate an efficient size reduction of the network, by pruning those attention heads that are deemed less relevant by our theory.

cs.LG↗

arXiv2023

Hidden connectivity structures control collective network dynamics

Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are naturally encoded in the space that more directly relates to network dynamics - the space of the connectivity eigenmodes. We develop a mathematical theory to impose eigenmode structures on connectivity, systematically characterizing their effect on network dynamics. We find the density of nearly-critical eigenvalues to be a particularly fundamental structure. It flexibly controls the power-law scaling of dynamical observables, in analogy with the system's spatial dimension in classical critical phenomena. This mechanism provides control over observables which are found to be fine-tuned in brain networks, but remained so far unexplained by traditionally studied structures, such as connectivity motifs. Specifically, the slope of the principal component spectrum of neural activity can be fine-tuned, as observed in primary visual cortex of mice. Furthermore, a novel transition between high and low dimensional activity allows for a wide and flexible tuning of dimensionality, as observed throughout cortex. The here discovered structures thus largely complement motifs. In fact, they are of a different, collective nature: they are not reflected by any local motif configuration. This result shows that many functionally relevant structures can remain hidden within the apparent randomness of highly heterogeneous cortical circuits. Our methods enable revealing these structures and investigate their effect on network dynamics.

cond-mat.dis-nn↗

arXiv2021

Gell-Mann-Low criticality in neural networks

Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the interaction between degrees of freedom across all length scales, which allows for complex nonlinear computation. We present a renormalized theory of a prototypical neural field theory, the stochastic Wilson-Cowan equation. We compute the flow of couplings, which parameterize interactions on increasing length scales. Despite similarities with the Kardar-Parisi-Zhang model, the theory is of a Gell-Mann-Low type, the archetypal form of a renormalizable quantum field theory. Here, nonlinear couplings vanish, flowing towards the Gaussian fixed point, but logarithmically slowly, thus remaining effective on most scales. We show this critical structure of interactions to implement a desirable trade-off between linearity, optimal for information storage, and nonlinearity, required for computation.

cond-mat.dis-nn↗

arXiv2017

Synchronization Patterns in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control

Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators' natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples.

math.OC↗