arXiv subjects

Matteo Ciarchi

Publications and source records attributed to Matteo Ciarchi.

6 recordsLinked to original sources

arXiv2026

A Bifurcation Theory for the Equilibria of Modern Hopfield Networks

Modern Hopfield networks provide a unifying framework for associative memory, transformer attention, diffusion-based generative models, and biological attractor dynamics, linking these systems through a common energy-based dynamics in which states are updated toward weighted combinations of stored patterns. Across these settings, network dynamics is determined by the organization of the energy landscape and the bifurcations of its fixed points. Despite their central role, a general theory of these bifurcations has remained unavailable beyond specific architectures and idealized pattern ensembles. Here we derive stability and bifurcation criteria for the fixed points of general convex-dual Modern Hopfield networks for a general statistics of the stored patterns. Applying this framework to random, block-correlated, and infinitely hierarchical pattern ensembles, we show how memory correlations systematically organize the emergence of hierarchical attractors through successive bifurcations. We further demonstrate that these predictions quantitatively describe retrieval bifurcations in MHNs storing patterns sampled from MNIST, and recapitulate the hierarchical organization of hematopoietic cell identities. Our results establish a general bifurcation theory for Modern Hopfield networks and identify the organization of fixed points as a unifying principle underlying their computational and biological behavior.

cond-mat.dis-nn↗

arXiv2026

Active fluctuations induce buckling of living surfaces

Active tissues exhibit tension fluctuations that are correlated in space and time. We study a minimal overdamped surface model in which such fluctuations enter as a zero-mean, multiplicative modulation of the local surface tension. Although the deterministic elastic dynamics (tension plus bending) stabilizes the flat state for all nonzero wave numbers, we find that sufficiently persistent active fluctuations generate positive ensemble growth rates for a finite band of Fourier modes, leading to stochastic buckling with wavelength selection. A non-Markovian theory based on the Novikov--Furutsu theorem captures the instability threshold and unstable band observed in simulations.

cond-mat.soft↗

arXiv2024

Phase behavior of Cacio e Pepe sauce

``Pasta alla Cacio e pepe'' is a traditional Italian dish made with pasta, pecorino cheese, and pepper. Despite its simple ingredient list, achieving the perfect texture and creaminess of the sauce can be challenging. In this study, we systematically explore the phase behavior of Cacio e pepe sauce, focusing on its stability at increasing temperatures for various proportions of cheese, water, and starch. We identify starch concentration as the key factor influencing sauce stability, with direct implications for practical cooking. Specifically, we delineate a regime where starch concentrations below 1\% (relative to cheese mass) lead to the formation of system-wide clumps, a condition determining what we term the ``Mozzarella Phase'' and corresponding to an unpleasant and separated sauce. Additionally, we examine the impact of cheese concentration relative to water at a fixed starch level, observing a lower critical solution temperature that we theoretically rationalized by means of a minimal effective free-energy model. \tcr{We further analyze the effect of a less traditional stabilizer, trisodium citrate, and observe a sharp transition from the Mozzarella Phase to a completely smooth and stable sauce, in contrast to starch-stabilized mixtures, where the transition is more gradual.} Finally, we present a scientifically optimized recipe based on our findings, enabling a consistently flawless execution of this classic dish.

cond-mat.soft↗

arXiv2024

Flocking by Turning Away

Flocking, as paradigmatically exemplified by birds, is the coherent collective motion of active agents. As originally conceived, flocking emerges through alignment interactions between the agents. Here, we report that flocking can also emerge through interactions that turn agents away from each other. Combining simulations, kinetic theory, and experiments, we demonstrate this mechanism of flocking in self-propelled Janus colloids with stronger repulsion on the front than on the rear. The polar state is stable because particles achieve a compromise between turning away from left and right neighbors. Unlike for alignment interactions, the emergence of polar order from turn-away interactions requires particle repulsion. At high concentration, repulsion produces flocking Wigner crystals. Whereas repulsion often leads to motility-induced phase separation of active particles, here it combines with turn-away torques to produce flocking. Therefore, our findings bridge the classes of aligning and non-aligning active matter. Our results could help to reconcile the observations that cells can flock despite turning away from each other via contact inhibition of locomotion. Overall, our work shows that flocking is a very robust phenomenon that arises even when the orientational interactions would seem to prevent it.

cond-mat.soft↗

arXiv2023

Clonal dynamics of surface-driven growing tissues

The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or cells in the bulk, is possible in cell culture experiments, but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers have become important experimental tools to study cell fate in vivo. Here, we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone-size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone-size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results show how the mode of tissue growth can be inferred from genetic tracing experiments.

q-bio.QM↗

arXiv2023

Unraveling active baths through their hidden degrees of freedom

The dynamics of a probe particle is highly influenced by the nature of the bath in which it is immersed. In particular, baths composed by active (e.g., self-propelled) particles induce intriguing out-of-equilibrium effects on tracer's motion that are customarily described by integrating out the dynamics of the bath's degrees of freedom (DOFs). However, thermodynamic quantities, such as the entropy production rate, are generally severely affected by coarse-graining procedures. Here, we show that active baths are associated with the presence of entropic DOFs exhibiting non-reciprocal interactions with a probe particle. Surprisingly, integrating out these DOFs inevitably results into a system-dependent increase or reduction of the entropy production rate. On the contrary, it stays invariant after integrating out non-entropic DOFs. As a consequence, they determine the dimensionality of isoentropic hypersurfaces in the parameter space. Our results shed light on the nature of active baths, revealing that the presence of a typical correlation time-scale is not a sufficient condition to have non-equilibrium effects on a probe particle, and draws a path towards the understanding of thermodynamically-consistent procedures to derive effective dynamics of observed DOFs.

cond-mat.stat-mech↗