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Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and…
Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit…
We discover an instability mechanism in suspensions of self-propelled particles that does not involve active stress. Instead, it is driven by a subtle interplay of inertia, swimmer motility, and concentration fluctuations, through a crucial…
Trained attention layers exhibit striking and reproducible spectral structure of the weights, including low-rank collapse, bulk deformation, and isolated spectral outliers, yet the origin of these phenomena and their implications for…
The success of self-attention lies in its ability to capture long-range dependencies and enhance context understanding, but it is limited by its computational complexity and challenges in handling sequential data with inherent…
Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The `energy-weighted' density matrix embedding theory (EwDMET) was established…
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…
We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
Self-attention mechanisms have revolutionised deep learning architectures, yet their core mathematical structures remain incompletely understood. In this work, we develop a category-theoretic framework focusing on the linear components of…
We study the spectral properties of sample covariance matrices constructed from pooled sequence representations, where token embeddings are drawn from a fixed two-class Gaussian mixture table and pooled via (fixed) attention weights.…
Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying…
We classify all spherically symmetric spacetimes admitting a kinematic self-similar vector of the second, zeroth or infinite kind. We assume that the perfect fluid obeys either a polytropic equation of state or an equation of state of the…
Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. By considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to…
We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting…
We describe a new approach based on semiclassical molecular dynamics that allows to simulate infrared absorption or emission spectra of molecular systems with inclusion of anharmonic intensities. This is achieved from semiclassical power…
The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary…