Related papers: On a phase transition in general order spline regr…
Consider a spiked random tensor obtained as a mixture of two components: noise in the form of a symmetric Gaussian $p$-tensor for $p\geq 3$ and signal in the form of a symmetric low-rank random tensor. The latter is defined as a linear…
In many extensions of the Standard Model electroweak phase transitions at high temperatures can be described in a minimal dimensionally reduced effective theory with SU(2) gauge field and fundamental Higgs scalar. In this effective theory,…
We have determined the phase diagram of the simplest version of a lattice model introduced in the recent work of Kazakov and Migdal. If $m_0$ and $\lambda$ are the bare mass and self coupling of the scalar field in the model respectively,…
The deconfining transition in $SU(3)$ gauge theory, traditionally interpreted through the Gross-Witten-Wadia (GWW) model as a sharp third-order phase transition in the large-$N_c$ limit, appears as a smooth crossover in lattice QCD. This…
We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…
The generalized Dickman distribution ${\cal D}_\theta$ with parameter $\theta>0$ is the unique solution to the distributional equality $W=_d W^*$, where \begin{eqnarray} W^*=_d U^{1/\theta}(W+1) \qquad (1) \end{eqnarray} with $W$…
We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of…
Policy evaluation in reinforcement learning is often conducted using two-timescale stochastic approximation, which results in various gradient temporal difference methods such as GTD(0), GTD2, and TDC. Here, we provide convergence rate…
We study the phase transition in the abelian lattice gauge theory using the Wilson-Polyakov line as the order parameter. The Wilson-Polyakov line remains very small at strong coupling and becomes non-zero at weak coupling, signalling a…
We study phase transitions in $SU(\infty)$ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the…
We consider the optimization problem of minimizing the logistic loss with gradient descent to train a linear model for binary classification with separable data. With a budget of $T$ iterations, it was recently shown that an accelerated…
We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling $g^2$ and a gauge index $N$, as a system passes through a large $N$ phase transition, using the universal example of the…
The dynamics of Deep Linear Networks (DLNs) is dramatically affected by the variance $\sigma^2$ of the parameters at initialization $\theta_0$. For DLNs of width $w$, we show a phase transition w.r.t. the scaling $\gamma$ of the variance…
We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific…
We consider the decentralized stochastic optimization problems, where a network of $n$ nodes, each owning a local cost function, cooperate to find a minimizer of the globally-averaged cost. A widely studied decentralized algorithm for this…
We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum…
We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We provide an effective theory for approximating the Bayes-optimal…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…