Related papers: Phase transitions in optimal unsupervised learning
We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry breaking binary direction $\bm{B}\in\{-1,+1\}^{N}$, onto which the projections have a Gaussian…
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the…
We propose a systematic methodology to identify the topological phase transition through a self-supervised machine learning model, which is trained to correlate system parameters to the non-local observables in time-of-flight experiments of…
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…
The application of machine learning in the study of phase transitions has achieved remarkable success in both equilibrium and non-equilibrium systems. It is widely recognized that unsupervised learning can retrieve phase transition…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques…
Entropy and order parameter are two key concepts in phase transition theory. This paper proposes an unified method to both find order parameter and estimate entropy automatically with unsupervised learning. The contributions of this paper…
Learning curves are a fundamental primitive in supervised learning, describing how an algorithm's performance improves with more data and providing a quantitative measure of its generalization ability. Formally, a learning curve plots the…
We propose an optimization method of mutual learning which converges into the identical state of optimum ensemble learning within the framework of on-line learning, and have analyzed its asymptotic property through the statistical mechanics…
Symmetry is a powerful tool for understanding phases of matter in equilibrium. Quantum circuits with measurements have recently emerged as a platform for novel states of matter intrinsically out of equilibrium. Can symmetry be used as an…
We study a simple model of unsupervised learning where the single symmetry breaking vector has binary components $\pm 1$. We calculate exactly the Bayes-optimal performance of an estimator which is required to lie in the same discrete…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of…
Supervised Learning has been successfully used to produce phase diagrams and identify phase boundaries when local order parameters are unavailable. Here, we apply unsupervised learning to this task. By using readily available clustering…
This paper presents a global trajectory optimization framework for minimizing lap time in autonomous racing under uncertain vehicle dynamics. Optimizing the trajectory over the full racing horizon is computationally expensive, and tracking…
In this Letter, we present a new strategy for applying the learning machine to study phase transitions. We train the learning machine with samples only obtained at a non-critical parameter point, aiming to establish intrinsic correlations…
We address the problem of active optical steering of structural phase transitions in solids. We demonstrate that existing reinforcement learning approaches can derive optimal time-dependent electric fields in optically-driven dissipative…
In recent years, developing unsupervised machine learning for identifying phase transition is a research direction. In this paper, we introduce a two-times clustering method that can help select perfect configurations from a set of…
In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…
This work carries out a detailed transient analysis of the learning behavior of multi-agent networks, and reveals interesting results about the learning abilities of distributed strategies. Among other results, the analysis reveals how…