Related papers: Finite size scaling in neural networks
For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of…
Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to…
Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general…
The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial…
In a class of methods for measurement of available path capacity and other capacity-related metrics in a network, trains of probe packets are transmitted from a sender to a receiver across a network path, and the sequences of time stamps at…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm…
The storage capacity of the Hopfield model is about 15% of the network size. It can be increased significantly in the Potts-glass model of the associative memory only. In this model neurons can be in more than two different states. We show…
We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation. The latter enforces imperviousness to change in units of measure whereas the former…
A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary…
We study the large-$r$ behavior of the bulk order-parameter correlation function $G(\bf{r})$ for $T>T_c$ within the lattice $\phi^4$ theory. We also study the large-$L$ behavior of the susceptibility $\chi$ of the confined lattice system of…
The network scale-up method enables researchers to estimate the size of hidden populations, such as drug injectors and sex workers, using sampled social network data. The basic scale-up estimator offers advantages over other size estimation…
Identifying the brain's neuronal cluster size to be presented as nodes in a network computation is critical to both neuroscience and artificial intelligence, as these define the cognitive blocks required for building intelligent…
Many machine learning models require setting a parameter that controls their size before training, e.g. number of neurons in DNNs, or inducing points in GPs. Increasing capacity typically improves performance until all the information from…
Finite-size scaling (FSS) is applied to net-baryon cumulant ratios $C_2/C_1$, $C_3/C_2$, $C_4/C_2$, $C_3/C_1$, and $C_4/C_1$ measured in Au+Au collisions over the Beam Energy Scan Phase~I range $\sqrt{s_{NN}}=7.7$--$200$~GeV to constrain…
We calculate universal finite size scaling functions for the order parameter and the longitudinal susceptibility of the three-dimensional O(4) model. The phase transition of this model is supposed to be in the same universality class as the…
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…
Diffusion on a T fractal lattice under the influence of topological biasing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormalization group approach on…