Related papers: A canonical ensemble approach to graded-response p…
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…
We present nonlinear photonic circuit models for constructing programmable linear transformations and use these to realize a coherent Perceptron, i.e., an all-optical linear classifier capable of learning the classification boundary…
Ensemble learning of $K$ nonlinear perceptrons, which determine their outputs by sign functions, is discussed within the framework of online learning and statistical mechanics. One purpose of statistical learning theory is to theoretically…
We analyze the generalization performance of a student in a model composed of nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We calculate the generalization error of the student analytically or numerically using…
We investigate the generalization ability of a perceptron with non-monotonic transfer function of a reversed-wedge type in on-line mode. This network is identical to a parity machine, a multilayer network. We consider several learning…
In this paper, we introduce the gated perceptron, an enhancement of the conventional perceptron, which incorporates an additional input computed as the product of the existing inputs. This allows the perceptron to capture non-linear…
The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the…
We investigate a quantum perceptron implemented on a quantum circuit using a repeat until method. We evaluate this from the perspective of capacity, one of the performance evaluation measures for perceptions. We assess a Gardner volume,…
In order to solve the problem of non-ideal training sets (i.e., the less-complete or over-complete sets) and implement one-iteration learning, a novel efficient quantum perceptron algorithm based on unitary weights is proposed, where the…
We study the on-line AdaTron learning of linearly non-separable rules by a simple perceptron. Training examples are provided by a perceptron with a non-monotonic transfer function which reduces to the usual monotonic relation in a certain…
Learning representations of two views of data such that the resulting representations are highly linearly correlated is appealing in machine learning. In this paper, we present a canonical correlation guided learning framework, which allows…
The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can…
Many experimentally-accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous…
Within the framework of on-line learning, we study the generalization error of an ensemble learning machine learning from a linear teacher perceptron. The generalization error achieved by an ensemble of linear perceptrons having homogeneous…
The concept of a recently proposed Forward-Forward learning algorithm for fully connected artificial neural networks is applied to a single multi output perceptron for classification. The parameters of the system are trained with respect to…
Perceptrons have been known for a long time as a promising tool within the neural networks theory. The analytical treatment for a special class of perceptrons started in seminal work of Gardner \cite{Gar88}. Techniques initially employed to…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…