Minibatch training of neural network ensembles via trajectory sampling

Most iterative neural network training methods use estimates of the loss function over small random subsets (or minibatches) of the data to update the parameters, which aid in decoupling the training time from the (often very large) size of the training datasets. Here, we show that a minibatch approach can also be used to train neural network ensembles (NNEs) via trajectory methods in a highly efficent manner. We illustrate this approach by training NNEs to classify images in the MNIST datasets. This method gives an improvement to the training times, allowing it to scale as the ratio of the size of the dataset to that of the average minibatch size which, in the case of MNIST, gives a computational improvement typically of two orders of magnitude. We highlight the advantage of using longer trajectories to represent NNEs, both for improved accuracy in inference and reduced update cost in terms of the samples needed in minibatch updates.Comment: 11 pages, 4 figures, 1 algorith

Optimal sampling of dynamical large deviations in two dimensions via tensor networks

We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open boundaries, in lattices of up to 40x40 sites. We show that at long-times both models have phase transitions between active and inactive dynamical phases. For the 2D East model we find that this trajectory transition is of the first-order, while for the SSEP we find indications of a second order transition. We then show how the PEPS can be used to implement a trajectory sampling scheme capable of directly accessing rare trajectories. We also discuss how the methods described here can be extended to study rare events at finite times.Comment: 6 pages, 4 figure

Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model

We study a one-dimensional classical stochastic kinetically constrained model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbours is excited. We call this model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) model. We describe the dynamics of the XOR-FA model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.Comment: 13+2 pages, 7+1 figure

Boundary conditions dependence of the phase transition in the quantum Newman-Moore model

We study the triangular plaquette model (TPM, also known as the Newman-Moore model) in the presence of a transverse magnetic field on a lattice with periodic boundaries in both spatial dimensions. We consider specifically the approach to the ground state phase transition of this quantum TPM (QTPM, or quantum Newman-Moore model) as a function of the system size and type of boundary conditions. Using cellular automata methods, we obtain a full characterization of the minimum energy configurations of the TPM for arbitrary tori sizes. For the QTPM, we use these cycle patterns to obtain the symmetries of the model, which we argue determine its quantum phase transition: we find it to be a first-order phase transition, with the addition of spontaneous symmetry breaking for system sizes which have degenerate classical ground states. For sizes accessible to numerics, we also find that this classification is consistent with exact diagonalization, Matrix Product States and Quantum Monte Carlo simulations.Comment: fixed unclear point, given the correct credit to citatio

Expertise differences in anticipatory judgements during a temporally and spatially occluded dynamic task

There is contradictory evidence surrounding the role of critical cues in the successful anticipation of penalty kick outcome. In the current study, skilled and less-skilled soccer goalkeepers were required to anticipate spatially (full body; hip region) and temporally (–160 ms, –80 ms before, foot–ball contact) occluded penalty kicks. The skilled group outperformed the less-skilled group in all conditions. Both groups performed better in the full body, compared to hip region condition. Later temporal occlusion conditions were associated with increased performance in the correct response and correct side analysis, but not for correct height. These data suggest that there is enough postural information from the hip region for skilled goalkeepers to make highly accurate predictions of penalty kick direction, however, other regions are needed in order to make predictions of height. These data demonstrate the evolution of cues over time and have implications for anticipation training

Experimental verification of dose enhancement effects in a lung phantom from inline magnetic fields.

BACKGROUND AND PURPOSE: To present experimental evidence of lung dose enhancement effects caused by strong inline magnetic fields. MATERIALS AND METHODS: A permanent magnet device was utilised to generate 0.95T-1.2T magnetic fields that encompassed two small lung-equivalent phantoms of density 0.3g/cm3. Small 6MV and 10MV photon beams were incident parallel with the magnetic field direction and Gafchromic EBT3 film was placed inside the lung phantoms, perpendicular to the beam (experiment 1) and parallel to the beam (experiment 2). Monte Carlo simulations of experiment 1 were also performed. RESULTS: Experiment 1: The 1.2T inline magnetic field induced a 12% (6MV) and 14% (10MV) increase in the dose at the phantom centre. The Monte Carlo modelling matched well (±2%) to the experimentally observed results. Experiment 2: A 0.95T field peaked at the phantom centroid (but not at the phantom entry/exit regions) details a clear dose increase due to the magnetic field of up to 25%. CONCLUSIONS: This experimental work has demonstrated how strong inline magnetic fields act to enhance the dose to lower density mediums such as lung tissue. Clinically, such scenarios will arise in inline MRI-linac systems for treatment of small lung tumours

Slow dynamics and large deviations in classical stochastic Fredkin chains

The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground-state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPSs). The stochastic model displays slow dynamics, including power-law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations - which we compute accurately via numerical MPSs - including an active-inactive phase transition and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice

Optimal sampling of dynamical large deviations via matrix product states

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions

The effect of anxiety on anticipation, allocation of attentional resources, and visual search behaviours

Successful sports performance requires athletes to be able to mediate any detrimental effects of anxiety whilst being able to complete tasks simultaneously. In this study, we examine how skill level influences the ability to mediate the effects of anxiety on anticipation performance and the capacity to allocate attentional resources to concurrent tasks. We use a counterbalanced, repeated measures design that required expert and novice badminton players to complete a film-based anticipation test in which they predicted serve direction under high- and low-anxiety conditions. On selected trials, participants completed an auditory secondary task. Visual search data were recorded and the Mental Readiness Form v-3 was used to measure cognitive anxiety, somatic anxiety and self-confidence. The Rating Scale of Mental Effort was used to measure mental effort. The expert players outperformed their novice counterparts on the anticipation task across both anxiety conditions, with both groups anticipation performance deteriorating under high- compared to low-anxiety. This decrease across anxiety conditions was significantly greater in the novice compared to the expert group. High-anxiety resulted in a shorter final visual fixation duration for both groups when compared to low-anxiety. Anxiety had a negative impact on secondary task performance for the novice, but not the expert group. Our findings suggest that expert athletes more effectively allocated attentional resources during performance under high-anxiety conditions. In contrast, novice athletes used more attentional resources when completing the primary task and, therefore, were unable to maintain secondary task performance under high-anxiety

Finite time large deviations via matrix product states

Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics of dynamical observables at arbitrary finite time. This is a harder problem because, in contrast to the infinite time case where only the extremal eigenstate of a tilted Markov generator is relevant, for finite time the whole spectrum plays a role. We show that finite time dynamical partition sums can be computed efficiently and accurately in one dimension using matrix product states, and describe how to use such results to generate rare event trajectories on demand. We apply our methods to the Fredrickson-Andersen (FA) and East kinetically constrained models, and to the symmetric simple exclusion process (SSEP), unveiling dynamical phase diagrams in terms of counting field and trajectory time. We also discuss extensions of this method to higher dimensions