The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting, that is, accurate predictions despite overfitting training data. In this article, we survey recent progress in statistical learning theory that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behaviour of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favourable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

Through diversity of composition, sequence, and interfacial structure, hybrid materials greatly expand the palette of materials available to access novel functionality. The NSF Division of Materials Research recently supported a workshop (October 17–18, 2019) aiming to (1) identify fundamental questions and potential solutions common to multiple disciplines within the hybrid materials community; (2) initiate interfield collaborations between hybrid materials researchers; and (3) raise awareness in the wider community about experimental toolsets, simulation capabilities, and shared facilities that can accelerate this research. This article reports on the outcomes of the workshop as a basis for cross-community discussion. The interdisciplinary challenges and opportunities are presented, and followed with a discussion of current areas of progress in subdisciplines including hybrid synthesis, functional surfaces, and functional interfaces.

Astrophysics Telescope for Large Area Spectroscopy Probe is a concept for a National Aeronautics and Space Administration probe-class space mission that will achieve ground-breaking science in the fields of galaxy evolution, cosmology, Milky Way, and the Solar System. It is the follow-up space mission to Wide Field Infrared Survey Telescope (WFIRST), boosting its scientific return by obtaining deep 1–4 μm slit spectroscopy for ∼70% of all galaxies imaged by the ∼2 000 deg2 WFIRST High Latitude Survey at z > 0.5. Astrophysics Telescope for Large Area Spectroscopy will measure accurate and precise redshifts for ∼200 M galaxies out to z < 7, and deliver spectra that enable a wide range of diagnostic studies of the physical properties of galaxies over most of cosmic history. Astrophysics Telescope for Large Area Spectroscopy Probe and WFIRST together will produce a 3D map of the Universe over 2 000 deg2, the definitive data sets for studying galaxy evolution, probing dark matter, dark energy and modifications of General Relativity, and quantifying the 3D structure and stellar content of the Milky Way. Astrophysics Telescope for Large Area Spectroscopy Probe science spans four broad categories: (1) Revolutionising galaxy evolution studies by tracing the relation between galaxies and dark matter from galaxy groups to cosmic voids and filaments, from the epoch of reionisation through the peak era of galaxy assembly; (2) Opening a new window into the dark Universe by weighing the dark matter filaments using 3D weak lensing with spectroscopic redshifts, and obtaining definitive measurements of dark energy and modification of General Relativity using galaxy clustering; (3) Probing the Milky Way’s dust-enshrouded regions, reaching the far side of our Galaxy; and (4) Exploring the formation history of the outer Solar System by characterising Kuiper Belt Objects. Astrophysics Telescope for Large Area Spectroscopy Probe is a 1.5 m telescope with a field of view of 0.4 deg2, and uses digital micro-mirror devices as slit selectors. It has a spectroscopic resolution of R = 1 000, and a wavelength range of 1–4 μm. The lack of slit spectroscopy from space over a wide field of view is the obvious gap in current and planned future space missions; Astrophysics Telescope for Large Area Spectroscopy fills this big gap with an unprecedented spectroscopic capability based on digital micro-mirror devices (with an estimated spectroscopic multiplex factor greater than 5 000). Astrophysics Telescope for Large Area Spectroscopy is designed to fit within the National Aeronautics and Space Administration probe-class space mission cost envelope; it has a single instrument, a telescope aperture that allows for a lighter launch vehicle, and mature technology (we have identified a path for digital micro-mirror devices to reach Technology Readiness Level 6 within 2 yr). Astrophysics Telescope for Large Area Spectroscopy Probe will lead to transformative science over the entire range of astrophysics: from galaxy evolution to the dark Universe, from Solar System objects to the dusty regions of the Milky Way.

Burnout symptoms, which are characterized by exhaustion, cynicism, and a reduced sense of professional efficacy, may deleteriously affect cognitive function in military personnel. A total of 32 U.S. Military Special Operations personnel enrolled in Survival School completed measures of trauma history, dissociation, and burnout before training. They then completed the Groton Maze Learning Test (GMLT), a neuropsychological measure of integrative visuospatial executive function during three field-based phases of Survival School—enemy evasion, captivity/interrogation, and escape/release from captivity. Lower pre-training perceptions of professional efficacy were associated with reduced executive function during all of the field-based phases of Survival School, even after adjustment for years of education, cynicism, and baseline GMLT scores. Magnitudes of decrements in executive function in Marines with low efficacy relative to those with high efficacy increased as training progressed and ranged from .58 during enemy evasion to .99 during escape/release from captivity. Pre-training perceptions of burnout may predict visuospatial executive function during naturalistic training-related stress in military personnel. Assessment of burnout symptoms, particularly perceptions of professional efficacy, may help identify military personnel at risk for stress-related executive dysfunction. (JINS, 2011, 17, 494–501)

We study sample-based estimates of the expectation of the functionproduced by the empirical minimization algorithm. We investigate theextent to which one can estimate the rate of convergence of theempirical minimizer in a data dependent manner. We establish threemain results. First, we provide an algorithm that upper bounds theexpectation of the empirical minimizer in a completelydata-dependent manner. This bound is based on a structural resultdue to Bartlett and Mendelson, which relates expectations to sampleaverages. Second, we show that these structural upper bounds can beloose, compared to previous bounds. In particular, we demonstrate aclass for which the expectation of the empirical minimizer decreasesas O(1/n) for sample size n, although the upper bound based onstructural properties is Ω(1). Third, we show that thislooseness of the bound is inevitable: we present an example thatshows that a sharp bound cannot be universally recovered fromempirical data.

The benefits of a strong proximal social network for people as they advance in age are well documented, but the continuation or development of social networks may be challenged when people relocate to a new home on retirement. This paper explores the personal network development of older residents who have moved to a new suburban (but not age-specific) residential development in a general urban setting. Drawing on a case study of a new outer-suburban ‘master planned estate’ in Brisbane, Queensland, the findings from interviews with 51 older residents and participant observations of a community group are presented. The study suggests that a traditional ideal of unreflexive community of place was an unreliable source of durable social bonds in contemporary fragmented and mobile social conditions, where the proximity of family members, durability of tenure and strong neighbourly ties are not inevitable. One successful resolution was found in a group of older residents who through exercising agency had joined a group the sole focus of which was social companionship. The theoretical bases of this type of group are discussed and its relevance is examined for retirees who have chosen to live in a residential environment for lifestyle and amenity reasons, away from their lifelong social networks.

Let and be sets of functions from domain X to ℝ. We say that validly generalises from approximate interpolation if and only if for each η > 0 and ∈, δ ∈ (0,1) there is m0(η, ∈, δ) such that for any function t ∈ and any probability distribution on X, if m > m0 then with m-probability at least 1 – δ, a sample X = (x1, X2,…,xm) ∈ Xm satisfies

We find conditions that are necessary and sufficient for to validly generalise from approximate interpolation, and we obtain bounds on the sample length m0{η,∈,δ) in terms of various parameters describing the expressive power of .

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.We gratefully acknowledge the support of the NSF under award DMS-0434383. Thanks also to three anonymous reviewers for useful comments that improved the presentation.

Reduced food availability in pregnancy influences fetal growth, obstetric outcomes and offspring health in both developing and developed countries. The objective of the present study was to determine responses to moderate global maternal nutrient restriction (MNR) during pregnancy in baboons (Papio hamadryas) – an established non-human primate model for pregnancy-related research. Starting at 30 d gestation (dG), twelve pregnant baboons received 70 % of food (MNR group) consumed by twenty ad libitum-fed pregnant controls. Maternal body weight, BMI, food intake and physical activity were measured before pregnancy, at 90 dG and at 165 dG (full-term 180 dG). Fetal and placental weights were recorded at the time of Caesarean section (90 and 165 dG). Activity patterns were also evaluated in fourteen non-pregnant female baboons. Behavioural observations were made in five non-pregnant, six control and four MNR animals. Pregnant baboons decreased overall physical activity and energy-expensive behaviours compared with non-pregnant baboons. In the MNR group, maternal weight, weight gain and maternal physical activity were reduced compared with the control animals. MNR decreased placental weight and volume compared with control, while fetal weight and length were unaffected. We conclude that decreased physical activity and increased usage of maternal available body stores play an important role in the maternal response to pregnancy. Also, adaptations in maternal behaviour and energy utilisation protect fetal growth during moderate MNR.