Nested Rollout Policy Adaptation (NRPA) is a Monte Carlo search algorithm for single player games. In this paper we propose to modify NRPA in order to improve the stability of the algorithm. Experiments show it improves the algorithm for different application domains: SameGame, Traveling Salesman with Time Windows and Expression Discovery.

This tutorial paper surveys training alternatives to end-to-end backpropagation (E2EBP) -- the de facto standard for training deep architectures. Modular training refers to strictly local training without both the forward and the backward pass, i.e., dividing a deep architecture into several nonoverlapping modules and training them separately without any end-to-end operation. Between the fully global E2EBP and the strictly local modular training, there are "weakly modular" hybrids performing training without the backward pass only. These alternatives can match or surpass the performance of E2EBP on challenging datasets such as ImageNet, and are gaining increased attention primarily because they offer practical advantages over E2EBP, which will be enumerated herein. In particular, they allow for greater modularity and transparency in deep learning workflows, aligning deep learning with the mainstream computer science engineering that heavily exploits modularization for scalability. Modular training has also revealed novel insights about learning and may have further implications on other important research domains. Specifically, it induces natural and effective solutions to some important practical problems such as data efficiency and transferability estimation.

A large fraction of textual data available today contains various types of 'noise', such as OCR noise in digitized documents, noise due to informal writing style of users on microblogging sites, and so on. To enable tasks such as search/retrieval and classification over all the available data, we need robust algorithms for text normalization, i.e., for cleaning different kinds of noise in the text. There have been several efforts towards cleaning or normalizing noisy text; however, many of the existing text normalization methods are supervised and require language-dependent resources or large amounts of training data that is difficult to obtain. We propose an unsupervised algorithm for text normalization that does not need any training data / human intervention. The proposed algorithm is applicable to text over different languages, and can handle both machine-generated and human-generated noise. Experiments over several standard datasets show that text normalization through the proposed algorithm enables better retrieval and stance detection, as compared to that using several baseline text normalization methods. Implementation of our algorithm can be found at https://github.com/ranarag/UnsupClean.

The Group-By query is an important kind of query, which is common and widely used in data warehouses, data analytics, and data visualization. Approximate query processing is an effective way to increase the querying efficiency on big data. The answer to a group-by query involves multiple values, which makes it difficult to provide sufficiently accurate estimations for all the groups. Stratified sampling improves the accuracy compared with the uniform sampling, but the samples chosen for some special queries cannot work for other queries. Online sampling chooses samples for the given query at query time, but it requires a long latency. Thus, it is a challenge to achieve both accuracy and efficiency at the same time. Facing such challenge, in this work, we propose a sample generation framework based on a conditional generative model. The sample generation framework can generate any number of samples for the given query without accessing the data. The proposed framework based on the lightweight model can be combined with stratified sampling and online aggregation to improve the estimation accuracy for group-by queries. The experimental results show that our proposed methods are both efficient and accurate.

After affecting the world in unexpected ways, COVID-19 has started mutating which is evident with the insurgence of its new variants. The governments, hospitals, schools, industries, and humans, in general, are looking for a potential solution in the vaccine which will eventually be available but its timeline for eradicating the virus is yet unknown. Several researchers have encouraged and recommended the use of good practices such as physical healthcare monitoring, immunity-boosting, personal hygiene, mental healthcare, and contact tracing for slowing down the spread of the virus. In this article, we propose the use of wearable/mobile sensors integrated with the Internet of Everything to cover the spectrum of good practices in an automated manner. We present hypothetical frameworks for each of the good practice modules and propose the COvid-19 Resistance Framework using the Internet of Everything (CORFIE) to tie all the individual modules in a unified architecture. We envision that CORFIE would be influential in assisting people with the new normal for current and future pandemics as well as instrumental in halting the economic losses, respectively. We also provide potential challenges and their probable solutions in compliance with the proposed CORFIE.

We propose the combination of forward shape derivatives and the use of an iterative inversion scheme for Bayesian optimization to find optimal designs of nanophotonic devices. This approach widens the range of applicability of Bayesian optmization to situations where a larger number of iterations is required and where derivative information is available. This was previously impractical because the computational efforts required to identify the next evaluation point in the parameter space became much larger than the actual evaluation of the objective function. We demonstrate an implementation of the method by optimizing a waveguide edge coupler.

Tests for detecting severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) were developed within days of the release of the virus genome ([ 1 ][1]). Multiple countries have been successful at controlling SARS-CoV-2 transmission by investing in large-scale testing capacity ([ 2 ][2]). Most testing has focused on quantitative polymerase chain reaction (qPCR) assays, which are capable of detecting minute amounts of viral RNA. Although powerful, these molecular tools cannot be scaled to meet demands for more extensive public health testing. To combat COVID-19, the “one-size-fits-all” approach that has dominated and confused decision-making with regard to testing and the evaluation of tests is unsuitable: Diagnostics, screening, and surveillance serve different purposes, demand distinct strategies, and require separate approval mechanisms. By supporting the innovation, approval, manufacturing, and distribution of simpler and cheaper screening and surveillance tools, it will be possible to more effectively limit the spread of COVID-19 and respond to future pandemics. Many types of tests are available for COVID-19 for clinical and public health use (see the figure). Testing can be performed in a central laboratory, at the point of care (POC), or in the community at the workplace, school, or home. COVID-19 testing begins with specimen collection. For medical use, a nasopharyngeal swab collected by a health care professional has been used for detection of virus infections. Demands on testing throughput for COVID-19, however, have driven new collection approaches, including saliva and less invasive nasal swabs. COVID-19 tests include molecular tests such as qPCR, isothermal amplification, and CRISPR, as well as antigen tests that detect SARS-CoV-2 proteins directly. Although rapid antigen tests have lower analytical sensitivity (i.e., require greater amounts of virus material to turn positive) than qPCR-based tests, their ability to detect infectious individuals with culturable virus is as high as for qPCR ([ 3 ][3]). Specificity (i.e., correctly identifying those not infected with SARS-CoV-2) of antigen tests achieves comparable results to molecular tests ([ 4 ][4]). Diagnostic testing for COVID-19 focuses on accurately identifying patients who are infected with SARS-CoV-2 to establish the presence or absence of disease and is performed on symptomatic patients or asymptomatic individuals who are at high risk of infection. This type of testing requires assays that are highly sensitive, so as to not miss COVID-19 patients (false negatives), and specific, so as to not wrongly diagnose SARS-CoV-2–negative individuals as having COVID-19 (false positives). These tests are typically performed by centralized high-complexity laboratories with specialized equipment using qPCR assays, with results that can be reported within 12 to 48 hours. Major bottlenecks in testing, however, have led to turnaround times exceeding 5 to 10 days in some regions, making such tests useless to prevent transmission. POC diagnostic testing at medical facilities can be qPCR assays, isothermal amplification, or antigen-based ([ 4 ][4]). These POC tests often require instruments that run a limited number of tests and can return results in under an hour. The need for an instrument limits the number of tests that can be performed and where they can be used. However, newer antigen tests are becoming available that do not require instruments or skilled operators, potentially allowing for much more distributed POC testing. Surveillance testing of populations can be used both as a tool for understanding historical exposures and as a measure of ongoing community transmission. For the former, serological testing of individuals for the presence of SARS-CoV-2–specific antibodies is used to identify those previously infected. For the latter, surveillance testing can be an effective way to monitor real-time SARS-CoV-2 spread in communities. One promising method is wastewater surveillance, which has been used to assess community transmission of poliovirus ([ 5 ][5]) and has shown potential for COVID-19 ([ 6 ][6]). qPCR testing of wastewater is used to detect SARS-CoV-2, and frequency dynamics of viral genetic material indicate COVID-19 infections in a community. Surveillance can also be performed from swab or saliva samples taken directly from individuals, and, in populations with low COVID-19 prevalence, pooling can be used to increase capacity and lower cost. For surveillance testing, the goal is not identification of every case but rather the collection of data from representative samples that accurately measure prevalence and serve to inform public health policy and resource allocation. Because the focus is on extrapolations to the population and not the individual, tests with known deviations from 100% sensitivity and specificity are still appropriate when the variance can be statistically corrected ([ 7 ][7]). To be most effective, results should include reported qPCR cycle thresholds, which is an estimate of viral load ([ 7 ][7]), to model epidemic trajectory and allow for real-time evaluation of mitigation programs ([ 8 ][8]), including once vaccination programs have begun. Screening testing of asymptomatic individuals to detect people who are likely infectious has been critically underused yet is one of the most promising tools to combat the COVID-19 pandemic ([ 9 ][9]). Infection with SARS-CoV-2 does not lead to symptoms in ∼20 to 40% of cases, and symptomatic disease is preceded by a presymptomatic incubation period ([ 10 ][10]). However, asymptomatic and presymptomatic cases are key contributors to virus spread, complicating our ability to break transmission chains ([ 10 ][10]). Entry screening to detect infectious individuals before accessing facilities (e.g., nursing homes, restaurants, and airports), along with symptom screening and temperature checks, can be beneficial, particularly in high-risk facilities such as skilled nursing facilities. When used strategically, entry-screening measures can be effective at suppressing transmission. Entry screening requires testing that provides rapid results—ideally within 15 min—to be most effective. The required sensitivity and specificity of entry-screening tests are, like all tests, context dependent. Entry-screening tests for a nursing home, for example, must be highly sensitive because the consequences of bringing SARS-CoV-2 into a nursing home can be devastating. Such tests must also be highly specific because the consequences of grouping a false-positive person with COVID-19–positive individuals could be deadly. Conversely, because children have substantially reduced mortality from COVID-19, entry screening into schools might require greater compromise that balances resources and sensitivity to test as many individuals as possible with a need to minimize disruptive false positives. Key to use of tests for entrance screening is that a negative test alone should not be considered sufficient to enter—that should be based on satisfying other requirements, including masks and physical distancing. Conversely, a positive test should be sufficient to bar entry in most settings. Public health screening is potentially the most powerful form of COVID-19 testing, aimed at outbreak suppression through maximizing detection of infectious individuals. This type of screening entails frequent serial testing of large fractions of the population, through self-administered at-home rapid tests, or in the community at high-contact settings, such as schools and workplaces ([ 9 ][9]). Public health screening can achieve herd effects by stopping onward spread through detection of asymptomatic or presymptomatic cases (fig. S1). Notably, not every transmission chain needs to be severed to achieve herd effects. Mathematical models that incorporate relevant variation in viral loads and test accuracy suggest that with frequent testing of a large fraction of a population, a sufficient number of cases could be detected to create herd effects ([ 11 ][11]). For example, Slovakia undertook public health screening to address COVID-19 ([ 12 ][12]): During a 2-week period, ∼80% of the population was screened using rapid antigen tests. With 50,000 cases identified, combined with other public health measures, it reduced incidence by 82% within 2 weeks ([ 12 ][12]). An important feature of large-scale public health screening is that centrally controlled reporting and contact tracing programs are not essential to induce herd effects as they are for surveillance testing. In a robust public health screening program, sufficient numbers of people are routinely testing themselves, such that contact tracing is subsumed by the screening program ([ 11 ][11]). Similar to home pregnancy tests, screening tests should be easy to obtain and administer, fast, and cheap. Like diagnostic tests, these tests must produce very low false-positive rates. If a screening test does not achieve high-enough specificity (e.g., >99.9%), screening programs can be paired with secondary confirmatory testing. Unlike diagnostic tests, however, the sensitivity of screening tests should not be determined based on their ability to diagnose patients but rather by their ability to accurately identify people who are most at risk of transmitting SARS-CoV-2. Such individuals tend to have higher viral loads ([ 13 ][13]), which makes the virus easier to detect ([ 14 ][14]). A focus on identifying infectious people means that frequency and abundance of tests should be prioritized above achieving high analytical sensitivity ([ 11 ][11]). Indeed, loss in sensitivity of individual tests, within reason, can be compensated for by frequency of testing and wider dissemination of tests ([ 9 ][9]). In addition, public health messaging should ensure appropriate expectations of screening, particularly around sensitivity and specificity so that false negatives and false positives do not erode public trust. ![Figure][15] COVID-19 testing strategies Testing for SARS-CoV-2 can be for personal or population health. Collection can be from symptomatic or asymptomatic individuals, as well as from wastewater and swabs of surfaces. The tests may be performed in central laboratories, at the POC, or using rapid tests. Attributes of tests differ according to application. GRAPHIC: KELLIE HOLOSKI/ SCIENCE Tests for public health screening require rapid, decentralized solutions that can be scaled for frequent screening of large numbers of asymptomatic individuals. Lateral-flow antigen tests and upcoming paper-based synthetic biology and CRISPR-based assays fit these needs and could be scaled to tens of millions of daily tests ([ 9 ][9]). These tests are simple and cheap, can be self-administered, and do not require machines to run and return results. The Abbott BinaxNOW rapid antigen test, which recently received an Emergency Use Authorization (EUA) in the United States as a diagnostic device, also comes with a smartphone app, allowing self-reporting of COVID-19 status that could be used instead of centralized reporting by public health agencies. Critically, despite being shown to be highly effective at detecting infectious individuals ([ 14 ][14]), very few of these tests are currently approved for screening of asymptomatic individuals, substantially limiting their utility. If such tests were made available direct to consumer (priced to allow equitable access) or produced and provided free of charge by governments, individuals could obtain their COVID-19 status at their own choosing and without complex medical decisions. Testing is a central pillar of clinical and public health response to global health emergencies, including the COVID-19 pandemic. Nearly all testing modalities have a role, and the one-size-fits-all approach to testing by many Western countries has failed. Many lower- and middle-income countries—including Senegal, Vietnam, and Ghana—have fared far better in their COVID-19 response, often using strong testing programs. The focus on diagnostic tests and the use of preexisting authorization pathways focused on qPCR-based clinical diagnostics not only slows the development and deployment of new surveillance and screening tests but also confuses the picture of what metrics effective public health tools should achieve. Testing to diagnose a patient with COVID-19 is fundamentally different from testing a person to prevent onward transmission. Regulatory pathways should be modified to incorporate these differences so that public health and screening tests are appropriately evaluated. It is necessary to be innovative and produce, distribute, and continuously improve the tests that exist to save lives and gain control of the COVID-19 pandemic. [science.sciencemag.org/content/371/6525/126/suppl/DC1][16] 1. [↵][17]1. V. M. Corman et al ., Euro. Surveill. 25, 2000045 (2020). [OpenUrl][18][CrossRef][19][PubMed][20] 2. [↵][21]1. M. G. Baker et al ., N. Engl. J. Med. 383, e56 (2020). [OpenUrl][22][CrossRef][23][PubMed][24] 3. [↵][25]1. A. Pekosz et al ., medRxiv 10.1101/2020.10.02.20205708 (2020). 4. [↵][26]1. R. Weissleder et al ., Sci. Transl. Med. 12, abc1931 (2020). [OpenUrl][27][CrossRef][28] 5. [↵][29]1. H. Asghar et al ., J. Infect. Dis. 210, S294 (2014). [OpenUrl][30][CrossRef][31][PubMed][32] 6. [↵][33]1. A. Nemudryi et al ., Cell Rep. Med. 1, 100098 (2020). [OpenUrl][34][CrossRef][35][PubMed][36] 7. [↵][37]1. R. Kahn et al ., medRxiv 10.1101/2020.05.02.20088765 (2020). 8. [↵][38]1. J. A. Hay et al ., medRxiv 10.1101/2020.10.08.20204222 (2020). 9. [↵][39]1. M. J. Mina et al ., N. Engl. J. Med. 383, e120 (2020). [OpenUrl][40][PubMed][41] 10. [↵][42]1. X. He et al ., Nat. Med. 26, 672 (2020). [OpenUrl][43][CrossRef][44][PubMed][41] 11. [↵][45]1. D. B. Larremore et al ., Sci. Adv. 10.1126/sciadv.abd5393 (2020). 12. [↵][46]1. M. Pavelka et al ., “The effectiveness of population-wide, rapid antigen test based screening in reducing SARS-CoV-2 infection prevalence in Slovakia,” CMMID Repository, 11 November 2020; . 13. [↵][47]1. E. A. Meyerowitz et al ., Ann. Intern. Med. 10.7326/M20-5008 (2020). 14. [↵][48]1. V. M. Corman et al ., medRxiv 10.1101/2020.11.12.20230292 (2020). [1]: #ref-1 [2]: #ref-2 [3]: #ref-3 [4]: #ref-4 [5]: #ref-5 [6]: #ref-6 [7]: #ref-7 [8]: #ref-8 [9]: #ref-9 [10]: #ref-10 [11]: #ref-11 [12]: #ref-12 [13]: #ref-13 [14]: #ref-14 [15]: pending:yes [16]: http://science.sciencemag.org/content/371/6525/126/suppl/DC1 [17]: #xref-ref-1-1 "View reference 1 in text" [18]: {openurl}?query=rft.jtitle%253DEuro.%2BSurveill.%26rft.volume%253D25%26rft.spage%253D2000045%26rft_id%253Dinfo%253Adoi%252F10.2807%252F1560-107917.ES.2020.25.3.2000045%26rft_id%253Dinfo%253Apmid%252F31992387%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [19]: /lookup/external-ref?access_num=10.2807/1560-107917.ES.2020.25.3.2000045&link_type=DOI [20]: /lookup/external-ref?access_num=31992387&link_type=MED&atom=%2Fsci%2F371%2F6525%2F126.atom [21]: #xref-ref-2-1 "View reference 2 in text" [22]: {openurl}?query=rft.jtitle%253DN.%2BEngl.%2BJ.%2BMed.%26rft.volume%253D383%26rft.spage%253De56%26rft_id%253Dinfo%253Adoi%252F10.1056%252FNEJMc2025203%26rft_id%253Dinfo%253Apmid%252F32767891%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [23]: /lookup/external-ref?access_num=10.1056/NEJMc2025203&link_type=DOI [24]: /lookup/external-ref?access_num=32767891&link_type=MED&atom=%2Fsci%2F371%2F6525%2F126.atom [25]: #xref-ref-3-1 "View reference 3 in text" [26]: #xref-ref-4-1 "View reference 4 in text" [27]: {openurl}?query=rft.jtitle%253DSci.%2BTransl.%2BMed.%26rft.volume%253D12%26rft.spage%253Dabc1931%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscitranslmed.abc1931%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [28]: /lookup/external-ref?access_num=10.1126/scitranslmed.abc1931&link_type=DOI [29]: #xref-ref-5-1 "View reference 5 in text" [30]: {openurl}?query=rft.jtitle%253DJ.%2BInfect.%2BDis.%26rft_id%253Dinfo%253Adoi%252F10.1093%252Finfdis%252Fjiu384%26rft_id%253Dinfo%253Apmid%252F25316848%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [31]: /lookup/external-ref?access_num=10.1093/infdis/jiu384&link_type=DOI [32]: /lookup/external-ref?access_num=25316848&link_type=MED&atom=%2Fsci%2F371%2F6525%2F126.atom [33]: #xref-ref-6-1 "View reference 6 in text" [34]: {openurl}?query=rft.jtitle%253DCell%2BRep.%2BMed.%26rft.volume%253D1%26rft.spage%253D100098%26rft_id%253Dinfo%253Adoi%252F10.1016%252Fj.xcrm.2020.100098%26rft_id%253Dinfo%253Apmid%252F32904687%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [35]: /lookup/external-ref?access_num=10.1016/j.xcrm.2020.100098&link_type=DOI [36]: /lookup/external-ref?access_num=32904687&link_type=MED&atom=%2Fsci%2F371%2F6525%2F126.atom [37]: #xref-ref-7-1 "View reference 7 in text" [38]: #xref-ref-8-1 "View reference 8 in text" [39]: #xref-ref-9-1 "View reference 9 in text" [40]: {openurl}?query=rft.jtitle%253DN.%2BEngl.%2BJ.%2BMed.%26rft.volume%253D383%26rft.spage%253De120%26rft_id%253Dinfo%253Apmid%252Fhttp%253A%252F%252Fwww.n%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [41]: /lookup/external-ref?access_num=http://www.n&link_type=MED&atom=%2Fsci%2F371%2F6525%2F126.atom [42]: #xref-ref-10-1 "View reference 10 in text" [43]: {openurl}?query=rft.jtitle%253DNat.%2BMed.%26rft.volume%253D26%26rft.spage%253D672%26rft_id%253Dinfo%253Adoi%252F10.7326%252FM20-3012%26rft_id%253Dinfo%253Apmid%252Fhttp%253A%252F%252Fwww.n%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [44]: /lookup/external-ref?access_num=10.7326/M20-3012&link_type=DOI [45]: #xref-ref-11-1 "View reference 11 in text" [46]: #xref-ref-12-1 "View reference 12 in text" [47]: #xref-ref-13-1 "View reference 13 in text" [48]: #xref-ref-14-1 "View reference 14 in text"

Cyber-physical systems (CPS) and Internet-of-Things (IoT) devices are increasingly being deployed across multiple functionalities, ranging from healthcare devices and wearables to critical infrastructures, e.g., nuclear power plants, autonomous vehicles, smart cities, and smart homes. These devices are inherently not secure across their comprehensive software, hardware, and network stacks, thus presenting a large attack surface that can be exploited by hackers. In this article, we present an innovative technique for detecting unknown system vulnerabilities, managing these vulnerabilities, and improving incident response when such vulnerabilities are exploited. The novelty of this approach lies in extracting intelligence from known real-world CPS/IoT attacks, representing them in the form of regular expressions, and employing machine learning (ML) techniques on this ensemble of regular expressions to generate new attack vectors and security vulnerabilities. Our results show that 10 new attack vectors and 122 new vulnerability exploits can be successfully generated that have the potential to exploit a CPS or an IoT ecosystem. The ML methodology achieves an accuracy of 97.4% and enables us to predict these attacks efficiently with an 87.2% reduction in the search space. We demonstrate the application of our method to the hacking of the in-vehicle network of a connected car. To defend against the known attacks and possible novel exploits, we discuss a defense-in-depth mechanism for various classes of attacks and the classification of data targeted by such attacks. This defense mechanism optimizes the cost of security measures based on the sensitivity of the protected resource, thus incentivizing its adoption in real-world CPS/IoT by cybersecurity practitioners.

The training of two-layer neural networks with nonlinear activation functions is an important non-convex optimization problem with numerous applications and promising performance in layerwise deep learning. In this paper, we develop exact convex optimization formulations for two-layer neural networks with second degree polynomial activations based on semidefinite programming. Remarkably, we show that semidefinite lifting is always exact and therefore computational complexity for global optimization is polynomial in the input dimension and sample size for all input data. The developed convex formulations are proven to achieve the same global optimal solution set as their non-convex counterparts. More specifically, the globally optimal two-layer neural network with polynomial activations can be found by solving a semidefinite program (SDP) and decomposing the solution using a procedure we call Neural Decomposition. Moreover, the choice of regularizers plays a crucial role in the computational tractability of neural network training. We show that the standard weight decay regularization formulation is NP-hard, whereas other simple convex penalties render the problem tractable in polynomial time via convex programming. We extend the results beyond the fully connected architecture to different neural network architectures including networks with vector outputs and convolutional architectures with pooling. We provide extensive numerical simulations showing that the standard backpropagation approach often fails to achieve the global optimum of the training loss. The proposed approach is significantly faster to obtain better test accuracy compared to the standard backpropagation procedure.

Fox News Flash top entertainment and celebrity headlines are here. Check out what's clicking today in entertainment. Even Drew Barrymore struggles in the dating world. The 45-year-old star welcomed comedian Nikki Glaser on her talk show on Monday and they talked about dating, which the actress said is "one of my favorite subjects ever to dissect." The two first chatted about dating apps, and Glaser explained that "guys do not come across great on dating apps."