This paper sheds light on the risk landscape of unsupervised least squares in the context of deep auto-encoding neural nets. We formally establish an equivalence between unsupervised least squares and principal manifolds. This link provides insight into the risk landscape of auto--encoding under the mean squared error, in particular all non-trivial critical points are saddlepoints. Finding saddlepoints is in itself difficult, overcomplete auto-encoding poses the additional challenge that the saddlepoints are degenerate. Within this context we discuss regularization of auto-encoders, in particular bottleneck, denoising and contraction auto-encoding and propose a new optimization strategy that can be framed as particular form of contractive regularization.

Daniely and Schacham recently showed that gradient descent finds adversarial examples on random undercomplete two-layers ReLU neural networks. The term "undercomplete" refers to the fact that their proof only holds when the number of neurons is a vanishing fraction of the ambient dimension. We extend their result to the overcomplete case, where the number of neurons is larger than the dimension (yet also subexponential in the dimension). In fact we prove that a single step of gradient descent suffices. We also show this result for any subexponential width random neural network with smooth activation function.

Knowledge bases often consist of facts which are harvested from a variety of sources, many of which are noisy and some of which conflict, resulting in a level of uncertainty for each triple. Knowledge bases are also often incomplete, prompting the use of embedding methods to generalize from known facts, however, existing embedding methods only model triple-level uncertainty, and reasoning results lack global consistency. To address these shortcomings, we propose BEUrRE, a novel uncertain knowledge graph embedding method with calibrated probabilistic semantics. BEUrRE models each entity as a box (i.e. axis-aligned hyperrectangle) and relations between two entities as affine transforms on the head and tail entity boxes. The geometry of the boxes allows for efficient calculation of intersections and volumes, endowing the model with calibrated probabilistic semantics and facilitating the incorporation of relational constraints. Extensive experiments on two benchmark datasets show that BEUrRE consistently outperforms baselines on confidence prediction and fact ranking due to its probabilistic calibration and ability to capture high-order dependencies among facts.

This paper presents our submission to SemEval-2021 Task 5: Toxic Spans Detection. The purpose of this task is to detect the spans that make a text toxic, which is a complex labour for several reasons. Firstly, because of the intrinsic subjectivity of toxicity, and secondly, due to toxicity not always coming from single words like insults or offends, but sometimes from whole expressions formed by words that may not be toxic individually. Following this idea of focusing on both single words and multi-word expressions, we study the impact of using a multi-depth DistilBERT model, which uses embeddings from different layers to estimate the final per-token toxicity. Our quantitative results show that using information from multiple depths boosts the performance of the model. Finally, we also analyze our best model qualitatively.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has the capacity to generate variants with major genomic changes. The UK variant B.1.1.7 (also known as VOC 202012/01) has many mutations that alter virus attachment and entry into human cells. Using a variety of statistical and dynamic modeling approaches, Davies et al. characterized the spread of the B.1.1.7 variant in the United Kingdom. The authors found that the variant is 43 to 90% more transmissible than the predecessor lineage but saw no clear evidence for a change in disease severity, although enhanced transmission will lead to higher incidence and more hospital admissions. Large resurgences of the virus are likely to occur after the easing of control measures, and it may be necessary to greatly accelerate vaccine roll-out to control the epidemic. Science , this issue p. [eabg3055][1] ### INTRODUCTION Several novel variants of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes COVID-19, emerged in late 2020. One of these, Variant of Concern (VOC) 202012/01 (lineage B.1.1.7), was first detected in southeast England in September 2020 and spread to become the dominant lineage in the United Kingdom in just a few months. B.1.1.7 has since spread to at least 114 countries worldwide. ### RATIONALE The rapid spread of VOC 202012/01 suggests that it transmits more efficiently from person to person than preexisting variants of SARS-CoV-2. This could lead to global surges in COVID-19 hospitalizations and deaths, so there is an urgent need to estimate how much more quickly VOC 202012/01 spreads, whether it is associated with greater or lesser severity of disease, and what control measures might be effective in mitigating its impact. We used social contact and mobility data, as well as demographic indicators linked to SARS-CoV-2 community testing data in England, to assess whether the spread of the new variant may be an artifact of higher baseline transmission rates in certain geographical areas or among specific demographic subpopulations. We then used a series of complementary statistical analyses and mathematical models to estimate the transmissibility of VOC 202012/01 across multiple datasets from the UK, Denmark, Switzerland, and the United States. Finally, we extended a mathematical model that has been extensively used to forecast COVID-19 dynamics in the UK to consider two competing SARS-CoV-2 lineages: VOC 202012/01 and preexisting variants. By fitting this model to a variety of data sources on infections, hospitalizations, and deaths across seven regions of England, we assessed different hypotheses for why the new variant appears to be spreading more quickly, estimated the severity of disease associated with the new variant, and evaluated control measures including vaccination and nonpharmaceutical interventions. Combining multiple lines of evidence allowed us to draw robust inferences. ### RESULTS The rapid spread of VOC 202012/01 is not an artifact of geographical differences in contact behavior and does not substantially differ by age, sex, or socioeconomic stratum. We estimate that the new variant has a 43 to 90% higher reproduction number (range of 95% credible intervals, 38 to 130%) than preexisting variants. Similar increases are observed in Denmark, Switzerland, and the United States. The most parsimonious explanation for this increase in the reproduction number is that people infected with VOC 202012/01 are more infectious than people infected with a preexisting variant, although there is also reasonable support for a longer infectious period and multiple mechanisms may be operating. Our estimates of severity are uncertain and are consistent with anything from a moderate decrease to a moderate increase in severity (e.g., 32% lower to 20% higher odds of death given infection). Nonetheless, our mathematical model, fitted to data up to 24 December 2020, predicted a large surge in COVID-19 cases and deaths in 2021, which has been borne out so far by the observed burden in England up to the end of March 2021. In the absence of stringent nonpharmaceutical interventions and an accelerated vaccine rollout, COVID-19 deaths in the first 6 months of 2021 were projected to exceed those in 2020 in England. ### CONCLUSION More than 98% of positive SARS-CoV-2 infections in England are now due to VOC 202012/01, and the spread of this new variant has led to a surge in COVID-19 cases and deaths. Other countries should prepare for potentially similar outcomes. ![Figure][2] Impact of SARS-CoV-2 Variant of Concern 202012/01. ( A ) Spread of VOC 202012/01 (lineage B.1.1.7) in England. ( B ) The estimated relative transmissibility of VOC 202012/01 (mean and 95% confidence interval) is similar across the United Kingdom as a whole, England, Denmark, Switzerland, and the United States. ( C ) Projected COVID-19 deaths (median and 95% confidence interval) in England, 15 December 2020 to 30 June 2021. Vaccine rollout and control measures help to mitigate the burden of VOC 202012/01. A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in September 2020 and is rapidly spreading toward fixation. Using a variety of statistical and dynamic modeling approaches, we estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine rollout, COVID-19 hospitalizations and deaths across England in the first 6 months of 2021 were projected to exceed those in 2020. VOC 202012/01 has spread globally and exhibits a similar transmission increase (59 to 74%) in Denmark, Switzerland, and the United States. [1]: /lookup/doi/10.1126/science.abg3055 [2]: pending:yes

Human brains are larger than and structurally different from the brains of the great apes. Ponce de León et al. explored the timing of the origins of the structurally modern human brain (see the Perspective by Beaudet). By comparing endocasts, representations of the inner surface of fossil brain cases, from early Homo from Africa, Georgia, and Southeast Asia, they show that these structural innovations emerged later than the first dispersal of the genus from Africa, and were probably in place by 1.7 to 1.5 million years ago. The modern humanlike brain organization emerged in cerebral regions thought to be related to toolmaking, social cognition, and language. Their findings suggest that brain reorganization was not a prerequisite for dispersals from Africa, and that there might have been more than one long-range dispersal of early Homo . Science , this issue p. [165][1]; see also p. [124][2] The brains of modern humans differ from those of great apes in size, shape, and cortical organization, notably in frontal lobe areas involved in complex cognitive tasks, such as social cognition, tool use, and language. When these differences arose during human evolution is a question of ongoing debate. Here, we show that the brains of early Homo from Africa and Western Asia (Dmanisi) retained a primitive, great ape–like organization of the frontal lobe. By contrast, African Homo younger than 1.5 million years ago, as well as all Southeast Asian Homo erectus , exhibited a more derived, humanlike brain organization. Frontal lobe reorganization, once considered a hallmark of earliest Homo in Africa, thus evolved comparatively late, and long after Homo first dispersed from Africa. [1]: /lookup/doi/10.1126/science.aaz0032 [2]: /lookup/doi/10.1126/science.abi4661

Following the recent progress in Terahertz (THz) signal generation and radiation methods, joint THz communications and sensing applications are shaping the future of wireless systems. Towards this end, THz spectroscopy is expected to be carried over user equipment devices to identify material and gaseous components of interest. THz-specific signal processing techniques should complement this re-surged interest in THz sensing for efficient utilization of the THz band. In this paper, we present an overview of these techniques, with an emphasis on signal pre-processing (standard normal variate normalization, min-max normalization, and Savitzky-Golay filtering), feature extraction (principal component analysis, partial least squares, t-distributed stochastic neighbor embedding, and nonnegative matrix factorization), and classification techniques (support vector machines, k-nearest neighbor, discriminant analysis, and naive Bayes). We also address the effectiveness of deep learning techniques by exploring their promising sensing capabilities at the THz band. Lastly, we investigate the performance and complexity trade-offs of the studied methods in the context of joint communications and sensing; we motivate the corresponding use-cases, and we present few future research directions in the field.

This paper describes the acquisition, preprocessing, segmentation, and alignment of an Amharic-English parallel corpus. It will be useful for machine translation of an under-resourced language, Amharic. The corpus is larger than previously compiled corpora; it is released for research purposes. We trained neural machine translation and phrase-based statistical machine translation models using the corpus. In the automatic evaluation, neural machine translation models outperform phrase-based statistical machine translation models.

The joy, anxiety, and anticipation of getting a COVID vaccine in America culminates, quite anticlimactically, with a piece of white cardstock. Some have already lost their vaccine cards or never got them to begin with. Others have their names misspelled and crossed out on it. Many are having trouble reconciling how something so simple--and easily forged--can carry such import and weight. The White House has recently clarified that there will be no federal vaccine passport.

Despite only being early in the year, significant events have already taken place in 2021. Mass vaccinations for Covid-19 have begun around the world, and new strains of the disease have surfaced in the United Kingdom, South Africa and Brazil. For companies, this news has had a direct impact on their ability to conduct business while further placing their pandemic response under the public microscope. How companies are being talked and written about is changing as the pandemic unfolds, and these nuances could reveal more than simply how effective an organization's marketing department is. What if shifts in sentiment could help traders make more informed financial decisions?