The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require exponentially more samples than the information-theoretic rate, or they use fewer samples but require solving NP-hard problems for which there are no known practical algorithms. A recent approach, based on integer programming, resolves this tension for nonnegative tensor completion. It achieves the information-theoretic sample complexity rate and deploys the Blended Conditional Gradients algorithm, which requires a linear (in numerical tolerance) number of oracle steps to converge to the global optimum. The tradeoff in this approach is that, in the worst case, the oracle step requires solving an integer linear program. Despite this theoretical limitation, numerical experiments show that this algorithm can, on certain instances, scale up to 100 million entries while running on a personal computer. The goal of this paper is to further enhance this algorithm, with the intention to expand both the breadth and scale of instances that can be solved. We explore several variants that can maintain the same theoretical guarantees as the algorithm, but offer potentially faster computation. We consider different data structures, acceleration of gradient descent steps, and the use of the Blended Pairwise Conditional Gradients algorithm. We describe the original approach and these variants, and conduct numerical experiments in order to explore various tradeoffs in these algorithmic design choices.

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Former federal prosecutor Trey Gowdy gives his take on the Alex Murdaugh trial and Hunter Biden's attorney calling for criminal probe of the laptop on'The Story.' High-profile lawyer Abbe Lowell again entered the national spotlight this week representing Hunter Biden in the legal battle involving his infamous laptop, and Lowell's hiring signals how seriously Biden is taking his situation, an attorney tells Fox News Digital. "Abbe is not cheap, and you don't bring in Abbe unless you want to go to war or prevent one," said the source who's worked with Lowell. He hasn't been charged with anything, but they're trying to prevent that because that would be bad for [President] Biden and Hunter." Lowell made a splash this week with letters urging prosecutors to launch state and federal investigations into John Paul Mac Isaac, who he accused of "unlawfully" accessing the younger Biden's personal data on his laptop after it was left at his repair shop in 2019. Former President Donald Trump's lawyer Rudy Giuliani, Steve Bannon and other notable Biden critics were also listed in the lawsuit for their role in disseminating the information to the public. Mac Isaac chose to work with President Donald Trump's personal lawyer to weaponize Mr. Biden's personal computer data against his father, Joseph R. Biden, by unlawfully causing the provision of Mr. Biden's personal data to the New York Post," Lowell wrote Wednesday.

In the classroom of the future--if there still are any--it's easy to imagine the endpoint of an arms race: an artificial intelligence that generates the day's lessons and prompts, a student-deployed A.I. that will surreptitiously do the assignment, and finally, a third-party A.I. that will determine if any of the pupils actually did the work with their own fingers and brain. Loop complete; no humans needed. If you were to take all the hype about ChatGPT at face value, this might feel inevitable. But a response to the hit software demo, released by OpenAI in November to instant fanfare, is coming. You only have to look at how schools dealt with the potential externalities of newly essential tech during the pandemic to see how a similarly paranoid reaction to chatbots like ChatGPT could go--and how it shouldn't. When schools had to shift on the fly to remote learning three years ago, there was a massive turn to what at that point was mainly enterprise software: Zoom.

By incorporating the residual of the differential equation into the loss function of a neural network-based surrogate model, PINNs can seamlessly combine measured data with physical constraints given by differential equations. PINNs can also be viewed as a surrogate model for solving differential equations by incorporating additional data or as a data-driven correction (or even discovery) of the underlying physical system. By the end of the year 2022, we had experienced several waves of the COVID-19 pandemic with different variants of the virus prevailing at different time intervals. Various levels of interventions and protective measures were implemented to counteract the uncontrolled spreading of the disease. We focus exemplarily on the time until the fourth wave (i.e., the omicron wave) of the COVID-19 pandemic in Germany that had its peak in February and March 2022. The B.1.617.2 (delta) variant of SARS-CoV-2, which is characterized by a higher contagiosity than the previous B.1.1.7 (alpha), B.1.351

3D face reconstruction algorithms from images and videos are applied to many fields, from plastic surgery to the entertainment sector, thanks to their advantageous features. However, when looking at forensic applications, 3D face reconstruction must observe strict requirements that still make unclear its possible role in bringing evidence to a lawsuit. Shedding some light on this matter is the goal of the present survey, where we start by clarifying the relation between forensic applications and biometrics. To our knowledge, no previous work adopted this relation to make the point on the state of the art. Therefore, we analyzed the achievements of 3D face reconstruction algorithms from surveillance videos and mugshot images and discussed the current obstacles that separate 3D face reconstruction from an active role in forensic applications.

According to the authors, such integration is like riding a bicycle made for two, also known as a tandem. This kind of vehicle requires a strong collaboration between the two riders to pedal synchronically and the one in front must be able and willing to drive the tandem towards a common destination, on which both riders agree. The structure of the bicycle should suit a diversity of users: tall and short; married couples and perfect strangers; sportspeople and lazy ones. The way it can be used must adapt to any kind of road, dirt trails and urban well-paved streets alike. Cycling metaphors aside, the convergence and integration of two different disciplines puts requirements to the method and the attitude of both and of all participants.

Despite the tremendous success of convolutional neural networks (CNNs) in computer vision, the mechanism of CNNs still lacks clear interpretation. Currently, class activation mapping (CAM), a famous visualization technique to interpret CNN's decision, has drawn increasing attention. Gradient-based CAMs are efficient while the performance is heavily affected by gradient vanishing and exploding. In contrast, gradient-free CAMs can avoid computing gradients to produce more understandable results. However, existing gradient-free CAMs are quite time-consuming because hundreds of forward interference per image are required. In this paper, we proposed Cluster-CAM, an effective and efficient gradient-free CNN interpretation algorithm. Cluster-CAM can significantly reduce the times of forward propagation by splitting the feature maps into clusters in an unsupervised manner. Furthermore, we propose an artful strategy to forge a cognition-base map and cognition-scissors from clustered feature maps. The final salience heatmap will be computed by merging the above cognition maps. Qualitative results conspicuously show that Cluster-CAM can produce heatmaps where the highlighted regions match the human's cognition more precisely than existing CAMs. The quantitative evaluation further demonstrates the superiority of Cluster-CAM in both effectiveness and efficiency.

Recent progress in scaling up large language models has shown impressive capabilities in performing few-shot learning across a wide range of text-based tasks. However, a key limitation is that these language models fundamentally lack visual perception - a crucial attribute needed to extend these models to be able to interact with the real world and solve vision tasks, such as in visual-question answering and robotics. Prior works have largely connected image to text through pretraining and/or fine-tuning on curated image-text datasets, which can be a costly and expensive process. In order to resolve this limitation, we propose a simple yet effective approach called Language-Quantized AutoEncoder (LQAE), a modification of VQ-VAE that learns to align text-image data in an unsupervised manner by leveraging pretrained language models (e.g., BERT, RoBERTa). Our main idea is to encode image as sequences of text tokens by directly quantizing image embeddings using a pretrained language codebook. We then apply random masking followed by a BERT model, and have the decoder reconstruct the original image from BERT predicted text token embeddings. By doing so, LQAE learns to represent similar images with similar clusters of text tokens, thereby aligning these two modalities without the use of aligned text-image pairs. This enables few-shot image classification with large language models (e.g., GPT-3) as well as linear classification of images based on BERT text features. To the best of our knowledge, our work is the first work that uses unaligned images for multimodal tasks by leveraging the power of pretrained language models.

We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for nongeometric data, as well as novel RPEs operating on the sequences of tokens embedded in higher-dimensional Euclidean spaces (e.g. point clouds). FLTs construct the optimal RPE mechanism implicitly by learning its spectral representation. As opposed to other architectures combining efficient low-rank linear attention with RPEs, FLTs remain practical in terms of their memory usage and do not require additional assumptions about the structure of the RPE-mask. FLTs allow also for applying certain structural inductive bias techniques to specify masking strategies, e.g. they provide a way to learn the so-called local RPEs introduced in this paper and providing accuracy gains as compared with several other linear Transformers for language modeling. We also thoroughly tested FLTs on other data modalities and tasks, such as: image classification and 3D molecular modeling. For 3D-data FLTs are, to the best of our knowledge, the first Transformers architectures providing RPE-enhanced linear attention.