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Supplementary to " Approximation with CNNs in Sobolev Space: with Applications to Classification "

Neural Information Processing Systems

In the Supplementary materials, we include detailed descriptions on convex surrogate losses,convolutional neural networks, non-asymptotic error bounds for commonly used loss functions, and prove Theorems 2.1,2.2, A toy example on the numerical performance of CNN approximation is presented in Appendix D. We next give a brief review of the convex surrogate loss functions and discuss in details on the connection between the excess risk with respect to the ฯ•-loss and that of 0-1 loss [28, 4]. Let ฯ•be a given convex univariate function ฯ•: R [0,). Instead of minimizing the excess risk R over H, we consider minimizing the risk with respect to the loss ฯ•(ฯ•-risk) R(f):= E{ฯ•(Yf(X))} over a certain class of functions F, where ฯ•: R [0,) is some generic loss function. For the special case when H = {h: h(x) = sign(f(x)),f F} and ฯ•() is a step function, i.e., ฯ•(x) = 1 Guohao Shen and Yuling Jiao contributed equally to this work Corresponding authors 36th Conference on Neural Information Processing Systems (NeurIPS 2022). As shown in [28] and [4], for a properly chosen ฯ•, ห†fn can indeed help reduce the 0-1 excess risk R (ห†hn) R (h0). More precisely, let R0:= inff measurable R(f), then for a proper ฯ•, we have ฯˆ(R (ห†hn) R (h0)) R(ห†fn) R(f0), where ฯˆ: [ 1,1] [0,)is a nonnegative continuous function, invertible on [0,1], and achieves its minimum at 0 with ฯˆ(0) = 0. A wide variety of popular classification methods are based on this tactic.



Designer Baby Companies Are in Turmoil

WIRED

Bootstrap Bio and Manhattan Genomics, which were pursuing gene editing in human embryos to prevent serious disease, have shut down. Two companies that launched last year with plans to create gene-edited babies have already shut down, citing money issues and internal conflict. One of them, Manhattan Genomics of New York, closed abruptly shortly after announcing a team of scientific advisers in October that included a prominent fertility doctor, a data scientist who worked for de-extinction company Colossal Biosciences, and a scientist who pioneered a "three-parent" IVF technique. The other, California-based Bootstrap Bio, said it ceased operations in late 2025, as first reported by Mother Jones. Manhattan Genomics and Bootstrap Bio had ambitions to edit DNA in human embryos with the goal of preventing serious disease in babies.



'Chemical-spraying' drones reportedly stolen from New Jersey facility sparks fears of 'nightmare scenario'

Daily Mail - Science & tech

Rob Reiner's son Jake shares horrific new details from night of his parents' murders and says it is'almost impossible to process' that his brother Nick has been charged with the killings Bloodbath on the streets as millions of dogs are'massacred' by firing squad ahead of the World Cup Tucker Carlson's secret heiress sister reveals bitter feud over family fortune: He says'I don't know her'... but trove of photos tells a very different story Lesbian sex secrets of Kristi Noem's ICE leader: Ex lover claims jealous rages over men, screaming through hotel walls... and vile tight bodysuit demand Hidden cameras at NYC's live animal markets expose filthy conditions, disease risks, and brutal treatment of chickens, ducks, rabbits and sheep MAUREEN CALLAHAN: Dark indisputable Michael Jackson truths Hollywood STILL covers up. His own daughter reportedly now thinks he was a pedophile, so why's this so hard to say? Scandal after high-ranking female prison officer gave birth to twins... as shocking rumor spreads about identity of their father My senior government source has told me why these scientists may REALLY be going missing. This is so serious even the President is being kept on a'need-to-know basis': KENNEDY Former NFL quarterback Tim Tebow announces tragic news of dad's death after battle with Parkinson's in heartbreaking post Reclusive Athina Onassis, heiress to $2.7billion fortune who stepped away from public life after humiliating heartbreak, breaks cover at Barcelona Bridal Week in rare public appearance Sam's Club just launched a perk that targets Costco's biggest flaw Disappointed customers reveal the most'overrated' chain restaurants... do YOU have good taste? Woke author who boasted about shoplifting from Whole Foods flies into foul-mouthed RAGE when confronted outside her $2.2m Brooklyn brownstone Sherrone Moore's ex-mistress reveals pregnancy as she details night fired Michigan coach came to her apartment Troubling past of'father of the year' who murdered son, 11, in airport bathroom... as grieving grandpa reveals warning sign that something awful was about to happen US threatens to'review' UK claim to Falklands Islands and ban Spain from NATO as punishment for failure to back Iran War'Chemical-spraying' drones reportedly stolen from New Jersey facility sparks fears of'nightmare scenario' An alarm has erupted after 15 powerful agricultural spray drones were stolen in a suspected coordinated heist in New Jersey last month. A report from The High Side claimed the FBI is investigating the theft amid fears the machines could be used to disperse dangerous materials.


Understanding Programmatic Weak Supervision via Source-aware Influence Function

Neural Information Processing Systems

Programmatic Weak Supervision (PWS) aggregates the source votes of multiple weak supervision sources into probabilistic training labels, which are in turn used to train an end model. With its increasing popularity, it is critical to have some tool for users to understand the influence of each component (e.g., the source vote or training data) in the pipeline and interpret the end model behavior. To achieve this, we build on Influence Function (IF) and propose source-aware IF2, which leverages the generation process of the probabilistic labels to decompose the end model's training objective and then calculate the influence associated with each (data, source, class) tuple. These primitive influence score can then be used to estimate the influence of individual component of PWS, such as source vote, supervision source, and training data. On datasets of diverse domains, we demonstrate multiple use cases: (1) interpreting incorrect predictions from multiple angles that reveals insights for debugging the PWS pipeline, (2) identifying mislabeling of sources with a gain of 9%-37% over baselines, and (3) improving the end model's generalization performance by removing harmful components in the training objective (13%-24% better than ordinary IF).




Anytime-Valid Inference For Multinomial Count Data

Neural Information Processing Systems

Many experiments compare count outcomes among treatment groups. Examples include the number of successful signups in conversion rate experiments or the number of errors produced by software versions in canary tests. Observations typically arrive in a sequence and practitioners wish to continuously monitor their experiments, sequentially testing hypotheses while maintaining Type I error probabilities under optional stopping and continuation. These goals are frequently complicated in practice by non-stationary time dynamics. We provide practical solutions through sequential tests of multinomial hypotheses, hypotheses about many inhomogeneous Bernoulli processes and hypotheses about many timeinhomogeneous Poisson counting processes. For estimation, we further provide confidence sequences for multinomial probability vectors, all contrasts among probabilities of inhomogeneous Bernoulli processes and all contrasts among intensities of time-inhomogeneous Poisson counting processes. Together, these provide an "anytime-valid" inference framework for a wide variety of experiments dealing with count outcomes, which we illustrate with several industry applications.


Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization

Neural Information Processing Systems

Graph neural networks (GNNs) have achieved superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards their transferability. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as the goal of transferable GNN training, which motivates the design of EGI (Ego-Graph Information maximization) to analytically achieve this goal. Secondly, when node features are structure-relevant, we conduct an analysis of EGI transferability regarding the difference between the local graph Laplacians of the source and target graphs. We conduct controlled synthetic experiments to directly justify our theoretical conclusions. Comprehensive experiments on two real-world network datasets show consistent results in the analyzed setting of direct-transfering, while those on large-scale knowledge graphs show promising results in the more practical setting of transfering with fine-tuning.1