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The impact of inference-time data perturbation (e.g., adversarial attacks) has been extensively studied in machine learning, leading to well-established certification techniques for adversarial robustness. In contrast, certifying models against training data perturbations remains a relatively under-explored area. These perturbations can arise in three critical contexts: adversarial data poisoning, where an adversary manipulates training samples to corrupt model performance; machine unlearning, which requires certifying model behavior under the removal of specific training data; and differential privacy, where guarantees must be given with respect to substituting individual data points. This work introduces Abstract Gradient Training (AGT), a unified framework for certifying robustness of a given model and training procedure to training data perturbations, including bounded perturbations, the removal of data points, and the addition of new samples. By bounding the reachable set of parameters, i.e., establishing provable parameter-space bounds, AGT provides a formal approach to analyzing the behavior of models trained via first-order optimization methods.

The Chinese Communist Party is a geopolitical cancer that will metastasize unless America can contain it with a once-in-a-generation investment in our national defense. Already, the CCP is actively colluding with Russia, prolonging Putin's war against Ukraine by blunting the impact of Western sanctions; it reaffirmed its support for Iran even after the deadly Oct. 7 attacks against Israel; and it has an explicit defense treaty with Kim Jung Un's North Korean dictatorship. To make matters even more dire, Chinese President Xi Jinping has instructed his People's Liberation Army to be ready to invade Taiwan by 2027. Chinese President Xi Jinping has instructed his People's Liberation Army to be ready to invade Taiwan by 2027. As George Washington counseled Congress in the nation's first ever inaugural address, "to be prepared for war is the most effectual means of preserving the peace."

Much of the tech industry's focus on the National Defense Authorization Act has revolved around President Trump's threat to veto the must-pass defense spending bill because it does not repeal Section 230. But the final version of the NDAA, passed by a vast majority of both chambers this week, contains a little-noticed provision that promises to reverberate across the industry: a pledge to increase government spending on artificial intelligence, quantum computing and 5G technology by $10 billion annually over the next five years. It's unclear exactly how much the government spends to bolster those technologies today, but it's likely closer to $1.5 billion. The Industries of the Future Act of 2020, which was supported by IBM and software industry trade group BSA, was introduced earlier this year amid a broader push from the White House -- and Ivanka Trump -- to invest more government resources in "industries of the future," meaning emerging technologies like quantum computing and artificial intelligence. It's part of a broader effort to funnel more resources toward ensuring the U.S. has a leg up on China in the so-called "race" to technological dominance.

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