'There's this deep mystery of what, actually, is this thing?': the philosopher inside Google DeepMind AI Since 2017, Iason Gabriel has worked at the tech giant, trying to anticipate - and think through - the impact of AI. But as commercial and geopolitical pressures escalate, can ethicists make any difference? In 2017, a 33-year-old political philosopher named Iason Gabriel was told by a friend that he ought to apply for a job at DeepMind, the London-based subsidiary of Google where much of its AI research was concentrated. The suggestion was not an obvious one. Gabriel was a cheerful but intense junior academic with a passion for Vipassana meditation and what his brother calls "enthusiastic" rock climbing. At the University of Oxford, where he was a fellow at St John's College, Gabriel taught courses on political theory and wrote papers on the moral contortions of "yuppie ethics" and the ethical blind spots of effective altruism. When he wasn't there, he did crisis work for the United Nations Development Programme in Sudan and Lebanon. DeepMind, meanwhile, was the world's leading AI research lab. In part, this was because it had the financial and computational backing of Google, which had bought the company in 2014 for $650m. In part, it was because DeepMind had recently shown it could put those resources to stunning use. In Seoul, in 2016, a DeepMind system called AlphaGo defeated Lee Sedol, a South Korean Go champion, in a five-game match. The victory was significant not least because of Go's legendary complexity; the game has more possible configurations than there are atoms in the universe. Thanks to the fuss around AlphaGo, Gabriel was aware of DeepMind.

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This raises a fundamental dilemma of statistical-computational tradeoffs: removing all samples from an unwanted domain may be computationally prohibitive, while randomly removing a subset may not provide distribution-level statistical guarantees. We propose a statistical framework for distributional unlearning, in which domains are modeled as probability distributions, and the goal is to remove a carefully chosen subset of samples that reduces the effect of an unwanted distribution while preserving performance on a desired one. We formalize this using a hypothesis test of the edited data with the desired and unwanted domains, leading to an interpretable and robust criterion for selecting samples to remove. Within this statistical framework, we characterize the fundamental region of the allowable edited data distributions and the removal-preservation Pareto frontier for a broad class of distribution families. This includes parametric families such as shifted Gaussians of arbitrary dimension, a one-dimensional location family with log-concave noise, and the one-dimensional Poisson family. It also includes nonparametric families such as the Gaussian white noise model, a canonical model for nonparametric regression. We prove composition rules that describe how distributional unlearning behaves across multimodal unwanted domains, and introduce a central-limit behavior for the removal-preservation baselines when composing a large number of such families. Finally, we provide finite sample guarantees by providing Pareto frontiers for some selection algorithms, and observe an information-computation gap.

We start by fleshing out the connection between strong convexity and smoothness charted in Lemma 1: Lemma 1. If F is -strongly convex w.r.t.

We show that if the conditional distribution p(C | T) factors through a sufficient statistic ϕ(T), then the Information Bottleneck (IB) problem for (T, C) is exactly equivalent to the IB problem for (ϕ(T), C). The reduction is loss-free: it preserves the full IB curve, the Lagrangian optimum at every trade-off parameter \b{eta}, and the optimal representations up to pullback through ϕ. As a result, the computational complexity of solving the IB problem is governed by the dimension of the sufficient statistic rather than the ambient dimension of the source. This identifies an exact structural condition under which the generic IB problem becomes tractable, and gives a formal bridge between the discrete and linear-Gaussian regimes. We then show that the classical Gaussian IB solution of Chechik, Globerson, Tishby and Weiss is an immediate corollary of this reduction, and we state a nonlinear-Gaussian generalisation. A small numerical example illustrates the practical consequence: when a low-dimensional sufficient statistic is available, the exact IB curve can be computed on the reduced problem at a cost determined by the statistic rather than by the ambient source dimension.

As people increasingly rely on AI chatbots for guidance, even on financial matters, a healthy dose of skepticism is critical. I've used ChatGPT to help me build a budget before, and it was genuinely helpful. After I input my monthly salary as well as my standard utilities and recurring expenses, the chatbot drafted a few solid options, and I tweaked them into penny-pinching perfection. "Millions of people turn to ChatGPT with money-related questions, from understanding debt to building budgets and learning financial concepts," says Niko Felix, an OpenAI spokesperson, when reached for comment. "ChatGPT can be a helpful tool for exploring options, preparing questions, and making financial topics easier to understand, but it is not a substitute for licensed financial professionals." OpenAI's Terms of Use state that the AI tool is not meant to replace professional financial advice.

Random forests are learning algorithms that build large collections of random trees and make predictions by averaging the individual tree predictions. In this paper, we consider various tree constructions and examine how the choice of parameters affects the generalization error of the resulting random forests as the sample size goes to infinity. We show that subsampling of data points during the tree construction phase is important: Forests can become inconsistent with either no subsampling or too severe subsampling. As a consequence, even highly randomized trees can lead to inconsistent forests if no subsampling is used, which implies that some of the commonly used setups for random forests can be inconsistent. As a second consequence we can show that trees that have good performance in nearest-neighbor search can be a poor choice for random forests.