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There is an eerie low hum that emanates from data centres, where tens of thousands of chips make trillions of computations a second to help drive the artificial intelligence (AI) revolution. These chips power the text, images and video generated by the queries made by the world of the advanced AI models. Their computations, which are in effect the switching on and off of microscopic silicon transistors that make up a chip, are actually silent. But, as with all computers, almost every watt of the significant electricity powering this process leaves as heat, and the sound you can hear is the slow whir of thousands of fans required to prevent the heat from frying the racks of servers. Depending on the size of the site, you may also hear the thrum of transformers in substations channelling electricity.

When you purchase through links in our articles, we may earn a small commission. AI subscriptions are the electric bill. You're always going to pay for cloud AI, so why not invest in yourself? The AI pendulum has swung back and forth throughout the last few years, from ChatGPT and Copilot in the cloud, then back to local AI and the PC's newfound NPU, then back to independent agents like Claude. Now it's headed the way of the PC once again, abandoning privacy arguments (which still stand strong!) for a more straightforward argument: It's better for your wallet.

Human writers are expensive, and they eventually die. AI is cheaper, and will never join a union. I have been thinking about this for close to 20 minutes, and I have concluded that human writing is finished. Let me begin with an anecdote, because that is how serious arguments begin. Last Tuesday I asked a machine to write me a birthday message for my sister-in-law.

If AI systems are viewed as too advanced to control, the companies that build them can't held liable for the harms they cause. "Runaway" AI, "rogue" agents, and "autonomous" actors--the current rhetoric would have you believe that AI agents are not only awake and aware, but angry at their creators. Prominent tech leaders such as Demis Hassabis, Dario Amodei, and Sam Altman push for regulation of these seemingly "superhuman" systems, while a separate faction, led by policy organizations and academic philosophers often aligned with the effective altruism movement, debates whether humanity holds the moral right to govern them at all. Upon closer inspection, they are all calling for the same thing: a view of AI systems as being so advanced and capable that no entity, human or corporate, could possibly be responsible for their actions. While these perspectives seem at odds, they are inadvertently aligned on one goal: making sure the companies that build these systems escape meaningful liability for the harms they already cause. This narrative is gaining traction as AI models become more complex and frontier labs reveal their incapability of containing the agents they've built.

It also alleges that Google "downloaded web scrapes of virtually the entire internet, including from known pirate sources and from behind legitimate paywalls". It further alleges that Google copied those works without permission to train its AI models and continues to do so, despite those uses allegedly falling outside the scope of existing agreements. The suit claims the company was fully aware of the legal risks, alleging that internal documents warned using books to train AI models was "highly problematic for Google," and could lead to as much as $100bn in fines. "At no point did Google inform authors and publishers that Google was copying their works as source material to develop and train AI models," the suit alleges. "It's an interesting issue that has a lot of complex dimensions, in no small part because it can be hard to prove what was or wasn't in a training corpus."

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We study uniform-in-time propagation-of-chaos for continuous-time Stein Variational Gradient Descent (SVGD). Classical finite-time propagation-of-chaos estimates for mean-field systems typically deteriorate rapidly with time and therefore do not directly explain the long-time relation between the finite-particle system and its mean-field limit. We obtain two complementary classes of uniform-in-time propagation-of-chaos results. For broad distributional metrics, we introduce a cutoff strategy which combines finite-time propagation-of-chaos estimates up to an $N$-dependent horizon with independent quantitative long-time convergence estimates for the finite-particle and mean-field SVGD flows. This yields uniform-in-averaging-time propagation-of-chaos bounds in Langevin kernel Stein discrepancy, Wasserstein-1 distance, and Wasserstein-2 distance, with logarithmic or iterated-logarithmic rates depending on the metric, target and kernel class. We also develop a finite-dimensional theory for matrix-valued finite-rank kernels. For Gaussian targets with bilinear kernels, the SVGD dynamics close exactly on first and second moments, yielding genuine uniform-in-physical-time parametric propagation-of-chaos rates in finite-dimensional Stein-feature metrics. We then prove a conjugacy principle showing that these feature-level estimates transfer to conjugate target-kernel pairs under orientation-preserving diffeomorphisms, thereby extending the theory to broad classes of nonlinear, including multimodal, targets. Together, these results highlight the contrast between generic distributional metrics, for which our general approach yields logarithmic rates, and closed finite-dimensional Stein observables, for which parametric $N^{-1/2}$ propagation-of-chaos rates persist uniformly in time.

We develop a framework for analyzing the learning dynamics of $\ell_2$-adversarial training of single-index models on Gaussian mixtures in the high-dimensional limit under streaming stochastic gradient descent (SGD). We derive deterministic equivalents for a broad class of statistics of the SGD iterates, including the adversarial risk and distance to adversarial optimality, in terms of the solution to a system of ODEs. We use them to study two idealized learning rate schedules: the Polyak stepsize and exact line search. In the case of $\ell_2$-adversarial least squares with a single class, we show that, unlike noiseless standard least squares, no constant learning rate guarantees monotone descent of SGD towards a minimizer of the adversarial risk. We identify anisotropic covariance and a mismatch in ridge parameters as the main sources of suboptimality of exact line search relative to the Polyak stepsize. We also introduce a stochastic differential equation (SDE), called adversarial homogenized SGD, that captures the evolution of statistics of the iterates of SGD. For $\ell_2$-adversarial least squares, using this SDE, we show the evolution of the risk is equivalent, up to dimension-free constants, to that of SGD on standard least squares with an adaptive learning rate and adaptive $\ell_2$-regularization. When the dynamics converge, the limiting adversarial risk and SGD iterate are determined by a fixed-point equation, with the limiting iterate being equivalent to the solution of a ridge regression problem whose regularization parameter is the limiting effective regularization of SGD.

Follow this section to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW? Smart Alerts: Get notified about major news as it happens. Follow this tag to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW?