We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing deep learning approaches either assume access to the driving noise or initial condition, or rely on deterministic surrogate models that fail to capture intrinsic stochasticity. We propose a structured latent-variable formulation that requires only observations of solution realizations and learns the underlying randomly forced dynamics. Our approach combines a spectral Galerkin projection with a […]

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arXiv:2601.22359v1 Announce Type: new Abstract: Machine unlearning offers a practical alternative to avoid full model re-training by approximately removing the influence of specific user data. While existing methods certify unlearning via statistical indistinguishability from re-trained models, these guarantees do not naturally extend to model outputs when inputs are adversarially perturbed. In particular, slight perturbations of forget samples may still be correctly recognized by the unlearned model – even when a re-trained model fails to do so – revealing […]

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With Google Opal AI, an experimental tool that assists users in making light “mini-apps” by means of a visual, AI-assisted workflow, Google has quietly made its entrance into the expanding universe of AI-powered app development. Opal places itself in the middle of rush coding, no-code platforms, and AI app creators, growing as a fast and user-friendly way to prototype functioning micro-apps without needing a lot of engineering.  Google Opal AI does not compete with full-stack app builders directly. […]

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arXiv:2507.15112v4 Announce Type: replace-cross Abstract: Machine learning systems increasingly face requirements to remove entire domains of information–such as toxic language or biases–rather than individual user data. This task presents a dilemma: full removal of the unwanted domain data is computationally expensive, while random partial removal is statistically inefficient. We find that a domain’s statistical influence is often concentrated in a small subset of its data samples, suggesting a path between ineffective partial removal and unnecessary complete removal. We […]

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arXiv:2602.05035v1 Announce Type: new Abstract: Multilingual language models (LMs) sometimes under-perform their monolingual counterparts, possibly due to capacity limitations. We quantify this “multilingual penalty” for lexical disambiguation–a task requiring precise semantic representations and contextualization mechanisms–using controlled datasets of human relatedness judgments for ambiguous words in both English and Spanish. Comparing monolingual and multilingual LMs from the same families, we find consistently reduced performance in multilingual LMs. We then explore three potential capacity constraints: representational (reduced embedding isotropy), attentional […]

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arXiv:2601.13191v1 Announce Type: new Abstract: In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected empirical risk subject to an $f$-divergence constraint are established. The proposed approach extends applicability to a broader class of $f$-divergences than previously reported and yields theoretical results that recover previously known results. Additionally, the difference between the expected empirical […]

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arXiv:2601.00172v1 Announce Type: new Abstract: Forecasting high-dimensional spatiotemporal systems remains computationally challenging for recurrent neural networks (RNNs) and long short-term memory (LSTM) models due to gradient-based training and memory bottlenecks. Reservoir Computing (RC) mitigates these challenges by replacing backpropagation with fixed recurrent layers and a convex readout optimization, yet conventional RC architectures still scale poorly with input dimensionality. We introduce a Sequential Reservoir Computing (Sequential RC) architecture that decomposes a large reservoir into a series of smaller, interconnected […]

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Each of us today has the opportunity to benefit in various ways from the vast amount of free knowledge available on the Internet. Despite this, many people use only a small portion of this technology. With artificial intelligence, more or less the same pattern is repeating: some people fully exploit its potential, while others limit themselves to asking simple questions to ChatGPT, much like what happened with Google. We have in our hands a tool with enormous potential: […]

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