Mathematicians stunned by AI's biggest breakthrough in mathematics yet An 80-year-old maths conjecture that has eluded the world's greatest mathematicians has been cracked by an artificial intelligence model built by OpenAI. The result has stunned experts and is being hailed as a seismic moment for AI's mathematical ability. "This is a problem that I didn't expect to see solved in my lifetime," says Misha Rudnev at the University of Bristol, UK. "It's absolutely a bomb." Tim Gowers at the University of Cambridge wrote that the solution is "a milestone in AI mathematics" in a blog post accompanying the work . "If a human had written the paper and submitted it to the and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that."

Given a set of calibrated images of a scene, we present an approach that produces a simple, compact, and actionable 3D world representation by means of 3D primitives. While many approaches focus on recovering high-fidelity 3D scenes, we focus on parsing a scene into mid-level 3D representations made of a small set of textured primitives. Such representations are interpretable, easy to manipulate and suited for physics-based simulations. Moreover, unlike existing primitive decomposition methods that rely on 3D input data, our approach operates directly on images through differentiable rendering.

Machine learning models are often personalized by using group attributes that encode personal characteristics (e.g., sex, age group, HIV status). In such settings, individuals expect to receive more accurate predictions in return for disclosing group attributes to the personalized model. We study when we can tell that a personalized model upholds this principle for every group who provides personal data. We introduce a metric called the benefit of personalization (BoP) to measure the smallest gain in accuracy that any group expects to receive from a personalized model. We describe how the BoP can be used to carry out basic routines to audit a personalized model, including: (i) hypothesis tests to check that a personalized model improves performance for every group; (ii) estimation procedures to bound the minimum gain in personalization. We characterize the reliability of these routines in a finite-sample regime and present minimax bounds on both the probability of error for BoP hypothesis tests and the mean-squared error of BoP estimates. Our results show that we can only claim that personalization improves performance for each group who provides data when we explicitly limit the number of group attributes used by a personalized model. In particular, we show that it is impossible to reliably verify that a personalized classifier with k 19 binary group attributes will benefit every group who provides personal data using a dataset of n = 8 109 samples - one for each person in the world.

Neural Information Processing Systems http://nips.cc/

We provide the guidelines presented to the users for the creation of the dataset. To see some examples of how the guidelines can be applied, visit the examples document. You can use it to rate each guideline and leave feedback for each task. The user should be allowed to refuse to give up any information. Ask the user to elaborate or rephrase instead.

In Figure 1, we compare our LMC framework with the baseline Softmax, and present qualitative results on the TinyImageNet dataset. Below, we discuss them in more detail. AUROC is a widely-used threshold-independent evaluation metric. Both authors contributed equally to the work. Before entering the inference process, similar to our framework, Softmax also pre-stores certain CLIP and DINO features to make the inference process more efficient.