We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly define a relationship between the optimal classifier and the target quasiprobabilistic density ratio which is discontinuous or not surjective. We address these problems by introducing a convex loss function that is well-suited for both probabilistic and quasiprobabilistic density ratio estimation. To quantify performance, an extended version of the Sliced-Wasserstein distance is introduced which is compatible with quasiprobability distributions. We demonstrate our approach on a real-world example from particle physics, of di-Higgs production in association with jets via gluon-gluon fusion, and achieve state-of-the-art results.

It's still not aliens, but the interstellar comet keeps getting weirder. Breakthroughs, discoveries, and DIY tips sent every weekday. As comet 3I/ATLAS continues its exciting journey through our solar system, scientists are still learning everything they can about this special space rock. It is only the second interstellar object ever tracked through our solar system and is among the fastest comets ever observed. As the 3I/ATLAS nears its closest distance to Earth, an international team of astronomers now says the space rock may be covered in active, icy cryovolcanoes.

This paper presents a method for uncovering hidden analytic relationships among the fundamental parameters of the Standard Model (SM), a foundational theory in physics that describes the fundamental particles and their interactions, using symbolic regression and genetic programming. Using this approach, we identify the simplest analytic relationships connecting pairs of these constants and report several notable expressions obtained with relative precision better than 1%. These results may serve as valuable inputs for model builders and artificial intelligence methods aimed at uncovering hidden patterns among the SM constants, or potentially used as building blocks for a deeper underlying law that connects all parameters of the SM through a small set of fundamental constants.

Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This simplified model enables uncluttered mathematical analysis, revealing two key properties: root value distributions asymptotically collapse to a single fixed value for finite-valued trees, and all reasonable algorithms achieve global optimality. However, these findings are artifacts of the model's design: its long criticized independence assumption strips games of structural complexity, producing trivial instances where no algorithm faces meaningful challenges. To address this limitation, we introduce a simple probabilistic model that incrementally constructs game-trees using a fixed level-wise conditional distribution. By enforcing ancestor dependencies, a critical structural feature of real-world games, our framework generates problems with adjustable difficulty while retaining some form of analytical tractability. For several algorithms, including AlphaBeta and Scout, we derive recursive formulas characterizing their average-case complexities under this model. These allow us to rigorously compare algorithms on deep game-trees, where Monte-Carlo simulations are no longer feasible. While asymptotically, all algorithms seem to converge to identical branching factor (a result analogous to that of independence-based models), deep finite trees reveal stark differences: AlphaBeta incurs a significantly larger constant multiplicative factor compared to algorithms like Scout, leading to a substantial practical slowdown. Our framework sheds new light on classical game-solving algorithms, offering rigorous evidence and analytical tools to advance the understanding of these methods under a richer, more challenging, and yet tractable model.

Large language models (LLMs) have raised hopes for automated end-to-end fact-checking, but prior studies report mixed results. As mainstream chatbots increasingly ship with reasoning capabilities and web search tools -- and millions of users already rely on them for verification -- rigorous evaluation is urgent. We evaluate 15 recent LLMs from OpenAI, Google, Meta, and DeepSeek on more than 6,000 claims fact-checked by PolitiFact, comparing standard models with reasoning- and web-search variants. Standard models perform poorly, reasoning offers minimal benefits, and web search provides only moderate gains, despite fact-checks being available on the web. In contrast, a curated RAG system using PolitiFact summaries improved macro F1 by 233% on average across model variants. These findings suggest that giving models access to curated high-quality context is a promising path for automated fact-checking.

During training, models can exploit spurious correlations as shortcuts, resulting in poor generalization performance when shortcuts do not persist. In this work, assuming access to a representation based on domain knowledge ( i.e., known

Section 3.2, as we trace down the associated inequality bound in Recall that we have defined in Section 3.1 the notion of output Using the notation in Section 3.1, we have In the following proof for Theorem 2, we apply similar steps in Appendix A.2 and consider the difference between set of pairwise margin under natural and weight perturbation setting, recall in We now offer a similar proof for convolutional neural networks. We note that each convolution operation can be described as matrix multiplication of a doubly block Toeplitz matrix. We now provide a proof for Lemma 2. Recall the definition of ramp function in Section 3.4.1, We further consider the case of cross entropy and prove an upper bound for it. We've also conducted the experiment of convolution-layer based model training on CIFAR-10 using As shown in Table 4, the standard model's performance rapidly degrades in 5-folds when the perturbation radius is The experiment setting follows Figure 1(b).