Justin Tan

Per Berglund, Giorgi Butbaia, Tristan Hübsch et al.

Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric within a given Kähler class. In this paper we investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces and Calabi-Yau threefolds. Using these Ricci-flat metric approximations for the Cefalú family of quartic twofolds and the Dwork family of quintic threefolds, we study characteristic forms on these geometries. We observe that the numerical stability of the numerically computed topological characteristic is heavily influenced by the choice of the neural network model, in particular, we briefly discuss a different neural network model, namely Spectral networks, which correctly approximate the topological characteristic of a Calabi-Yau. Using persistent homology, we show that high curvature regions of the manifolds form clusters near the singular points. For our neural network approximations, we observe a Bogomolov--Yau type inequality $3c_2 \geq c_1^2$ and observe an identity when our geometries have isolated $A_1$ type singularities. We sketch a proof that $χ(X~\smallsetminus~\mathrm{Sing}\,{X}) + 2~|\mathrm{Sing}\,{X}| = 24$ also holds for our numerical approximations.

Challenger Mishra, Justin Tan

We compute solutions to the Hermitian Yang-Mills equations on holomorphic vector bundles $V$ via an alternating optimisation procedure founded on geometric machine learning. The proposed method is fully general with respect to the rank and structure group of $V$, requiring only the ability to enumerate a basis of global sections for a given bundle. This enables us to compute the physically normalised Yukawa couplings in a broad class of heterotic string compactifications. Using this method, we carry out this computation in full for a heterotic compactification incorporating a gauge bundle with non-Abelian structure group.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Team Phoenix, Arka Ray, Askar Ali Mohamed Jawad et al.

We introduce Phoenix-VL 1.5 Medium, a 123B-parameter natively multimodal and multilingual foundation model, adapted to regional languages and the Singapore context. Developed as a sovereign AI asset, it demonstrates that deep domain adaptation can be achieved with minimal degradation to broad-spectrum intelligence and alignment. Continued pretraining was performed on Mistral Medium 3.1 using a localized 1-trillion tokens multimodal corpus, followed by a 250-billion tokens long-context extension phase. Subsequent post-training incorporated a novel human-annotated Singapore multimodal dataset and curated textual corpus on Singapore culture, knowledge, and legislation, totaling 22-billion tokens. An additional 5 billion tokens of model alignment was performed through Online Direct Preference Optimization. Phoenix-VL 1.5 Medium achieves state-of-the-art performance for its size on Singapore multimodal, legal, and government policy benchmarks while remaining globally competitive on general multimodal intelligence, multilingual, and STEM benchmarks. We also introduce a novel evaluation suite encompassing localized knowledge benchmarks and an institutionally aligned model behavior and safety framework. We report the data curation principles, training methodology, and highlight benchmark and inference performance.

Per Berglund, Giorgi Butbaia, Tristan Hübsch et al.

We introduce \texttt{cymyc}, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. \texttt{cymyc} includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.