Casey Zhao | Searcharxiv

arXiv2025

GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models

We present GLM-4.5, an open-source Mixture-of-Experts (MoE) large language model with 355B total parameters and 32B activated parameters, featuring a hybrid reasoning method that supports both thinking and direct response modes. Through multi-stage training on 23T tokens and comprehensive post-training with expert model iteration and reinforcement learning, GLM-4.5 achieves strong performance across agentic, reasoning, and coding (ARC) tasks, scoring 70.1% on TAU-Bench, 91.0% on AIME 24, and 64.2% on SWE-bench Verified. With much fewer parameters than several competitors, GLM-4.5 ranks 3rd overall among all evaluated models and 2nd on agentic benchmarks. We release both GLM-4.5 (355B parameters) and a compact version, GLM-4.5-Air (106B parameters), to advance research in reasoning and agentic AI systems. Code, models, and more information are available at https://github.com/zai-org/GLM-4.5.

cs.CL↗

arXiv2022

Infinite $\{3,7\}$-surface in $\mathbb{H}^3$

Objects with large symmetry groups have been an interest for many mathematicians. A classical question in geometry is whether a surface with certain geometric features, such as completeness, curvature, etc..., can embed in $\mathbb{R}^3.$ In a recent paper, Lee constructs an infinite $\{3,7\}$-surface in $\mathbb{R}^3$ by gluing together prisms and antiprisms, in an attempt to find a periodic surface in $\mathbb{R}^3$ that is cover of Klein's quartic. While Lee's construction shows that such construction self-intersects in $\mathbb{R}^3$, it does not prove nor disprove the possibility of an embedding. In this paper, we explore a possible embedding of the genus three Klein's quartic, or its cover, in hyperbolic space.

math.DG↗