Daily Papers

The quadratic complexity and weak length extrapolation of Transformers limits their ability to scale to long sequences, and while sub-quadratic solutions like linear attention and state space models exist, they empirically underperform Transformers in pretraining efficiency and downstream task accuracy. We introduce Megalodon, a neural architecture for efficient sequence modeling with unlimited context length. Megalodon inherits the architecture of Mega (exponential moving average with gated attention), and further introduces multiple technical components to improve its capability and stability, including complex exponential moving average (CEMA), timestep normalization layer, normalized attention mechanism and pre-norm with two-hop residual configuration. In a controlled head-to-head comparison with Llama2, Megalodon achieves better efficiency than Transformer in the scale of 7 billion parameters and 2 trillion training tokens. Megalodon reaches a training loss of 1.70, landing mid-way between Llama2-7B (1.75) and 13B (1.67). Code: https://github.com/XuezheMax/megalodon

De novo 3D molecule generation is a pivotal task in drug discovery. However, many recent geometric generative models struggle to produce high-quality 3D structures, even if they maintain 2D validity and topological stability. To tackle this issue and enhance the learning of effective molecular generation dynamics, we present Megalodon-a family of scalable transformer models. These models are enhanced with basic equivariant layers and trained using a joint continuous and discrete denoising co-design objective. We assess Megalodon's performance on established molecule generation benchmarks and introduce new 3D structure benchmarks that evaluate a model's capability to generate realistic molecular structures, particularly focusing on energetics. We show that Megalodon achieves state-of-the-art results in 3D molecule generation, conditional structure generation, and structure energy benchmarks using diffusion and flow matching. Furthermore, doubling the number of parameters in Megalodon to 40M significantly enhances its performance, generating up to 49x more valid large molecules and achieving energy levels that are 2-10x lower than those of the best prior generative models.

Designing a unified neural network to efficiently and inherently process sequential data with arbitrary lengths is a central and challenging problem in sequence modeling. The design choices in Transformer, including quadratic complexity and weak length extrapolation, have limited their ability to scale to long sequences. In this work, we propose Gecko, a neural architecture that inherits the design of Mega and Megalodon (exponential moving average with gated attention), and further introduces multiple technical components to improve its capability to capture long range dependencies, including timestep decay normalization, sliding chunk attention mechanism, and adaptive working memory. In a controlled pretraining comparison with Llama2 and Megalodon in the scale of 7 billion parameters and 2 trillion training tokens, Gecko achieves better efficiency and long-context scalability. Gecko reaches a training loss of 1.68, significantly outperforming Llama2-7B (1.75) and Megalodon-7B (1.70), and landing close to Llama2-13B (1.67). Notably, without relying on any context-extension techniques, Gecko exhibits inherent long-context processing and retrieval capabilities, stably handling sequences of up to 4 million tokens and retrieving information from contexts up to 4times longer than its attention window. Code: https://github.com/XuezheMax/gecko-llm

This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.