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A Mathematical Theory of the Jacobian Lens

arXiv:2610.31955v1 Announce Type: new Abstract: Recent work from Anthropic introduced a new interpretability tool, called the Jacobian lens (J-lens, Gurnee et al., 2026). This method identified linear directions in the hidden states of frontier language models that had properties reminiscent of working memory-like representations. However, it is unclear what mechanistic properties of such features make them detectable to the J-lens. To this end, we introduce a mathematical theory of the J-lens, and show that it preferentially identifies coherent features -- directions that act like leading, spatially coherent Lyapunov modes. Small perturbations along these directions amplify across layers, remain roughly constant across token positions, and are consistent across different contexts. While w

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PRISM: Promoting Sampling Diversity of Large Language Models with Implicit Stochastic Modulation

arXiv:2610.32101v1 Announce Type: new Abstract: Large language models (LLMs) exhibit mode collapse, where their output distribution concentrates on familiar semantic modes. When diversity disappears, repeated sampling becomes semantic repetition rather than discovery, making rare but stronger solutions unlikely to surface and leaving self-evolution and continual learning difficult to sustain. Most remedies intervene only at inference time, shaping sam- ples without making diversity a model capability. We propose PRISM, a training-time framework that internalizes diversity within the model. PRISM combines (i) submodular curation that pairs each prompt with diverse-yet-correct multi-teacher solutions, and (ii) stochastic embedding modulation, which turns special-token perturbations into impl

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Putting Transformer Theories to the Test

arXiv:2610.32104v1 Announce Type: new Abstract: Several formal theories have been developed to characterize the capabilities and limitations of the transformer architecture, each employing different abstractions that capture different features of the architecture. Due to the differences in their underlying assumptions and conceptual frameworks, these theories can disagree in their predictions about what tasks transformers find easy or hard. We map out seven theories of transformer capability (Star-free, $\mathsf{AC}^0$, $\mathsf{TC}^0$, C-RASP, MPC, BAPO, and Sensitivity) and translate their results into a common matrix of predictions across a suite of tasks covering different computational structures. We provide new theoretical results to complete this matrix. We then evaluate theoretical

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Kevin Roose is AGI-pilled. Why aren’t you?

Today, I’m talking to Kevin Roose, journalist and author of the new book The AGI Chronicles, which details the recent and explosive transformation of the AI industry. Kevin was a longtime New York Times reporter and host of the popular podcast Hard Fork, but he and friend of the show Casey Newton just left the […]

Kevin Roose is AGI-pilled. Why aren’t you?Kevin Roose is AGI-pilled. Why aren’t you?
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Collaborative In-Context Learning for Indoor Radio Map Estimation

arXiv:2610.31702v1 Announce Type: new Abstract: Indoor radio map estimation (RME) is essential for wireless applications such as coverage planning, localization, and network deployment. However, most existing methods follow a supervised learning paradigm that requires costly labeled data and task-specific model training. Moreover, indoor environments involve privacy-sensitive information, such as building layouts and structures, that often cannot be centralized. To address these challenges, we make the first attempt to formulate indoor RME as a collaborative in-context learning (ICL) problem. We propose Poly-Ripple, a framework in which multiple clients perform ICL using large autoregressive vision models (LAVMs) without model updates. Each client is prompted by its private demonstrations

Collaborative In-Context Learning for Indoor Radio Map Estimation
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When and How Does Muon Precondition? The Role of Structured Gradient Noise

arXiv:2610.31728v1 Announce Type: new Abstract: Muon has become a popular optimizer for large language model training, yet its theoretical foundations remain poorly understood. In this work, we study how gradient noise geometry shapes Muon's preconditioning benefits. We first show, theoretically and empirically, that under the classical isotropic noise assumption, Muon offers no acceleration beyond a rescaling of the learning rate. This motivates us to investigate structured noise arising from mini-batch sampling in associative memory with heterogeneous task frequencies. We establish an exact balancing threshold for two tasks and extend the analysis to multiple tasks, revealing how task coverage and gradient reliability jointly shape learning. Our analysis shows that Muon can soften the de

When and How Does Muon Precondition? The Role of Structured Gradient Noise
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IMF Bangkok Conference Speech Sparks Heated Debate: Former Co-Founders of OpenAI and Anthropic Claim “The Singularity Has Already Begun”

On October 17, 2026, a former OpenAI employee and co-founder of Anthropic delivered a speech at the IMF conference in Bangkok, arguing that “the technological singularity has already begun,” citing AI systems’ demonstrated capacity for autonomous research in fields such as mathematics, biology, physics, and robotics. The data cited—such as TheoPhysEval’s 98% score and Humanity’s Last Exam rising to 67.7%—were sourced from the speaker himself and affiliated institutions, with no third-party verification. The speech underscored the AI-driven transformation of scientific paradigms and its economic implications, while explicitly stating that this assessment reflects a subjective viewpoint rather than a scientific consensus.

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Can your Postgres survive a bad query?

How do Postgres providers handle a query that exhausts memory? A recursive query benchmark compares query failures and cluster survival across ClickHouse Managed Postgres, Cloud SQL, PlanetScale, and Amazon RDS.

Extending the Context Length to 1M Tokens!

API Documentation (Chinese) HuggingFace Demo ModelScope Demo Introduction After the release of Qwen2.5, we heard the community’s demand for processing longer contexts. In recent months, we have made many optimizations for the model capabilities and inference performance of extremely long context. Today, we are proud to introduce the new Qwen2.5-Turbo version, which features: Longer Context Support: We have extended the model’s context length from 128k to 1M, which is approximately 1 million English words or 1.