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Superconductivity from Doping Symmetric Mass Generation Insulators: Application to La$$_3$$Ni$$_2$$O$$_7$$ under Pressure 

We consider a DA-type surgery of the famous Lorenz attractor in dimension 4. This kind of surgery was first used by Smale [Differentiable dynamical systems. Bull. Amer. Math. Soc. (N.S.) 73(6) (1967), 747–817] and Mañé [Contributions to the stability conjecture. Topology 17(4) (1978), 383–396] to give important examples in the study of partially hyperbolic systems. Our construction gives the first example of a singular chain recurrence class which is Lyapunov stable, away from homoclinic tangencies, and exhibits robustly heterodimensional cycles. Moreover, the chain recurrence class has the following interesting property: there exists robustly a two-dimensional sectionally expanding subbundle (containing the flow direction) of the tangent bundle such that it is properly included in a subbundle of the finest dominated splitting for the tangent flow. 

We develop KnowThyself, an agentic assistant that advances large language model (LLM) interpretability. Existing tools provide useful insights but remain fragmented and code-intensive. KnowThyself consolidates these capabilities into a chat-based interface, where users can upload models, pose natural language questions, and obtain interactive visualizations with guided explanations. At its core, an orchestrator LLM first reformulates user queries, an agent router further directs them to specialized modules, and the outputs are finally contextualized into coherent explanations. This design lowers technical barriers and provides an extensible platform for LLM inspection. By embedding the whole process into a conversational workflow, KnowThyself offers a robust foundation for accessible LLM interpretability. 

Catastrophic forgetting is a longstanding challenge in continual learning, where models lose knowledge from earlier tasks when learning new ones. While various mitigation strategies have been proposed for Multi-Layer Perceptrons (MLPs), recent architectural advances like Kolmogorov-Arnold Networks (KANs) have been suggested to offer intrinsic resistance to forgetting by leveraging localized spline-based activations. However, the practical behavior of KANs under continual learning remains unclear, and their limitations are not well understood. To address this, we present a comprehensive study of catastrophic forgetting in KANs and develop a theoretical framework that links forgetting to activation support overlap and intrinsic data dimension. We validate these analyses through systematic experiments on synthetic and vision tasks, measuring forgetting dynamics under varying model configurations and data complexity. Further, we introduce KAN-LoRA, a novel adapter design for parameter-efficient continual fine-tuning of language models, and evaluate its effectiveness in knowledge editing tasks. Our findings reveal that while KANs exhibit promising retention in low-dimensional algorithmic settings, they remain vulnerable to forgetting in high-dimensional domains such as image classification and language modeling. These results advance the understanding of KANs’ strengths and limitations, offering practical insights for continual learning system design. 

We study the existence and uniqueness of equilibrium states for continuous flows on a compact, locally maximal invariant set under weak, non-uniform versions of specification, expansivity, and the Bowen property, further improving the Climenhaga-Thompson Criterion [8], [9]. 

Large language models (LLMs) have shown re2 markable performance in tackling natural language 3 tasks, yet the internal mechanisms that enable their 4 impressive generalization and reasoning abilities 5 remain opaque. This lack of transparency presents 6 significant challenges in fundamentally eliminating 7 undesirable behaviors such as hallucinations and 8 toxicity, hindering the safe and beneficial deploy9 ment of LLMs. This survey paper aims to un10 cover the internal working mechanisms underly11 ing LLM functionality through the lens of explain12 ability. First, we review how knowledge is en13 coded within LLMs via mechanistic interpretabil14 ity techniques. Then, we summarize what knowl15 edge is embedded in LLMrepresentations by lever16 aging probing techniques and representation engi17 neering. Additionally, we investigate the training 18 dynamics to explore models' generalization abili19 ties through grokking and memorization. Finally, 20 we explore how the insights gained from these ex21 planations can further enhance LLM performance 22 through model editing, improve efficiency through 23 pruning, and better align with human values.