Complex Bounded Operators
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Complex Bounded Operators in Isabelle/HOL
Announce Type: replace Abstract: We present a formalization of bounded operators on complex vector spaces in Isabelle/HOL. Our formalization contains material on complex vector spaces (normed spaces, Banach spaces, Hilbert spaces) that complements and goes beyond the developments of real vectors spaces in the Isabelle/HOL standard library. We define the type of bounded operators between complex vector spaces (cblinfun) and develop the theory of unitaries, projectors, extension of bounded...
Quantum Time Lower Bounds by Permutation Invariance
arXiv:2606.05099v1 Announce Type: cross Abstract: Tight bounds on quantum sample complexity and quantum query complexity have been known for various computational problems in the literature, whereas tight bounds on quantum time complexity (i.e., the size of quantum circuits) remain unresolved. In this paper, we provide a framework to establish lower bounds on the quantum time complexity for testing permutation-invariant properties of quantum states, via a reduction from quantum sample...
Excitation of control-affine systems and Koopman error bounds
arXiv:2511.03734v2 Announce Type: replace Abstract: The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework...
The American Missile Crisis
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CacheRAG: A Semantic Caching System for Retrieval-Augmented Generation in Knowledge Graph Question Answering
arXiv:2604.26176v4 Announce Type: replace Abstract: The integration of Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) has significantly advanced Knowledge Graph Question Answering (KGQA). However, existing LLM-driven KGQA systems act as stateless planners, generating retrieval plans in isolation without exploiting historical query patterns: analogous to a database system that optimizes every query from scratch without a plan cache. This fundamental design flaw leads...
CacheRAG: A Semantic Caching System for Retrieval-Augmented Generation in Knowledge Graph Question Answering
arXiv:2604.26176v3 Announce Type: replace Abstract: The integration of Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) has significantly advanced Knowledge Graph Question Answering (KGQA). However, existing LLM-driven KGQA systems act as stateless planners, generating retrieval plans in isolation without exploiting historical query patterns: analogous to a database system that optimizes every query from scratch without a plan cache. This fundamental design flaw leads...
CacheRAG: A Semantic Caching System for Retrieval-Augmented Generation in Knowledge Graph Question Answering
Announce Type: replace Abstract: The integration of Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) has significantly advanced Knowledge Graph Question Answering (KGQA). However, existing LLM-driven KGQA systems act as stateless planners, generating retrieval plans in isolation without exploiting historical query patterns: analogous to a database system that optimizes every query from scratch without a plan cache. This fundamental design flaw leads to schema...
A Variational Framework for the Complexity of PDE Solutions
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Understand and Accelerate Memory Processing Pipeline for Large Language Model Inference
Announce Type: replace Abstract: Modern large language models (LLMs) increasingly depends on efficient long-context processing and generation mechanisms, including sparse attention, retrieval-augmented generation (RAG), and compressed contextual memory, to support complex reasoning. We show that these optimizations can be unified into a four-step memory processing pipeline: Prepare Memory, Compute Relevancy, Retrieval, and Apply to Inference. Through systematic profiling, we identify a...