On IVF Approximating Spaces

We introduce the concept of IVF approximating spaces and obtain decision conditions that every IVF topological space is an IVF approximating space

HDIdx: High-Dimensional Indexing for Efficient Approximate Nearest Neighbor Search

Fast Nearest Neighbor (NN) search is a fundamental challenge in large-scale data processing and analytics, particularly for analyzing multimedia contents which are often of high dimensionality. Instead of using exact NN search, extensive research efforts have been focusing on approximate NN search algorithms. In this work, we present "HDIdx", an efficient high-dimensional indexing library for fast approximate NN search, which is open-source and written in Python. It offers a family of state-of-the-art algorithms that convert input high-dimensional vectors into compact binary codes, making them very efficient and scalable for NN search with very low space complexity

Learning a Complete Image Indexing Pipeline

To work at scale, a complete image indexing system comprises two components: An inverted file index to restrict the actual search to only a subset that should contain most of the items relevant to the query; An approximate distance computation mechanism to rapidly scan these lists. While supervised deep learning has recently enabled improvements to the latter, the former continues to be based on unsupervised clustering in the literature. In this work, we propose a first system that learns both components within a unifying neural framework of structured binary encoding

Learning a Complete Image Indexing Pipeline

To work at scale, a complete image indexing system comprises two components: An inverted file index to restrict the actual search to only a subset that should contain most of the items relevant to the query; An approximate distance computation mechanism to rapidly scan these lists. While supervised deep learning has recently enabled improvements to the latter, the former continues to be based on unsupervised clustering in the literature. In this work, we propose a first system that learns both components within a unifying neural framework of structured binary encoding

Martingale-coboundary decomposition for stationary random fields

We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one dimensional processes from 1975. For Lp spaces with 2 \leq p < \infty we give a necessary and sufficient condition which extends Volny's result from 1993 to random fields and improves condition of El Machkouri and Giraudo from 2016 (arXiv:1410.3062). In application, new weak invariance principle and estimates of large deviations are found.Comment: Stochastics and Dynamics 201

Landau levels in wrinkled and rippled graphene sheets

We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different average space curvatures and shown to obey a linear relation. The study is carried out with a quantum lattice Boltzmann method, solving the Dirac equation on curved manifolds.Comment: 6 pages, 4 figures, 27th International Conference on Discrete Simulation of Fluid Dynamic

Co-design Hardware and Algorithm for Vector Search

Vector search has emerged as the foundation for large-scale information retrieval and machine learning systems, with search engines like Google and Bing processing tens of thousands of queries per second on petabyte-scale document datasets by evaluating vector similarities between encoded query texts and web documents. As performance demands for vector search systems surge, accelerated hardware offers a promising solution in the post-Moore's Law era. We introduce \textit{FANNS}, an end-to-end and scalable vector search framework on FPGAs. Given a user-provided recall requirement on a dataset and a hardware resource budget, \textit{FANNS} automatically co-designs hardware and algorithm, subsequently generating the corresponding accelerator. The framework also supports scale-out by incorporating a hardware TCP/IP stack in the accelerator. \textit{FANNS} attains up to 23.0$\times$ and 37.2$\times$ speedup compared to FPGA and CPU baselines, respectively, and demonstrates superior scalability to GPUs, achieving 5.5$\times$ and 7.6$\times$ speedup in median and 95\textsuperscript{th} percentile (P95) latency within an eight-accelerator configuration. The remarkable performance of \textit{FANNS} lays a robust groundwork for future FPGA integration in data centers and AI supercomputers.Comment: 11 page

Boundary values of holomorphic semigroups of unbounded operators and similarity of certain perturbations

AbstractWe obtain sufficient conditions for a “holomorphic” semigroup of unbounded operators to possess a boundary group of bounded operators. The theorem is applied to generalize to unbounded operators results of Kantorovitz about the similarity of certain perturbations. Our theory includes a result of Fisher on the Riemann-Liouville semigroup in Lp(0, ∞) 1 < p < ∞. In this particular case we give also an alternative approach, where the boundary group is obtained as the limit of groups in the weak operator topology

Boundary values of holomorphic semigroups of unbounded operators and similarity of certain perturbations

AbstractWe obtain sufficient conditions for a “holomorphic” semigroup of unbounded operators to possess a boundary group of bounded operators. The theorem is applied to generalize to unbounded operators results of Kantorovitz about the similarity of certain perturbations. Our theory includes a result of Fisher on the Riemann-Liouville semigroup in Lp(0, ∞) 1 < p < ∞. In this particular case we give also an alternative approach, where the boundary group is obtained as the limit of groups in the weak operator topology