arXiv subjects

Karthik V.

Publications and source records attributed to Karthik V..

2 recordsLinked to original sources

arXiv2024

Convolutional restricted Boltzmann machine (CRBM) correlated variational wave function for the Hubbard model on a square lattice: Mott metal-insulator transition

We use a convolutional restricted Boltzmann machine (CRBM) neural network to construct a variational wave function (WF) for the Hubbard model on a square lattice and study it using the variational Monte Carlo (VMC) method. In the wave function, the CRBM acts as a correlation factor to a mean-field BCS state. The number of variational parameters in the WF does not grow automatically with the lattice size and it is computationally much more efficient compared to other neural network based WFs. We find that in the intermediate to strong coupling regime of the model at half-filling, the wave function outperforms even the highly accurate long range backflow-Jastrow correlated wave function. Using the WF, we study the ground state of the half-filled model as a function of onsite Coulomb repulsion $U$. We consider two cases for the next-nearest-neighbor hopping parameter, e.g., $t'=0$ as well as a frustrated model case with $t'\neq 0$. By examining several quantities, e.g., double occupancy, charge gap, momentum distribution, and spin-spin correlations, we find that the weekly correlated phase in both cases is paramagnetic metallic (PM). As $U$ is increased, the system undergoes a first-order Mott transition to an insulating state at a critical $U_c$, the value of which depends upon $t'$. The Mott state in both cases is spin gapped with long range antiferromagnetic (AF) order. Remarkably, the AF order emerges spontaneously from the wave function which does not have any explicitly broken symmetry in it. Apart from some quantitative differences in the results for the two values of $t'$, we find some interesting qualitative differences in the way the Mott transition takes place in the two cases.

cond-mat.str-el↗

arXiv2024

BANG: Billion-Scale Approximate Nearest Neighbor Search using a Single GPU

Approximate Nearest Neighbour Search (ANNS) is a subroutine in algorithms routinely employed in information retrieval, pattern recognition, data mining, image processing, and beyond. Recent works have established that graph-based ANNS algorithms are practically more efficient than the other methods proposed in the literature. The growing volume and dimensionality of data necessitates designing scalable techniques for ANNS. To this end, the prior art has explored parallelising graph-based ANNS on GPU, leveraging its massive parallelism. The current state-of-the-art GPU-based ANNS algorithms either (i) require both the dataset and the generated graph index to reside entirely in the GPU memory, or (ii) they partition the dataset into small independent shards, each of which can fit in GPU memory, and perform the search on these shards on the GPU. While the first approach fails to handle large datasets due to the limited memory available on the GPU, the latter delivers poor performance on large datasets due to high data traffic over the low-bandwidth PCIe interconnect. We introduce BANG, a first-of-its-kind technique for graph-based ANNS on GPU for billion-scale datasets, that cannot entirely fit in the GPU memory. BANG stands out by harnessing a compressed form of the dataset on a single GPU to perform distance computations while efficiently accessing the graph index kept on the host memory, enabling efficient ANNS on large graphs within the limited GPU memory. BANG incorporates highly optimised GPU kernels and proceeds in phases that run concurrently on the GPU and CPU, taking advantage of their architectural specificities. Using a single NVIDIA Ampere A100 GPU, BANG achieves throughputs 50x-400x higher than competing methods for a recall of 0.9 on three popular billion-scale datasets.

cs.DC↗