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We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
Ground-state auxiliary-field quantum Monte Carlo (AFQMC) methods have become key numerical tools for studying quantum phases and phase transitions in interacting many-fermion systems. Despite the broad applicability, the efficiency of these…
When simulating a lattice system near its critical temperature, local algorithms for modeling the system's evolution can introduce very large autocorrelation times into sampled data. This critical slowing down places restrictions on the…
With high computation power and memory bandwidth, graphics processing units (GPUs) lend themselves to accelerate data-intensive analytics, especially when such applications fit the single instruction multiple data (SIMD) model. However,…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
Training LLMs presents significant memory challenges due to growing size of data, weights, and optimizer states. Techniques such as data and model parallelism, gradient checkpointing, and offloading strategies address this issue but are…
We describe several additions to the ENIGMA system that guides clause selection in the E automated theorem prover. First, we significantly speed up its neural guidance by adding server-based GPU evaluation. The second addition is motivated…
We present an implementation of the hierarchical tree algorithm on the individual timestep algorithm (the Hermite scheme) for collisional $N$-body simulations, running on GRAPE-9 system, a special-purpose hardware accelerator for…
In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (10pJ/word on-die to 10,000pJ/word on the network). To increase memory locality at the hardware level and reduce…
With the widespread use of self-consistent field methods, including Hartree-Fock and Density Functional Theory, the implications of accelerating these methods are immense. To this end, we develop a tensor hypercontraction construction with…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on…
A Hessian based optimal control method is presented in Liouville space to mitigate previously undesirable polynomial scaling of computation time. This new method, an improvement to the state-of-the-art Newton-Raphson GRAPE method, is…
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…
We present Sapporo, a library for performing high-precision gravitational N-body simulations on NVIDIA Graphical Processing Units (GPUs). Our library mimics the GRAPE-6 library, and N-body codes currently running on GRAPE-6 can switch to…
In this paper we consider the time complexity of computing the sum and product of two $n$-bit numbers within the tile self-assembly model. The (abstract) tile assembly model is a mathematical model of self-assembly in which system…