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Paxos is a prominent theory of state machine replication. Recent data intensive Systems those implement state machine replication generally require high throughput. Earlier versions of Paxos as few of them are classical Paxos, fast Paxos…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
TUnfold is a tool for correcting migration and background effects in high energy physics for multi-dimensional distributions. It is based on a least square fit with Tikhonov regularisation and an optional area constraint. For determining…
Recent advances in large language models (LLMs) have introduced latent reasoning as a promising alternative to autoregressive reasoning. By performing internal computation with hidden states from previous steps, latent reasoning benefit…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
Large language models have demonstrated strong reasoning capabilities in complex tasks through tool integration, which is typically framed as a Markov Decision Process and optimized with trajectory-level RL algorithms such as GRPO. However,…
Polynomial Krylov subspace methods are among the most widely used methods for approximating $f(A)b$, the action of a matrix function on a vector, in particular when $A$ is large and sparse. When $A$ is Hermitian positive definite, the…
Transistor topology optimization is a critical step in standard cell design, directly dictating diffusion sharing efficiency and downstream routability. However, identifying optimal topologies remains a persistent bottleneck, as…
In this paper the author introduces a new domain decomposition method for the solution of discretised integral equation eigenvalue problems. The new domain decomposition method is motivated by the so-called automated multi-level…
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…
Signal temporal logic (STL) is a powerful formalism for specifying various temporal properties in dynamical systems. However, existing methods, such as mixed-integer programming and nonlinear programming, often struggle to efficiently solve…
This paper introduces a simple and scalable approach to improve the data efficiency of large language model (LLM) training by augmenting existing text data with thinking trajectories. The compute for pre-training LLMs has been growing at an…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…
We consider the problem of low-rank approximation of massive dense non-negative tensor data, for example to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting…
We analyze the efficiency of parallelization and restart mechanisms for stochastic simulations in model-free settings, where the underlying system dynamics are unknown. Such settings are common in Reinforcement Learning (RL) and rare event…
We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guarantees…
A new code for nuclear shell-model calculations, "KSHELL", is developed. It aims at carrying out both massively parallel computation and single-node computation in the same manner. We solve the Schr\"{o}dinger's equation in the $M$-scheme…
Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…