Related papers: Parallel Galton Watson Process
Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…
We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
The surge in availability of genomic data holds promise for enabling determination of genetic causes of observed individual traits, with applications to problems such as discovery of the genetic roots of phenotypes, be they molecular…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
The rapid advancement in Large Language Models has been met with significant challenges in their training processes, primarily due to their considerable computational and memory demands. This research examines parallelization techniques…
After learning a concept, humans are also able to continually generalize their learned concepts to new domains by observing only a few labeled instances without any interference with the past learned knowledge. In contrast, learning…
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…
As deep neural networks (DNNs) become deeper, the training time increases. In this perspective, multi-GPU parallel computing has become a key tool in accelerating the training of DNNs. In this paper, we introduce a novel methodology to…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 47:15--32, 2015]) are compact indices for texts over an alphabet $[0,\sigma)$ that support rank, select and access queries in $O(\lg \sigma)$ time.…
A major obstacle to developing artificial intelligence applications capable of true lifelong learning is that artificial neural networks quickly or catastrophically forget previously learned tasks when trained on a new one. Numerous methods…
We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and…
We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to…
The Galton-Watson process is a model for population growth which assumes that individuals reproduce independently according to the same offspring distribution. Inference usually focuses on the offspring average as it allows to classify the…
Graph foundation models using graph neural networks promise sustainable, efficient atomistic modeling. To tackle challenges of processing multi-source, multi-fidelity data during pre-training, recent studies employ multi-task learning, in…
Recent work showed that compiling functional programs to use dense, serialized memory representations for recursive algebraic datatypes can yield significant constant-factor speedups for sequential programs. But serializing data in a…
Deep research agents, which synthesize information across diverse sources, are significantly constrained by the sequential nature of reasoning. This bottleneck results in high latency, poor runtime adaptability, and inefficient resource…
It is shown in this work how the Wang-Landau algorithm can be parallelized through the concept of the micromagnetic ensemble, when the Hamiltonian contains both spin interaction and the external field terms, and thus energy-magnetization…