Related papers: Fast Computation of Zigzag Persistence
Coverage-guided fuzzers are powerful automated bug-finding tools. They mutate program inputs, observe coverage, and save any input that hits an unexplored path for future mutation. Unfortunately, without knowledge of input formats--for…
Diffusion models have achieved unprecedented success in text-aligned generation, largely driven by Classifier-Free Guidance (CFG). However, standard CFG operates strictly on instantaneous gradients, omitting the intrinsic curvature of the…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
Certifiable robustness gives the guarantee that small perturbations around an input to a classifier will not change the prediction. There are two approaches to provide certifiable robustness to adversarial examples: a) explicitly training…
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…
Text-to-image generation models have made significant progress in producing high-quality images from textual descriptions, yet they continue to struggle with maintaining subject consistency across multiple images, a fundamental requirement…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
Decompressing a file made by the gzip program at an arbitrary location is in principle impossible, due to the nature of the DEFLATE compression algorithm. Consequently, no existing program can take advantage of parallelism to rapidly…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
Objective: Spike sorting is a fundamental step in analysing extracellular recordings, enabling the isolation of single-neuron activity. However, it remains a challenging problem because extracellular traces mix overlapping spikes from…
The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we…
The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…
The persistent homology pipeline includes the reduction of a, so-called, boundary matrix. We extend the work of Bauer et al. (2014) and Chen et al. (2011) where they show how to use dependencies in the boundary matrix to adapt the reduction…
Markov chain Monte Carlo (MCMC) is a key algorithm in computational statistics, and as datasets grow larger and models grow more complex, many popular MCMC algorithms become too computationally expensive to be practical. Recent progress has…
It has been shown that $1$-parameter persistence modules have a very simple classification, namely there is a discrete invariant called a barcode that completely characterizes $1$-parameter persistence modules up to isomorphism. In…
Temporal graphs are commonly used to represent complex systems and track the evolution of their constituents over time. Visualizing these graphs is crucial as it allows one to quickly identify anomalies, trends, patterns, and other…
Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
Storing and archiving data produced by next-generation sequencing (NGS) is a huge burden for research institutions. Reference-based compression algorithms are effective in dealing with these data. Our work focuses on compressing FASTQ…
We consider the problem of producing compact architectures for text classification, such that the full model fits in a limited amount of memory. After considering different solutions inspired by the hashing literature, we propose a method…