We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines $p$-adic numbers with topological data analysis. Each DNA sequence is encoded along two complementary axes: a $p$-adic distance on $k$-mer prefixes, which captures hierarchical positional structure, and a compositional $L_1$ distance on $k$-mer frequencies, which captures local sequence content.
arXiv:2606. 06117v1 Announce Type: cross Abstract: We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines $p$-adic numbers with topological data analysis.
arXiv:2606. 14737v1 Announce Type: cross Abstract: Molecular dynamics (MD) simulations generate trajectories in a high-dimensional configuration space whose analysis critically depends on molecular descriptors, typically handcrafted observables or learned kinetic embeddings.
arXiv:2511. 04873v2 Announce Type: replace-cross Abstract: Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data.
arXiv:2606. 06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations.
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
arXiv:2607. 20657v1 Announce Type: cross Abstract: Unique and rapid classification of knots and links is an open mathematical problem that is relevant to a range of (bio)physical systems, including polymer melts, DNA, and proteins.
arXiv:2607. 25680v1 Announce Type: cross Abstract: We propose Rashomon Alignment (RA), a new measure to assess functional similarity between two models.
The growing number of medical vision foundation models highlights the need for effective model selection. However, mainstream selection methods rely on exhaustive fine-tuning, which is computationally expensive.
arXiv:2607. 16553v1 Announce Type: new Abstract: Protein fold classification can be approached via sequence-based representations or structural descriptors, but direct comparisons between lightweight handcrafted descriptors and pretrained protein language model embeddings remain limited.
We propose Rashomon Alignment (RA), a new measure to assess functional similarity between two models. Existing functional similarity measures are distributional, quantifying differences between outputs of models applied to real-world data.
arXiv:2608. 00697v1 Announce Type: cross Abstract: Variational autoencoders (VAEs) trained on multiple sequence alignments (MSAs) have emerged as powerful generative models for biological sequences, with applications ranging from disease variant prediction to functional RNA design.
arXiv:2608. 08485v1 Announce Type: new Abstract: Current LLM safety guardrails face a fundamental tension: fine-tuning distorts pre-trained representations while generative judges incur prohibitive inference costs.