Invariant Point Attention (IPA) is a key algorithm for geometry-aware modeling in structural biology, central to many protein and RNA models. However, its quadratic complexity limits the input sequence length. We introduce FlashIPA, a factorized reformulation of IPA that leverages hardware-efficient FlashAttention to achieve linear scaling in GPU memory and wall-clock time with sequence length. FlashIPA matches or exceeds standard IPA performance while substantially reducing computational costs. FlashIPA extends training to previously unattainable lengths, and we demonstrate this by re-training generative models without length restrictions and generating structures of thousands of residues. FlashIPA is available at https://github.com/flagshippioneering/flash_ipa.

Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference: when exposed to a high-dimensional signal S, a system of interest computes a representation R of that signal, which is then observed through a noisy measurement M. From a large number of signals and measurements, we wish to infer the "filter" that maps S to R. However, the standard method for solving such problems, likelihood-based inference, requires perfect a priori knowledge of the "noise function" mapping R to M. In practice such noise functions are usually known only approximately, if at all, and using an incorrect noise function will typically bias the inferred filter. Here we show that in the large data limit, this need for a precharacterized noise function can be circumvented by searching for filters that instead maximize the mutual information I[M; R] between observed measurements and predicted representations. Moreover, if the correct filter lies within the space of filters being explored, maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the data processing inequality. It is important to note that maximizing mutual information will typically leave a small number of directions in parameter space unconstrained. We term these directions diffeomorphic modes and present an equation that allows these modes to be derived systematically. The presence of diffeomorphic modes reflects a fundamental and nontrivial substructure within parameter space, one that is obscured by standard likelihood-based inference.

BACKGROUND: The evolutionary pressures that underlie the large-scale functional organization of the genome are not well understood in eukaryotes. Recent evidence suggests that functionally similar genes may colocalize (cluster) in the eukaryotic genome, suggesting the role of chromatin-level gene regulation in shaping the physical distribution of coordinated genes. However, few of the bioinformatic tools currently available allow for a systematic study of gene colocalization across several, evolutionarily distant species. Furthermore, most tools require the user to input manually curated lists of gene position information, DNA sequence or gene homology relations between species. With the growing number of sequenced genomes, there is a need to provide new comparative genomics tools that can address the analysis of multi-species gene colocalization. RESULTS: Kerfuffle is a web tool designed to help discover, visualize, and quantify the physical organization of genomes by identifying significant gene colocalization and conservation across the assembled genomes of available species (currently up to 47, from humans to worms). Kerfuffle only requires the user to specify a list of human genes and the names of other species of interest. Without further input from the user, the software queries the e!Ensembl BioMart server to obtain positional information and discovers homology relations in all genes and species specified. Using this information, Kerfuffle performs a multi-species clustering analysis, presents downloadable lists of clustered genes, performs Monte Carlo statistical significance calculations, estimates how conserved gene clusters are across species, plots histograms and interactive graphs, allows users to save their queries, and generates a downloadable visualization of the clusters using the Circos software. These analyses may be used to further explore the functional roles of gene clusters by interrogating the enriched molecular pathways associated with each cluster. CONCLUSIONS: Kerfuffle is a new, easy-to-use and publicly available tool to aid our understanding of functional genomics and comparative genomics. This software allows for flexibility and quick investigations of a user-defined set of genes, and the results may be saved online for further analysis. Kerfuffle is freely available at http://atwallab.org/kerfuffle, is implemented in JavaScript (using jQuery and jsCharts libraries) and PHP 5.2, runs on an Apache server, and stores data in flat files and an SQLite database.

What happens to the optimal interpretation of noisy data when there exists more than one equally plausible interpretation of the data? In a Bayesian model-learning framework the answer depends on the prior ex- pectations of the dynamics of the model parameter that is to be inferred from the data. Local time constraints on the priors are insufficient to pick one interpretation over another. On the other hand, nonlocal time constraints, induced by a 1/f noise spectrum of the priors, is shown to permit learning of a specific model parameter even when there are in- finitely many equally plausible interpretations of the data. This transition is inferred by a remarkable mapping of the model estimation problem to a dissipative physical system, allowing the use of powerful statisti- cal mechanical methods to uncover the transition from indeterminate to determinate model learning.