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Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a “biologically plausible” region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simplemore »geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.« less

Detecting when the underlying distribution changes for the observed time series is a fundamental problem arising in a broad spectrum of applications. In this paper, we study multiple change-point localization in the high-dimensional regression setting, which is particularly challenging as no direct observations of the parameter of interest is available. Specifically, we assume we observe {xt,yt}nt=1 where {xt}nt=1 are p-dimensional covariates, {yt}nt=1 are the univariate responses satisfying 𝔼(yt)=x⊤tβ∗t for 1≤t≤n and {β∗t}nt=1 are the unobserved regression coefficients that change over time in a piecewise constant manner. We propose a novel projection-based algorithm, Variance Projected Wild Binary Segmentation~(VPWBS), which transforms the original (difficult) problem of change-point detection in p-dimensional regression to a simpler problem of change-point detection in mean of a one-dimensional time series. VPWBS is shown to achieve sharp localization rate Op(1/n) up to a log factor, a significant improvement from the best rate Op(1/n‾√) known in the existing literature for multiple change-point localization in high-dimensional regression. Extensive numerical experiments are conducted to demonstrate the robust and favorable performance of VPWBS over two state-of-the-art algorithms, especially when the size of change in the regression coefficients {β∗t}nt=1 is small.

The physical architectures of information storage systems often dictate how information is encoded, databases are organized, and files are accessed. Here we show that a simple architecture comprised of a T7 promoter and a single-stranded overhang domain (ss-dsDNA), can unlock dynamic DNA-based information storage with powerful capabilities and advantages. The overhang provides a physical address for accessing specific DNA strands as well as implementing a range of in-storage file operations. It increases theoretical storage densities and capacities by expanding the encodable sequence space and simplifies the computational burden in designing sets of orthogonal file addresses. Meanwhile, the T7 promoter enables repeatable information access by transcribing information from DNA without destroying it. Furthermore, saturation mutagenesis around the T7 promoter and systematic analyses of environmental conditions reveal design criteria that can be used to optimize information access. This simple but powerful ss-dsDNA architecture lays the foundation for information storage with versatile capabilities.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

Changepoint detection methods are used in many areas of science and engineering, for example, in the analysis of copy number variation data to detect abnormalities in copy numbers along the genome. Despite the broad array of available tools, methodology for quantifying our uncertainty in the strength (or the presence) of given changepointspost‐selectionare lacking. Post‐selection inference offers a framework to fill this gap, but the most straightforward application of these methods results in low‐powered hypothesis tests and leaves open several important questions about practical usability. In this work, we carefully tailor post‐selection inference methods toward changepoint detection, focusing on copy number variation data. To accomplish this, we study commonly used changepoint algorithms: binary segmentation, as well as two of its most popular variants, wild and circular, and the fused lasso. We implement some of the latest developments in post‐selection inference theory, mainly auxiliary randomization. This improves the power, which requires implementations of Markov chain Monte Carlo algorithms (importance sampling and hit‐and‐run sampling) to carry out our tests. We also provide recommendations for improving practical useability, detailed simulations, and example analyses on array comparative genomic hybridization as well as sequencing data.