Related papers: Bayesian interpolation for power laws in neural da…

There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We…

The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…

Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…

Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that…

Neural networks encode information through their collective spiking activity in response to external stimuli. This population response is noisy and strongly correlated, with complex interplay between correlations induced by the stimulus,…

Queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns. The main predictions are the existence of a power-law distribution for the interevent time of human actions and two…

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…

In materials science, data are scarce and expensive to generate, whether computationally or experimentally. Therefore, it is crucial to identify how model performance scales with dataset size and model capacity to distinguish between data-…

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…

The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the…

Recent advancements in deep learning have been primarily driven by the use of large models trained on increasingly vast datasets. While neural scaling laws have emerged to predict network performance given a specific level of computational…

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise…

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds…

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…

Recent works have shown that machine learning models improve at a predictable rate with the total amount of training data, leading to scaling laws that describe the relationship between error and dataset size. These scaling laws can help…

The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic…

Memory and forgetting constitute two sides of the same coin, and although the first has been rigorously investigated, the latter is often overlooked. A number of experiments under the realm of psychology and experimental neuroscience have…

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…

Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and…