Related papers: The baseline for response latency distributions

We study a reaction diffusion system where we consider a non-gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with tails approaching to zero faster than a power law, the usual…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

For Large Language Models (LLMs) to be reliably deployed, models must effectively know when not to answer: abstain. Reasoning models, in particular, have gained attention for impressive performance on complex tasks. However, reasoning…

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported…

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty $, is given in the form of a power law…

The problem of regression extrapolation, or out-of-distribution generalization, arises when predictions are required at test points outside the range of the training data. In such cases, the non-parametric guarantees for regression methods…

We consider scheduling in the M/G/1 queue with unknown job sizes. It is known that the Gittins policy minimizes mean response time in this setting. However, the behavior of the tail of response time under Gittins is poorly understood, even…

Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…

Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…

In this paper, we consider the state-dependent reflecting random walk on a half-strip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed…

The performance of Large Language Models (LLMs) often degrades when crucial information is in the middle of a long context, a "lost-in-the-middle" phenomenon that mirrors the primacy and recency effects in human memory. We propose that this…

Symmetric random walks in $R^d$ and $Z^d$ are considered. It is assumed that the jump distribution density has moderate tails, i.e., several density moments are finite, including the second one. The global (for all $x$ and $t$) asymptotic…

The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…

Ordinal response model is a popular and commonly used regression for ordered categorical data in a wide range of fields such as medicine and social sciences. However, it is empirically known that the existence of ``outliers'', combinations…

Many tasks are accomplished via random processes. The completion time of such a task can be profoundly affected by restart: the occasional resetting of the task's underlying random process. Consequently, determining when restart will impede…

Despite recent progress in training long-chain-of-thought reasoning models via scaling reinforcement learning (RL), its underlying training dynamics remain poorly understood, and several counterintuitive behaviors persist. This work focuses…

Information processing in the brain requires integration of information over time. Such an integration can be achieved if signals are maintained in the network activity for the required period, as quantified by the intrinsic timescale.…

In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…

Estimating the location and scale parameters is common in statistics, using, for instance, the well-known sample mean and standard deviation. However, inference can be contaminated by the presence of outliers if modeling is done with…

We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…