2 citations · 8 across the 16 of their papers we have counts for
20 papers
Log-Likelihood, Simpson's Paradox, and the Detection of Machine-Generated Text
Tom Kempton, Viktor Drobnyi, Maeve Madigan +1
The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploi…
TempTest: Local Normalization Distortion and the Detection of Machine-generated Text
Tom Kempton, Stuart Burrell, Connor Cheverall
Existing methods for the zero-shot detection of machine-generated text are dominated by three statistical quantities: log-likelihood, log-rank, and entropy. As language models mimi…
Local Normalization Distortion and the Thermodynamic Formalism of Decoding Strategies for Large Language Models
Tom Kempton, Stuart Burrell
Advances in hardware and language model architecture have spurred a revolution in natural language generation. However, autoregressive models compute probability distributions over…
Local dimension spectrum for dominated planar self-affine sets
Alex Batsis, Antti Käenmäki, Tom Kempton
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this…
The Dynamics of the Fibonacci Partition Function
Tom Kempton
In this article we study the local structure of the Fibonacci Partition Function by relating it to a cocycle over an irrational rotation.
Towards Absolutely Continuous Bernoulli Convolutions
Alex Batsis, Tom Kempton
We show how to turn the question of the absolute continuity of Bernoulli convolutions into one of counting the growth of the number of overlaps in the system. When the contraction…
Measures on the Spectra of Algebraic Integers
Tom Kempton, Alex Batsis
Given a real number beta > 1, the spectrum of beta is a well studied dynamical object. In this article we show the existence of a certain measure on the spectrum of beta related to…
Computing Garsia Entropy for Bernoulli Convolutions with Algebraic Parameters
Kevin G. Hare, Tom Kempton, Tomas Persson +1
We introduce a parameter space containing all algebraic integers that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this…
Intermediate dimensions
Kenneth J. Falconer, Jonathan M. Fraser, Tom Kempton
We introduce a continuum of dimensions which are `intermediate' between the familiar Hausdorff and box dimensions. This is done by restricting the families of allowable covers in t…
On the Hausdorff Dimension of Bernoulli Convolutions
Shigeki Akiyama, De-Jun Feng, Tom Kempton +1
We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows…
On the L^q Dimensions of Measures on Hueter-Lalley Type Self-Affine Sets
Jonathan Fraser, Tom Kempton
We study the L^q -dimensions of self-affine measures and the Kaenmaki measure on a class of self-affine sets similar to the class considered by Hueter and Lalley. We give simple, c…
The dimension of projections of self-affine sets and measures
Kenneth Falconer, Tom Kempton
Let E be a plane self-affine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if mu is a Bernoulli measure on E with di…
The random continued fraction transformation
Charlene Kalle, Tom Kempton, Evgeny Verbitskiy
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We…
The Scenery Flow for Self-Affine Measures
Tom Kempton
We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely…
Planar self-affine sets with equal Hausdorff, box and affinity dimensions
Kenneth Falconer, Tom Kempton
Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-…
Bernoulli Convolutions and 1D Dynamics
Tom Kempton, Tomas Persson
We describe a family of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are p…
Sets of beta-expansions and the Hausdorff Measure of Slices through Fractals
Tom Kempton
We study natural measures on sets of beta-expansions and on slices through self similar sets. In the setting of beta-expansions, these allow us to better understand the measure of…
On the Invariant Density of the Random Beta-Transformation
Tom Kempton
We construct a Lebesgue measure preserving natural extension of the random beta-transformation. This allows us to give a formula for the density of the absolutely continuous invari…
Digit Frequencies and Bernoulli Convolutions
Tom Kempton
It is well known that the Bernoulli convolution associated to the golden mean has Hausdorff dimension less than 1, i.e. that there exists a set with and $dim_H…
Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions
Tom Kempton
We study the typical growth rate of the number of words of length n which can be extended to beta-expansions of x. In the general case we give a lower bound for the growth rate, wh…