The title of this paper really is a complete summary of what it's about!
But that does hide just how much went into this: it's 31 pages with 218 numbered equations and an average citation year of 1982 (before I was born… just). Or, to put it more directly, the cross entropy (also, KL-divergence and entropy) of piecewise linear functions turns out to be a lot more work than you initially think it's going to be. Was surprised to discover nobody had derived this previously (I expected to find it in a table on Wikipedia!), and then I did the derivation and ended up a lot less surprised… anyway, the equation itself:

It's not the nicest result: there is a singularity when a linear segment is flat, which is not where you expect to find one for an information theoretic equation. In practice it doesn't matter (see paper), and pushing gradients through it to train a neural network is demonstrated. One thing learned from all of this is that writing "piecewise linear probability density function" many times gets annoying, and while it only just about appears in the paper I've started referring to such distributions as orograms. That is, histogram but "histo", meaning a wooden post (the bars of a histogram), has been replaced with "oro", meaning a mountain (which is what your prototypical piecewise linear PDF looks like). This is what I've called the generic library that I coded and used to generate all of the results in the paper:

Orogram — A library for working with 1D piecewise linear probability density functions

Link to OpenReview version: The Cross-entropy of Piecewise Linear Probability Density Functions by Tom S. F. Haines, TMLR, 2024.

Link to version on this web server: The Cross-entropy of Piecewise Linear Probability Density Functions by Tom S. F. Haines, TMLR, 2024.

And here's an image of the entire paper, just because it would feel weird to have nothing visual, even if it's nightmare inducing:

You can find me in the first 30 minutes of the below podcast, talking about 3Dami and teaching Blender:

A follow up to the previous paper! This time around Oscar is experimenting with synthetic data, of varying levels of realism, in an attempt to build a model that can generate realistic output (a re-view autoencoder), to improve confidence in its correctness when used for classification. Because SAS has a view direction (with what can be thought of as a shadow), and the data often has multiple views this model lets you merge all data and then pick the view direction when reconstructing the input, to get a novel view. The representation is then used to classify the existence, or not, and type, of munition.

Link to conference version (open access): Automatic recognition of underwater munitions from multi-view sonar surveys using semi supervised machine learning: a simulation study

Link to local version, in case the above breaks: Automatic recognition of underwater munitions from multi-view sonar surveys using semi supervised machine learning: a simulation study

Not going to say a massive amount about this one; title is basically an entire abstract anyway! A dataset paper, going over challenges specific to SAS scans of underwater weapon dumps from WW2. Most interesting part, at least as judged from my point of view, is what you do when ground truth labels are unreliable going on impossible. Paper is also very much in anticipation of future fun, when we unleash the kittens of machine learning onto the problem:-)

Link to journal version: Challenges of Labelling Unknown Seabed Munition Dumpsites from Acoustic and Optical Surveys: A Case Study at Skagerrak

Link to version on this web server: Challenges of Labelling Unknown Seabed Munition Dumpsites from Acoustic and Optical Surveys: A Case Study at Skagerrak
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