Unigram tokenizer: how does it work?
The explanation in the documentation of the Huggingface Transformers library seems more approachable:

Unigram is a subword tokenization algorithm introduced in Subword Regularization: Improving Neural Network Translation Models with Multiple Subword Candidates (Kudo, 2018). In contrast to BPE or WordPiece, Unigram initializes its base vocabulary to a large number of symbols and progressively trims down each symbol to obtain a smaller vocabulary. The base vocabulary could for instance correspond to all pre-tokenized words and the most common substrings. Unigram is not used directly for any of the models in the transformers, but it’s used in conjunction with SentencePiece.
At each training step, the Unigram algorithm defines a loss (often defined as the log-likelihood) over the training data given the current vocabulary and a unigram language model. Then, for each symbol in the vocabulary, the algorithm computes how much the overall loss would increase if the symbol was to be removed from the vocabulary. Unigram then removes p (with p usually being 10% or 20%) percent of the symbols whose loss increase is the lowest, i.e. those symbols that least affect the overall loss over the training data. This process is repeated until the vocabulary has reached the desired size. The Unigram algorithm always keeps the base characters so that any word can be tokenized.
Because Unigram is not based on merge rules (in contrast to BPE and WordPiece), the algorithm has several ways of tokenizing new text after training. As an example, if a trained Unigram tokenizer exhibits the vocabulary:
[&quot;b&quot;, &quot;g&quot;, &quot;h&quot;, &quot;n&quot;, &quot;p&quot;, &quot;s&quot;, &quot;u&quot;, &quot;ug&quot;, &quot;un&quot;, &quot;hug&quot;],
&quot;hugs&quot; could be tokenized both as [&quot;hug&quot;, &quot;s&quot;], [&quot;h&quot;, &quot;ug&quot;, &quot;s&quot;] or [&quot;h&quot;, &quot;u&quot;, &quot;g&quot;, &quot;s&quot;]. So which one to choose? Unigram saves the probability of each token in the training corpus on top of saving the vocabulary so that the probability of each possible tokenization can be computed after training. The algorithm simply picks the most likely tokenization in practice, but also offers the possibility to sample a possible tokenization according to their probabilities.
Those probabilities are defined by the loss the tokenizer is trained on. Assuming that the training data consists of the words 1,…, and that the set of all possible tokenizations for a word  is defined as (), then the overall loss is defined as
$\mathcal{L} = -\sum_{i=1}^{N} \log \left ( \sum_{x \in S(x_{i})} p(x) \right )$

There are some parts that are not very detailed, though, for instance, how it initializes the base (seed) vocabulary to a large number of symbols&quot;.
This part is more clearly explained in the original article by the end of section 3.2:

There are several ways to prepare the seed vocabulary. The natural choice is to use the union of all characters and the most frequent substrings in the corpus. Frequent substrings can be enumerated in $O(T)$ time and $O(20T)$ space with the Enhanced Suffix Array algorithm (Nong et al., 2009), where T is the size of the corpus.

About the details of the expectation maximization algorithm used to compute probabilities, this is what happens:

[Expectation] Estimate each subword probability by the corresponding frequency counts in the vocabulary
[Maximization] Use the Viterbi algorithm to segment the corpus, returning the optimal segments.

You can check the details, together with practical examples, in this tutorial.