How is hashing implemented in SGNN (Self-Governing Neural Networks)?

So I've read the paper named Self-Governing Neural Networks for On-Device Short Text Classification which presents an embedding-free approach to projecting words into a neural representation. To quote them:

The key advantage of SGNNs over existing work is that they surmount the need for pre-trained word embeddings and complex networks with huge parameters. [...] our method is a truly embedding-free approach unlike majority of the widely-used state-of-the-art deep learning techniques in NLP

Basically, from what I understand, they proceed as follow:

1. You'd first need to compute n-grams (side-question: is that skip-gram like old skip-gram, or new skip-gram like word2vec? I assume it's the first one for what remains) on words' characters to obtain a featurized representation of words in a text, so as an example, with 4-grams you could yield a 1M-dimensional sparse feature vector per word. Hopefully, it's sparse so memory needn't to be fully used for that because it's almost one-hot (or count-vectorized, or tf-idf vectorized ngrams with lots of zeros).
2. Then you'd need to hash those n-grams sparse vectors using Locality-sensitive hashing (LSH). They seem to use Random Projection from what I've understood. Also, instead of ngram-vectors, they instead use tuples of n-gram feature index and its value for non-zero n-gram feature (which is also by definition a "sparse matrix" computed on-the-fly such as from a Default Dictionary of non-zero features instead of a full vector).
3. I found an implementation of Random Projection in scikit-learn. From my tests, it doesn't seem to yield a binary output, although the whole thing is using sparse on-the-fly computations within scikit-learn's sparse matrices as expected for a memory-efficient (non-zero dictionnary-like features) implementation I guess.

What doesn't work in all of this, and where my question lies, is in how they could end up with binary features from the sparse projection (the hashing). They seem to be saying that the hashing is done at the same time of computing the features, which is confusing, I would have expected the hashing to come in the order I wrote above as in 1-2-3 steps, but their steps 1 and 2 seems to be somehow merged.

My confusion arises mostly from the paragraphs starting with the phrase "On-the-fly Computation." at page 888 (PDF's page 2) of the paper in the right column. Here is an image depicting the passage that confuses me:

I'd like to convey my school project to a success (trying to mix BERT with SGNNs instead of using word embeddings). So, how would you demystify that? More precisely, how could a similar random hashing projection be achieved with scikit-learn, or TensorFlow, or with PyTorch? Trying to connect the dots here, I've significantly researched but their paper doesn't give implementation details, which is what I'd like to reproduce. I at least know that the SGNN uses 80 fourten-dimensionnal LSHes on character-level n-grams of words (is my understanding right in the first place?).

Thanks!

EDIT: after starting to code, I realized that the output of scikit-learn's SparseRandomProjection() looks like this:

[0.7278244729081154,
 -0.7278244729081154,
 0.0,
 0.0,
 0.7278244729081154,
 0.0,
 ...
]

For now, this looks fine, it's closer to binary but it would still be castable to an integer instead of a float by using the good ratio in the first place. I still wonder about the skip-gram thing, I assume n-gram of characters of words for now but it's probably wrong. Will post code soon to GitHub.

EDIT #2: I coded something here, but with n-grams instead of skip-grams: https://github.com/guillaume-chevalier/SGNN-Self-Governing-Neural-Networks-Projection-Layer

More discussion threads on this here: https://github.com/guillaume-chevalier/SGNN-Self-Governing-Neural-Networks-Projection-Layer/issues?q=is%3Aissue