[1] https://stackoverflow.com/questions/57960995/how-are-the-tok...

Old school word embedding models (like Word2Vec) come up with embeddings by using masked word predictions. You can embed a whole sentence by taking the average of all the word embeddings in the sentence.

There are many scenarios where this average fails to distinguish between multiple meanings of a word. For example “fine weather” and “fine hair” both contain “fine” but mean different things.

Transformers are great at producing better embeddings by considering context, and using the words in the rest of the sentence to produce a better representation of each word. BERT is a great model to do this.

The problem is that if you want to use BERT by itself to compute relevance you need to perform a lot of compute per query because you have to concatenate the query and the document vector to produce a long sequence that can then be “embedded” by BERT. Figure 2c in the ColBERT paper [1]

What ColBERT does is to use the fact that BERT can use context from the entire sentence and its attention heads to produce a more nuanced representation of any token in its input. It does this once for all documents in its index. So for example (assuming “fine” was a token) it would embed the “fine” in the sentence “we’re having fine weather today” to a different vector than the fine in “Sarah has fine blond hair”. In ColBERT the size of the output embeddings are usually much smaller than the typical 1024 you might expect from a Word2Vec.

Now, if you have a query, you can do the same and produce token level embeddings for all the tokens in the query.

Once you have these two contextualised embeddings, you can check for the presence of the particular meaning of a word in the document using the dot product. For example the query “which children have fine hair” matches the document “Sarah had fine blond hair” because the token “fine” is used in the exact same context in both the query and the document and should be picked up by the MaxSim operation.

[1] https://arxiv.org/pdf/2004.12832

Investment bank trading desks in the pre-2008 era, partnership at the big strategy consulting firms and even “multi-strategy hedge funds” now are actually all collections of very incentive aligned businesses. They share the Creo quality of making lots of millionaires and people looking back on their time there as one of great freedom and achievement.

In all these places, employees are paid according to the revenue they generate, with seemingly no ceiling to what you can take home. It is true that the size of any one cell doesn’t scale beyond a small number of people. But all the organisations I mentioned above scale by having units tackling small pieces of vast markets.

The main lesson I took away from reading “Barbarians at the Gate” is that big companies hugely suffer from the principal agent problem, where management is mostly out to enrich themselves at the expense of shareholders and employees (sometimes). This looting is however only possible at a company that was established by a founder with a deep vision and passion for the product and has set up systems and culture that generates sufficient cash for the professional management to leech off.

What I have not read yet is a systematic study of these “cellular organizations” and what the common features are that make them successful. My guess is that the key is that each “unit” or “cell” has measurable economics that makes it possible to share the economic value over a sustained period of time. A bit like why sales people get paid a lot.

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As with all things, practice is an essential part of improving!

Then, there's learning from some real achievements. Fast inverse square root, or the 55GB/s Fizzbuzz example: https://codegolf.stackexchange.com/questions/215216/high-thr...

But in general it seems to be very hard to beat the bang for buck from generating C and compiling that - even with something simple like tcc

[1] https://www.eecs.harvard.edu/%7Emichaelm/postscripts/tr-02-0... [2] https://stackoverflow.com/questions/70963247/bloom-filters-w...

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