Some of the earlier computers of the 20th centure were analog computers, not digital.
At some point analog died however, and "computer" basically by default started meaning just "digital computer".
As of the 2010's and forward, with the limit of Moore's law and the rise of machine learning, people have started looking again into analog computing as a possile way forward. A key insight is that huge floating point precision is not that crucial in many deep learning applications, e.g. many new digital designs have tried 16-bit floating point as opposed to the more traditional 32-bit minium. Some papers are even looking into 8-bit: dl.acm.org/doi/10.5555/3327757.3327866
As an example, the Lightmatter company was trying to implement silicon photonics-based matrix multiplication.
A general intuition behind this type of development is that the human brain, the holy grail of machine learning, is itself an analog computer.
Ordinals are inscriptions created with the protocol described at: docs.ordinals.com/inscriptions.html The protocol was designed by developer Casey Rodarmor, and shares a few similarities with the AtomSea & EMBII protocol.
The protocol also includes a way to have ownership over inscriptions, effectively creating an NFT system on top of the bitcoin blockchain. AtomSea & EMBII also already had such a system however. In either case, Ciro Santilli couldn't give less of a fuck about who owns some random publicly viewable digital asset.
For whatever reason, orinals became extremelly popular compared to the AtomSea & EMBII format, leading to millions os inscriptions, and 10k+ images as of block 830k. They also started to take up a substatial portion of the available block space.
This in turn led to a lot of child porn rediscussion, and people linking back to this page to view earlier inscriptions: incoming links.
Unfortunately, unlike AtomSea & EMBII and even cryptograffiti.info uploads, most ordinals are designed to be just souless bulk collectibles, as with as much artistic merit as any random collectible card set or postage stamps you may find at a newpaper stall. To make things worse many of them are likely algorithmically generated. Eternal September had truly arrived to the Bitcoin blockchain. As a result, machine learning would be almost essential in order to find interesting uploads amidst such bulk.
The source code for the reference uploader and indexer is at: github.com/ordinals/ord
The reference viewer server for the runs at: ordinals.com.
The
i0
at the end of the URL above means "inscription 0". This is because a single transaction can have multiple inscriptions.Some of them have sold for high prices. Magic Eden is a popular interface for trading them:
- 2023-12-08: #8 was sold dor 10.4 BTC[ref] (~$450,000 at the time)
The ordinals also started taking up large portions of the Bitcoin blockchain:
Apparently the "Taproot" Bitcoin update made it easier to upload image-sized data once again, which had become prohibitively expensive 2023 and much earlier:
- protos.com/did-taproot-ruin-bitcoin-with-nft-inscriptions-of-monkey-jpegs/
- ordinals.com/ appears to index some types of ordinals
Bibliography:
- blocktelegraph.io/parent-child-bitcoin-inscriptions/ parent-child relationshipsi are possible between two ordinals
- ordinals.com/
- bitcoin.stackexchange.com/questions/117018/understanding-how-ordinals-work-with-the-bitcoin-blockchain-what-is-exactly-sto
- bitcoin.stackexchange.com/questions/118405/read-ordinal-transaction-data
- bitcoin.stackexchange.com/questions/118247/can-someone-explain-the-byte-composition-of-an-inscription-reveal-transaction
- nftnow.com/guides/bitcoin-nfts-most-notable-ordinals-inscriptions/
A parameter that you choose which determines how the algorithm will perform.
In the case of machine learning in particular, it is not part of the training data set.
Hyperparameters can also be considered in domains outside of machine learning however, e.g. the step size in partial differential equation solver is entirely independent from the problem itself and could be considered a hyperparamter. One difference from machine learning however is that step size hyperparameters in numerical analysis are clearly better if smaller at a higher computational cost. In machine learning however, there is often an optimum somewhere, beyond which overfitting becomes excessive.
Given a bunch of points in dimensions, PCA maps those points to a new dimensional space with .
is a hyperparameter, and are common choices when doing dataset exploration, as they can be easily visualized on a planar plot.
The mapping is done by projecting all points to a dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.
The hyperplane choice is done as follows:
- the hyperplane will have origin at the mean point
- the first axis is picked along the direction of greatest variance, i.e. where points are the most spread out.Intuitively, if we pick an axis of small variation, that would be bad, because all the points are very close to one another on that axis, so it doesn't contain as much information that helps us differentiate the points.
- then we pick a second axis, orthogonal to the first one, and on the direction of second largest variance
- and so on until orthogonal axes are taken
www.sartorius.com/en/knowledge/science-snippets/what-is-principal-component-analysis-pca-and-how-it-is-used-507186 provides an OK-ish example with a concrete context. In there, each point is a country, and the input data is the consumption of different kinds of foods per year, e.g.:so in this example, we would have input points in 4D.
- flour
- dry codfish
- olive oil
- sausage
The question is then: we want to be able to identify the country by what they eat.
Suppose that every country consumes the same amount of flour every year. Then, that number doesn't tell us much about which country each point represents (has the least variance), and the first PCA axes would basically never point anywhere near that direction.
Another cool thing is that PCA seems to automatically account for linear dependencies in the data, so it skips selecting highly correlated axes multiple times. For example, suppose that dry codfish and olive oil consumption are very high in Portugal and Spain, but very low in Germany and Poland. Therefore, the variation is very high in those two parameters, and contains a lot of information.
However, suppose that dry codfish consumption is also directly proportional to olive oil consumption. Because of this, it would be kind of wasteful if we selected:since the information about codfish already tells us the olive oil. PCA apparently recognizes this, and instead picks the first axis at a 45 degree angle to both dry codfish and olive oil, and then moves on to something else for the second axis.
- dry codfish as the first axis
- olive oil as the second axis
We can see that much like the rest of machine learning, PCA can be seen as a form of compression.
The approach of this channel of exposing recent research papers is a "honking good idea" that should be taken to other areas beyond just machine learning. It takes a very direct stab at the missing link between basic and advanced!