pytorch.org/vision/0.13/models.html has a minimal runnable example adapted to python/pytorch/resnet_demo.py.

That example uses a ResNet pre-trained on the COCO dataset to do some inference, tested on Ubuntu 22.10:This first downloads the model, which is currently 167 MB.

We know it is COCO because of the docs: pytorch.org/vision/0.13/models/generated/torchvision.models.detection.fasterrcnn_resnet50_fpn_v2.html which explains that is an alias for:

The runtime is relatively slow on P51, about 4.7s.

After it finishes, the program prints the recognized classes:so we get the expected bird, but also the more intriguing banana.

By looking at the output image with bounding boxes, we understand where the banana came from!

www.gelifesciences.com/en/us/shop/protein-analysis/protein-sample-preparation/protein-enrichment/magrack-6-p-05761 (archive).

Given a bunch of points in $n$ dimensions, PCA maps those points to a new $p$ dimensional space with $p\le n$.

$p$ is a hyperparameter, $p=1$ and $p=2$ 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 $p$ dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.

The hyperplane choice is done as follows:

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.

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.

We can see that much like the rest of machine learning, PCA can be seen as a form of compression.

Fixed quantum angular momentum in a given direction.

Can range between $\pm l$.

E.g. consider gallium which is 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1:

The z component of the quantum angular momentum is simply:so e.g. again for gallium:

Note that this direction is arbitrary, since for a fixed azimuthal quantum number (and therefore fixed total angular momentum), we can only know one direction for sure. $z$ is normally used by convention.

At twitter.com/togelius/status/1328404390114435072 called out on DeepMind Lab2D for not giving them credit on prior work!As seen from web.archive.org/web/20220331022932/http://gvgai.net/ though, DeepMind sponsored them at some point.

Basically ensuring that good AI alignment allows us to survive the singularity.