The wave equation contains the entire state of a particle.
From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.
And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.
More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.
When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.
This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".
Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in due to Carleson's theorem.
Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle
In precise terms, the uncertainty principle talks about the standard deviation of two measures.
We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:
- to localize the wave in space at position 0 to reduce the space uncertainty, we have to reduce the support. However, doing so makes the momentum variation on the edges more and more important, as the slope will go up and down faster (higher top, and less x space for descent), leading to a larger variance (note that average momentum is still 0, due to to symmetry of the bump function)
- to localize the momentum as much as possible at 0, we can make the support wider and wider. This makes the bumps at the edges smaller and smaller. However, this also obviously delocalises the wave function more and more, increasing the variance of x
Bibliography:
- www.youtube.com/watch?v=bIIjIZBKgtI&list=PL54DF0652B30D99A4&index=59 "K2. Heisenberg Uncertainty Relation" by doctorphys (2011)
- physics.stackexchange.com/questions/132111/uncertainty-principle-intuition Uncertainty Principle Intuition on Physics Stack Exchange
This is the first thing you have to know about supervised learning:Both of those already have hardware acceleration available as of the 2010s.
- training is when you learn model parameters from input. This literally means learning the best value we can for a bunch of number input numbers of the model. This can easily be on the hundreds of thousands.
- inference is when we take a trained model (i.e. with the parameters determined), and apply it to new inputs
An IBM made/pushed term, but that matches Ciro Santilli's general view of how we should move forward AGI.
Interesting layer skip architecture thing.
Apparently destroyed ImageNet 2015 and became very very famous as such.
Someone should package this better for end user "just works after Conda install" image generation, it is currently much more of a library setup.
Tested on Amazon EC2 on a g5.xlarge machine, which has an Nvidia A10G, using the AWS Deep Learning Base GPU AMI (Ubuntu 20.04) image.
First install Conda as per Section "Install Conda on Ubuntu", and then just follow the instructions from the README, notably the Reference sampling script section.This took about 2 minutes and generated 6 images under
git clone https://github.com/runwayml/stable-diffusion
cd stable-diffusion/
git checkout 08ab4d326c96854026c4eb3454cd3b02109ee982
conda env create -f environment.yaml
conda activate ldm
mkdir -p models/ldm/stable-diffusion-v1/
wget -O models/ldm/stable-diffusion-v1/model.ckpt https://huggingface.co/CompVis/stable-diffusion-v-1-4-original/resolve/main/sd-v1-4.ckpt
python scripts/txt2img.py --prompt "a photograph of an astronaut riding a horse" --plmsoutputs/txt2img-samples/samples, includining an image outputs/txt2img-samples/grid-0000.png which is a grid montage containing all the six images in one:
A quick attempt at removing their useless safety features (watermark and NSFW text filter) is:but that produced 4 black images and only two unfiltered ones. Also likely the lack of sexual training data makes its porn suck, and not in the good way.
diff --git a/scripts/txt2img.py b/scripts/txt2img.py
index 59c16a1..0b8ef25 100644
--- a/scripts/txt2img.py
+++ b/scripts/txt2img.py
@@ -87,10 +87,10 @@ def load_replacement(x):
def check_safety(x_image):
safety_checker_input = safety_feature_extractor(numpy_to_pil(x_image), return_tensors="pt")
x_checked_image, has_nsfw_concept = safety_checker(images=x_image, clip_input=safety_checker_input.pixel_values)
- assert x_checked_image.shape[0] == len(has_nsfw_concept)
- for i in range(len(has_nsfw_concept)):
- if has_nsfw_concept[i]:
- x_checked_image[i] = load_replacement(x_checked_image[i])
+ #assert x_checked_image.shape[0] == len(has_nsfw_concept)
+ #for i in range(len(has_nsfw_concept)):
+ # if has_nsfw_concept[i]:
+ # x_checked_image[i] = load_replacement(x_checked_image[i])
return x_checked_image, has_nsfw_concept
@@ -314,7 +314,7 @@ def main():
for x_sample in x_checked_image_torch:
x_sample = 255. * rearrange(x_sample.cpu().numpy(), 'c h w -> h w c')
img = Image.fromarray(x_sample.astype(np.uint8))
- img = put_watermark(img, wm_encoder)
+ # img = put_watermark(img, wm_encoder)
img.save(os.path.join(sample_path, f"{base_count:05}.png"))
base_count += 1- torchvision ResNet
- MLperf v2.1 ResNet contains a pre-trained ResNet ONNX at zenodo.org/record/4735647/files/resnet50_v1.onnx for its inference benchmark. We've tested it at: Run MLperf v2.1 ResNet on Imagenette.
catalog.ngc.nvidia.com/orgs/nvidia/resources/resnet_50_v1_5_for_pytorch explains:
The difference between v1 and v1.5 is that, in the bottleneck blocks which requires downsampling, v1 has stride = 2 in the first 1x1 convolution, whereas v1.5 has stride = 2 in the 3x3 convolution.This difference makes ResNet50 v1.5 slightly more accurate (~0.5% top1) than v1, but comes with a small performance drawback (~5% imgs/sec).
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact