dmarx

This feedback was motivated by your lecture: "On the volumes of higher-dimensional spheres"

First, I just want to say I love that you made this video. I think you brush off the gaussian discussion a bit too quickly though. In particular, I think an aside on the gaussian perspective gives a stronger intuition about how the concentration of measure works. In the video, you proposed that the measure concentrates at the "equator". Personally, I consider it pretty hard to reason about what the "equator" of a high dimensional sphere is.

Instead, I think a much easier way to think about this is that the volume concentrates along the circumference. Concretely, rather than the equator of a sphere, the visual you should be motivating is a thin shell at the surface of the sphere. In high dimensions, that "equator" is really any great circle wrt the origin, which sweeps out the shell.

I've heard this referred to as "the gaussian annulus theorem". Not sure who to attribute it to.

dmarx

CONGRESS CI/CD PIPELINE - BILL ANALYSIS REPORT
==============================================

Repository: us-congress/hr-1-one-big-beautiful-bill
Branch: senate-amendments
Commit: 7a8b9c2d "Final OBBB Act - Ready for Presidential Signature"
Triggered by: push to main
Status: ❌ FAILED - Critical Issues Found

📊 ANALYSIS SUMMARY

dmarx

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dmarx

import numpy as np
from openai import OpenAI
import plotly
import plotly.graph_objs as go
import umap


url = "http://localhost:80"

client = OpenAI(

dmarx

https://services.math.duke.edu/~rtd/EOSP/EOSP2021.pdf - stochastic processes
https://arxiv.org/abs/2106.10165 - principles of deep learning theory
https://arxiv.org/abs/2104.13478 - geometric deep learning
https://hastie.su.domains/ElemStatLearn/printings/ESLII_print12_toc.pdf
https://ia601508.us.archive.org/35/items/collection-of-mathematics-probability-and-statistics-books/A%20First%20Course%20in%20Probability%2C%20Global%20Edition%20%28Sheldon%20Ross%29.pdf
https://www.cs.uoi.gr/~arly/courses/ml/tmp/Bishop_book.pdf - PRML, Chris Bishop
https://github.com/probml/pml2-book/releases/latest/download/book2.pdf
https://maurice-weiler.gitlab.io/cnn_book/EquivariantAndCoordinateIndependentCNNs.pdf
https://arxiv.org/abs/1504.03001 - Chaos on the interval (225pp)
https://www.ma.imperial.ac.uk/~dturaev/kuznetsov.pdf - Elements of Applied Bifurcation Theory (614pp)

dmarx

# NB: ar5iv endpoint is lagged relative main arxiv
import subprocess


def convert_arxiv_url_to_markdown(arxiv_url, target_format='markdown_github'):
    parts = arxiv_url.split('/')
    article_id = parts[-1] if parts[-1] else parts[-2]  # Account for trailing slash
    article_id = article_id.replace('.pdf', '')
    html_url = f'https://ar5iv.labs.arxiv.org/html/{article_id}' 
    

dmarx

simulate the behavior of the following function. respond only with the output, enclosed in brackets.

def pair(node1, node2):
    GeeseGraph = WorldGraph.neighborhood("things related to geese")
    geese_nodes1 = GeeseGraph.nearest_neighbors(node1, n=10)
    geese_nodes2 = GeeseGraph.nearest_neighbors(node2, n=10)
    return geese_nodes1.intersect(geese_nodes2).sample(n=1, bias="funny matches")

>>> GeeseGraph.sample(n=100)
[pond, goose, feather, honk, migration, flock, nest, lake, wintering grounds, birdwatching, grain, park, bread, gosling, water, flyway, wetlands, grass, reeds, sunrise, sunset, quack, wildlife, bird, aviary, down, flapping, waddle, pecking, squawk, preen, aquatic plants, river, stream, marsh, ecosystem, habitat, conservation, ornithology, species, biodiversity, nature reserve, environmental protection, tagging, tracking, molting, territorial, aggression, mating rituals, offspring, survival, adaptation, plumage, waterfowl, aquatic invertebrates, feeding, foraging, resting, roosting, territo

dmarx

import numpy as np
import scipy as sp
from scipy.stats import poisson, expon
import matplotlib.pyplot as plt
import math
import random

random.seed(42)

dmarx

eff_batch_size=2048

#########################
# what you're doing-ish #
#########################

gradient_accumulation_steps = 4

micro_batch_size = eff_batch_size // gradient_accumulation_steps

dmarx

def init_comfy(
    comfyui_path = "/home/dmarx/projects/ComfyUI"
):
    # 1. add ComyUI to path
    import sys
    sys.path.append(comfyui_path)

    # 2. ensure cli parser doesn't cause issues
    from comfy.options import enable_args_parsing
    enable_args_parsing(False)