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https://x.com/jxbz/status/1857145985480438073

import torch

def polar_factor_newton_schulz(M, max_iter=50):

M_t = M / M.norm(p='fro')
for _ in range(max_iter):
M_t = 1.5 * M_t - 0.5 * M_t @ M_t.T @ M_t
return M_t

cloneofsimo

# batch_eigendecomp.py
import torch
from torch.utils.cpp_extension import load_inline
import argparse
import os
import shutil

def clear_cuda_cache():
    cache_path = os.path.expanduser('~/.cache/torch_extensions')
    if os.path.exists(cache_path):

cloneofsimo

#!/bin/bash

# Install required packages if not present
check_and_install_dependencies() {
    local packages=("inotify-tools" "texlive" "texlive-latex-extra" "biber")
    
    echo "Checking and installing dependencies..."
    for package in "${packages[@]}"; do
        if ! dpkg -l | grep -q "^ii  $package "; then
            sudo apt-get install -y "$package"

cloneofsimo

import torch
import torch.nn as nn
import torch.nn.functional as F
from torchvision import datasets, transforms
import numpy as np
import math


def compute_activation_std(model, dataset, device='cpu', batch_size=32, num_workers=0, layer_names=None):
    activations = {}

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import torch
import time

torch.backends.cuda.matmul.allow_tf32 = True
torch.backends.cudnn.allow_tf32 = True
torch.backends.cuda.matmul.allow_bf16_reduced_precision_reduction = False

@torch.no_grad()
def benchmark_gemm(m, k, n, dtype=torch.bfloat16, allow_bf16_reduce=True):
    torch.backends.cuda.matmul.allow_bf16_reduced_precision_reduction = allow_bf16_reduce

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import torch
import triton
import triton.language as tl
from triton.language.extra import libdevice

@triton.jit
def fractal_kernel(
    zr_ptr, zi_ptr, cr_ptr, ci_ptr, output_ptr,
    alpha_ptr, beta_ptr, poly0_ptr, poly1_ptr, poly2_ptr, poly3_ptr, p_ptr, R, max_iter,
    H, W,

cloneofsimo

Polynomial Maps from $S^n$ to $S^n$

Motivated by https://x.com/gabrielpeyre/status/1837156819799577034

---

Understanding Polynomial Maps on Spheres

cloneofsimo

Variant of AM-GM for Minimization

When dealing with functions of the form $f(x) = x^a + \frac{1}{x^b}$, a variant of the AM-GM inequality can be used to find the minimum. Specifically, if you have:

$$ f(x) = c_1 \cdot x^a + c_2 \cdot \frac{1}{x^b} $$

The minimum occurs at:

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Summarization:

As a professional summarizer, create a concise and comprehensive summary of the provided text, be it an article, post, conversation, or passage, while adhering to these guidelines:

Craft a summary that is detailed, thorough, in-depth, and complex, while maintaining clarity and conciseness.

Incorporate main ideas and essential information, eliminating extraneous language and focusing on critical aspects.

Rely strictly on the provided text, without including external information.

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def plot_lr_final_loss_batchsize(file_path):
    # Load the data
    data = pd.read_csv(file_path)
    
    # Extract columns that match 'val_loss/val_loss_'
    val_loss_columns = [col for col in data.columns if col.startswith('val_loss/val_loss_')]
    
    # Sort val_loss_columns by K (numeric value after 'val_loss/val_loss_') in increasing order