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A Trick for Backpropagation of Linear Transformations

Linear transformations such as sums, matrix products, dot products, Hadamard products, and many more can often be represented using an einsum (short for Einstein summation). This post explains a simple trick to backpropagate through any einsum, regardless of what operations it represents. Example Einsum For example, an einsum for matrix multiplication can be written like so: import numpy as np A = np.arange(2 * 3).reshape(2, 3) # A = [ # [0, 1, 2], # [3, 4, 5] # ] B = np.arange(3 * 4).reshap

Topics: einsum ik jnp np uses

‘Terrifier’ Makes an Undeniable Mark on Halloween Horror Nights Hollywood

The gates of Universal Studios Halloween Horror Nights Hollywood have opened, and this year’s event has some of the theme park’s biggest debuts. Between Terrifier and Five Nights at Freddy’s, the headliner haunted houses really pack a punch, with the terror titan-led Jason Universe house, based on the Friday the 13th franchise, also helping to power a killer season start. But that’s not to say there were some lows; surprisingly, HHN’s anticipated Fallout offering fell short of expectations. Som

About Containers and VMs

About containers and VMs¶ Incus provides support for two different types of instances: system containers and virtual machines. Incus uses features of the Linux kernel (such as namespaces and cgroups ) in the implementation of system containers. These features provide a software-only way to isolate and restrict a running system container. A system container can only be based on the Linux kernel. When running a virtual machine, Incus uses hardware features of the the host system as a way to iso

Octopolis and Octlantis

Settlements of gloomy octopuses in Australia Octopolis and Octlantis are two non-human settlements occupied by gloomy octopuses (Octopus tetricus) in Jervis Bay, on the south coast of New South Wales. The first site, named "Octopolis" by biologists, was found in 2009. Octopolis consists of a bed of shells (mainly scallop shells) in an ellipse shape, 2–3 meters diameter on its longer axis, with a single piece of anthropogenic detritus, believed to be scrap metal, within the site. Octopuses build

A simple pixel physics simulator in Rust using Macroquad

Sbixel Sbixel is a very simple pixel physics simulator I made to learn Rust. It uses macroquad for drawing — and I was pleasantly surprised by how simple and awesome it is! Quick demo (click for youtube link): ⚠️ This project is very basilar and doesn't have much ambition to go anywhere — it's mainly a learning sandbox. How It Works The simulation uses a "sector" system to reduce unnecessary processing by only simulating active areas of pixels. All settings related to simulation and perfo

19% of California houses are owned by investors

Relatively speaking, California is not a hot spot for housing investors. That’s a conclusion from my trusty spreadsheet’s review of data on investor activity across the nation from BatchData, a small data tracker that digs deeper into property records than many traditional real estate analysts. BatchData reviewed California ownership records to identify the state’s owner-occupied residences compared to houses controlled by investors. This study included properties for short-term or long-term r

All the Biggest Theme Park News of July You May Have Missed

The vacation season at the theme parks is winding down as Halloween begins to creep into the dead of summer, with its fall events arriving sooner than later. Here’s a roundup of this month’s happenings at major amusement parks and immersive experiences featuring Disneyland 70, Universal Horrors, and a Wednesday x Wendy’s not-so-happy meal coming soon to a drive-thru near you. Universal Studios Resorts – Hollywood and Orlando Let’s kick things off with the biggest news: Halloween Horror Nights

Can Macs Get Viruses in 2025? Do You Need Antivirus for Your Mac?

Remember those old I’m a Mac, I’m a PC ads? In one, the Mac looks on, concerned, while the PC keeps sneezing from a virus it's caught, eventually crashing backward onto the ground. For a while, Macs did seem mostly immune to computer viruses. But when Apple’s market share ballooned, with it came a new fan club: hackers. Yes, MacOS comes with XProtect, Gatekeeper and other tools, and most Mac owners get by just fine with these plus a dash of skepticism. Still, security firms keep spotting fresh

Can Macs Get Viruses in 2025? Do You Need an Antivirus for Your Mac?

Remember those old I’m a Mac, I’m a PC ads? In one, the Mac looks on, concerned, while the PC keeps sneezing from a virus it's caught, eventually crashing backward onto the ground. For a while, Macs did seem mostly immune to computer viruses. But when Apple’s market share ballooned, with it came a new fan club: hackers. Yes, MacOS comes with XProtect, Gatekeeper and other tools, and most Mac owners get by just fine with these plus a dash of skepticism. Still, security firms keep spotting fresh

Bus Bunching

When two or more buses are scheduled at regular intervals on the same route, planners may expect that each will make the same progress, pausing at each stop for the same interval (1). But if Bus B is delayed by traffic congestion (2), it incurs a penalty: Because it arrives late to the next stop, it will pick up some passengers who’d planned to take Bus C (3). Accommodating these passengers delays Bus B even longer, putting it even further behind schedule. Meanwhile, Bus C begins to make unusual

Leprechauns, root causes, and other fairy tales

This is a short talk I gave a while ago about how complex systems fail, and root cause analysis. Transcript is below. Transcript We’re going to talk about root causes today, but since I only have about 10 minutes, I wanted to start with some stories from a book I’m writing called Bedtime Stories To Put Your Children To Sleep Instantly And Also Yourself. This first story is about leprechauns. Once upon a time, there was a company with a new employee, and one day the employee asked their manage

US AI Action Plan

America must have the most powerful AI systems in the world, but we must also lead the world in creative and transformative application of those systems. Ultimately, it is the uses of technology that create economic growth, new jobs, and scientific advancements. America must invent and embrace productivity enhancing AI uses that the world wants to emulate. Achieving this requires the Federal government to create the conditions where private sector-led innovation can flourish.

What happens when an octopus engages with art?

CNN — When the Japanese artist Shimabuku was 31 years old, he took an octopus on a tour of Tokyo. After catching it from the sea with the help of a local fisherman in Akashi, a coastal city over 3 hours away from the Japanese capital by train, he transported the live creature in a temperature-controlled tank of seawater to show it the sights of Tokyo before returning it safely to its home the same day. “I thought it would be nice,” the artist, now 56, said about the experience, over a video ca

Robot Vacuum Tips to Help You Keep a Tidy Home (2025)

In the past few years, no other gadget—headphones, electric bicycle, literally anything at all—has improved as dramatically as the humble robot vacuum. The hardware and software have improved beyond all imagining. There are self-emptying bins, multilevel mapping abilities, and all sorts of bells and whistles, like an automated robot arm! Prices on the entry-level models have dropped significantly, to the point where robot vacuums are now an accessible household tool instead of a statement of bou

Cross-Compilation Toolchains for Linux

About This site provides a large number of ready-to-use cross-compilation toolchains, targetting the Linux operating system on a large number of architectures. Based on gcc and binutils, those toolchains are provided in several variants with the glibc, uClibc-ng and musl C libraries. The toolchains are built using the Buildroot build system. Most toolchains are tested by building a Linux kernel and Linux userspace, and booting it under Qemu. This is of course not possible on some CPU architec