The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many datasets, the stable coloring is reached after a few iterations and the optimal number of iterations for machine learning tasks is typically even lower. This suggests that the colors diverge too fast, defining a similarity that is too coarse. We generalize the concept of color refinement and propose a framework for gradual neighborhood refinement, which allows a slower convergence to the stable coloring and thus provides a more fine-grained refinement hierarchy and vertex similarity. We assign new colors by clustering vertex neighborhoods, replacing the original injective color assignment function. Our approach is used to derive new variants of existing graph kernels and to approximate the graph edit distance via optimal assignments regarding vertex similarity. We show that in both tasks, our method outperforms the original color refinement with only a moderate increase in running time advancing the state of the art.

Once in a blue moon, Sonos releases its speakers in some fun colors or finishes, but most of the time, people just have to pick between black and white. But starting today, you can get the portable Sonos Roam in three new shades; Wave, Sunset and Olive. As you might guess, Wave is a chill shade of light blue, Sunset straddles the line between orange and pink and olive is a cactus sort of green. Aside from these colors, there's nothing else new with the $179 speaker -- it has a built-in battery for about 10 hours of play time, Bluetooth for when you're away from WiFi, a microphone for voice commands via Alexa and Google Assistant and auto Trueplay technology to tune the speaker for optimal sound wherever you place it. I really liked the speaker when I reviewed it last year, and even though it costs $10 more than it did when it launched, I still think it's a great portable speaker that is a smart addition if you're already using other Sonos products.

Apple will soon offer the HomePod mini in three new colors. Announced during the company's Unleased event on Monday, the new yellow, orange and blue colorways will join the existing white and space gray models in November. The price will remain unchanged at $99 in the US. Apple first announced the HomePod mini last fall. As you'd expect, the speaker comes with deep integration with the company's other products. In addition to Siri support, its built-in U1 ultra-wideband chip allows you to quickly and easily hand off audio from your iPhone to the speaker.

"I opened the oven and my eyes just watered," she told me. I had never tasted such a horrible chocolate thing in my whole life." Shane, 33, is not a professional artificial-intelligence researcher. During the day, she works with laser beams for a small research company in Boulder, Colorado. But she plays around with artificial intelligence in her free time.