These are my favorites, whether you're new to fitness, an athlete, or a parent shopping for your kid. It's been five years since Google officially acquired Fitbit for a reported $2.1 billion, grabbing hardware and software teams that also absorbed assets from Pebble, which Fitbit itself acquired in 2016. So, how have things changed? Well, for starters, Fitbit is now Google Fitbit. It's not the most imaginative of name changes, and it hasn't stuck in consumers' minds, but the good news is that Fitbit devices remain some of the most user-friendly and welcoming fitness trackers available.

A nature-loving 10-year-old girl who found an endangered amphibian under a bridge has left her mum in shock, surprise and disbelief. Melanie Hill said her daughter, Evie, discovered the nine-inch Mexican axolotl as they spent the day near the River Ogmore in Bridgend. She said Evie was always finding things like newts and bugs, but said the axolotl discovery was a surprise. It is the first documented discovery of an axolotl in the wild in the UK with only 50 to 1,000 individuals left globally today, according to experts. Axolotls as pets have seen a surge in popularity in recent years after they were introduced to video games such as Minecraft and Roblox.

I've recently introduced a few friends to the power of a great robot vacuum. One of my friends calls hers a marriage saver, while the other was both thrilled and horrified by how many stains the vacuum's AI found on her floors. Personally, my robot vacuums keep me from wanting to set the litter box on fire, since my cat is on a mission to create his own navigational trail of litter through my home. The best robot vacuums these days aren't just vacuuming your floors, nor are they blindly bumping around your house like they used to. These gadgets are mopping, scrubbing away stains, lifting themselves off of obstacles, and even reminding you to clean the dirtier areas in your home more frequently. A good robot vacuum can cost a pretty penny, but it doesn't have to, depending on what you're looking for. I've been testing every new robot vacuum I can in my three-story home filled with three adults, a preschooler, and a cat who's on a mission to get litter all over the house.

Deep learning methods achieve state-of-the-art performance in many application scenarios. Yet, these methods require a significant amount of hyperparameters tuning in order to achieve the best results. In particular, tuning the learning rates in the stochastic optimization process is still one of the main bottlenecks. In this paper, we propose a new stochastic gradient descent procedure for deep networks that does not require any learning rate setting. Contrary to previous methods, we do not adapt the learning rates nor we make use of the assumed curvature of the objective function. Instead, we reduce the optimization process to a game of betting on a coin and propose a learning rate free optimal algorithm for this scenario. Theoretical convergence is proven for convex and quasi-convex functions and empirical evidence shows the advantage of our algorithm over popular stochastic gradient algorithms.

What Will It Take to Get A.I. Out of Schools? The tech world assumes that A.I.-aided education is necessary and inevitable. A growing number of parents, educators, and cognitive scientists say the opposite. I don't like A.I., and I am raising my children not to like it. I've been telling them for years now that chatbots are manipulative and dangerous, that A.I.-image generators are loosening our collective grip on reality, that large language models are built atop industrial-scale intellectual-property theft. At times, I find myself speaking with my kids about A.I. in the same terms that we might discuss a creepy neighbor who lives down the block: avoid eye contact, cross the street when you walk past his house, and, when in doubt, call on a trusted adult. Yes, I, too, have suspected that the creepy neighbor walks on cloven hooves inside his Yeezy Boosts, but he probably isn't going anywhere--in fact, he keeps buying up properties around town--so just try your best not to engage. Somehow, I was not prepared for the creepy neighbor to start hanging around my kids' schools; somehow, I thought we had until high school.

Will fusion power get cheap? New research suggests that cost declines could be slow for the technology. Fusion power could provide a steady, zero-emissions source of electricity in the future--if companies can get plants built and running. But a new study suggests that even if that future arrives, it might not come cheap. Technologies tend to get less expensive over time. Lithium-ion batteries are now about 90% cheaper than they were in 2013.

Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly. In this work we study the limits of computationally efficient low-rank kernel approximation. We show that for a broad class of kernels, including the popular Gaussian and polynomial kernels, computing a relative error $k$-rank approximation to $K$ is at least as difficult as multiplying the input data matrix $A \in R^{n \times d}$ by an arbitrary matrix $C \in R^{d \times k}$. Barring a breakthrough in fast matrix multiplication, when $k$ is not too large, this requires $\Omega(nnz(A)k)$ time where $nnz(A)$ is the number of non-zeros in $A$. This lower bound matches, in many parameter regimes, recent work on subquadratic time algorithms for low-rank approximation of general kernels [MM16,MW17], demonstrating that these algorithms are unlikely to be significantly improved, in particular to $O(nnz(A))$ input sparsity runtimes. At the same time there is hope: we show for the first time that $O(nnz(A))$ time approximation is possible for general radial basis function kernels (e.g., the Gaussian kernel) for the closely related problem of low-rank approximation of the kernelized dataset.

We study connections between Dykstra's algorithm for projecting onto an intersection of convex sets, the augmented Lagrangian method of multipliers or ADMM, and block coordinate descent. We prove that coordinate descent for a regularized regression problem, in which the penalty is a separable sum of support functions, is exactly equivalent to Dykstra's algorithm applied to the dual problem. ADMM on the dual problem is also seen to be equivalent, in the special case of two sets, with one being a linear subspace. These connections, aside from being interesting in their own right, suggest new ways of analyzing and extending coordinate descent. For example, from existing convergence theory on Dykstra's algorithm over polyhedra, we discern that coordinate descent for the lasso problem converges at an (asymptotically) linear rate. We also develop two parallel versions of coordinate descent, based on the Dykstra and ADMM connections.

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