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Explainer details math behind the Softmax function and its derivative

A technical post explains the Softmax function, which converts an N-dimensional vector of real numbers into another N-dimensional vector of values between 0 and 1 that sum to 1. Using worked numeric examples, it shows how Softmax acts as a smoothed version of the maximum function, giving the largest input a disproportionately larger share of the output while still assigning smaller shares to other elements.

Study: butterfly wing patterns create motion illusions that foil predators

Researchers from the University of Exeter and University of Essex, publishing in Nature, found that butterflies' wing patterns combine with their flight to produce visual illusions that distort predators' perception of speed and direction. The team says this helps explain why few predators specialise in catching butterflies mid-flight, unlike moths, which are preyed on by many aerial hunters.

Cramer picks Akamai over Cloudflare, Fastly as AI traffic play

Jim Cramer highlighted Cloudflare, Akamai and Fastly as beneficiaries of surging internet traffic driven by AI agents, with Fastly up 159% year to date, Cloudflare up 78%, and Akamai up 22%. He noted Akamai's recent $11.6 billion, seven-year computing capacity deal with Anthropic, and said Cloudflare's CEO reported AI agent traffic has already exceeded human traffic on its network.

Oxygen Forensics execs charged over hidden Russian ownership tied to UK, US police use

US prosecutors arrested Oxygen Forensics' American CEO Lion Reiber and Russian national Vladimir Davydov, alleging the Virginia-based company concealed Russian ownership to win US government contracts, including a five-year deal with the Secret Service awarded in September 2024. British police, including specialist Metropolitan Police units, have also used Oxygen's phone-unlocking software during live investigations, according to public documents. Prosecutors say Reiber falsely told US officials in 2022, 2023 and again in March that the company had no top-level owner and no Russian involvement in building the software.

St. Lucie County, Florida finds 11 unpermitted Flock cameras of unknown origin

After St. Lucie County, Florida decided to stop using Flock surveillance cameras and began removing them, officials discovered 14 devices beyond the 52 they believed were installed. The Sheriff's Office later claimed three of those unpermitted cameras without explaining the lack of paperwork, leaving 11 cameras whose owners remain unidentified.

OpenAI adds virtual clothing try-on to ChatGPT shopping features

OpenAI has introduced a Virtual Try On feature in ChatGPT that lets users upload a selfie and full-body photo to see themselves wearing clothing items shown in chat, including items from uploaded screenshots. The feature runs on OpenAI's ChatGPT Images 2.5 model released in September, and the app now also lets users save liked products to a Library for later.

Researchers trace Venus' lower haze to cosmic dust, not volcanic ash

A team led by planetary scientist Hiroki Karyu at Tohoku University used a microphysical model to explain the yellowish haze in Venus' lower atmosphere, first seen by Venera and Pioneer Venus probes in the 1970s. The study, published in Nature Astronomy, found the haze forms when sulfuric acid reacts with dust particles left behind by meteorites burning up in the atmosphere, ruling out volcanic ash or surface dust as the source.

Federal judge blocks Utah's anti-VPN age verification law

A federal court issued a preliminary injunction halting enforcement of Utah's SB 73, which required adult websites to detect and block VPN users or verify the physical location of visitors using privacy tools, and banned instructions on using VPNs to bypass age checks. The judge found the law likely violates the Constitution's restriction on states burdening people and businesses outside their borders, since it would effectively force sites to age-verify every visitor nationwide in case they were an obfuscating Utah resident.

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