Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a linear associative memory that maps $p$ input embeddings in $\mathbb{R}^d$ to their corresponding~$d$-dimensional targets via a single layer, requiring each mapped input to be well separated from all other targets. Unlike in supervised classification, this strict separation induces~$p$ constraints per association and produces strong correlations between constraints that make a direct characterisation of the storage capacity difficult. Here, we provide a precise characterisation of this capacity in the following way. We first introduce a decoupled model in which each input has its own independent set of competing outputs, and provide numerical and analytical evidence that this decoupled model is equivalent to the original model in terms of storage capacity, spectra of the learnt weights, and storage mechanism. Using tools from statistical physics, we show that the decoupled model can store up to $p_c \log p_c / d^2 = 1 / 2$ associations, and generalise the computation of $p_c$ to linear two-layer architectures. Our analysis also gives mechanistic insight into how the optimal solution improves over a naïve Hebbian learning rule: rather than boosting input-output alignments with broad fluctuations, the optimal solution raises the correct scores just above the extreme-value threshold set by the competing outputs. These findings give a sharp statistical-physics characterisation of factual storage in linear networks and provide a baseline for understanding the memory capacity of more realistic neural architectures.

Ilya Sutskever Stands by His Role in Sam Altman's OpenAI Ouster: 'I Didn't Want It to Be Destroyed' The former OpenAI chief scientist may be estranged from the company, but he still came to its defense as he testified on Monday. Elon Musk's trial against OpenAI and Microsoft entered its final stretch on Monday, with testimony from Microsoft CEO Satya Nadella, former OpenAI chief scientist Ilya Sutskever, and current OpenAI chairman Bret Taylor. Sutskever drew the spotlight, revealing an ownership stake in OpenAI's $850-billion for-profit arm that is currently worth about $7 billion. That makes him one of the largest known individual shareholders of OpenAI. Earlier in the trial, OpenAI president Greg Brockman acknowledged for the first time that he has around $30 billion worth of OpenAI shares .

Security around Beijing's historic Tiananmen Square has been heightened for days, with rumours on social media swirling of a special parade or some big, choreographed event. Preparations for this major event have started with a whisper, but China appears ready to put on a show for US President Donald Trump. The visit will include talks, a banquet, and a visit to the Temple of Heaven, a complex of imperial temples where emperors would pray for a good harvest. And both Trump and Chinese President Xi Jinping will be hoping the visit will bear fruit. This summit between the world's two most powerful leaders is set to be one of the most consequential encounters for years.

Environment Animals Wildlife Birds Jackie and Shadow's eaglets can now see like their parents More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. They grow up so fast. Sandy and Luna pictured last week. Breakthroughs, discoveries, and DIY tips sent six days a week. High above Big Bear Lake in southern California, a pair of eaglets' eyesight is coming into focus.

Yes, it works--if you have small fingers. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Fitting everything inside resembles a game of'Tetris.' Breakthroughs, discoveries, and DIY tips sent six days a week. Leftover Altoid tins are staple components in all types of handy, DIY projects . Once you eat the mints, the aluminum containers routinely house basic first aid kits, miniature speakers, sewing accessories, and even watercolor paints.

Testing for'Bad Cholesterol' Doesn't Tell the Whole Story So why don't more doctors use it? For decades, assessing cholesterol risk has been built around a simple idea: Lower "bad" cholesterol, lower your chance of a heart attack . The test at the center of that approach measures how much low-density lipoprotein, or LDL cholesterol, is circulating in part of the blood. It has shaped everything from clinical guidelines to the widespread use of statins, medications that reduce LDL. Lowering LDL cholesterol reduces heart attacks, strokes, and early death.

We can now add cybercrimes to the list of growing concerns associated with artificial intelligence. Google's Threat Intelligence Group (GTIG) said it discovered, for the first time ever, a threat actor using a zero-day exploit that it believes was developed by AI. Zero-day vulnerabilities are often the most dangerous since they're unknown to the targets, leaving them with zero days to prepare for the attack. Google said in the report the threat actor was planning to use it in a mass exploitation event, but its proactive discovery may have prevented its use. Google added that it doesn't believe its own Gemini models were used, but still has high confidence an AI model was part of discovering the vulnerability and weaponizing an exploit.

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The complaints, obtained by WIRED, described Bad Bunny's performance as being overly sexual and protested that the show was in Spanish. Bad Bunny performs during halftime of Super Bowl LX at Levi's Stadium in Santa Clara, California. Even before Bad Bunny took to the field, his Super Bowl halftime performance drew controversy, especially from MAGA influencers upset over the Puerto Rican star's comments against Immigration and Customs Enforcement and the fact that he sings in Spanish. Following the performance, which was watched by more than 128 million people, those complaints continued--but they were largely focused on perceived vulgarity in the artist's performance. Following a Freedom of Information Act (FOIA) request from WIRED, the Federal Communications Commission, which regulates communications including broadcast, released 2,155 complaints the agency received about the Super Bowl, most of which were about the halftime show.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. There are 26 different bitter receptors in the human body. Breakthroughs, discoveries, and DIY tips sent six days a week. Regular coffee drinkers know there is a big difference between a brew's aroma and its taste. A cup may smell warm and full-bodied only to leave you with a lingering bitterness behind the first sip.