Complex dynamical systems, from macromolecules to ecosystems, are often modeled by stochastic differential equations. To learn such models from data, a common approach involves sparse selection among a large function library. However, we show that overfitting arises - not just from individual model complexity, but also from the combinatorial growth of possible models. To address this, we introduce Parsimonious Stochastic Inference (PASTIS), a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters. PASTIS outperforms existing methods and reliably identifies minimal models, even with low sampling rates or measurement error. It extends to stochastic partial differential equations, and applies to ecological networks and reaction-diffusion dynamics.

The marketing departments of financial institutions strive to craft products and services that cater to the diverse needs of businesses of all sizes. However, it is evident upon analysis that larger corporations often receive a more substantial portion of available funds. This disparity arises from the relative ease of assessing the risk of default and bankruptcy in these more prominent companies. Historically, risk analysis studies have focused on data from publicly traded or stock exchange-listed companies, leaving a gap in knowledge about small and medium-sized enterprises (SMEs). Addressing this gap, this study introduces a method for evaluating SMEs by generating images for processing via a convolutional neural network (CNN). To this end, more than 10,000 images, one for each company in the sample, were created to identify scenarios in which the CNN can operate with higher assertiveness and reduced training error probability. The findings demonstrate a significant predictive capacity, achieving 97.8% accuracy, when a substantial number of images are utilized. Moreover, the image creation method paves the way for potential applications of this technique in various sectors and for different analytical purposes.

The White House said on Tuesday that it was investigating the national security implications of DeepSeek's rapid rise. The Chinese AI startup released an open-sourced problem-solving model, R1, that has wowed Silicon Valley. According to the company, the model uses far less computing power and far fewer chips – therefore far less money – to achieve the same or better results as its US counterparts. DeepSeek's app, an AI assistant, has rocketed to the top of app stores in the US and UK, though it suffered a cyberattack on Monday that led the company to limit registrations. The tech sector saw its stock prices decline by a whopping 1tn in response on Monday.

This article is part of The D.C. Brief, TIME's politics newsletter. Sign up here to get stories like this sent to your inbox. Stop me if you've heard this one: a tech tool owned by a foreign adversary is thrusting its tentacles into the devices in tens of millions of Americans' pockets, giving its owners the chance to harvest vast amounts of data about them while shaping how they interpret the world around them, either real or imagined. That was, in essence, why the U.S. Supreme Court just this month unanimously upheld a law effectively banning TikTok--because Congress saw it as a national security risk that stood to benefit China. Given the challenges coming from Beijing, justices said Washington was within its power to deny it one of its strongest toeholds out of concern that it could be used to surveil Americans, steal their secrets, and feed them a stream of propaganda useful to China's big-picture goals.

White House press secretary Karoline Leavitt shared a message from President Donald Trump on the source of drone sightings reported over New Jersey. The White House on Tuesday revealed that some of the drones seen flying over New Jersey and other parts of the country in November were authorized to be flown by the Federal Aviation Administration. Press secretary Karoline Leavitt shared an update "directly" from President Donald Trump that clarified the origin of the drones, which caused a national stir and captured headlines for weeks late last year. "After research and study, the drones that were flying over New Jersey in large numbers were authorized by the FAA for research and various other reasons," Leavitt said. White House Press Secretary Karoline Leavitt holds her first news conference in the Brady Press Briefing Room at the White House on Jan. 28, 2025, in Washington, D.C.

OpenAI has begun offering a version of ChatGPT designed for US government agencies. ChatGPT Gov includes many of the same features found in the Enterprise offering of the chatbot, including access to the company's GPT-4o model. "By making our products available to the US government, we aim to ensure AI serves the national interest and the public good, aligned with democratic values, while empowering policymakers to responsibly integrate these capabilities to deliver better services to the American people," OpenAI said in a blog post published Tuesday. Before today, US government employees were already using ChatGPT in their day-to-day work. According to the company, federal, state and local government workers at 3,500 agencies across the country have sent more than 18 million messages since 2024.

OpenAI CEO Sam Altman sits down with Shannon Bream to discuss the positives and potential negatives of artificial intelligence and the importance of maintaining a lead in the A.I. industry over China. OpenAI has announced a new "ChatGPT for Gov" product that the company says will provide U.S. government agencies an additional way to access their frontier large language models (LLMs) while maintaining internal security standards. "We believe the U.S. government's adoption of artificial intelligence can boost efficiency and productivity and is crucial for maintaining and enhancing America's global leadership in this technology. This includes making our models available to support public sector work that benefits society – such as public health, energy and the environment, transportation and infrastructure, consumer protection, and national security," OpenAI wrote in a Tuesday press release. The company believes that partnering with the U.S. government is key to ensuring rapidly developing AI capabilities are well understood by policymakers and responsibly integrated to deliver services to American citizens.

Experts have urged caution over rapidly embracing the Chinese artificial intelligence platform DeepSeek, citing concerns about it spreading misinformation and how the Chinese state might exploit users' data. The new low-cost AI wiped 1tn off the leading US tech stock index this week and it rapidly became the most downloaded free app in the UK and the US. Donald Trump called it a "wake-up call" for tech firms. Its emergence has shocked the tech world by apparently showing it can achieve a similar performance to widely used platforms such as ChatGPT at a fraction of the cost. Michael Wooldridge, a professor of the foundations of AI at Oxford University, said it was not unreasonable to assume data inputted into the chatbot could be shared with the Chinese state. He said: "I think it's fine to download it and ask it about the performance of Liverpool football club or chat about the history of the Roman empire, but would I recommend putting anything sensitive or personal or private on them?

There was a lot of news last week. The Guardian's journalism is independent. We will earn a commission if you buy something through an affiliate link. Donald Trump, Sam Altman, Masayoshi Son and Larry Ellison announced a 500bn initiative to expand infrastructure supporting artificial intelligence dubbed Stargate. On its heels came a press release from Meta vowing to expand its capital expenditure to 65bn in the coming year to expand its data centers.

If you ask a historian what happened on June 4, 1989, you will learn that this was the date that hundreds of protesters were killed in the Tiananmen Square Massacre. However, if you ask China's controversial ChatGPT rival, DeepSeek, you are unlikely to get any response at all. During testing, MailOnline watched in real-time as answers to sensitive questions were scrubbed and replaced with evasive replies. On topics censored by the Chinese Communist Party (CCP), the bot briefly attempts to respond before wiping away its own answers in front of the user's eyes. DeepSeek actively censors topics related to protests such as the White Paper Movement and Hong Kong's pro-democratic Umbrella Movement.