As intelligent systems are developed across diverse substrates - from machine learning models and neuromorphic hardware to in vitro neural cultures - understanding what gives a system agency has become increasingly important. Existing definitions, however, tend to rely on top-down descriptions that are difficult to quantify. We propose a bottom-up framework grounded in a system's information-processing order: the extent to which its transformation of input evolves over time. We identify three orders of information processing. Class I systems are reactive and memoryless, mapping inputs directly to outputs. Class II systems incorporate internal states that provide memory but follow fixed transformation rules. Class III systems are adaptive; their transformation rules themselves change as a function of prior activity. While not sufficient on their own, these dynamics represent necessary informational conditions for genuine agency. This hierarchy offers a measurable, substrate-independent way to identify the informational precursors of agency. We illustrate the framework with neurophysiological and computational examples, including thermostats and receptor-like memristors, and discuss its implications for the ethical and functional evaluation of systems that may exhibit agency.

Modern AI systems increasingly operate inside markets and institutions where data, behavior, and incentives are endogenous. This paper develops an economic foundation for multi-agent learning by studying a principal-agent interaction in a Markov decision process with strategic externalities, where both the principal and the agent learn over time. We propose a two-phase incentive mechanism that first estimates implementable transfers and then uses them to steer long-run dynamics; under mild regret-based rationality and exploration conditions, the mechanism achieves sublinear social-welfare regret and thus asymptotically optimal welfare. Simulations illustrate how even coarse incentives can correct inefficient learning under stateful externalities, highlighting the necessity of incentive-aware design for safe and welfare-aligned AI in markets and insurance.

This paper, introducing a novel method in philo-matics, draws on Wittgenstein's concept of family resemblance from analytic philosophy to develop a clustering algorithm for machine learning. According to Wittgenstein's Philosophical Investigations (1953), family resemblance holds that members of a concept or category are connected by overlapping similarities rather than a single defining property. Consequently, a family of entities forms a chain of items sharing overlapping traits. This philosophical idea naturally lends itself to a graph-based approach in machine learning. Accordingly, we propose the Wittgenstein's Family Resemblance (WFR) clustering algorithm and its kernel variant, kernel WFR. This algorithm computes resemblance scores between neighboring data instances, and after thresholding these scores, a resemblance graph is constructed. The connected components of this graph define the resulting clusters. Simulations on benchmark datasets demonstrate that WFR is an effective nonlinear clustering algorithm that does not require prior knowledge of the number of clusters or assumptions about their shapes.

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.

Blind inverse problems arise in many experimental settings where the forward operator is partially or entirely unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward manner. Recently, data-driven approaches have been proposed to address blind inverse problems, demonstrating strong empirical performance and adaptability. However, these methods often lack interpretability and are not supported by rigorous theoretical guarantees, limiting their reliability in applied domains such as imaging inverse problems. In this work, we shed light on learning in blind inverse problems within the simplified yet insightful framework of Linear Minimum Mean Square Estimators (LMMSEs). We provide an in-depth theoretical analysis, deriving closed-form expressions for optimal estimators and extending classical results. In particular, we establish equivalences with suitably chosen Tikhonov-regularized formulations, where the regularization depends explicitly on the distributions of the unknown signal, the noise, and the random forward operators. We also prove convergence results under appropriate source condition assumptions. Furthermore, we derive rigorous finite-sample error bounds that characterize the performance of learned estimators as a function of the noise level, problem conditioning, and number of available samples. These bounds explicitly quantify the impact of operator randomness and reveal the associated convergence rates as this randomness vanishes. Finally, we validate our theoretical findings through illustrative numerical experiments that confirm the predicted convergence behavior.

BBC Verify has been tracking the Marinera for weeks. Housing, Europe ties, economy... what Canadians are hopeful for in 2026 The BBC spoke to people in Toronto and Montreal to find out what they're optimistic about heading into the new year. The powerful storm system brought blizzard conditions to areas of the Midwest and East Coast causing some travel delays. Governor Gavin Newsom has declared a state of emergency for parts of California, including Los Angeles, San Bernardino and San Diego. The White Settlement Police Department is searching for two suspects.

Website of Claude seen in an iPhone screen on 21 May 2023. Website of Claude seen in an iPhone screen on 21 May 2023. Anthropic is planning a $10bn fundraise that would value the Claude chatbot maker at $350bn, according to multiple reports published on Wednesday. The new valuation represents an increase of nearly double from about four months ago, per CNBC, which reported that the company had signed a term sheet that stipulated the $350bn figure. The round could close within weeks, although the size and terms could change.

Grok Is Generating Sexual Content Far More Graphic Than What's on X A WIRED review of outputs hosted on Grok's official website shows it's being used to create violent sexual images and videos, as well as content that includes apparent minors. Elon Musk's Grok chatbot has drawn outrage and calls for investigation after being used to flood X with "undressed" images of women and sexualized images of what appear to be minors. However, that's not the only way people have been using the AI to generate sexualized images. Grok's website and app, which are are separate from X, include sophisticated video generation that is not available on X and is being used to produce extremely graphic, sometimes violent, sexual imagery of adults that is vastly more explicit than images created by Grok on X. It may also have been used to create sexualized videos of apparent minors.

NASA astronaut Nichole Ayers spotted the summer storm while aboard the International Space Station. Breakthroughs, discoveries, and DIY tips sent every weekday. Lightning is one of Earth's most impressive phenomena. The sudden discharges of superheated plasma occur even in seemingly sunny conditions, rip apart air molecules, and can easily span hundreds of miles . But while there is still a lot to learn about lightning from our perspective here on Earth, there's also much to glean by observing it from high above.

Be cautious if you opt to use it. OpenAI is launching a new facet for its AI chatbot called ChatGPT Health . This new feature will allow users to connect medical records and wellness apps to ChatGPT in order to get more tailored responses to queries about their health. The company noted that there will be additional privacy safeguards for this separate space within ChatGPT, and said that it will not use conversations held in Health for training foundational models. ChatGPT Health is currently in a testing stage, and there are some regional restrictions on which health apps can be connected to the AI company's platform.