Given a text description, we immediately imagine an overall visual impression using this prior and, based on this, we draw a picture by progressively adding more andmore details.

Predicting the most likely route from asource location to adestination is acore functionality inmapping services. Although theproblem hasbeenstudied inthe literature, two key limitations remain to be addressed.

The Math on AI Agents Doesn't Add Up A research paper suggests AI agents are mathematically doomed to fail. The big AI companies promised us that 2025 would be "the year of the AI agents." It turned out to be the year of AI agents, and kicking the can for that transformational moment to 2026 or maybe later. But what if the answer to the question "When will our lives be fully automated by generative AI robots that perform our tasks for us and basically run the world?" is, like that New Yorker cartoon, "How about never?" That was basically the message of a paper published without much fanfare some months ago, smack in the middle of the overhyped year of "agentic AI." Entitled " Hallucination Stations: On Some Basic Limitations of Transformer-Based Language Models," it purports to mathematically show that "LLMs are incapable of carrying out computational and agentic tasks beyond a certain complexity."

How Do You Teach an AI to Be Good? A person holds a smartphone displaying the logo of "Claude," an AI language model by Anthropic A person holds a smartphone displaying the logo of "Claude," an AI language model by Anthropic Cheng Xin/Getty Images Getting AI models to behave used to be a thorny mathematical problem. These days, it looks a bit more like raising a child. That, at least, is according to Amanda Askell --a trained philosopher whose unique role within Anthropic is crafting the personality of Claude, the AI firm's rival to ChatGPT. "Imagine you suddenly realize that your six-year-old child is a kind of genius," Askell says.

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. Previous approaches have relied on multiscale generation to considerably accelerate SGMs. We explain how this acceleration results from an implicit factorization of the data distribution into a product of conditional probabilities of wavelet coefficients across scales. The resulting Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales, and its time complexity therefore grows linearly with the image size. This is proved mathematically for Gaussian distributions, and shown numerically for physical processes at phase transition and natural image datasets.

Machine learning algorithms are increasingly deployed in critical domains such as finance, healthcare, and criminal justice [1]. The increasing popularity of algorithmic decision-making has stimulated interest in algorithmic fairness within the academic community. Researchers have introduced various fairness definitions that quantify disparities between privileged and protected groups, use causal inference to determine the impact of race on model predictions, and that test calibration of probability predictions from the model. Existing literature does not provide a way in which to assess whether observed disparities between groups are statistically significant or merely due to chance. This paper introduces a rigorous framework for testing the statistical significance of fairness violations by leveraging k-fold cross-validation [2] to generate sampling distributions of fairness metrics. This paper introduces statistical tests that can be used to identify statistically significant violations of fairness metrics based on disparities between predicted and actual outcomes, model calibration, and causal inference techniques [1]. We demonstrate this approach by testing recidivism forecasting algorithms trained on data from the National Institute of Justice. Our findings reveal that machine learning algorithms used for recidivism forecasting exhibit statistically significant bias against Black individuals under several fairness definitions, while also exhibiting no bias or bias against White individuals under other definitions. The results from this paper underscore the importance of rigorous and robust statistical testing while evaluating algorithmic decision-making systems.

Modern vision-language models (VLMs) deliver impressive predictive accuracy yet offer little insight into 'why' a decision is reached, frequently hallucinating facts, particularly when encountering out-of-distribution data. Neurosymbolic frameworks address this by pairing black-box perception with interpretable symbolic reasoning, but current methods extract their symbols solely from task labels, leaving them weakly grounded in the underlying visual data. In this paper, we introduce a multi-agent system - Concept-RuleNet that reinstates visual grounding while retaining transparent reasoning. Specifically, a multimodal concept generator first mines discriminative visual concepts directly from a representative subset of training images. Next, these visual concepts are utilized to condition symbol discovery, anchoring the generations in real image statistics and mitigating label bias. Subsequently, symbols are composed into executable first-order rules by a large language model reasoner agent - yielding interpretable neurosymbolic rules. Finally, during inference, a vision verifier agent quantifies the degree of presence of each symbol and triggers rule execution in tandem with outputs of black-box neural models, predictions with explicit reasoning pathways. Experiments on five benchmarks, including two challenging medical-imaging tasks and three underrepresented natural-image datasets, show that our system augments state-of-the-art neurosymbolic baselines by an average of 5% while also reducing the occurrence of hallucinated symbols in rules by up to 50%.

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. Previous approaches have relied on multiscale generation to considerably accelerate SGMs. We explain how this acceleration results from an implicit factorization of the data distribution into a product of conditional probabilities of wavelet coefficients across scales.

This paper delves into recent advancements in Quantum Reinforcement Learning (QRL), particularly focusing on non-commutative environments, which represent uncharted territory in this field. Our research endeavors to redefine the boundaries of decision-making by introducing formulations and strategies that harness the inherent properties of quantum systems. At the core of our investigation characterization of the agent's state space within a Hilbert space ($\mathcal{H}$). Here, quantum states emerge as complex superpositions of classical state introducing non-commutative quantum actions governed by unitary operators, necessitating a reimagining of state transitions. Complementing this framework is a refined reward function, rooted in quantum mechanics as a Hermitian operator on $\mathcal{H}$. This reward function serves as the foundation for the agent's decision-making process. By leveraging the quantum Bellman equation, we establish a methodology for maximizing expected cumulative reward over an infinite horizon, considering the entangled dynamics of quantum systems. We also connect the Quantum Bellman Equation to the Degree of Non Commutativity of the Environment, evident in Pure Algebra. We design a quantum advantage function. This ingeniously designed function exploits latent quantum parallelism inherent in the system, enhancing the agent's decision-making capabilities and paving the way for exploration of quantum advantage in uncharted territories. Furthermore, we address the significant challenge of quantum exploration directly, recognizing the limitations of traditional strategies in this complex environment.