The first part of the proof follows the policy gradient theorem. This concludes the proof of Theorem 1.Theorem 2 Since the second-order derivative formulation as stated in Theorem 1 and Theorem 2 are both unbiased derivative estimate. The randomly initiated neural network uses ReLU layers as nonlinearity followed by a linear layer in the end. In order to train the optimal policy, in the gridworld example, we use tabular value-iteration algorithm to learn the Q value of each state action pair. So the number of available actions is 5, while the number of available states is 5 5 = 25 .

The first part of the proof follows the policy gradient theorem. This concludes the proof of Theorem 1.Theorem 2 Since the second-order derivative formulation as stated in Theorem 1 and Theorem 2 are both unbiased derivative estimate. The randomly initiated neural network uses ReLU layers as nonlinearity followed by a linear layer in the end. In order to train the optimal policy, in the gridworld example, we use tabular value-iteration algorithm to learn the Q value of each state action pair. So the number of available actions is 5, while the number of available states is 5 5 = 25 .

Human social behaviour is governed by complex interactions shaped by uncertainty, causality, and group dynamics. We propose Causal Spherical Hypergraph Networks (Causal-SphHN), a principled framework for socially grounded prediction that jointly models higher-order structure, directional influence, and epistemic uncertainty. Our method represents individuals as hyperspherical embeddings and group contexts as hyperedges, capturing semantic and relational geometry. Uncertainty is quantified via Shannon entropy over von Mises-Fisher distributions, while temporal causal dependencies are identified using Granger-informed subgraphs. Information is propagated through an angular message-passing mechanism that respects belief dispersion and directional semantics. Experiments on SNARE (offline networks), PHEME (online discourse), and AMIGOS (multimodal affect) show that Causal-SphHN improves predictive accuracy, robustness, and calibration over strong baselines. Moreover, it enables interpretable analysis of influence patterns and social ambiguity. This work contributes a unified causal-geometric approach for learning under uncertainty in dynamic social environments.

In this work, we consider the task of resolving object referents when given a comparative language description. We present a Multi-view Approach to Grounding in Context (MAGiC) that leverages transformers to pragmatically reason over both objects given multiple image views and a language description. In contrast to past efforts that attempt to connect vision and language for this task without fully considering the resulting referential context, MAGiC makes use of the comparative information by jointly reasoning over multiple views of both object referent candidates and the referring language expression. We present an analysis demonstrating that comparative reasoning contributes to SOTA performance on the SNARE object reference task.

Lily Xu is a PhD student at Harvard University, applying machine learning and game theory to wildlife conservation. She is particularly focused on the prevention of illegal wildlife poaching, and she told us about this interesting, and critically important, area of research. Green security is the challenge of environmental conservation under some unknown threat. The three domains that we focus on are illegal wildlife poaching, illegal logging and illegal fishing. Across all of these settings we have an environmental challenge, which is to preserve our natural ecosystems.

Artificial Intelligence (AI) for social good is a field of work which, broadly speaking, uses AI to make the world a better place. I had a chance to interview two leaders in the field, Dr. Bryan Wilder, who recently received his Ph.D. from Harvard (and will be joining the faculty at Carnegie Mellon next fall) and current Harvard Ph.D. student, Lily Xu. Both Bryan and Lily have been advised by Dr. Tambe, Gordon McKay Professor of Computer Science and Director of the Center for Research in Computation and Society (CRCS) at Harvard University and Director of AI for Social Good at Google Research India. While Bryan and Lily are both working at the intersection of AI and social good, they arrived at this junction via different paths. Bryan was studying computer science and looking for a field to apply his knowledge; his search led him to public health.

Seemingly simple natural language requests to a robot are generally underspecified, for example "Can you bring me the wireless mouse?" When viewing mice on the shelf, the number of buttons or presence of a wire may not be visible from certain angles or positions. Flat images of candidate mice may not provide the discriminative information needed for "wireless". The world, and objects in it, are not flat images but complex 3D shapes. If a human requests an object based on any of its basic properties, such as color, shape, or texture, robots should perform the necessary exploration to accomplish the task. In particular, while substantial effort and progress has been made on understanding explicitly visual attributes like color and category, comparatively little progress has been made on understanding language about shapes and contours. In this work, we introduce a novel reasoning task that targets both visual and non-visual language about 3D objects. Our new benchmark, ShapeNet Annotated with Referring Expressions (SNARE), requires a model to choose which of two objects is being referenced by a natural language description. We introduce several CLIP-based models for distinguishing objects and demonstrate that while recent advances in jointly modeling vision and language are useful for robotic language understanding, it is still the case that these models are weaker at understanding the 3D nature of objects -- properties which play a key role in manipulation. In particular, we find that adding view estimation to language grounding models improves accuracy on both SNARE and when identifying objects referred to in language on a robot platform.

The illegal animal trade is a global scourge but a lucrative one, worth $8 to 10 billion annually, according to the United Nations Office on Drugs and Crime (UNODC) -- trailing only human, drug and weapons trafficking in value. With so much money to be made, conservationists and wildlife rangers face overwhelming odds against well-organized poaching operations fueled by incessant demand for illicit animal products. The results of this protracted conflict have been nothing short of devastating for the species caught in the middle. At the start of the 20th century, more than 100,000 tigers are estimated to have roamed throughout Southeast Asia. Today, due to a combination of habitat loss and aggressive poaching, fewer than 4,000 currently remain in the wild.

This article is part of New York's Future Issue, a collection of predictions about the near future as seen through the recent past. Click here to read more. On June 21, 2017, electronic musician Holly Herndon and her husband, writer/philosopher/teacher Mat Dryhurst, welcomed a new addition to their family. "She's an inhuman child," Herndon tells me one afternoon, while seated in the offices of her record label, 4AD. Spawn is nascent machine intelligence, or AI. There's artificial intelligence being deployed for self-driving 18-wheelers, Netflix user-preference predictors, customer service preferences, handwriting recognition, and cyber-security to fight hackers using AI to create malware.

There are two kinds of elephants in Africa: the forest elephant and the savanna elephant (above), photographed this past spring in Liwonde National Park in Malawi. The Great Elephant Census found that Africa's savanna elephant population decreased by about a third in the seven years between 2007 and 2014. There are two kinds of elephants in Africa: the forest elephant and the savanna elephant (above), photographed this past spring in Liwonde National Park in Malawi. The Great Elephant Census found that Africa's savanna elephant population decreased by about a third in the seven years between 2007 and 2014. A few years ago, Paul Allen, the co-founder of Microsoft, published the results of something called the Great Elephant Census, which counted all the savanna elephants in Africa. What it found rocked the conservation world: In the seven years between 2007 and 2014, Africa's savanna elephant population decreased by about a third and was on track to disappear completely from some African countries in as few as 10 years. To reverse that trend, researchers landed on a technology that is rewriting the rules for everything from our household appliances to our cars: artificial intelligence. AI's ability to find patterns in enormous volumes of information is demystifying not just elephant behavior but human behavior -- specifically poacher behavior -- too.