This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.

This work was done when Mingyu was at MIT.

Finally,thepredictedoutput function is decoded by the inverse PhCA, given any query locations.

General physical scene understanding requires more than simply localizing and recognizing objects -- it requires knowledge that objects can have different latent properties (e.g., mass or elasticity), and that those properties affect the outcome of physical events. While there has been great progress in physical and video prediction models in recent years, benchmarks to test their performance typically do not require an understanding that objects have individual physical properties, or at best test only those properties that are directly observable (e.g., size or color). This work proposes a novel dataset and benchmark, termed Physion++, that rigorously evaluates visual physical prediction in artificial systems under circumstances where those predictions rely on accurate estimates of the latent physical properties of objects in the scene. Specifically, we test scenarios where accurate prediction relies on estimates of properties such as mass, friction, elasticity, and deformability, and where the values of those properties can only be inferred by observing how objects move and interact with other objects or fluids. We evaluate the performance of a number of state-of-the-art prediction models that span a variety of levels of learning vs. built-in knowledge, and compare that performance to a set of human predictions. We find that models that have been trained using standard regimes and datasets do not spontaneously learn to make inferences about latent properties, but also that models that encode objectness and physical states tend to make better predictions. However, there is still a huge gap between all models and human performance, and all models' predictions correlate poorly with those made by humans, suggesting that no state-of-the-art model is learning to make physical predictions in a human-like way. These results show that current deep learning models that succeed in some settings nevertheless fail to achieve human-level physical prediction in other cases, especially those where latent property inference is required.

This paper proposes DeepRule, an integrated framework for automated business rule generation in retail assortment and pricing optimization. Addressing the systematic misalignment between existing theoretical models and real-world economic complexities, we identify three critical gaps: (1) data modality mismatch where unstructured textual sources (e.g. negotiation records, approval documents) impede accurate customer profiling; (2) dynamic feature entanglement challenges in modeling nonlinear price elasticity and time-varying attributes; (3) operational infeasibility caused by multi-tier business constraints. Our framework introduces a tri-level architecture for above challenges. We design a hybrid knowledge fusion engine employing large language models (LLMs) for deep semantic parsing of unstructured text, transforming distributor agreements and sales assessments into structured features while integrating managerial expertise. Then a game-theoretic constrained optimization mechanism is employed to dynamically reconcile supply chain interests through bilateral utility functions, encoding manufacturer-distributor profit redistribution as endogenous objectives under hierarchical constraints. Finally an interpretable decision distillation interface leveraging LLM-guided symbolic regression to find and optimize pricing strategies and auditable business rules embeds economic priors (e.g. non-negative elasticity) as hard constraints during mathematical expression search. We validate the framework in real retail environments achieving higher profits versus systematic B2C baselines while ensuring operational feasibility. This establishes a close-loop pipeline unifying unstructured knowledge injection, multi-agent optimization, and interpretable strategy synthesis for real economic intelligence.

We derive the first closed-form condition under which artificial intelligence (AI) capital profits could sustainably finance a universal basic income (UBI) without relying on new taxation or the creation of new jobs. In a Solow-Zeira task-automation economy with a CES aggregator $σ< 1$, we introduce an AI capability parameter that scales the productivity of automatable tasks and obtain a tractable expression for the AI capability threshold -- the minimum productivity of AI relative to pre-AI automation required for a balanced transfer. Using current U.S. economic parameters, we find that even in the conservative scenario where no new tasks or jobs emerge, AI systems would only need to reach only 5-7 times today's automation productivity to fund an 11%-of-GDP UBI. Our analysis also reveals some specific policy levers: raising public revenue share (e.g. profit taxation) of AI capital from the current 15% to about 33% halves the required AI capability threshold to attain UBI to 3 times existing automation productivity, but gains diminish beyond 50% public revenue share, especially if regulatory costs increase. Market structure also strongly affects outcomes: monopolistic or concentrated oligopolistic markets reduce the threshold by increasing economic rents, whereas heightened competition significantly raises it. These results therefore offer a rigorous benchmark for assessing when advancing AI capabilities might sustainably finance social transfers in an increasingly automated economy.

Given demand models of multiple products, the role of optimization is to find the best price strategy.

Empirical scaling laws describe how test loss and other performance metrics depend on model size, dataset size, and compute. While such laws are consistent within specific regimes, apparently distinct scaling behaviors have been reported for related settings such as model compression. Motivated by recent progress in spectral analyses of neural representations, this paper develops a \emph{generalized spectral framework} that unifies learning dynamics and compression phenomena under a common functional ansatz. We generalize the spectral evolution function from the linear kernel form $g(λt)=λt$ to an asymptotically polynomial function $g(λ,t;β)$, characterized by an effective spectral--temporal elasticity $ρ(β)$. This framework recovers existing lazy and feature-learning theories as special cases and yields an invariant relation between learning and compression

Spin coating polymer thin films to achieve specific mechanical properties is inherently a multi-objective optimization problem. We present a framework that integrates an active Pareto front learning algorithm (PyePAL) with visualization and explainable AI techniques to optimize processing parameters. PyePAL uses Gaussian process models to predict objective values (hardness and elasticity) from the design variables (spin speed, dilution, and polymer mixture), guiding the adaptive selection of samples toward promising regions of the design space. To enable interpretable insights into the high-dimensional design space, we utilize UMAP (Uniform Manifold Approximation and Projection) for two-dimensional visualization of the Pareto front exploration. Additionally, we incorporate fuzzy linguistic summaries, which translate the learned relationships between process parameters and performance objectives into linguistic statements, thus enhancing the explainability and understanding of the optimization results. Experimental results demonstrate that our method efficiently identifies promising polymer designs, while the visual and linguistic explanations facilitate expert-driven analysis and knowledge discovery.