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We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only access to a black box simulator from which short bursts of simulation can be obtained, we design an algorithm that outputs an estimate of the invariant manifold, a process of the effective stochastic dynamics on it, which has averaged out the fast modes, and a simulator thereof. This simulator is efficient in that it exploits of the low dimension of the invariant manifold, and takes time steps of size dependent on the regularity of the effective process, and therefore typically much larger than that of the original simulator, which had to resolve the fast modes. The algorithm and the estimation can be performed on-the-fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.

We show that the use of large language models (LLMs) is prevalent among crowd workers, and that targeted mitigation strategies can significantly reduce, but not eliminate, LLM use. On a text summarization task where workers were not directed in any way regarding their LLM use, the estimated prevalence of LLM use was around 30%, but was reduced by about half by asking workers to not use LLMs and by raising the cost of using them, e.g., by disabling copy-pasting. Secondary analyses give further insight into LLM use and its prevention: LLM use yields high-quality but homogeneous responses, which may harm research concerned with human (rather than model) behavior and degrade future models trained with crowdsourced data. At the same time, preventing LLM use may be at odds with obtaining high-quality responses; e.g., when requesting workers not to use LLMs, summaries contained fewer keywords carrying essential information. Our estimates will likely change as LLMs increase in popularity or capabilities, and as norms around their usage change. Yet, understanding the co-evolution of LLM-based tools and users is key to maintaining the validity of research done using crowdsourcing, and we provide a critical baseline before widespread adoption ensues.

Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adjacency matrix. The neural network is equipped with a novel projection layer that ensures the output matrices are sparse and satisfy a recently developed characterization of acyclicity. We devise a scalable computational framework for learning contextual DAGs and provide a convergence guarantee and an analytical gradient for backpropagating through the projection layer. Our experiments suggest that the new approach can recover the true context-specific graph where existing approaches fail.

We propose task-adaptive tokenization as a way to adapt the generation pipeline to the specifics of a downstream task and enhance long-form generation in mental health. Inspired by insights from cognitive science, our task-adaptive tokenizer samples variable segmentations from multiple outcomes, with sampling probabilities optimized based on task-specific data. We introduce a strategy for building a specialized vocabulary and introduce a vocabulary merging protocol that allows for the integration of task-specific tokens into the pre-trained model's tokenization step. Through extensive experiments on psychological question-answering tasks in both Chinese and English, we find that our task-adaptive tokenization approach brings a significant improvement in generation performance while using up to 60% fewer tokens. Preliminary experiments point to promising results when using our tokenization approach with very large language models.

In this series of works we establish homogenized lattice Boltzmann methods (HLBM) for the simulation of fluid flow through porous media. Our contributions in part I are twofold. First, we assemble the targeted partial differential equation system by formally unifying the governing equations for nonstationary fluid flow in porous media. To this end, a matrix of regularly arranged obstacles of equal size is placed into the domain to model fluid flow through structures of different porosities that is governed by the incompressible nonstationary Navier--Stokes equations. Depending on the ratio of geometric parameters in the matrix arrangement, several cases of homogenized equations are obtained. We review the existing methods to homogenize the nonstationary Navier--Stokes equations for specific porosities and interpret connections between the resulting model equations from the perspective of applicability. Consequently, the homogenized Navier--Stokes equations are formulated as targeted partial differential equations which jointly incorporate the derived aspects. Second, we propose a kinetic model, named homogenized Bhatnagar--Gross--Krook Boltzmann equation, which approximates the homogenized nonstationary Navier--Stokes equations. We formally prove that the zeroth and first order moments of the kinetic model provide solutions to the mass and momentum balance variables of the macrocopic model up to specific orders in the scaling parameter. Based on the present contributions, in the sequel (part II) the homogenized Navier--Stokes equations are consistently approximated by deriving a limit consistent HLBM discretization of the homogenized Bhatnagar--Gross--Krook Boltzmann equation.

We introduce Multi-view Ancestral Sampling (MAS), a method for generating consistent multi-view 2D samples of a motion sequence, enabling the creation of its 3D counterpart. MAS leverages a diffusion model trained solely on 2D data, opening opportunities to exciting and diverse fields of motion previously under-explored as 3D data is scarce and hard to collect. MAS works by simultaneously denoising multiple 2D motion sequences representing the same motion from different angles. Our consistency block ensures consistency across all views at each diffusion step by combining the individual generations into a unified 3D sequence, and projecting it back to the original views for the next iteration. We demonstrate MAS on 2D pose data acquired from videos depicting professional basketball maneuvers, rhythmic gymnastic performances featuring a ball apparatus, and horse obstacle course races. In each of these domains, 3D motion capture is arduous, and yet, MAS generates diverse and realistic 3D sequences without textual conditioning. As we demonstrate, our ancestral sampling-based approach offers a more natural integration with the diffusion framework compared to popular denoising optimization-based approaches, and avoids common issues such as out-of-domain sampling, lack of details and mode-collapse. //guytevet.github.io/mas-page/

To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best among alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programmed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it! Despite their simplicity, mathematical tractability made models like the voter model (VM) and the local majority rule model (MR) useful to describe in simple terms such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbours in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, to reduce the cognitive load. Our analysis in grounded on the introduction of a model that generalises the two existing VM and MR models, showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show that another speed-accuracy trade-off is regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy

In this work a general semi-parametric multivariate model where the first two conditional moments are assumed to be multivariate time series is introduced. The focus of the estimation is the conditional mean parameter vector for discrete-valued distributions. Quasi-Maximum Likelihood Estimators (QMLEs) based on the linear exponential family are typically employed for such estimation problems when the true multivariate conditional probability distribution is unknown or too complex. Although QMLEs provide consistent estimates they may be inefficient. In this paper novel two-stage Multivariate Weighted Least Square Estimators (MWLSEs) are introduced which enjoy the same consistency property as the QMLEs but can provide improved efficiency with suitable choice of the covariance matrix of the observations. The proposed method allows for a more accurate estimation of model parameters in particular for count and categorical data when maximum likelihood estimation is unfeasible. Moreover, consistency and asymptotic normality of MWLSEs are derived. The estimation performance of QMLEs and MWLSEs is compared through simulation experiments and a real data application, showing superior accuracy of the proposed methodology.

Neural network models become increasingly popular as dynamic modeling tools in the control community. They have many appealing features including nonlinear structures, being able to approximate any functions. While most researchers hold optimistic attitudes towards such models, this paper questions the capability of (deep) neural networks for the modeling of dynamic systems using input-output data. For the identification of linear time-invariant (LTI) dynamic systems, two representative neural network models, Long Short-Term Memory (LSTM) and Cascade Foward Neural Network (CFNN) are compared to the standard Prediction Error Method (PEM) of system identification. In the comparison, four essential aspects of system identification are considered, then several possible defects and neglected issues of neural network based modeling are pointed out. Detailed simulation studies are performed to verify these defects: for the LTI system, both LSTM and CFNN fail to deliver consistent models even in noise-free cases; and they give worse results than PEM in noisy cases.

The coordination of autonomous vehicles is an open field that is addressed by different researches comprising many different techniques. In this paper we focus on decentralized approaches able to provide adaptability to different infrastructural and traffic conditions. We formalize an Emergent Behavior Approach that, as per our knowledge, has never been performed for this purpose, and a Decentralized Auction approach. We compare them against existing centralized negotiation approaches based on auctions and we determine under which conditions each approach is preferable to the others.