Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In this context, full order models (FOMs), such as those relying on the finite element method, can reach high levels of accuracy, however often yielding intensive simulations to run. For this reason, surrogate models are developed to replace computationally expensive solvers with more efficient ones, which can strike favorable trade-offs between accuracy and efficiency. This work explores the potential usage of graph neural networks (GNNs) for the simulation of time-dependent PDEs in the presence of geometrical variability. In particular, we propose a systematic strategy to build surrogate models based on a data-driven time-stepping scheme where a GNN architecture is used to efficiently evolve the system. With respect to the majority of surrogate models, the proposed approach stands out for its ability of tackling problems with parameter dependent spatial domains, while simultaneously generalizing to different geometries and mesh resolutions. We assess the effectiveness of the proposed approach through a series of numerical experiments, involving both two- and three-dimensional problems, showing that GNNs can provide a valid alternative to traditional surrogate models in terms of computational efficiency and generalization to new scenarios. We also assess, from a numerical standpoint, the importance of using GNNs, rather than classical dense deep neural networks, for the proposed framework.
We develop randomization-based tests for heterogeneous treatment effects in the presence of network interference. Leveraging the exposure mapping framework, we study a broad class of null hypotheses that represent various forms of constant treatment effects in networked populations. These null hypotheses, unlike the classical Fisher sharp null, are not sharp due to unknown parameters and multiple potential outcomes. Existing conditional randomization procedures either fail to control size or suffer from low statistical power in this setting. We propose a testing procedure that constructs a data-dependent focal assignment set and permits variation in focal units across focal assignments. These features complicate both estimation and inference, necessitating new technical developments. We establish the asymptotic validity of the proposed procedure under general conditions on the test statistic and characterize the asymptotic size distortion in terms of observable quantities. The procedure is applied to experimental network data and evaluated via Monte Carlo simulations.
The task of discerning between generated and natural texts is increasingly challenging. In this context, watermarking emerges as a promising technique for ascribing generated text to a specific model. It alters the sampling generation process so as to leave an invisible trace in the generated output, facilitating later detection. This research consolidates watermarks for large language models based on three theoretical and empirical considerations. First, we introduce new statistical tests that offer robust theoretical guarantees which remain valid even at low false-positive rates (less than 10$^{\text{-6}}$). Second, we compare the effectiveness of watermarks using classical benchmarks in the field of natural language processing, gaining insights into their real-world applicability. Third, we develop advanced detection schemes for scenarios where access to the LLM is available, as well as multi-bit watermarking.
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a definition of oracle computations based on meta-level functions rather than object-level models of computation, relying on the fact that in constructive systems such as CIC all definable functions are computable by construction. Such an approach lends itself well to machine-checked proofs, which we carry out in Coq. There is a tension in finding a good synthetic rendering of the higher-order notion of oracle computability. On the one hand, it has to be informative enough to prove central results, ensuring that all notions are faithfully captured. On the other hand, it has to be restricted enough to benefit from axioms for synthetic computability, which usually concern first-order objects. Drawing inspiration from a definition by Andrej Bauer based on continuous functions in the effective topos, we use a notion of sequential continuity to characterise valid oracle computations. As main technical results, we show that Turing reducibility forms an upper semilattice, transports decidability, and is strictly more expressive than truth-table reducibility, and prove that whenever both a predicate $p$ and its complement are semi-decidable relative to an oracle $q$, then $p$ Turing-reduces to $q$.
Head-related transfer function (HRTF) capture the information that a person uses to localize sound sources in space, and thus is crucial for creating personalized virtual acoustic experiences. However, practical HRTF measurement systems may only measure a person's HRTFs sparsely, and this necessitates HRTF upsampling. This paper proposes a physics-informed neural network (PINN) method for HRTF upsampling. The PINN exploits the Helmholtz equation, the governing equation of acoustic wave propagation, for regularizing the upsampling process. This helps the generation of physically valid upsamplings which generalize beyond the measured HRTF. Furthermore, the size (width and depth) of the PINN is set according to the Helmholtz equation and its solutions, the spherical harmonics (SHs). This makes the PINN have an appropriate level of expressive power and thus does not suffer from the over-fitting problem. Since the PINN is designed independent of any specific HRTF dataset, it offers more generalizability compared to pure data-driven methods. Numerical experiments confirm the better performance of the PINN method for HRTF upsampling in both interpolation and extrapolation scenarios in comparison with the SH method and the HRTF field method.
Deep learning in computational biochemistry has traditionally focused on molecular graphs neural representations; however, recent advances in language models highlight how much scientific knowledge is encoded in text. To bridge these two modalities, we investigate how molecular property information can be transferred from natural language to graph representations. We study property prediction performance gains after using contrastive learning to align neural graph representations with representations of textual descriptions of their characteristics. We implement neural relevance scoring strategies to improve text retrieval, introduce a novel chemically-valid molecular graph augmentation strategy inspired by organic reactions, and demonstrate improved performance on downstream MoleculeNet property classification tasks. We achieve a +4.26% AUROC gain versus models pre-trained on the graph modality alone, and a +1.54% gain compared to recently proposed molecular graph/text contrastively trained MoMu model (Su et al. 2022).
Financial analysis is an important tool for evaluating company performance. Practitioners work to answer financial questions to make profitable investment decisions, and use advanced quantitative analyses to do so. As a result, Financial Question Answering (QA) is a question answering task that requires deep reasoning about numbers. Furthermore, it is unknown how well pre-trained language models can reason in the financial domain. The current state-of-the-art requires a retriever to collect relevant facts about the financial question from the text and a generator to produce a valid financial program and a final answer. However, recently large language models like GPT-3 have achieved state-of-the-art performance on wide variety of tasks with just a few shot examples. We run several experiments with GPT-3 and find that a separate retrieval model and logic engine continue to be essential components to achieving SOTA performance in this task, particularly due to the precise nature of financial questions and the complex information stored in financial documents. With this understanding, our refined prompt-engineering approach on GPT-3 achieves near SOTA accuracy without any fine-tuning.
Debiased machine learning estimators for nonparametric inference of smooth functionals of the data-generating distribution can suffer from excessive variability and instability. For this reason, practitioners may resort to simpler models based on parametric or semiparametric assumptions. However, such simplifying assumptions may fail to hold, and estimates may then be biased due to model misspecification. To address this problem, we propose Adaptive Debiased Machine Learning (ADML), a nonparametric framework that combines data-driven model selection and debiased machine learning techniques to construct asymptotically linear, adaptive, and superefficient estimators for pathwise differentiable functionals. By learning model structure directly from data, ADML avoids the bias introduced by model misspecification and remains free from the restrictions of parametric and semiparametric models. While they may exhibit irregular behavior for the target parameter in a nonparametric statistical model, we demonstrate that ADML estimators provides regular and locally uniformly valid inference for a projection-based oracle parameter. Importantly, this oracle parameter agrees with the original target parameter for distributions within an unknown but correctly specified oracle statistical submodel that is learned from the data. This finding implies that there is no penalty, in a local asymptotic sense, for conducting data-driven model selection compared to having prior knowledge of the oracle submodel and oracle parameter. To demonstrate the practical applicability of our theory, we provide a broad class of ADML estimators for estimating the average treatment effect in adaptive partially linear regression models.
Misinformation on YouTube is a significant concern, necessitating robust detection strategies. In this paper, we introduce a novel methodology for video classification, focusing on the veracity of the content. We convert the conventional video classification task into a text classification task by leveraging the textual content derived from the video transcripts. We employ advanced machine learning techniques like transfer learning to solve the classification challenge. Our approach incorporates two forms of transfer learning: (a) fine-tuning base transformer models such as BERT, RoBERTa, and ELECTRA, and (b) few-shot learning using sentence-transformers MPNet and RoBERTa-large. We apply the trained models to three datasets: (a) YouTube Vaccine-misinformation related videos, (b) YouTube Pseudoscience videos, and (c) Fake-News dataset (a collection of articles). Including the Fake-News dataset extended the evaluation of our approach beyond YouTube videos. Using these datasets, we evaluated the models distinguishing valid information from misinformation. The fine-tuned models yielded Matthews Correlation Coefficient>0.81, accuracy>0.90, and F1 score>0.90 in two of three datasets. Interestingly, the few-shot models outperformed the fine-tuned ones by 20% in both Accuracy and F1 score for the YouTube Pseudoscience dataset, highlighting the potential utility of this approach -- especially in the context of limited training data.
Economic interactions often occur in networks where heterogeneous agents (such as workers or firms) sort and produce. However, most existing estimation approaches either require the network to be dense, which is at odds with many empirical networks, or they require restricting the form of heterogeneity and the network formation process. We show how the functional differencing approach introduced by Bonhomme (2012) in the context of panel data, can be applied in network settings to derive moment restrictions on model parameters and average effects. Those restrictions are valid irrespective of the form of heterogeneity, and they hold in both dense and sparse networks. We illustrate the analysis with linear and nonlinear models of matched employer-employee data, in the spirit of the model introduced by Abowd, Kramarz, and Margolis (1999).
Language models can be prompted to reason through problems in a manner that significantly improves performance. However, \textit{why} such prompting improves performance is unclear. Recent work showed that using logically \textit{invalid} Chain-of-Thought (CoT) prompting improves performance almost as much as logically \textit{valid} CoT prompting, and that editing CoT prompts to replace problem-specific information with abstract information or out-of-distribution information typically doesn't harm performance. Critics have responded that these findings are based on too few and too easily solved tasks to draw meaningful conclusions. To resolve this dispute, we test whether logically invalid CoT prompts offer the same level of performance gains as logically valid prompts on the hardest tasks in the BIG-Bench benchmark, termed BIG-Bench Hard (BBH). We find that the logically \textit{invalid} reasoning prompts do indeed achieve similar performance gains on BBH tasks as logically valid reasoning prompts. We also discover that some CoT prompts used by previous works contain logical errors. This suggests that covariates beyond logically valid reasoning are responsible for performance improvements.
We investigate the ability of individuals to visually validate statistical models in terms of their fit to the data. While visual model estimation has been studied extensively, visual model validation remains under-investigated. It is unknown how well people are able to visually validate models, and how their performance compares to visual and computational estimation. As a starting point, we conducted a study across two populations (crowdsourced and volunteers). Participants had to both visually estimate (i.e, draw) and visually validate (i.e., accept or reject) the frequently studied model of averages. Across both populations, the level of accuracy of the models that were considered valid was lower than the accuracy of the estimated models. We find that participants' validation and estimation were unbiased. Moreover, their natural critical point between accepting and rejecting a given mean value is close to the boundary of its 95% confidence interval, indicating that the visually perceived confidence interval corresponds to a common statistical standard. Our work contributes to the understanding of visual model validation and opens new research opportunities.
Heretofore, learning the directed acyclic graphs (DAGs) that encode the cause-effect relationships embedded in observational data is a computationally challenging problem. A recent trend of studies has shown that it is possible to recover the DAGs with polynomial time complexity under the equal variances assumption. However, this prohibits the heteroscedasticity of the noise, which allows for more flexible modeling capabilities, but at the same time is substantially more challenging to handle. In this study, we tackle the heteroscedastic causal structure learning problem under Gaussian noises. By exploiting the normality of the causal mechanisms, we can recover a valid causal ordering, which can uniquely identify the causal DAG using a series of conditional independence tests. The result is HOST (Heteroscedastic causal STructure learning), a simple yet effective causal structure learning algorithm that scales polynomially in both sample size and dimensionality. In addition, via extensive empirical evaluations on a wide range of both controlled and real datasets, we show that the proposed HOST method is competitive with state-of-the-art approaches in both the causal order learning and structure learning problems.
This paper studies the possibilities made open by the use of Lazy Clause Generation (LCG) based approaches to Constraint Programming (CP) for tackling sequential classical planning. We propose a novel CP model based on seminal ideas on so-called lifted causal encodings for planning as satisfiability, that does not require grounding, as choosing groundings for functions and action schemas becomes an integral part of the problem of designing valid plans. This encoding does not require encoding frame axioms, and does not explicitly represent states as decision variables for every plan step. We also present a propagator procedure that illustrates the possibilities of LCG to widen the kind of inference methods considered to be feasible in planning as (iterated) CSP solving. We test encodings and propagators over classic IPC and recently proposed benchmarks for lifted planning, and report that for planning problem instances requiring fewer plan steps our methods compare very well with the state-of-the-art in optimal sequential planning.
Textual content around us is growing on a daily basis. Numerous articles are being written as we speak on online newspapers, blogs, or social media. Similarly, recent advances in the AI field, like language models or traditional classic AI approaches, are utilizing all the above to improve their learned representation to tackle NLP challenges with human-like accuracy. It is commonly accepted that it is crucial to have access to well-written text from valid sources to tackle challenges like text summarization, question-answering, machine translation, or even pronoun resolution. For instance, to summarize well, one needs to select the most important sentences in order to concatenate them to form the summary. However, what happens if we do not have access to well-formed English sentences or even non-valid sentences? Despite the importance of having access to well-written sentences, figuring out ways to validate them is still an open area of research. To address this problem, we present a simplified way to validate English sentences through a novel neural-symbolic approach. Lately, neural-symbolic approaches have triggered an increasing interest towards tackling various NLP challenges, as they are demonstrating their effectiveness as a central component in various AI systems. Through combining Classic with Modern AI, which involves the blending of grammatical and syntactical rules with language models, we effectively tackle the Corpus of Linguistic Acceptability (COLA), a task that shows whether or not a sequence of words is an English grammatical sentence. Among others, undertaken experiments effectively show that blending symbolic and non-symbolic systems helps the former provide insights about the latter's accuracy results.
Choice modeling is at the core of understanding how changes to the competitive landscape affect consumer choices and reshape market equilibria. In this paper, we propose a fundamental characterization of choice functions that encompasses a wide variety of extant choice models. We demonstrate how non-parametric estimators like neural nets can easily approximate such functionals and overcome the curse of dimensionality that is inherent in the non-parametric estimation of choice functions. We demonstrate through extensive simulations that our proposed functionals can flexibly capture underlying consumer behavior in a completely data-driven fashion and outperform traditional parametric models. As demand settings often exhibit endogenous features, we extend our framework to incorporate estimation under endogenous features. Further, we also describe a formal inference procedure to construct valid confidence intervals on objects of interest like price elasticity. Finally, to assess the practical applicability of our estimator, we utilize a real-world dataset from S. Berry, Levinsohn, and Pakes (1995). Our empirical analysis confirms that the estimator generates realistic and comparable own- and cross-price elasticities that are consistent with the observations reported in the existing literature.
We address the problem of generating realistic 3D motions of humans interacting with objects in a scene. Our key idea is to create a neural interaction field attached to a specific object, which outputs the distance to the valid interaction manifold given a human pose as input. This interaction field guides the sampling of an object-conditioned human motion diffusion model, so as to encourage plausible contacts and affordance semantics. To support interactions with scarcely available data, we propose an automated synthetic data pipeline. For this, we seed a pre-trained motion model, which has priors for the basics of human movement, with interaction-specific anchor poses extracted from limited motion capture data. Using our guided diffusion model trained on generated synthetic data, we synthesize realistic motions for sitting and lifting with several objects, outperforming alternative approaches in terms of motion quality and successful action completion. We call our framework NIFTY: Neural Interaction Fields for Trajectory sYnthesis.
The objective of clusterability evaluation is to check whether a clustering structure exists within the data set. As a crucial yet often-overlooked issue in cluster analysis, it is essential to conduct such a test before applying any clustering algorithm. If a data set is unclusterable, any subsequent clustering analysis would not yield valid results. Despite its importance, the majority of existing studies focus on numerical data, leaving the clusterability evaluation issue for categorical data as an open problem. Here we present TestCat, a testing-based approach to assess the clusterability of categorical data in terms of an analytical $p$-value. The key idea underlying TestCat is that clusterable categorical data possess many strongly associated attribute pairs and hence the sum of chi-squared statistics of all attribute pairs is employed as the test statistic for $p$-value calculation. We apply our method to a set of benchmark categorical data sets, showing that TestCat outperforms those solutions based on existing clusterability evaluation methods for numeric data. To the best of our knowledge, our work provides the first way to effectively recognize the clusterability of categorical data in a statistically sound manner.
Stochastic Gradient Descent (SGD) is one of the most popular algorithms in statistical and machine learning due to its computational and memory efficiency. Various averaging schemes have been proposed to accelerate the convergence of SGD in different settings. In this paper, we explore a general averaging scheme for SGD. Specifically, we establish the asymptotic normality of a broad range of weighted averaged SGD solutions and provide asymptotically valid online inference approaches. Furthermore, we propose an adaptive averaging scheme that exhibits both optimal statistical rate and favorable non-asymptotic convergence, drawing insights from the optimal weight for the linear model in terms of non-asymptotic mean squared error (MSE).
Knowledge Graph Embedding (KGE) models are used to learn continuous representations of entities and relations. A key task in the literature is predicting missing links between entities. However, Knowledge Graphs are not just sets of links but also have semantics underlying their structure. Semantics is crucial in several downstream tasks, such as query answering or reasoning. We introduce the subgraph inference task, where a model has to generate likely and semantically valid subgraphs. We propose IntelliGraphs, a set of five new Knowledge Graph datasets. The IntelliGraphs datasets contain subgraphs with semantics expressed in logical rules for evaluating subgraph inference. We also present the dataset generator that produced the synthetic datasets. We designed four novel baseline models, which include three models based on traditional KGEs. We evaluate their expressiveness and show that these models cannot capture the semantics. We believe this benchmark will encourage the development of machine learning models that emphasize semantic understanding.