3D instance segmentation is crucial for applications demanding comprehensive 3D scene understanding. In this paper, we introduce a novel method that simultaneously learns coefficients and prototypes. Employing an overcomplete sampling strategy, our method produces an overcomplete set of instance predictions, from which the optimal ones are selected through a Non-Maximum Suppression (NMS) algorithm during inference. The obtained prototypes are visualizable and interpretable. Our method demonstrates superior performance on S3DIS-blocks, consistently outperforming existing methods in mRec and mPrec. Moreover, it operates 32.9% faster than the state-of-the-art. Notably, with only 0.8% of the total inference time, our method exhibits an over 20-fold reduction in the variance of inference time compared to existing methods. These attributes render our method well-suited for practical applications requiring both rapid inference and high reliability.
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In (Dzanic, J. Comp. Phys., 508:113010, 2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.
The method of multivariable Mendelian randomization uses genetic variants to instrument multiple exposures, to estimate the effect that a given exposure has on an outcome conditional on all other exposures included in a linear model. Unfortunately, the inclusion of every additional exposure makes a weak instruments problem more likely, because we require conditionally strong genetic predictors of each exposure. This issue is well appreciated in practice, with different versions of F-statistics routinely reported as measures of instument strength. Less transparently, however, these F-statistics are sometimes used to guide instrument selection, and even to decide whether to report empirical results. Rather than discarding findings with low F-statistics, weak instrument-robust methods can provide valid inference under weak instruments. For multivariable Mendelian randomization with two-sample summary data, we encourage use of the inference strategy of Andrews (2018) that reports both robust and non-robust confidence sets, along with a statistic that measures how reliable the non-robust confidence set is in terms of coverage. We also propose a novel adjusted-Kleibergen statistic that corrects for overdispersion heterogeneity in genetic associations with the outcome.
In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, are widely used in describing many physical phenomena with long-range interactions. The ND problem is the nonlocal analog of the classic diffusion problem, and as the interaction radius (horizon) vanishes, then the nonlocality disappears and the ND problem converges to the classic diffusion problem. Under certain conditions, the exact solution to the ND problem may exhibit discontinuities, setting it apart from the classic diffusion problem. Since the DG method shows its great advantages in resolving problems with discontinuities in computational fluid dynamics over the past several decades, it is natural to adopt the DG method to compute the ND problems. Based on [Du-Ju-Lu-Tian-CAMC2020], we develop the DG methods with different penalty terms, ensuring that the proposed DG methods have local counterparts as the horizon vanishes. This indicates the proposed methods will converge to the existing DG schemes as the horizon vanishes, which is crucial for achieving asymptotic compatibility. Rigorous proofs are provided to demonstrate the stability, error estimates, and asymptotic compatibility of the proposed DG schemes. To observe the effect of the nonlocal diffusion, we also consider the time-dependent convection-diffusion problems with nonlocal diffusion. We conduct several numerical experiments, including accuracy tests and Burgers' equation with nonlocal diffusion, and various horizons are taken to show the good performance of the proposed algorithm and validate the theoretical findings.
In this paper, we propose nonlocal diffusion models with Dirichlet boundary. These nonlocal diffusion models preserve the maximum principle and also have corresponding variational form. With these good properties, we can prove the well-posedness and the vanishing nonlocality convergence. Furthermore, by specifically designed weight function, we can get a nonlocal diffusion model with second order convergence which is optimal for nonlocal diffusion models.
Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep latent variable models, we show theoretically that confounding can be detected and corrected under the assumption that the observed data is a piecewise affine transformation of a latent Gaussian mixture model and that the identity of the mixture components is confounded. We provide a flow-based algorithm to estimate this model and perform deconfounding. Experimental results on synthetic and real-world data provide support for the effectiveness of our approach.
Do norms of rationality apply to machine learning models, in particular language models? In this paper we investigate this question by focusing on a special subset of rational norms: coherence norms. We consider both logical coherence norms as well as coherence norms tied to the strength of belief. To make sense of the latter, we introduce the Minimal Assent Connection (MAC) and propose a new account of credence, which captures the strength of belief in language models. This proposal uniformly assigns strength of belief simply on the basis of model internal next token probabilities. We argue that rational norms tied to coherence do apply to some language models, but not to others. This issue is significant since rationality is closely tied to predicting and explaining behavior, and thus it is connected to considerations about AI safety and alignment, as well as understanding model behavior more generally.
In this work, we use language modeling to investigate the factors that influence code-switching. Code-switching occurs when a speaker alternates between one language variety (the primary language) and another (the secondary language), and is widely observed in multilingual contexts. Recent work has shown that code-switching is often correlated with areas of high information load in the primary language, but it is unclear whether high primary language load only makes the secondary language relatively easier to produce at code-switching points (speaker-driven code-switching), or whether code-switching is additionally used by speakers to signal the need for greater attention on the part of listeners (audience-driven code-switching). In this paper, we use bilingual Chinese-English online forum posts and transcripts of spontaneous Chinese-English speech to replicate prior findings that high primary language (Chinese) information load is correlated with switches to the secondary language (English). We then demonstrate that the information load of the English productions is even higher than that of meaning equivalent Chinese alternatives, and these are therefore not easier to produce, providing evidence of audience-driven influences in code-switching at the level of the communication channel, not just at the sociolinguistic level, in both writing and speech.
In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual iteratively weighted least squares method in generalized linear models is presented. It is through the discussion of the asymptotic distribution of the proposed estimator and a set of statistics for testing linear hypothesis that it is possible to define standardized residuals using the mean-shift outlier model. In addition, robust versions of deviance function and the Akaike information criterion are defined with the aim of providing tools for model selection. Finally, the performance of the proposed methodology is illustrated through a simulation study and analysis of a real dataset.
Recent developments in the Byzantine Fault Tolerant consensus protocols have shown the DAG-based protocols to be a very promising technique. While early implementations of DAG-based protocols such as Narwhal/Bullshark trade high throughput for a low latency, the latest versions of DAG-based protocols such as Mysticeti and Shoal++ show that indeed a latency comparable to that of traditional consensus protocols such as HotStuff can be achieve with the DAG-based consensus protocols while still maintaining high throughput. Mysticeti in particular achieves a low latency by implementing a novel approach of using an uncertified DAG - a significant breakthrough comparing to the certified DAG used in the previous generations of the protocol. However, the uncertified DAG exposes the system to new vectors of attacks by Byzantine validators that did not exist in the certified DAG protocols. In this paper we describe those issues and present the Adelie protocol, that addresses issues that comes with an uncertified DAG. We also incorporate some of the techniques from the Shoal++ to reduce latency even further. This paper also presents an implementation of Adelie protocol - bftd that demonstrates yet another breakthrough in the maximum achieved TPS and low latency.
In this paper we propose an explicit fully discrete scheme to numerically solve the stochastic Allen-Cahn equation. The spatial discretization is done by a spectral Galerkin method, followed by the temporal discretization by a tamed accelerated exponential Euler scheme. Based on the time-independent boundedness of moments of numerical solutions, we present the weak error analysis in an infinite time interval by using Malliavin calculus. This provides a way to numerically approximate the invariant measure for the stochastic Allen-Cahn equation.
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