In this work, the use of t-SNE is proposed to embed 3D point clouds of plants into 2D space for plant characterization. It is demonstrated that t-SNE operates as a practical tool to flatten and visualize a complete 3D plant model in 2D space. The perplexity parameter of t-SNE allows 2D rendering of plant structures at various organizational levels. Aside from the promise of serving as a visualization tool for plant scientists, t-SNE also provides a gateway for processing 3D point clouds of plants using their embedded counterparts in 2D. In this paper, simple methods were proposed to perform semantic segmentation and instance segmentation via grouping the embedded 2D points. The evaluation of these methods on a public 3D plant data set conveys the potential of t-SNE for enabling of 2D implementation of various steps involved in automatic 3D phenotyping pipelines.
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Personalisation of language models for dialogue sensitises them to better capture the speaking patterns of people of specific characteristics, and/or in specific environments. However, rich character annotations are difficult to come by and to successfully leverage. In this work, we release and describe a novel set of manual annotations for 863 speakers from the popular Cornell Movie Dialog Corpus, including features like characteristic quotes and character descriptions, and a set of six automatically extracted metadata for over 95% of the featured films. We perform extensive experiments on two corpora and show that such annotations can be effectively used to personalise language models, reducing perplexity by up to 8.5%. Our method can be applied even zero-shot for speakers for whom no prior training data is available, by relying on combinations of characters' demographic characteristics. Since collecting such metadata is costly, we also contribute a cost-benefit analysis to highlight which annotations were most cost-effective relative to the reduction in perplexity.
Stochastic gradient descent samples uniformly the training set to build an unbiased gradient estimate with a limited number of samples. However, at a given step of the training process, some data are more helpful than others to continue learning. Importance sampling for training deep neural networks has been widely studied to propose sampling schemes yielding better performance than the uniform sampling scheme. After recalling the theory of importance sampling for deep learning, this paper reviews the challenges inherent to this research area. In particular, we propose a metric allowing the assessment of the quality of a given sampling scheme; and we study the interplay between the sampling scheme and the optimizer used.
We propose a new distributed algorithm that combines heavy-ball momentum and a consensus-based gradient method to find a Nash equilibrium (NE) in a class of non-cooperative convex games with unconstrained action sets. In this approach, each agent in the game has access to its own smooth local cost function and can exchange information with its neighbors over a communication network. The proposed method is designed to work on a general sequence of time-varying directed graphs and allows for non-identical step-sizes and momentum parameters. Our work is the first to incorporate heavy-ball momentum in the context of non-cooperative games, and we provide a rigorous proof of its geometric convergence to the NE under the common assumptions of strong convexity and Lipschitz continuity of the agents' cost functions. Moreover, we establish explicit bounds for the step-size values and momentum parameters based on the characteristics of the cost functions, mixing matrices, and graph connectivity structures. To showcase the efficacy of our proposed method, we perform numerical simulations on a Nash-Cournot game to demonstrate its accelerated convergence compared to existing methods.
The view inconsistency problem in score-distilling text-to-3D generation, also known as the Janus problem, arises from the intrinsic bias of 2D diffusion models, which leads to the unrealistic generation of 3D objects. In this work, we explore score-distilling text-to-3D generation and identify the main causes of the Janus problem. Based on these findings, we propose two approaches to debias the score-distillation frameworks for robust text-to-3D generation. Our first approach, called score debiasing, involves gradually increasing the truncation value for the score estimated by 2D diffusion models throughout the optimization process. Our second approach, called prompt debiasing, identifies conflicting words between user prompts and view prompts utilizing a language model and adjusts the discrepancy between view prompts and object-space camera poses. Our experimental results show that our methods improve realism by significantly reducing artifacts and achieve a good trade-off between faithfulness to the 2D diffusion models and 3D consistency with little overhead.
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. Remarkably, we show that minimization of these quadratic objectives leads to control of the likelihood for any of our generative models built upon stochastic dynamics. By contrast, we establish that generative models based upon a deterministic dynamics must, in addition, control the Fisher divergence between the target and the model. We also construct estimators for the likelihood and the cross-entropy of interpolant-based generative models, discuss connections with other stochastic bridges, and demonstrate that such models recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant.
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for time-harmonic Maxwell equations, we analyze an analogous discretization of convolution operators with strongly singular kernels. For a class of kernel functions that includes the finite Hilbert transformation in 1D and the principal part of the Maxwell volume integral operator used for DDA in dimensions 2 and 3, we show that the method, which does not fit into known frameworks of projection methods, can nevertheless be considered as a finite section method for an infinite block Toeplitz matrix. The symbol of this matrix is given by a Fourier series that does not converge absolutely. We use Ewald's method to obtain an exponentially fast convergent series representation of this symbol and show that it is a bounded function, thereby allowing to describe the spectrum and the numerical range of the matrix. It turns out that this numerical range includes the numerical range of the integral operator, but that it is in some cases strictly larger. In these cases the discretization method does not provide a spectrally correct approximation, and while it is stable for a large range of the spectral parameter $\lambda$, there are values of $\lambda$ for which the singular integral equation is well posed, but the discretization method is unstable.
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize the test level and power in relation to the kernel bandwidth, the number of samples, and the intrinsic dimensionality of the manifold. Specifically, we show that when data densities are supported on a $d$-dimensional sub-manifold $\mathcal{M}$ embedded in an $m$-dimensional space, the kernel two-sample test for data sampled from a pair of distributions $p$ and $q$ that are H\"older with order $\beta$ (up to 2) is powerful when the number of samples $n$ is large such that $\Delta_2 \gtrsim n^{- { 2 \beta/( d + 4 \beta ) }}$, where $\Delta_2$ is the squared $L^2$-divergence between $p$ and $q$ on manifold. We establish a lower bound on the test power for finite $n$ that is sufficiently large, where the kernel bandwidth parameter $\gamma$ scales as $n^{-1/(d+4\beta)}$. The analysis extends to cases where the manifold has a boundary, and the data samples contain high-dimensional additive noise. Our results indicate that the kernel two-sample test does not have a curse-of-dimensionality when the data lie on or near a low-dimensional manifold. We validate our theory and the properties of the kernel test for manifold data through a series of numerical experiments.
We present the free and open source software TAS-Paths, a novel system which calculates optimal, collision-free paths for the movement of triple-axis spectrometers. The software features an easy to use graphical user interface, but can also be scripted and used as a library. It allows the user to plan and visualise the motion of the instrument before the experiment and can be used during measurements to circumvent obstacles. The instrument path is calculated in angular configuration space in order to keep a maximum angular distance from any obstacle.
The solution of the governing equation representing the drawdown in a horizontal confined aquifer, where groundwater flow is unsteady, is provided in terms of the exponential integral, which is famously known as the Well function. For the computation of this function in practical applications, it is important to develop not only accurate but also a simple approximation that requires evaluation of the fewest possible terms. To that end, introducing Ramanujan's series expression, this work proposes a full-range approximation to the exponential integral using Ramanujan's series for the small argument (u \leq 1) and an approximation based on the bound of the integral for the other range (u \in (1,100]). The evaluation of the proposed approximation results in the most accurate formulae compared to the existing studies, which possess the maximum percentage error of 0.05\%. Further, the proposed formula is much simpler to apply as it contains just the product of exponential and logarithm functions. To further check the efficiency of the proposed approximation, we consider a practical example for evaluating the discrete pumping kernel, which shows the superiority of this approximation over the others. Finally, the authors hope that the proposed efficient approximation can be useful for groundwater and hydrogeological applications.
Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.
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