Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.
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Processing 是一門開源編程語言和與之配套的集成開發環境（IDE）的名稱。Processing 在電子藝術和視覺設計社區被用來教授編程基礎，并運用于大量的新媒體和互動藝術作品中。
Mixture of Experts (MoE) models have emerged as a primary solution for reducing the computational cost of Large Language Models. In this work, we analyze their scaling properties, incorporating an expanded range of variables. Specifically, we introduce a new hyperparameter, granularity, whose adjustment enables precise control over the size of the experts. Building on this, we establish scaling laws for fine-grained MoE, taking into account the number of training tokens, model size, and granularity. Leveraging these laws, we derive the optimal training configuration for a given computational budget. Our findings not only show that MoE models consistently outperform dense Transformers but also highlight that the efficiency gap between dense and MoE models widens as we scale up the model size and training budget. Furthermore, we demonstrate that the common practice of setting the size of experts in MoE to mirror the feed-forward layer is not optimal at almost any computational budget.
The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes. However, curse of dimensionality (CoD) poses challenge when dealing with high-dimensional FP PDEs. Although Monte Carlo and vanilla Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimension increases, surpassing the precision of numerical simulations and resulting in substantial errors. Moreover, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a difficult HJB equation, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in SDEs. The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling. Three fitting methods, Score Matching (SM), Sliced SM (SSM), and Score-PINN, are introduced. The proposed score-based SDE solver operates in two stages: first, employing SM, SSM, or Score-PINN to acquire the score; and second, solving the LL via an ODE using the obtained score. Comparative evaluations across these methods showcase varying trade-offs. The proposed method is evaluated across diverse SDEs, including anisotropic OU processes, geometric Brownian, and Brownian with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy. The numerical results demonstrate the score-based SDE solver's stability, speed, and performance across different settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.
The Sibson and Arimoto capacity, which are based on the Sibson and Arimoto mutual information (MI) of order {\alpha}, respectively, are well-known generalizations of the channel capacity C. In this study, we derive novel alternating optimization algorithms for computing these capacities by providing new variational characterizations of the Sibson MI and Arimoto MI. Moreover, we prove that all iterative algorithms for computing these capacities are equivalent under appropriate conditions imposed on their initial distributions.
Gender-neutral translation (GNT) that avoids biased and undue binary assumptions is a pivotal challenge for the creation of more inclusive translation technologies. Advancements for this task in Machine Translation (MT), however, are hindered by the lack of dedicated parallel data, which are necessary to adapt MT systems to satisfy neutral constraints. For such a scenario, large language models offer hitherto unforeseen possibilities, as they come with the distinct advantage of being versatile in various (sub)tasks when provided with explicit instructions. In this paper, we explore this potential to automate GNT by comparing MT with the popular GPT-4 model. Through extensive manual analyses, our study empirically reveals the inherent limitations of current MT systems in generating GNTs and provides valuable insights into the potential and challenges associated with prompting for neutrality.
Intra-fraction motion in radiotherapy is commonly modeled using deformable image registration (DIR). However, existing methods often struggle to balance speed and accuracy, limiting their applicability in clinical scenarios. This study introduces a novel approach that harnesses Neural Graphics Primitives (NGP) to optimize the displacement vector field (DVF). Our method leverages learned primitives, processed as splats, and interpolates within space using a shallow neural network. Uniquely, it enables self-supervised optimization at an ultra-fast speed, negating the need for pre-training on extensive datasets and allowing seamless adaptation to new cases. We validated this approach on the 4D-CT lung dataset DIR-lab, achieving a target registration error (TRE) of 1.15\pm1.15 mm within a remarkable time of 1.77 seconds. Notably, our method also addresses the sliding boundary problem, a common challenge in conventional DIR methods.
Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation
Natural policy gradient (NPG) methods with entropy regularization achieve impressive empirical success in reinforcement learning problems with large state-action spaces. However, their convergence properties and the impact of entropy regularization remain elusive in the function approximation regime. In this paper, we establish finite-time convergence analyses of entropy-regularized NPG with linear function approximation under softmax parameterization. In particular, we prove that entropy-regularized NPG with averaging satisfies the \emph{persistence of excitation} condition, and achieves a fast convergence rate of $\tilde{O}(1/T)$ up to a function approximation error in regularized Markov decision processes. This convergence result does not require any a priori assumptions on the policies. Furthermore, under mild regularity conditions on the concentrability coefficient and basis vectors, we prove that entropy-regularized NPG exhibits \emph{linear convergence} up to a function approximation error.
The recognition performance of biometric systems strongly depends on the quality of the compared biometric samples. Motivated by the goal of establishing a common understanding of face image quality and enabling system interoperability, the committee draft of ISO/IEC 29794-5 introduces expression neutrality as one of many component quality elements affecting recognition performance. In this study, we train classifiers to assess facial expression neutrality using seven datasets. We conduct extensive performance benchmarking to evaluate their classification and face recognition utility prediction abilities. Our experiments reveal significant differences in how each classifier distinguishes "neutral" from "non-neutral" expressions. While Random Forests and AdaBoost classifiers are most suitable for distinguishing neutral from non-neutral facial expressions with high accuracy, they underperform compared to Support Vector Machines in predicting face recognition utility.
Spatio-temporal forecasting, pivotal in numerous fields, hinges on the delicate equilibrium between isolating nuanced patterns and sifting out noise. To tackle this, we introduce Sparse Regression-based Vector Quantization (SVQ), a novel technique that leverages sparse regression for succinct representation, an approach theoretically and practically favored over classical clustering-based vector quantization methods. This approach preserves critical details from the original vectors using a regression model while filtering out noise via sparse design. Moreover, we approximate the sparse regression process using a blend of a two-layer MLP and an extensive codebook. This approach not only substantially cuts down on computational costs but also grants SVQ differentiability and training simplicity, resulting in a notable enhancement of performance. Our empirical studies on five spatial-temporal benchmark datasets demonstrate that SVQ achieves state-of-the-art results. Specifically, on the WeatherBench-S temperature dataset, SVQ improves the top baseline by 7.9%. In video prediction benchmarks-Human, KTH, and KittiCaltech-it reduces MAE by an average of 9.4% and improves image quality by 17.3% (LPIPS).
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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