Bayesian optimization (BO) is a powerful framework to optimize black-box expensive-to-evaluate functions via sequential interactions. In several important problems (e.g. drug discovery, circuit design, neural architecture search, etc.), though, such functions are defined over large $\textit{combinatorial and unstructured}$ spaces. This makes existing BO algorithms not feasible due to the intractable maximization of the acquisition function over these domains. To address this issue, we propose $\textbf{GameOpt}$, a novel game-theoretical approach to combinatorial BO. $\textbf{GameOpt}$ establishes a cooperative game between the different optimization variables, and selects points that are game $\textit{equilibria}$ of an upper confidence bound acquisition function. These are stable configurations from which no variable has an incentive to deviate$-$ analog to local optima in continuous domains. Crucially, this allows us to efficiently break down the complexity of the combinatorial domain into individual decision sets, making $\textbf{GameOpt}$ scalable to large combinatorial spaces. We demonstrate the application of $\textbf{GameOpt}$ to the challenging $\textit{protein design}$ problem and validate its performance on four real-world protein datasets. Each protein can take up to $20^{X}$ possible configurations, where $X$ is the length of a protein, making standard BO methods infeasible. Instead, our approach iteratively selects informative protein configurations and very quickly discovers highly active protein variants compared to other baselines.
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This study aims to optimize the existing retrieval-augmented generation model (RAG) by introducing a graph structure to improve the performance of the model in dealing with complex knowledge reasoning tasks. The traditional RAG model has the problem of insufficient processing efficiency when facing complex graph structure information (such as knowledge graphs, hierarchical relationships, etc.), which affects the quality and consistency of the generated results. This study proposes a scheme to process graph structure data by combining graph neural network (GNN), so that the model can capture the complex relationship between entities, thereby improving the knowledge consistency and reasoning ability of the generated text. The experiment used the Natural Questions (NQ) dataset and compared it with multiple existing generation models. The results show that the graph-based RAG model proposed in this paper is superior to the traditional generation model in terms of quality, knowledge consistency, and reasoning ability, especially when dealing with tasks that require multi-dimensional reasoning. Through the combination of the enhancement of the retrieval module and the graph neural network, the model in this study can better handle complex knowledge background information and has broad potential value in multiple practical application scenarios.
We investigate experimental design for randomized controlled trials (RCTs) with both equal and unequal treatment-control assignment probabilities. Our work makes progress on the connection between the distributional discrepancy minimization (DDM) problem introduced by Harshaw et al. (2024) and the design of RCTs. We make two main contributions: First, we prove that approximating the optimal solution of the DDM problem within even a certain constant error is NP-hard. Second, we introduce a new Multiplicative Weights Update (MWU) algorithm for the DDM problem, which improves the Gram-Schmidt walk algorithm used by Harshaw et al. (2024) when assignment probabilities are unequal. Building on the framework of Harshaw et al. (2024) and our MWU algorithm, we then develop the MWU design, which reduces the worst-case mean-squared error in estimating the average treatment effect. Finally, we present a comprehensive simulation study comparing our design with commonly used designs.
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs are coupled through a dynamic boundary condition, posed on the interface, that relates the normal gradients of the solutions to the time derivative of their jump. This system is referred to as the Extracellular Membrane Intracellular model or the cell-by-cell model. Due to the dynamic nature of the interface condition and to the presence of corner singularities, the analysis of discontinuous Galerkin methods is non-standard. We prove the existence and uniqueness of solutions by a reformulation of the problem to one posed on the membrane. Convergence is shown by utilizing face-to-element lifting operators and notions of weak consistency suitable for solutions with low spatial regularity. Further, we present parameter-robust preconditioned iterative solvers. Numerical examples in idealized geometries demonstrate our theoretical findings, and simulations in multiple cells portray the robustness of the method.
Semantic segmentation models are typically trained on a fixed set of classes, limiting their applicability in open-world scenarios. Class-incremental semantic segmentation aims to update models with emerging new classes while preventing catastrophic forgetting of previously learned ones. However, existing methods impose strict rigidity on old classes, reducing their effectiveness in learning new incremental classes. In this work, we propose Taxonomy-Oriented Poincar\'e-regularized Incremental-Class Segmentation (TOPICS) that learns feature embeddings in hyperbolic space following explicit taxonomy-tree structures. This supervision provides plasticity for old classes, updating ancestors based on new classes while integrating new classes at fitting positions. Additionally, we maintain implicit class relational constraints on the geometric basis of the Poincar\'e ball. This ensures that the latent space can continuously adapt to new constraints while maintaining a robust structure to combat catastrophic forgetting. We also establish eight realistic incremental learning protocols for autonomous driving scenarios, where novel classes can originate from known classes or the background. Extensive evaluations of TOPICS on the Cityscapes and Mapillary Vistas 2.0 benchmarks demonstrate that it achieves state-of-the-art performance. We make the code and trained models publicly available at //topics.cs.uni-freiburg.de.
Modern optimizers such as AdamW, equipped with momentum and adaptive learning rate, are designed to escape local minima and explore the vast parameter space. This exploration is beneficial for finding good loss basins when training from scratch. It is not necessarily ideal when resuming from a powerful foundation model because it can lead to large deviations from the pre-trained initialization and, consequently, worse robustness and generalization. At the same time, strong regularization on all parameters can lead to under-fitting. We hypothesize that selectively regularizing the parameter space is the key to fitting and retraining the pre-trained knowledge. This paper proposes a new weight decay technique, Selective Projection Decay (SPD), that selectively imposes a strong penalty on certain layers while allowing others to change freely. Intuitively, SPD expands and contracts the parameter search space for layers with consistent and inconsistent loss reduction, respectively. Experimentally, when equipped with SPD, Adam consistently provides better in-distribution generalization and out-of-distribution robustness performance on multiple popular vision and language benchmarks. Code available at~\url{//github.com/GT-RIPL/Selective-Projection-Decay.git}
We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficient s in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.
Achieving the effective design and improvement of reward functions in reinforcement learning (RL) tasks with complex custom environments and multiple requirements presents considerable challenges. In this paper, we propose ERFSL, an efficient reward function searcher using LLMs, which enables LLMs to be effective white-box searchers and highlights their advanced semantic understanding capabilities. Specifically, we generate reward components for each numerically explicit user requirement and employ a reward critic to identify the correct code form. Then, LLMs assign weights to the reward components to balance their values and iteratively adjust the weights without ambiguity and redundant adjustments by flexibly adopting directional mutation and crossover strategies, similar to genetic algorithms, based on the context provided by the training log analyzer. We applied the framework to an underwater data collection RL task without direct human feedback or reward examples (zero-shot learning). The reward critic successfully corrects the reward code with only one feedback instance for each requirement, effectively preventing unrectifiable errors. The initialization of weights enables the acquisition of different reward functions within the Pareto solution set without the need for weight search. Even in cases where a weight is 500 times off, on average, only 5.2 iterations are needed to meet user requirements. The ERFSL also works well with most prompts utilizing GPT-4o mini, as we decompose the weight searching process to reduce the requirement for numerical and long-context understanding capabilities
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.
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.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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