Efficient Symmetry-Aware Materials Generation via Hierarchical Generative Flow Networks

Discovering new solid-state materials requires rapidly exploring the vast space of crystal structures and locating stable regions. Generating stable materials with desired properties and compositions is extremely difficult as we search for very small isolated pockets in the exponentially many possibilities, considering elements from the periodic table and their 3D arrangements in crystal lattices. Materials discovery necessitates both optimized solution structures and diversity in the generated material structures. Existing methods struggle to explore large material spaces and generate diverse samples with desired properties and requirements. We propose the Symmetry-aware Hierarchical Architecture for Flow-based Traversal (SHAFT), a novel generative model employing a hierarchical exploration strategy to efficiently exploit the symmetry of the materials space to generate crystal structures given desired properties. In particular, our model decomposes the exponentially large materials space into a hierarchy of subspaces consisting of symmetric space groups, lattice parameters, and atoms. We demonstrate that SHAFT significantly outperforms state-of-the-art iterative generative methods, such as Generative Flow Networks (GFlowNets) and Crystal Diffusion Variational AutoEncoders (CDVAE), in crystal structure generation tasks, achieving higher validity, diversity, and stability of generated structures optimized for target properties and requirements.

Generating Realistic Tabular Data with Large Language Models

While most generative models show achievements in image data generation, few are developed for tabular data generation. Recently, due to success of large language models (LLM) in diverse tasks, they have also been used for tabular data generation. However, these methods do not capture the correct correlation between the features and the target variable, hindering their applications in downstream predictive tasks. To address this problem, we propose a LLM-based method with three important improvements to correctly capture the ground-truth feature-class correlation in the real data. First, we propose a novel permutation strategy for the input data in the fine-tuning phase. Second, we propose a feature-conditional sampling approach to generate synthetic samples. Finally, we generate the labels by constructing prompts based on the generated samples to query our fine-tuned LLM. Our extensive experiments show that our method significantly outperforms 10 SOTA baselines on 20 datasets in downstream tasks. It also produces highly realistic synthetic samples in terms of quality and diversity. More importantly, classifiers trained with our synthetic data can even compete with classifiers trained with the original data on half of the benchmark datasets, which is a significant achievement in tabular data generation.

Stable Hadamard Memory: Revitalizing Memory-Augmented Agents for Reinforcement Learning

Effective decision-making in partially observable environments demands robust memory management. Despite their success in supervised learning, current deep-learning memory models struggle in reinforcement learning environments that are partially observable and long-term. They fail to efficiently capture relevant past information, adapt flexibly to changing observations, and maintain stable updates over long episodes. We theoretically analyze the limitations of existing memory models within a unified framework and introduce the Stable Hadamard Memory, a novel memory model for reinforcement learning agents. Our model dynamically adjusts memory by erasing no longer needed experiences and reinforcing crucial ones computationally efficiently. To this end, we leverage the Hadamard product for calibrating and updating memory, specifically designed to enhance memory capacity while mitigating numerical and learning challenges. Our approach significantly outperforms state-of-the-art memory-based methods on challenging partially observable benchmarks, such as meta-reinforcement learning, long-horizon credit assignment, and POPGym, demonstrating superior performance in handling long-term and evolving contexts.

Robust Transfer Learning for Active Level Set Estimation with Locally Adaptive Gaussian Process Prior

The objective of active level set estimation for a black-box function is to precisely identify regions where the function values exceed or fall below a specified threshold by iteratively performing function evaluations to gather more information about the function. This becomes particularly important when function evaluations are costly, drastically limiting our ability to acquire large datasets. A promising way to sample-efficiently model the black-box function is by incorporating prior knowledge from a related function. However, this approach risks slowing down the estimation task if the prior knowledge is irrelevant or misleading. In this paper, we present a novel transfer learning method for active level set estimation that safely integrates a given prior knowledge while constantly adjusting it to guarantee a robust performance of a level set estimation algorithm even when the prior knowledge is irrelevant. We theoretically analyze this algorithm to show that it has a better level set convergence compared to standard transfer learning approaches that do not make any adjustment to the prior. Additionally, extensive experiments across multiple datasets confirm the effectiveness of our method when applied to various different level set estimation algorithms as well as different transfer learning scenarios.

Novel Kernel Models and Exact Representor Theory for Neural Networks Beyond the Over-Parameterized Regime

This paper presents two models of neural-networks and their training applicable to neural networks of arbitrary width, depth and topology, assuming only finite-energy neural activations; and a novel representor theory for neural networks in terms of a matrix-valued kernel. The first model is exact (un-approximated) and global, casting the neural network as an elements in a reproducing kernel Banach space (RKBS); we use this model to provide tight bounds on Rademacher complexity. The second model is exact and local, casting the change in neural network function resulting from a bounded change in weights and biases (ie. a training step) in reproducing kernel Hilbert space (RKHS) in terms of a local-intrinsic neural kernel (LiNK). This local model provides insight into model adaptation through tight bounds on Rademacher complexity of network adaptation. We also prove that the neural tangent kernel (NTK) is a first-order approximation of the LiNK kernel. Finally, and noting that the LiNK does not provide a representor theory for technical reasons, we present an exact novel representor theory for layer-wise neural network training with unregularized gradient descent in terms of a local-extrinsic neural kernel (LeNK). This representor theory gives insight into the role of higher-order statistics in neural network training and the effect of kernel evolution in neural-network kernel models. Throughout the paper (a) feedforward ReLU networks and (b) residual networks (ResNet) are used as illustrative examples.

Enhanced Bayesian Optimization via Preferential Modeling of Abstract Properties

Experimental (design) optimization is a key driver in designing and discovering new products and processes. Bayesian Optimization (BO) is an effective tool for optimizing expensive and black-box experimental design processes. While Bayesian optimization is a principled data-driven approach to experimental optimization, it learns everything from scratch and could greatly benefit from the expertise of its human (domain) experts who often reason about systems at different abstraction levels using physical properties that are not necessarily directly measured (or measurable). In this paper, we propose a human-AI collaborative Bayesian framework to incorporate expert preferences about unmeasured abstract properties into the surrogate modeling to further boost the performance of BO. We provide an efficient strategy that can also handle any incorrect/misleading expert bias in preferential judgments. We discuss the convergence behavior of our proposed framework. Our experimental results involving synthetic functions and real-world datasets show the superiority of our method against the baselines.

Active Level Set Estimation for Continuous Search Space with Theoretical Guarantee

A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and expensive to evaluate, the level sets need to be found in a minimum set of function evaluations. Existing methods often assume a discrete search space with a finite set of data points for function evaluations and estimating the level sets. When applied to a continuous search space, these methods often need to first discretize the space which leads to poor results while needing high computational time. While some methods cater for the continuous setting, they still lack a proper guarantee for theoretical convergence. To address this problem, we propose a novel algorithm that does not need any discretization and can directly work in continuous search spaces. Our method suggests points by constructing an acquisition function that is defined as a measure of confidence of the function being higher or lower than the given threshold. A theoretical analysis for the convergence of the algorithm to an accurate solution is provided. On multiple synthetic and real-world datasets, our algorithm successfully outperforms state-of-the-art methods.

Policy Learning for Off-Dynamics RL with Deficient Support

Reinforcement Learning (RL) can effectively learn complex policies. However, learning these policies often demands extensive trial-and-error interactions with the environment. In many real-world scenarios, this approach is not practical due to the high costs of data collection and safety concerns. As a result, a common strategy is to transfer a policy trained in a low-cost, rapid source simulator to a real-world target environment. However, this process poses challenges. Simulators, no matter how advanced, cannot perfectly replicate the intricacies of the real world, leading to dynamics discrepancies between the source and target environments. Past research posited that the source domain must encompass all possible target transitions, a condition we term full support. However, expecting full support is often unrealistic, especially in scenarios where significant dynamics discrepancies arise. In this paper, our emphasis shifts to addressing large dynamics mismatch adaptation. We move away from the stringent full support condition of earlier research, focusing instead on crafting an effective policy for the target domain. Our proposed approach is simple but effective. It is anchored in the central concepts of the skewing and extension of source support towards target support to mitigate support deficiencies. Through comprehensive testing on a varied set of benchmarks, our method's efficacy stands out, showcasing notable improvements over previous techniques.

PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks

Black-box optimization is a powerful approach for discovering global optima in noisy and expensive black-box functions, a problem widely encountered in real-world scenarios. Recently, there has been a growing interest in leveraging domain knowledge to enhance the efficacy of machine learning methods. Partial Differential Equations (PDEs) often provide an effective means for elucidating the fundamental principles governing the black-box functions. In this paper, we propose PINN-BO, a black-box optimization algorithm employing Physics-Informed Neural Networks that integrates the knowledge from Partial Differential Equations (PDEs) to improve the sample efficiency of the optimization. We analyze the theoretical behavior of our algorithm in terms of regret bound using advances in NTK theory and prove that the use of the PDE alongside the black-box function evaluations, PINN-BO leads to a tighter regret bound. We perform several experiments on a variety of optimization tasks and show that our algorithm is more sample-efficient compared to existing methods.

Root Cause Explanation of Outliers under Noisy Mechanisms

Identifying root causes of anomalies in causal processes is vital across disciplines. Once identified, one can isolate the root causes and implement necessary measures to restore the normal operation. Causal processes are often modelled as graphs with entities being nodes and their paths/interconnections as edge. Existing work only consider the contribution of nodes in the generative process, thus can not attribute the outlier score to the edges of the mechanism if the anomaly occurs in the connections. In this paper, we consider both individual edge and node of each mechanism when identifying the root causes. We introduce a noisy functional causal model to account for this purpose. Then, we employ Bayesian learning and inference methods to infer the noises of the nodes and edges. We then represent the functional form of a target outlier leaf as a function of the node and edge noises. Finally, we propose an efficient gradient-based attribution method to compute the anomaly attribution scores which scales linearly with the number of nodes and edges. Experiments on simulated datasets and two real-world scenario datasets show better anomaly attribution performance of the proposed method compared to the baselines. Our method scales to larger graphs with more nodes and edges.