Collective Variable Free Transition Path Sampling with Generative Flow Network

Understanding transition paths between meta-stable states in molecular systems is fundamental for material design and drug discovery. However, sampling these paths via molecular dynamics simulations is computationally prohibitive due to the high-energy barriers between the meta-stable states. Recent machine learning approaches are often restricted to simple systems or rely on collective variables (CVs) extracted from expensive domain knowledge. In this work, we propose to leverage generative flow networks (GFlowNets) to sample transition paths without relying on CVs. We reformulate the problem as amortized energy-based sampling over molecular trajectories and train a bias potential by minimizing the squared log-ratio between the target distribution and the generator, derived from the flow matching objective of GFlowNets. Our evaluation on three proteins (Alanine Dipeptide, Polyproline, and Chignolin) demonstrates that our approach, called TPS-GFN, generates more realistic and diverse transition paths than the previous CV-free machine learning approach.

Pessimistic Backward Policy for GFlowNets

This paper studies Generative Flow Networks (GFlowNets), which learn to sample objects proportionally to a given reward function through the trajectory of state transitions. In this work, we observe that GFlowNets tend to under-exploit the high-reward objects due to training on insufficient number of trajectories, which may lead to a large gap between the estimated flow and the (known) reward value. In response to this challenge, we propose a pessimistic backward policy for GFlowNets (PBP-GFN), which maximizes the observed flow to align closely with the true reward for the object. We extensively evaluate PBP-GFN across eight benchmarks, including hyper-grid environment, bag generation, structured set generation, molecular generation, and four RNA sequence generation tasks. In particular, PBP-GFN enhances the discovery of high-reward objects, maintains the diversity of the objects, and consistently outperforms existing methods.

Tackling Prevalent Conditions in Unsupervised Combinatorial Optimization: Cardinality, Minimum, Covering, and More

Combinatorial optimization (CO) is naturally discrete, making machine learning based on differentiable optimization inapplicable. Karalias & Loukas (2020) adapted the probabilistic method to incorporate CO into differentiable optimization. Their work ignited the research on unsupervised learning for CO, composed of two main components: probabilistic objectives and derandomization. However, each component confronts unique challenges. First, deriving objectives under various conditions (e.g., cardinality constraints and minimum) is nontrivial. Second, the derandomization process is underexplored, and the existing derandomization methods are either random sampling or naive rounding. In this work, we aim to tackle prevalent (i.e., commonly involved) conditions in unsupervised CO. First, we concretize the targets for objective construction and derandomization with theoretical justification. Then, for various conditions commonly involved in different CO problems, we derive nontrivial objectives and derandomization to meet the targets. Finally, we apply the derivations to various CO problems. Via extensive experiments on synthetic and real-world graphs, we validate the correctness of our derivations and show our empirical superiority w.r.t. both optimization quality and speed.

Gaussian Plane-Wave Neural Operator for Electron Density Estimation

This work studies machine learning for electron density prediction, which is fundamental for understanding chemical systems and density functional theory (DFT) simulations. To this end, we introduce the Gaussian plane-wave neural operator (GPWNO), which operates in the infinite-dimensional functional space using the plane-wave and Gaussian-type orbital bases, widely recognized in the context of DFT. In particular, both high- and low-frequency components of the density can be effectively represented due to the complementary nature of the two bases. Extensive experiments on QM9, MD, and material project datasets demonstrate GPWNO's superior performance over ten baselines.

Hybrid Neural Representations for Spherical Data

In this paper, we study hybrid neural representations for spherical data, a domain of increasing relevance in scientific research. In particular, our work focuses on weather and climate data as well as comic microwave background (CMB) data. Although previous studies have delved into coordinate-based neural representations for spherical signals, they often fail to capture the intricate details of highly nonlinear signals. To address this limitation, we introduce a novel approach named Hybrid Neural Representations for Spherical data (HNeR-S). Our main idea is to use spherical feature-grids to obtain positional features which are combined with a multilayer perception to predict the target signal. We consider feature-grids with equirectangular and hierarchical equal area isolatitude pixelization structures that align with weather data and CMB data, respectively. We extensively verify the effectiveness of our HNeR-S for regression, super-resolution, temporal interpolation, and compression tasks.

Triplet Edge Attention for Algorithmic Reasoning

This work investigates neural algorithmic reasoning to develop neural networks capable of learning from classical algorithms. The main challenge is to develop graph neural networks that are expressive enough to predict the given algorithm outputs while generalizing well to out-of-distribution data. In this work, we introduce a new graph neural network layer called Triplet Edge Attention (TEA), an edge-aware graph attention layer. Our algorithm works by precisely computing edge latent, aggregating multiple triplet messages using edge-based attention. We empirically validate our TEA layer in the CLRS benchmark and demonstrate a $5%$ improvement on average. In particular, we achieve a $30%$ improvement for the string algorithms compared to the state-of-the-art model.

A Simple and Scalable Representation for Graph Generation

Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches encounter significant limitations when generating large-scale graphs. This is due to their requirement to output the full adjacency matrices whose size grows quadratically with the number of nodes. In response to this challenge, we introduce a new, simple, and scalable graph representation named gap encoded edge list (GEEL) that has a small representation size that aligns with the number of edges. In addition, GEEL significantly reduces the vocabulary size by incorporating the gap encoding and bandwidth restriction schemes. GEEL can be autoregressively generated with the incorporation of node positional encoding, and we further extend GEEL to deal with attributed graphs by designing a new grammar. Our findings reveal that the adoption of this compact representation not only enhances scalability but also bolsters performance by simplifying the graph generation process. We conduct a comprehensive evaluation across ten non-attributed and two molecular graph generation tasks, demonstrating the effectiveness of GEEL.

Non-backtracking Graph Neural Networks

The celebrated message-passing updates for graph neural networks allow the representation of large-scale graphs with local and computationally tractable updates. However, the local updates suffer from backtracking, i.e., a message flows through the same edge twice and revisits the previously visited node. Since the number of message flows increases exponentially with the number of updates, the redundancy in local updates prevents the graph neural network from accurately recognizing a particular message flow for downstream tasks. In this work, we propose to resolve such a redundancy via the non-backtracking graph neural network (NBA-GNN) that updates a message without incorporating the message from the previously visited node. We further investigate how NBA-GNN alleviates the over-squashing of GNNs, and establish a connection between NBA-GNN and the impressive performance of non-backtracking updates for stochastic block model recovery. We empirically verify the effectiveness of our NBA-GNN on long-range graph benchmark and transductive node classification problems.

Learning Energy Decompositions for Partial Inference of GFlowNets

This paper studies generative flow networks (GFlowNets) to sample objects from the Boltzmann energy distribution via a sequence of actions. In particular, we focus on improving GFlowNet with partial inference: training flow functions with the evaluation of the intermediate states or transitions. To this end, the recently developed forward-looking GFlowNet reparameterizes the flow functions based on evaluating the energy of intermediate states. However, such an evaluation of intermediate energies may (i) be too expensive or impossible to evaluate and (ii) even provide misleading training signals under large energy fluctuations along the sequence of actions. To resolve this issue, we propose learning energy decompositions for GFlowNets (LED-GFN). Our main idea is to (i) decompose the energy of an object into learnable potential functions defined on state transitions and (ii) reparameterize the flow functions using the potential functions. In particular, to produce informative local credits, we propose to regularize the potential to change smoothly over the sequence of actions. It is also noteworthy that training GFlowNet with our learned potential can preserve the optimal policy. We empirically verify the superiority of LED-GFN in five problems including the generation of unstructured and maximum independent sets, molecular graphs, and RNA sequences.

Local Search GFlowNets

Generative Flow Networks (GFlowNets) are amortized sampling methods that learn a distribution over discrete objects proportional to their rewards. GFlowNets exhibit a remarkable ability to generate diverse samples, yet occasionally struggle to consistently produce samples with high rewards due to over-exploration on wide sample space. This paper proposes to train GFlowNets with local search which focuses on exploiting high rewarded sample space to resolve this issue. Our main idea is to explore the local neighborhood via destruction and reconstruction guided by backward and forward policies, respectively. This allows biasing the samples toward high-reward solutions, which is not possible for a typical GFlowNet solution generation scheme which uses the forward policy to generate the solution from scratch. Extensive experiments demonstrate a remarkable performance improvement in several biochemical tasks. Source code is available: \url{https://github.com/dbsxodud-11/ls_gfn}.