This paper investigates the application of Generative Flow Networks (GFlowNets) to lead optimization in drug discovery. GFlowNets provide a novel framework for generating diverse molecular structures while optimizing for desired properties, addressing the limitations of traditional methods in exploring vast chemical spaces. We adapt GFlowNets to incrementally modify lead compounds, integrating domain-specific heuristics to guide the generation process. Our method employs the trajectory balance objective on a graph neural network (GNN), to learn a policy that samples fragments based on a multi-objective reward. The reward function ensures increase in cell permeability and similarity to the starting molecule. The results on benchmark datasets of activity cliffs demonstrate that GFlowNets can generate diverse modifications, producing optimized candidate molecules with improvement in cell permeability. This work can be extended with other pharmacokinetic properties for lead optimization in early-stage drug development, potentially accelerating the discovery of novel therapeutics.
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A Hybrid Framework for Airfoil Optimization: Combining PINNs and Genetic Algorithm (Student Abstract)
PDF ↗Achieving optimal design is a crucial aspect of any design process for safe and efficient operation. Such tasks typically require numerous simulations over many iterations, which can become computationally expensive. This paper proposes a novel method that combines Physics-informed Neural Networks (PINNs) with a Genetic Algorithm to optimize the parameters of an airfoil that aims to achieve favourable aerodynamic conditions. Traditional solvers are computationally expensive for performing such tasks, but using PINNs can significantly reduce this while keeping accuracy high. The proposed approach shows the advantage of using PINNs in optimizing complex engineering problems.
A Renormalization Group Framework for Scale-Invariant Feature Learning in Deep Neural Networks (Student Abstract)
PDF ↗We propose a framework that uses renormalization group (RG) theory from statistical physics to analyze and optimize the hierarchical feature learning process in deep neural networks. Here, the layer-wise transformations in deep networks can be viewed as analogous to RG transformations, with each layer implementing a coarse-graining operation that extracts increasingly abstract features. We propose an approach to enforce scale invariance in neural networks, introduce scale-aware activation functions, and derive RG flow equations for network parameters. We show that our approach leads to fixed points corresponding to scale-invariant feature representations. Finally, we propose an RG-guided training procedure that converges to these fixed points while minimizing the loss function.
The neural tangent kernel (NTK) has emerged as an important tool in recent years, both for developing a theoretical understanding of deep learning as well as for various applications. Even though recursive closed form expressions have been derived for computing the NTK, these become computationally expensive as the complexity of a network increases. Recent papers have looked at reducing this complexity using various sketching techniques along with random features. Building on these techniques, we propose an additional optimization step which results in better approximation of the NTK.
Learning Logic Specifications for Policy Guidance in POMDPs: an Inductive Logic Programming Approach
PDF ↗Partially Observable Markov Decision Processes (POMDPs) are a powerful framework for planning under uncertainty. They allow to model state uncertainty as a belief probability distribution. Approximate solvers based on Monte Carlo sampling show great success to relax the computational demand and perform online planning. However, scaling to complex realistic domains with many actions and long planning horizons is still a major challenge, and a key point to achieve good performance is guiding the action-selection process with domain-dependent policy heuristics which are tailored for the specific application domain. We propose to learn high-quality heuristics from POMDP traces of executions generated by any solver. We convert the belief-action pairs to a logical semantics, and exploit data- and time-efficient Inductive Logic Programming (ILP) to generate interpretable belief-based policy specifications, which are then used as online heuristics. We evaluate thoroughly our methodology on two notoriously challenging POMDP problems, involving large action spaces and long planning horizons, namely, rocksample and pocman. Considering different state-of-the-art online POMDP solvers, including POMCP, DESPOT and AdaOPS, we show that learned heuristics expressed in Answer Set Programming (ASP) yield performance superior to neural networks and similar to optimal handcrafted task-specific heuristics within lower computational time. Moreover, they well generalize to more challenging scenarios not experienced in the training phase (e.g., increasing rocks and grid size in rocksample, incrementing the size of the map and the aggressivity of ghosts in pocman).
In coastal river systems, floods, often during major storms or king tides, severely threaten lives and property. However, hydraulic structures such as dams, gates, pumps, and reservoirs exist in these river systems, and these floods can be mitigated or even prevented by strategically releasing water before extreme weather events. A standard approach used by local water management agencies is the “rule-based” method, which specifies predetermined water prereleases based on historical human experience, but which tends to result in excessive or inadequate water release. Iterative optimization methods that rely on detailed physics-based models for prediction are an alternative approach. Whereas, such methods tend to be computationally intensive, requiring hours or even days to solve the problem optimally. In this paper, we propose a Forecast Informed Deep Learning Architecture, FIDLAR, to achieve rapid and near-optimal flood management with precise water prereleases. FIDLAR seamlessly integrates two neural network modules: one called the Flood Manager, which is responsible for generating water pre-release schedules, and another called the Flood Evaluator, which evaluates those generated schedules. The Evaluator module is pre-trained separately, and its gradient-based feedback is utilized to train the Manager model, ensuring near-optimal water pre-releases. We have conducted experiments with a flood-prone coastal area in South Florida. Results show that FIDLAR is several orders of magnitude faster than currently used physics-based approaches while outperforming baseline methods with improved water pre-release schedules.
Decision trees, owing to their interpretability, are attractive as control policies for (dynamical) systems. Unfortunately, constructing, or synthesising, such policies is a challenging task. Previous approaches do so by imitating a neural-network policy, approximating a tabular policy obtained via formal synthesis, employing reinforcement learning, or modelling the problem as a mixed-integer linear program. However, these works may require access to a hard-to-obtain accurate policy or a formal model of the environment (within reach of formal synthesis), and may not provide guarantees on the quality or size of the final tree policy. In contrast, we present an approach to synthesise optimal decision-tree policies given a deterministic black-box environment and specification, a discretisation of the tree predicates, and an initial set of states, where optimality is defined with respect to the number of steps to achieve the goal. Our approach is a specialised search algorithm which systematically explores the (exponentially large) space of decision trees under the given discretisation. The key component is a novel trace-based pruning mechanism that significantly reduces the search space. Our approach represents a conceptually novel way of synthesising small decision-tree policies with optimality guarantees even for black-box environments with black-box specifications.
Mathematical formulas are the language of communication between humans and nature. Discovering latent formulas from observed data is an important challenge in artificial intelligence, commonly known as symbolic regression(SR). The current mainstream SR algorithms regard SR as a combinatorial optimization problem and use Genetic Programming (GP) or Reinforcement Learning (RL) to solve the SR problem. These methods perform well on simple problems, but poorly on slightly more complex tasks. In addition, this class of algorithms ignores an important aspect: in SR tasks, symbols have explicit numerical meaning. So can we take full advantage of this important property and try to solve the SR problem with more efficient numerical optimization methods? Extrapolation and Learning Equation (EQL) replaces activation functions in neural networks with basic symbols and sparsifies connections to derive a simplified expression from a large network. However, EQL's fixed network structure can't adapt to the complexity of different tasks, often resulting in redundancy or insufficient, limiting its effectiveness. Based on the above analysis, we propose MetaSymNet, a tree-like network that employs the PANGU meta-function as its activation function. PANGU meta-function can evolve into various candidate functions during training. The network structure can also be adaptively adjusted according to different tasks. Then the symbol network evolves into a concise, interpretable mathematical expression. To evaluate the performance of MetaSymNet and five baseline algorithms, we conducted experiments across more than ten datasets, including SRBench. The experimental results show that MetaSymNet has achieved relatively excellent results on various evaluation metrics.
ConfigX: Modular Configuration for Evolutionary Algorithms via Multitask Reinforcement Learning
PDF ↗Recent advances in Meta-learning for Black-Box Optimization (MetaBBO) have shown the potential of using neural networks to dynamically configure evolutionary algorithms (EAs), enhancing their performance and adaptability across various BBO instances. However, they are often tailored to a specific EA, which limits their generalizability and necessitates retraining or redesigns for different EAs and optimization problems. To address this limitation, we introduce ConfigX, a new paradigm of the MetaBBO framework that is capable of learning a universal configuration agent (model) for boosting diverse EAs. To achieve so, our ConfigX first leverages a novel modularization system that enables the flexible combination of various optimization sub-modules to generate diverse EAs during training. Additionally, we propose a Transformer-based neural network to meta-learn a universal configuration policy through multitask reinforcement learning across a designed joint optimization task space. Extensive experiments verify that, our ConfigX, after large-scale pre-training, achieves robust zero-shot generalization to unseen tasks and outperforms state-of-the-art baselines. Moreover, ConfigX exhibits strong lifelong learning capabilities, allowing efficient adaptation to new tasks through fine-tuning. Our proposed ConfigX represents a significant step toward an automatic, all-purpose configuration agent for EAs.
We present Learn2Aggregate, a machine learning (ML) framework for optimizing the generation of Chvatal-Gomory (CG) cuts in mixed integer linear programming (MILP). The framework trains a graph neural network to classify useful constraints for aggregation in CG cut generation. The ML-driven CG separator selectively focuses on a small set of impactful constraints, improving runtimes without compromising the strength of the generated cuts. Key to our approach is the formulation of a constraint classification task which favours sparse aggregation of constraints, consistent with empirical findings. This, in conjunction with a careful constraint labeling scheme and a hybrid of deep learning and feature engineering, results in enhanced CG cut generation across five diverse MILP benchmarks. On the largest test sets, our method closes roughly twice as much of the integrality gap as the standard CG method while running 40% faster. This performance improvement is due to our method eliminating 75% of the constraints prior to aggregation.
Binary Neural Networks (BNNs) have garnered significant attention due to their immense potential for deployment on edge devices. However, the non-differentiability of the quantization function poses a challenge for the optimization of BNNs, as its derivative cannot be backpropagated. To address this issue, hypernetwork based methods, which utilize neural networks to learn the gradients of non-differentiable quantization functions, have emerged as a promising approach due to their adaptive learning capabilities to reduce estimation errors. However, existing hypernetwork based methods typically rely solely on current gradient information, neglecting the influence of historical gradients. This oversight can lead to accumulated gradient errors when calculating gradient momentum during optimization. To incorporate historical gradient information, we design a Historical Gradient Storage (HGS) module, which models the historical gradient sequence to generate the first-order momentum required for optimization. To further enhance gradient generation in hypernetworks, we propose a Fast and Slow Gradient Generation (FSG) method. Additionally, to produce more precise gradients, we introduce Layer Recognition Embeddings (LRE) into the hypernetwork, facilitating the generation of layer-specific fine gradients. Extensive comparative experiments on the CIFAR-10 and CIFAR-100 datasets demonstrate that our method achieves faster convergence and lower loss values, outperforming existing baselines.
In decision-making problems under uncertainty, predicting unknown parameters is often considered independent of the optimization part. Decision-focused learning (DFL) is a task-oriented framework that integrates prediction and optimization by adapting the predictive model to give better decisions for the corresponding task. Here, an inevitable challenge arises when computing the gradients of the optimal decision with respect to the parameters. Existing research copes with this issue by smoothly reforming surrogate optimization or constructing surrogate loss functions that mimic task loss. However, they are applied to restricted optimization domains. In this paper, we propose Locally Convex Global Loss Network (LCGLN), a global surrogate loss model that can be implemented in a general DFL paradigm. LCGLN learns task loss via a partial input convex neural network which is guaranteed to be convex for chosen inputs while keeping the non-convex global structure for the other inputs. This enables LCGLN to admit general DFL through only a single surrogate loss without any sense for choosing appropriate parametric forms. We confirm the effectiveness and flexibility of LCGLN by evaluating our proposed model with three stochastic decision-making problems.
Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.
Iterative preference optimization has recently become one of the de-facto training paradigms for large language models (LLMs), but the performance is still underwhelming due to too much noisy preference data yielded in the loop. To combat this issue, we present an Uncertainty-enhanced Preference Optimization (UPO) framework to make the LLM self-evolve with reliable feedback. The key idea is mitigating the noisy preference pairs derived from the current policy and reward models by performing pair-wise uncertainty estimation and judiciously reliable feedback sampling. To reach this goal, we thus introduce an estimator model, which incorporates Monte Carlo (MC) dropout in Bayesian neural network (BNN) to perform uncertainty estimation for the batch of preference pairs. Compared to the existing methods that directly filter generated responses based on the reward score, the estimator focuses on the model uncertainty in a pair-wise manner and effectively bypasses the confirmation bias problem of the reward model. Additionally, we also propose an uncertainty-enhanced self-evolution algorithm to better improve the LLM robustly align with these reliable feedback data. Extensive experiments over multiple benchmarks demonstrate our framework substantially improves the performance of iterative preference optimization.
Denoising diffusion probabilistic models (DDPMs) have gained popularity in devising neural vocoders and obtained outstanding performance. However, existing DDPM-based neural vocoders struggle to handle the prosody diversities due to their susceptibility to mode-collapse issues confronted with imbalanced data. We introduced Cauchy Diffusion, a model incorporating the Cauchy noises to address this challenge. The heavy-tailed Cauchy distribution exhibits better resilience to imbalanced speech data, potentially improving prosody modeling. Our experiments on the LJSpeech and VCTK datasets demonstrate that Cauchy Diffusion achieved state-of-the-art speech synthesis performance. Compared to existing neural vocoders, our Cauchy Diffusion notably improved speech diversity while maintaining superior speech quality. Remarkably, Cauchy Diffusion surpassed neural vocoders based on generative adversarial networks (GANs) that are explicitly optimized to improve diversity.
Multi-agent pathfinding (MAPF) is a problem that generally requires finding collision-free paths for multiple agents in a shared environment. Solving MAPF optimally, even under restrictive assumptions, is NP-hard, yet efficient solutions for this problem are critical for numerous applications, such as automated warehouses and transportation systems. Recently, learning-based approaches to MAPF have gained attention, particularly those leveraging deep reinforcement learning. Typically, such learning-based MAPF solvers are augmented with additional components like single-agent planning or communication. Orthogonally, in this work we rely solely on imitation learning that leverages a large dataset of expert MAPF solutions and transformer-based neural network to create a foundation model for MAPF called MAPF-GPT. The latter is capable of generating actions without additional heuristics or communication. MAPF-GPT demonstrates zero-shot learning abilities when solving the MAPF problems that are not present in the training dataset. We show that MAPF-GPT notably outperforms the current best-performing learnable MAPF solvers on a diverse range of problem instances and is computationally efficient during inference.
Over the last decade, graph neural networks (GNNs) have made significant progress in numerous graph machine learning tasks. In real-world applications, where domain shifts occur and labels are often unavailable for a new target domain, graph domain adaptation (GDA) approaches have been proposed to facilitate knowledge transfer from the source domain to the target domain. Previous efforts in tackling distribution shifts across domains have mainly focused on aligning the node embedding distributions generated by the GNNs in the source and target domains. However, as the core part of GDA approaches, the impact of the underlying GNN architecture has received limited attention. In this work, we explore this orthogonal direction, i.e., how to facilitate GDA with architectural enhancement. In particular, we consider a class of GNNs that are designed explicitly based on optimization problems, namely unfolded GNNs (UGNNs), whose training process can be represented as bi-level optimization. Empirical and theoretical analyses demonstrate that when transferring from the source domain to the target domain, the lower-level objective value generated by the UGNNs significantly increases, resulting in an increase in the upper-level objective as well. Motivated by this observation, we propose a simple yet effective strategy called cascaded propagation (CP), which is guaranteed to decrease the lower-level objective value. The CP strategy is widely applicable to general UGNNs, and we evaluate its efficacy with three representative UGNN architectures. Extensive experiments on five real-world datasets demonstrate that the UGNNs integrated with CP outperform state-of-the-art GDA baselines.
Adaptive optimizers such as Adam and RMSProp have gained attraction in complex neural networks, including generative adversarial networks (GANs) and Transformers, thanks to their stable performance and fast convergence compared to non-adaptive optimizers. A frequently overlooked limitation of adaptive optimizers is that adjusting the learning rate of each dimension individually would ignore the knowledge of the whole loss landscape, resulting in slow updates of parameters, invalidating the learning rate adjustment strategy and eventually leading to widespread insufficient convergence of parameters. In this paper, we propose HVAdam, a novel optimizer that associates all dimensions of the parameters to find a new parameter update direction, leading to a refined parameter update strategy for an increased convergence rate. We validated HVAdam in extensive experiments, showing its faster convergence, higher accuracy, and more stable performance on image classification, image generation, and natural language processing tasks. Particularly, HVAdam achieves a significant improvement on GANs compared with other state-of-the-art methods, especially in Wasserstein-GAN (WGAN) and its improved version with gradient penalty (WGAN-GP).
Scaling Deep Neural Networks (DNNs) requires significant computational resources in terms of GPU quantity and compute capacity. In practice, there usually exists a large number of heterogeneous GPU devices due to the rapid release cycle of GPU products. It is highly needed to efficiently and economically harness the power of heterogeneous GPUs, so that it can meet the requirements of DNN research and development. The paper introduces Poplar, a distributed training system that extends Zero Redundancy Optimizer (ZeRO) with heterogeneous-aware capabilities. We explore a broader spectrum of GPU heterogeneity, including compute capability, memory capacity, quantity and a combination of them. In order to achieve high computational efficiency across all heterogeneous conditions, Poplar conducts fine-grained measurements of GPUs in each ZeRO stage. We propose a novel batch allocation method and a search algorithm to optimize the utilization of heterogeneous GPUs clusters. Furthermore, Poplar implements fully automated parallelism, eliminating the need for deploying heterogeneous hardware and finding suitable batch size. Extensive experiments on three heterogeneous clusters, comprising six different types of GPUs, demonstrate that Poplar achieves a training throughput improvement of 1.02-3.92x over current state-of-the-art heterogeneous training systems.
DG-Mamba: Robust and Efficient Dynamic Graph Structure Learning with Selective State Space Models
PDF ↗Dynamic graphs exhibit intertwined spatio-temporal evolutionary patterns, widely existing in the real world. Nevertheless, the structure incompleteness, noise, and redundancy result in poor robustness for Dynamic Graph Neural Networks (DGNNs). Dynamic Graph Structure Learning (DGSL) offers a promising way to optimize graph structures. However, aside from encountering unacceptable quadratic complexity, it overly relies on heuristic priors, making it hard to discover underlying predictive patterns. How to efficiently refine the dynamic structures, capture intrinsic dependencies, and learn robust representations, remains under-explored. In this work, we propose the novel DG-Mamba, a robust and efficient Dynamic Graph structure learning framework with the Selective State Space Models (Mamba). To accelerate the spatio-temporal structure learning, we propose a kernelized dynamic message-passing operator that reduces the quadratic time complexity to linear. To capture global intrinsic dynamics, we establish the dynamic graph as a self-contained system with State Space Model. By discretizing the system states with the cross-snapshot graph adjacency, we enable the long-distance dependencies capturing with the selective snapshot scan. To endow learned dynamic structures more expressive with informativeness, we propose the self-supervised Principle of Relevant Information for DGSL to regularize the most relevant yet least redundant information, enhancing global robustness. Extensive experiments demonstrate the superiority of the robustness and efficiency of our DG-Mamba compared with the state-of-the-art baselines against adversarial attacks.